Fixed_Income_I.ipynb

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    "import pandas as pd\n",
    "import numpy as np\n",
    "from datetime import date\n",
    "from IPython.display import Image"
   ]
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    "# Fixed-Income Securities: Defining Elements\n",
    "Fixed-income securities (or `debt securities` or `bonds`) are the dominant means of raising capital. It is a way for corporations to borrow without relinquishing ownership. Investors use them to diversify equity risk and fund known payment streams.\n",
    "### Basic Feature of Bonds\n",
    "#### Issuer\n",
    "Entities that raise capital by issuing debt include \n",
    "- companies, \n",
    "- national (sovereign) governments, \n",
    "- sub-national (non-sovereign) governments: non-sovereign bonds are typically repaid from the issuer’s taxing authority or the cash flows of the project being financed\n",
    "- quasi-government agencies, and \n",
    "- supranational organizations (e.g., World Bank): The source of payment for bonds issued by supranational organizations is either the repayment of previous loans made by the organization or the paid-in capital of its member states. \n",
    "- Special purpose entities that are created to securitize assets (e.g., mortgage-backed securities) are typically treated as another type of issuer.\n",
    "\n",
    "#### Maturity\n",
    "The maturity date is the due date of the principal. The tenor is the time remaining until maturity. A 10-year bond issued 2 years ago has an 8-year tenor. Maturities range from overnight to 30+ years.\n",
    "\n",
    "Money market securities have maturities of less than one year, while longer-dated debt trades in the capital market. Perpetual bonds have no stated maturity. *The primary difference between a money market security and a capital market security is the maturity at issuance. Money market securities mature in one year or less, whereas capital market securities mature in more than one year.*\n",
    "#### Par Value\n",
    "The par value (or `principal amount` or `face value`) is the amount that must be repaid at maturity. Often the price of a bond is quoted as a percentage of the par value. Bonds selling below the par value are at a discount and bonds selling above the par value are at a premium.\n",
    "#### Coupon Rate and Frequency\n",
    "The issuer agrees to pay the coupon rate (`nominal rate`) each year. For example, a 5% coupon bond with a $1,000 par value pays $50 in coupons annually. If the frequency is annual, bondholders will receive a single $50 payment at the end of each year. If the frequency is semi-annual, the same bond would pay $25 coupons every six months until maturity. Mortgage-backed securities typically pay monthly coupons.\n",
    "- `Conventional bonds` pay a fixed interest rate, while \n",
    "- `Floating-rate notes` have coupon rates that change based on the performance of a reference rate (e.g., Libor). For example, a floating rate bond with a coupon rate of Libor + 1% will pay a 5% coupon if Libor is at 4%. If Libor falls to 2%, the bond's next coupon payment will be for 3% of par value. These spreads are often quoted in terms of `basis points`, which is 0.01%. Libor + 1% can be stated as Libor + 100 basis points.\n",
    "- A `zero-coupon bond` is called a pure discount bond because no coupons are paid. Instead, investors purchase these securities at a discount and receive their par value at maturity.\n",
    "\n",
    "#### Currency Denomination\n",
    "Bonds can be denominated in any currency, issuers are not required to use their domestic currency. Indeed, many foreign bond issues are denominated in USD or EUR to attract a wider pool of investors.\n",
    "- `Dual-currency issues` make coupon payments in one currency and principal payments in another. \n",
    "- `Currency option bonds` give bondholders the right to choose which of two currency denominations they prefer for coupons and principal repayments.\n",
    "\n",
    "### Yield Measures\n",
    "A bond's price is inversely related to its yield (i.e., a higher yield results in a lower price). Commonly-quoted yield measures include:\n",
    "#### Current Yield\n",
    "(a.k.a. `running yield`) is the annual coupon divided by the bond’s current price. The current yield is a measure of income that is analogous to the dividend yield for a common share.\n",
    "$$Current\\ Yield(as\\ \\%)=\\frac{Annual\\ Coupon}{Current\\ Price}$$\n",
    "$Annual\\ Coupon=Par\\ Value \\times Coupon\\ Rate$\n",
    "#### Yield to Maturity\n",
    "It is the internal rate of return (discount rate) that makes the present value of a bond's future cash flows equal to its current price. Also known as `redemption yield` or `yield to redemption`.\n",
    "\n",
    "The yield to maturity can be considered an estimate of the bond’s expected return; it reflects the annual return that an investor will earn on a bond if this investor purchases the bond today and holds it until maturity. \n",
    "\n",
    "#### Risks\n",
    "Bondholders are exposed to `credit risk`—that is, the risk of loss resulting from the issuer failing to make full and timely payments of *interest* and/or repayments of *principal*.\n",
    "\n",
    "Systemic risk is the risk of failure of the financial system. \n",
    "\n",
    "Interest rate risk is the risk that a change in market interest rate affects a bond’s value."
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    "## Legal and Regulatory and Tax Considerations\n",
    "### Bond Indenture\n",
    "The `trust deed` (or `bond indenture`) describes the obligations of the bond issuer and the rights of the bondholders. It specifies the principal value, coupon rate, maturity date, covenants, contingency provisions, collateral, and credit enhancements.\n",
    "\n",
    "The indenture is held by a `trustee`, which is typically a financial institution. The trustee is appointed by the issuer but acts in a fiduciary capacity for bondholders. The trustee duties are mainly administrative (e.g., maintaining records) unless a default occurs.\n",
    "\n",
    "#### Legal Identity of the Bond Issuer and its Legal Form\n",
    "A bond's issuer has contractual obligations to its bondholders. The indenture specifies exactly which legal entity is bound by the terms of the contract. For example, a parent company is not responsible for bonds issued by its subsidiaries unless this has been specified in the indenture.\n",
    "\n",
    "Financial institutions often create legally-separate special purpose entities (SPEs) as vehicles for securitizing their assets. This entity is typically thinly capitalized with no independent managers, but it owns the underlying assets that have been transferred from sponsoring financial institution. SPEs are bankruptcy-remote, meaning that the sponsor's creditors have no claim to the securitized assets.\n",
    "#### Source of Repayment Proceeds\n",
    "The indenture describes how the issuer will make interest and principal payments. Sovereign bonds are backed by national governments that have the authority to tax their citizens and print money. Non-sovereign government issuers may be able to service their debt obligations issues through general taxes, project cash flows, or special taxes. Corporate bonds are repaid with operating cash flows, while securitizations rely on cash flows from a pool of underlying assets.\n",
    "#### Asset or Collateral Backing and Seniority Ranking\n",
    "Investors must understand how they rank relative to other creditors. Senior debt has a higher claim than subordinated debt in the event of a bankruptcy. Similarly secured bonds rank above unsecured bonds.\n",
    "\n",
    "1. **Secured bonds** are backed by collateral that lenders can claim if the issuer defaults on its obligations. Collateral may be specifically identified assets. For example, \n",
    "  - `collateral trust bonds` are secured by financial assets (*securities, such as common shares, other bonds*), and \n",
    "  - `equipment trust certificates` are secured by physical assets. Alternatively, collateral can be broadly defined as \"general plant and equipment.\"\n",
    "2. **Unsecured bonds** have no collateral; bondholders have only a general claim on the issuer’s assets and cash flows.\n",
    "3. **Debentures** typically refers to secured bonds in the UK and its former colonies and unsecured bonds in the rest of the world.\n",
    "4. **Covered bonds** are like asset-backed securities in that a financial institution creates a segregated pool of assets (e.g., loans). However, these assets remain on the financial institution's `balance sheet`. If one of the assets stops generating cash flows, the issuer must replace it with a performing asset. \n",
    "\n",
    "#### Credit Enhancements\n",
    "Internal and external credit enhancements can be used to reduce credit risk. `Internal credit enhancements` include \n",
    "- `subordination` (`credit tranching`) (through waterfall structure): the cash flows generated by the assets are allocated with different priority to tranches of different seniority. \n",
    "- `over-collateralization`: posting more collateral than is needed to obtain or secure financing. \n",
    "- `reserve accounts` or `reserve funds`: two types of this include \n",
    "  - cash reserve fund, is a deposit of cash that can be used to absorb losses.\n",
    "  - excess spread account(s) (`excess interest cash flow`), allocation into an account of any amounts left over after paying out the interest to bondholders. (related: turboing)\n",
    "\n",
    "External credit enhancements such as \n",
    "- `surety bonds`: Bank guarantees and surety bonds are very similar in nature because they both reimburse bondholders for any losses incurred if the issuer defaults. However, there is usually a maximum amount that is guaranteed, called the penal sum. The major difference between a bank guarantee and a surety bond is that the former is issued by a bank, whereas the latter is issued by a rated and regulated insurance company.\n",
    "- bank guarantees\n",
    "- letters of credit or guarantees from financial institutions: The financial institution provides the issuer with a credit line to reimburse any cash flow shortfalls from the assets backing the issue.\n",
    "\n",
    "Bank guarantees, surety bonds, and letters of credit expose the investor to third-party (or counterparty) risk—that is, the possibility that a guarantor cannot meet its obligations. A `cash collateral account` mitigates this concern because the issuer immediately borrows the `credit-enhancement amount` and then invests that amount, usually in highly rated short-term commercial paper. Because a cash collateral account is an actual deposit of cash rather than a pledge of cash, a downgrade of the cash collateral account provider will not necessarily result in a downgrade of the bond issue backed by that provider.\n",
    "#### Covenants\n",
    "Covenants are clauses that specify the rights of the bondholders and any actions that the issuer is obligated to perform or prohibited from performing. They include both `affirmative (positive)` and `negative covenants`. \n",
    "- Affirmative covenants are usually administrative in nature. \n",
    "- Negative covenants typically restrict the issuer in areas such as additional debt issuance, changing claims on assets, shareholder distributions, asset disposals, risky investments, and mergers and acquisitions."
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    "### Legal and Regulatory Considerations\n",
    "The global bond markets consist of **national bond markets** and the **Eurobond market**. A national bond market includes all the bonds that are issued and traded in a specific country and denominated in the currency of that country. \n",
    "- Bonds issued by entities that are incorporated in that country are called domestic bonds, whereas \n",
    "- Bonds issued by entities that are incorporated in another country are called foreign bonds.\n",
    "\n",
    "Foreign bond nicknames:\n",
    "- “kangaroo bonds” in Australia\n",
    "- “maple bonds” in Canada\n",
    "- “panda bonds” in China\n",
    "- “Samurai bonds” in Japan\n",
    "- “kimchi bonds” in South Korea\n",
    "- “matrioshka bonds” in Russia\n",
    "- “matador bonds” in Spain\n",
    "- “bulldog bonds” in the United Kingdom\n",
    "- and “Yankee bonds” in the United States.\n",
    "\n",
    "Legal and regulatory requirements vary greatly by jurisdiction, so the location of issuance and trading matters. \n",
    "\n",
    "Eurobonds are traded on the Eurobond market and are typically less regulated. These bonds are named after the currency in which they are denominated in. *they are named after the currency in which they are denominated. For example, Eurodollar and Euroyen bonds are denominated in US dollars and Japanese yens, respectively. Bonds that are denominated in euros are called euro-denominated Eurobonds.*\n",
    "\n",
    "Eurobonds are usually unsecured bonds underwritten by a consortium of financial institutions known as a `syndicate`. \n",
    "- Most Eurobonds are `bearer bonds` – only the clearing system knows who owns the bonds. \n",
    "- Global bonds are simultaneously issued in the Eurobond market and at least one domestic market.\n",
    "\n",
    "### Tax Considerations\n",
    "The income portion of a bond investment is taxed at the `ordinary income tax rate`. However, some securities are `tax exempt`. \n",
    "- Capital gains and losses are treated differently than ordinary income. \n",
    "- Some countries differentiate between long-term and short-term gains. \n",
    "- `Original issue discounts` (for bonds issued at a discount) may include a portion of the accrued interest as interest income. \n",
    "$$original\\ issue\\ discount= par\\ value- original\\ issue\\ price$$\n",
    "\n",
    "(The purpose of an original issue discount tax provision is to tax investors in Company B’s bonds the same way as investors in Company A’s bonds.)"
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    "## Structure of a Bond's Cash Flows\n",
    "### Principal Repayment Structures\n",
    "#### Bullet, Fully Amortized, and Partially Amortized Bonds\n",
    "1. `Bullet bonds` (a.k.a. `plain vanilla bond`, is the most common type) repay the entire principal at maturity. Periodic coupon payments for interest are made prior to maturity.\n",
    "2. A `fully amortized bond` are structured to provide equal annuity-like payments that are split between interest and principal. Over time, the interest portion decreases and the principal portion increases.\n",
    "3. A `partially amortized bond` amortizes some principal in each of its periodic payments and makes a final balloon payment that includes any principal that has not already been amortized.\n",
    "\n",
    "#### Sinking Fund Arrangements\n",
    "1. `Sinking funds` can also be used to periodically retire the bond principal. The schedule usually specifies a percentage of a bond issue that must be retired each year. The trustee could choose which bonds to redeem randomly.\n",
    "\n",
    "*Typically, the issuer will forward repayment proceeds to the bond’s trustee. The trustee will then either redeem bonds to this value or select by lottery the serial numbers of bonds to be paid off.*\n",
    "2. `Call provisions` can also be used that allow the issuer to retire some percentage of the bonds early. The actual bonds within the issue to be repurchased are selected at random.\n",
    "\n",
    "*The issuer can usually repurchase the bonds at the market price, at par, or at a specified sinking fund price, whichever is the lowest.*\n",
    "\n",
    "Sinking fund provisions reduce credit risk for investors by reducing the risk associated with a single balloon payment. However, reinvestment risk increased because the amortized principal that is received before maturity may be reinvested at low yields.\n",
    "### Coupon Payment Structures\n",
    "Coupons are the interest payments made to the bondholders. Most sovereign and corporate bonds pay coupons semi-annually (twice a year). Eurobonds typically pay coupons annually. While most bonds pay fixed-rate coupons, there are many variations.\n",
    "#### Floating-Rate Notes (FRNs)\n",
    "Bonds with coupon rates linked to an external index are called floating-rate notes. Government-sponsored enterprises often issue FRNs. Most FRNs pay **quarterly** coupons and pay a fixed spread over the reference rate (e.g., Libor + 1.5%).\n",
    "\n",
    "Some FRNs, called `variable-rate notes`, have variable spreads. FRNs have virtually no interest rate risk because the coupon payments will increase when rates rise. Many FRNs have caps and floors to limit interest rate payments. `Inverse floaters` have coupon rates that move inversely with the reference rate.\n",
    "#### Step-Up Coupon Bonds\n",
    "Step-up coupon bonds pay coupons that increase periodically based on a set schedule. They offer investors protection against rising interest rates and give issuers an incentive to repurchase (call) bonds if interest rates remain stable or fall.\n",
    "#### Credit-Linked Coupon Bonds\n",
    "Bonds that have coupon rates tied to credit ratings are called credit-linked coupon bonds. The coupon rate will increase if the issuer gets downgraded and decrease if the issuer gets upgraded.\n",
    "#### Payment-in-Kind (PIK) Coupon Bonds\n",
    "PIK coupon bonds allow the issuer to pay coupons with more bonds rather than cash. Lenders expect higher yields on the bonds because borrowers increase their credit risk by issuing more bonds as in-kind coupon payments.\n",
    "#### Deferred Coupon Bonds\n",
    "Deferred coupon bonds, also called `split coupon bonds`, pay no coupons in the early years and then higher coupons in later years. This structure allows issuers to defer cash payments while investors can potentially defer their tax liability. `Zero-coupon bonds` are an extreme example of the deferred coupon structure.\n",
    "#### Index-Linked Bonds\n",
    "Indexed-linked bonds have the coupons tied to a specific index. While any index can be used, inflation-type indices are common. Governments are the major issuers of inflation-linked bonds. The effect of inflation may be reflected in changes to the coupons or principal.\n",
    "- Zero-coupon indexed bonds and have their principal adjusted.\n",
    "- Interest-indexed bonds have their coupons adjusted.\n",
    "- Capital-indexed bonds pay a fixed coupon rate that is applied to a principal amount that is adjusted for inflation.\n",
    "- Indexed-annuity bonds are amortizing bonds with annuity payments that are adjusted for inflation."
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    "## Bonds with Contingency Provisions\n",
    "A bond's indenture may contain contingency provisions that specify actions that may be taken under certain conditions. Provisions that may be embedded in bonds include call options, put options, and conversion options.\n",
    "### Callable Bonds\n",
    "Issuers want to borrow at the lowest possible rate. If a company issues a 10-year, 5% coupon bond, and investors subsequently only require a 4% yield, the company will be paying an above-market rate on its borrowed funds. If the bonds included a call option, the company could repurchase its outstanding debt and issue new debt at a lower interest rate. If the market yield rises above 5%, the company can simply choose not the exercise its call option.\n",
    "\n",
    "Of course, features that benefit borrowers generally do not benefit lenders. In the above scenario, the lenders would be forced to sell bonds that are paying 5% coupons at a time when the market has determined that a 4% yield is sufficient for that level of risk. To make matters worse, these investors would be forced to reinvest the funds from the called bonds in a low-yield environment. As compensation for this possibility, investors require issuers to pay higher coupon rates or charge a lower price on callable bonds compared to otherwise equivalent option-free bonds.\n",
    "\n",
    "When interest rates fall, the price of the embedded call option increases. *The price of a callable bond equals the price of an option-free bond minus the price of the embedded call option*. The price of the callable bond will not increase as much as an option-free bond because the price of the call option is increasing. **As interest rates fall, the bond is more likely to be called, limiting the upside price increase potential.** \\[?\\]\n",
    "\n",
    "Callable bonds often specify a `call protection period` during which the issuer is not permitted to exercise its call option. After the call protection period has expired, the issuer has the right to repurchase the bonds at a call price schedule that is outlined in the indenture.\n",
    "\n",
    "*For example, a 10-year callable bond may have a 5-year call protection period, at which point the issuer can repurchase it for a call price of 103 per 100 of par value. The call price may drop to 102 after 6 years, 101 after 7 years, and remain at 100 from the end of Year 8 until maturity.*\n",
    "\n",
    "Call options differ with respect to how much flexibility issuers have.\n",
    "- American-style call options can be exercised any time after the call protection period (if applicable) has expired. This structure is most valuable for issuers of callable bonds.\n",
    "- European-style call options can only be exercised on one specific call date. This structure is most restrictive for issuers.\n",
    "- Bermuda-style call options are more flexible than European-style options because they offer multiple call dates (e.g., every coupon payment date after the call protection period).\n",
    "\n",
    "Callable bonds may include a `make-whole provision` that compensates lenders with a lump-sum payment based on the present value of coupon payments that will not be received after if the call option is exercised. If borrowers offer such a provision, lenders will be willing to accept a lower call premium.\n",
    "### Putable Bonds\n",
    "Embedded put options give lenders the right to sell their bonds back to the issuer at a specified price (usually par) on set dates. Typically, put provisions are in effect for one- to five-year periods. A Bermuda-style put option gives investors multiple opportunities to sell their bonds back, while a European-style put option provides just one.\n",
    "\n",
    "Bondholders benefit from the opportunity to redeem their bonds if market rates rise or if the issuer's credit quality declines. In exchange for this protection, investors are willing to accept lower yields or pay a higher price on putable bonds compared to otherwise equivalent option-free bonds.\n",
    "### Convertible Bonds\n",
    "Convertible bonds grant lenders the right to convert their bonds into a specified number of the issuer's common shares. Bondholders will exercise this option when the issuer's stock does well.\n",
    "\n",
    "**A convertible bond is effectively an option-free bond plus an equity call option**. Investors are willing to accept lower yields because they enjoy both the `upside potential of equity` and the `downside protection of a fixed-income security`. For their part, issuers benefit from lower borrowing costs and the elimination of debt obligations when conversion options are exercised.\n",
    "\n",
    "Key features of convertible bonds include:\n",
    "- **Conversion price**: The share price at which bonds can be converted.\n",
    "- **Conversion ratio**: The number of common shares that will be received for each convertible bond. It is calculated as: $\\frac{Par\\ value}{Conversion\\ price}$\n",
    "- **Conversion value**: The value if converted immediately. It is calculated as: $Current\\ share\\ price\\times Conversion\\ ratio$\n",
    "- **Conversion premium**: $= convertible\\ bond’s\\ price - its\\ conversion$, `Conversion parity` exists if the conversion premium is zero. \n",
    "  1. If the convertible bond price is greater than the conversion value, there is a positive conversion premium and the conversion condition is described as `below parity`. \n",
    "  2. If the convertible bond price is less than the conversion value, the conversion premium is negative and the conversion condition is `above parity`.\n",
    "\n",
    "Most investors do not exercise their conversion option until maturity, even if the issuer's share price has risen above the conversion price. This is because the interest payments on convertible bonds are generally higher than any dividend payments that would be made to common shareholders. In order to avoid such a scenario, issuers may retain a call option that grants them the right to force a conversion if their stock price rises above a specified level.\n",
    "\n",
    "`Warrants` is like a conversion option in the sense that they allow the holder to purchase common shares at a specific price. However, they are often offered as \"sweeteners\" to reduce borrowing costs rather than being structured as embedded options. Warrants may be traded separately on public equity exchanges. (A warrant is a separate, tradable security that entitles the holder to buy the underlying common share of the issuing company. )\n",
    "\n",
    "`Contingent convertible bonds (CoCos)` have been issued by financial institutions. The bonds automatically convert to equity if a certain trigger is reached (e.g., the issuer's capitalization ratio falls below the regulatory minimum level). Lenders have no control over the timing of exercise and they are exposed to downside risk, so yields are relatively high compared to otherwise equivalent bonds."
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    "Example\n",
    "\n",
    "Assume that a convertible bond issued in South Korea has a par value of ₩1,000,000 and is currently priced at ₩1,100,000. The underlying share price is ₩40,000 and the conversion ratio is 25:1. The conversion condition for this bond is:"
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      "Below parity\n"
     ]
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   "source": [
    "# know that \n",
    "par_val = 1000000\n",
    "price = 1100000\n",
    "share_p = 40000\n",
    "convert_r = 25\n",
    "# conversion price \n",
    "convert_p = share_p\n",
    "# conversion value\n",
    "convert_v = share_p * convert_r\n",
    "# premium or discount?\n",
    "if convert_v > price:\n",
    "    print('Above parity')\n",
    "elif convert_v == price:\n",
    "    print('At parity')\n",
    "else:\n",
    "    print('Below parity')"
   ]
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   "source": [
    "# Fixed-Income Markets: Issuance, Trading, and Funding"
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    "## Overview of Global Fixed-Income Markets\n",
    "### Classification of Fixed-Income Markets\n",
    "#### Type of Issuer\n",
    "The four broad categories of bond issuers are:\n",
    "1. Government and government-related\n",
    "2. Financial institutions\n",
    "3. Non-financial corporations\n",
    "4. Households\n",
    "\n",
    "Debt profiles vary by country, but mature markets tend to have higher debt/GDP ratios than emerging markets.\n",
    "#### Credit Quality\n",
    "Classification can be made based on scores from credit rating agencies. Broadly, they can be categorized as investment grade (ratings of Baa3 or above by Moody’s Investors Service or BBB– or above by Standard & Poor’s and Fitch Ratings) or non-investment grade (junk, speculative, high yield). Because some institutional investors are only permitted to hold investment-grade bonds, these securities tend to be more liquid than bonds that trade in the non-investment grade segment of the market.\n",
    "#### Maturity\n",
    "- Maturities up to one year are money market securities. These include government bills and corporate commercial paper. \n",
    "- Longer-dated debt issues are called capital market securities.\n",
    "#### Currency Denomination\n",
    "Emerging market issuers (both corporations and, to a lesser extent, governments) have found it easier to borrow by issuing bonds denominated in foreign currencies (e.g., USD, EUR). The price of a USD-denominated bond issued by a Mexican company will be primarily influenced by US interest rates and the company's credit quality.\n",
    "#### Type of Coupon\n",
    "Some bonds pay a fixed rate of interest while others pay a floating rate. To manage their interest rate exposure, banks that issue floating-rate debt tend to make floating-rate loans and invest in floating-rate securities. Corporations often issue floating-rate debt rather as an alternative to drawing on their lines of credit.\n",
    "\n",
    "Coupon payments for floating-rate bonds are set relative to a reference rate. Beginning in the 1980s, the London Interbank Offered Rate (Libor) has been the benchmark reference rate for maturities of up to one-year in multiple currencies. Libor is the rate at which London-based banks believe that they could borrow unsecured funds from other banks. At the peak of its popularity, there were 150 Libor rates (15 maturities for 10 different currencies).\n",
    "\n",
    "**Reference Rates**\n",
    "*Libor reflects the rate at which a panel of banks believe they could borrow unsecured funds from other banks in the London interbank money market for different currencies and different borrowing periods ranging from overnight to one year—the interbank money market, or interbank market, is the market of loans and deposits between banks for maturities up to one year.*\n",
    "\n",
    "*Interbank offered rates are used as reference rates not only for floating-rate bonds, but also for other debt instruments including mortgages, derivatives such as interest rate and currency swaps, and many other financial contracts and products. *\n",
    "\n",
    "Problems with Libor emerged during the financial crisis of 2007-2009, when banks deliberately understated their borrowing costs to increase their perceived creditworthiness. Other banks manipulated their submissions to increase the value of their Libor-relative derivative positions. Since then, the administration of Libor has changed and market participants are preparing to adopt a secured overnight financing rate (SOFR) as a replacement. SOFR is based on transactions in the repo market.\n",
    "\n",
    "#### Geography\n",
    "Domestic bonds are issued in, denominated in, and sold in a particular country. Foreign bonds are issued by an issuer from another country. Eurobonds are issued outside the jurisdiction of any single country and may be denominated in any currency. Borrowers typically prefer to issue Eurobonds rather than foreign bonds because reporting and regulatory requirements are lower and the larger pool of potential investors reduces borrowing costs. Investors also distinguish between developed markets and emerging bond markets. Bonds that are issued in emerging markets tend to have different risks than developed market debt.\n",
    "\n",
    "#### Other\n",
    "Many other classification methods can be used, such as inflation-linked or tax-exempt status. For example, most municipal bonds issued in the United States are tax-exempt. Some countries choose to tax coupon income from government bonds, but not capital gains"
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    "### Fixed-Income Indices\n",
    "Fixed-income indices are constructed from securities that represent a bond market or sector. The Barclays Capital Global Aggregate Bond Index is one of the most popular. It has components including the U.S., Pan-European, and Asian-Pacific.\n",
    "\n",
    "### Investors in Fixed-Income Securities\n",
    "Bond prices are ultimately determined by both supply and demand. \n",
    "- Central banks\n",
    "- Institutional investors\n",
    "- Retail investors \n",
    "\n",
    "**Open market operations**\n",
    "Central banks implement monetary policy through open market operations. By purchasing bonds in the open market a central bank will increase its country's monetary base. Selling bonds has the opposite effect. By purchasing (selling) domestic bonds, central banks increase (decrease) the monetary base in the economy. Central banks may also purchase and sell bonds denominated in foreign currencies as part of their efforts to manage the relative value of the domestic currency and their country’s foreign reserves.\n",
    "\n",
    "Institutional investors include \n",
    "- pension funds \n",
    "- insurance companies\n",
    "- hedge funds\n",
    "- charitable foundations and endowments\n",
    "- `sovereign wealth funds`, which are state-owned investment funds that tend to have very long investment horizons and aim to preserve or create wealth for future generations.\n",
    "\n",
    "Retail investors often invest through mutual funds. Most bond trading occurs in the over-the-counter (OTC) market rather than on organized exchanges.\n",
    "\n",
    "**Retail investors**: \n",
    "- fixed-income mutual funds \n",
    "- exchange-traded funds (ETFs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Primary and Secondary Bond Markets\n",
    "### Primary Bond Markets\n",
    "Bonds are first sold to investors in the primary markets through `public offerings` and `private placements`. \n",
    "\n",
    "Public offerings are usually done via \n",
    "- underwritten offerings\n",
    "- best-effort offerings\n",
    "- auctions\n",
    "\n",
    "**Underwritten offerings** (also called `firm commitment offerings`) are underwritten by an investment bank. A bond issue that is underwritten by a group of investment banks is called a `syndicated offering`. The underwriting process includes the following six phases:\n",
    "1. The issuer determines the amount of funding needed and the type of bond offering.\n",
    "2. The issuer selects the underwriter, or the lead underwriter in the case of a syndicated offering. Underwriters buy bonds from the issuer and sell them to investors at a higher price, so offering prices are determined by negotiations between issuers and underwriters.\n",
    "3. The structure (such as terms, notional amount, coupon rate, price) is set, but may change before the pricing day. It is critical the price is not set too high or too low. The underwriter also completes the necessary regulatory forms.\n",
    "4. The underwriter must gauge the demand to help determine the final price. This could be done through advertisements, informal discussions, or trading in the `grey market`, which is an informal forward market for upcoming bond issues. Trading in the grey market provides underwriters with data that can be used to help set the price at which a new bond issue should be offered.\n",
    "5. The `pricing day` is the last day investors can commit to buying the bond. It is the day before the `offering day`, which is when the underwriter purchases the bond issue from the issuer.\n",
    "6. Bonds are delivered to investors about 14 days later.\n",
    "\n",
    "In contrast, in a **best effort offering**, the investment bank only serves as a broker. It only tries to sell the bond issue at the negotiated offering price if it is able to for a commission. Thus, the investment bank has less risk and correspondingly less incentive to sell the bonds in a best effort offering than in an underwritten offering.\n",
    "\n",
    "**Shelf registration** allows issuers to offer additional bonds without preparing a new offering circular. Because disclosure requirements are lower, only well-established issuers have access to shelf registration. Some jurisdictions limit sales of shelf offerings to qualified institutional investors.\n",
    "\n",
    "**Auctions** allow investors to bid on bonds, which helps to facilitate price discovery. **Most sovereign bonds are sold to investors through public auctions.**\n",
    "\n",
    "*The United States uses a single-price auction process, which results in a single price for both competitive and non-competitive bidders. Other countries (e.g., Canada, Germany) use a multi-price auction process that can result in multiple different prices and coupon rates for the same bond issue. In a single-price bond auction, a bidder that enters a competitive bid specifies the rate (yield) that is considered acceptable. If the rate specified in the competitive bid is above the rate (yield) determined at auction, the investor will not be offered any securities.*\n",
    "\n",
    "**Private placements** are usually unregistered bonds sold to a very small group of accredited investors. Trading in secondary markets is very limited, so liquidity is low. Investors in this market often have influence over the structure of the bonds.\n",
    "### Secondary Bond Markets (\"Aftermarket\")\n",
    "Bonds are traded among `institutional investors` and `central banks` in secondary markets. \n",
    "\n",
    "`Liquidity` refers to the ability to trade (buy or sell) securities quickly and easily at prices close to their fair market value.\n",
    "- Liquidity involves much more than “how quickly one can turn a bond into cash.” This statement implicitly assumes a long position, but some market participants need to buy quickly when covering a short position. \n",
    "- speed of trading alone does not constitute a liquid market. (In a liquid market, trading takes place quickly at prices close to the security’s fair market value.)\n",
    "\n",
    "#### Structure\n",
    "Liquid securities can be bought and sold at prices close to fair value. Most trading of bonds is done in the `over-the-counter market` rather than on `organised exchanges`. \n",
    "1. An organized exchange provides a place where buyers and sellers can meet to arrange their trades. Although buy or sell orders may come from anywhere, the transaction must take place at the exchange according to the rules imposed by the exchange. \n",
    "2. With OTC markets, buy and sell orders initiated from various locations are matched through a communications network. OTC markets need electronic trading platforms over which users submit buy and sell orders.\n",
    "\n",
    "The level of commitment to the different sectors of the market varies among market makers. The `bid–offer spread` or `bid–ask spread`, which reflects the prices at which dealers will buy from a customer (bid) and sell to a customer (offer or ask), is very often used as an indicator of liquidity. A low bid-ask spread indicates a liquid market. Some illiquid issues have no quoted bid and ask prices. \n",
    "\n",
    "**Settlement** is the process that occurs after the trade is made. The bonds are passed to the buyer and payment is received by the seller. Government bonds usually settle on a T+1 basis (settlement takes place the day after the trade date), while corporate bonds usually settle on a T+2 or T+3 basis.\n",
    "\n",
    "Trades clear within either or both of the two main clearing systems:\n",
    "- Euroclear \n",
    "- Clearstream\n",
    "Settlement occurs by means of a simultaneous exchange of bonds for cash on the books of the clearing system. An electronic bridge connecting Euroclear and Clearstream allows transfer of bonds from one system to the other, so it is not necessary to have accounts at both systems. Both systems operate on a paperless, computerized book-entry basis, although a bond issue is still represented by a physical document, the `global note`."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
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    "## Government Debt\n",
    "### Sovereign Bonds\n",
    "#### Characteristics of Sovereign Bonds\n",
    "Sovereign bonds are issued by national governments to fund spending when tax revenues are insufficient. They are often classified according to their maturity. In the United States:\n",
    "- Treasury bills (T-bills) have maturities of less than one year\n",
    "- Treasury notes have maturities of 1 to 10 years\n",
    "- Treasury bonds have maturities of longer than 10 years\n",
    "\n",
    "The most recent version of a particular government bond is called an `on-the-run issue`. For example, if the US Treasury conducts a new auction of 1-year T-bills every month, the January issue will be considered on-the-run until the February auction is conducted, at which point the February issue is considered on-the-run and the January issue is referred to as `off-the-run`. In general, on-the-run issues are more liquid because securities typically trade less frequently as they age.\n",
    "\n",
    "**On-the-run government bonds serve as a benchmark for corporate bonds.** For example, if a newly-issued 5-year government bond has a 5% yield, an equivalent 5-year corporate bond with a 7% spread is described as trading at a 2% spread over the benchmark rate.\n",
    "\n",
    "Money market securities, which have maturities of one year or less, are usually issued on a pure discount basis and redeemed at par. By contrast, capital market government securities typically make regular coupon payments (e.g., annually, semiannually).\n",
    "#### Credit Quality of Sovereign Bonds\n",
    "Sovereign bonds are usually issued with no collateral. Instead, they are backed by the national government's authority to raise revenues via taxation. Fiscal surpluses can be used to retire existing debt, while fiscal deficits are financed by issuing new debt and \"rolling over\" maturing debt issues. National governments have the unique ability to raise funds by printing more money.\n",
    "\n",
    "Of course, excessive reliance on taxation can overburden an economy and threaten a government's ability to repay its debts. Additionally, printing more money will devalue a currency relative to others. While sovereign bonds are generally considered to be free of default risk, certain countries (notably the United States) had their credit rating downgraded in the aftermath of the 2007-2009 financial crisis.\n",
    "\n",
    "National governments may choose to issue foreign currency-denominated debt when investors are willing to accept credit risk but not foreign exchange risk. For example, the Swedish government enjoys the highest possible credit ratings but still chooses to issue USD-denominated debt because demand among investors for Swedish krona is comparatively low. Emerging-market governments often find it easier to borrow by issuing debt denominated in major currencies. However, countries are more limited in their ability to repay foreign currency obligations. Because a government can much more readily obtain more of its own currency than a currency issued by another sovereign government, credit rating agencies tend to give higher ratings to otherwise equivalent bonds denominated in the government's local currency. Bonds issued in the sovereign’s currency and a strong domestic savings base are both favorable sovereign rating factors.\n",
    "#### Types of Sovereign Bonds\n",
    "- `Fixed-Rate Bonds` \n",
    "Sovereign bonds most commonly issue fixed-rate bonds. Zero-coupon bonds can be thought of as bonds that pay 0% coupons. Most short-term government debt obligations (i.e., maturities of less than one year) are pure discount securities. Longer-term bonds are usually fixed-rate obligations.\n",
    "- `Floating-Rate Bonds` \n",
    "Some countries issue floating-rate bonds to attract investors who want to reduce their exposure to interest rate risk. However, the vast majority of sovereign debt issues are fixed-rate securities.\n",
    "- `Inflation-Linked Bonds` (a.k.a `linkers`)\n",
    "Investors concerned about inflation risk prefer inflation-linked bonds. Adjustments are made to a bond's coupons and/or principal based on changes in the level of a specified price index. In the US, Treasury Inflation-Protected Securities (TIPS) are linked to the Consumer Price Index.\n",
    "\n",
    "`Consols` are bonds with no maturity (i.e., they are perpetuities)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Non-Sovereign Bonds \n",
    "Non-sovereign bonds are issued by `sub-national governments`, such as states and cities. They are often used to finance specific projects like schools or roads. They are referred to as `municipal bonds` in the United States. Non-sovereign governments can raise funds to service their debt obligations by taxing citizens who fall under their jurisdiction or by accessing a stream of cash flows from a project that was financed with debt. Although historical default rates are relatively low for these bonds, they carry greater credit risk than equivalent sovereign bonds and investors require higher yields as compensation.\n",
    "\n",
    "Non-sovereign bonds usually trade at a higher yield and lower price than sovereign bonds with similar characteristics. The higher yield is because of the higher credit risk associated with non-sovereign issuers relative to sovereign issuers, although default rates of local governments are historically low and their credit quality is usually high. The higher yield may also be a consequence of non-sovereign bonds being less liquid than sovereign bonds with similar characteristics.\n",
    "### Quasi-Government Bonds (Agency Bonds)\n",
    "Quasi-government agencies perform government functions but they are not true government entities. In the United States, such agencies include government-sponsored entities (e.g., Federal National Mortgage Association). Although most agency bonds do not carry an explicit government guarantee, investors often price them based on the assumption of an implicit guarantee. Quasi-government bonds generally enjoy high credit ratings due to historically low default rates in this sector.\n",
    "### Supranational Bonds\n",
    "Multilateral agencies like the World Bank and International Monetary Fund also issue bonds. Usually, these are plain vanilla bonds, although floating-rate notes and callable bonds are occasionally issued. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
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    "## Corporate Debt\n",
    "### Bank Loans, Syndicated Loans\n",
    "`Bilateral loans` (i.e., single lender to single borrower) are often made by banks to small and medium-sized companies. Syndicated loans are made by a group of lenders to a single borrower. This allows lenders to diversify credit risk. Some syndicated loans are securitized and marketed to investors.\n",
    "\n",
    "Both bilateral and syndicated loans are usually structured with floating rate interest payments that are determined by a reference rate and a spread to reflect the borrower's credit risk. For example, a large company may pay Libor + 2.0% while a smaller company pays Libor + 2.5%. The \"prime rate\" that banks offer to their most creditworthy clients tends to fluctuate with the rate at which banks can borrow from each other in the overnight market.\n",
    "### Commercial Paper\n",
    "#### Characteristics of Commercial Paper\n",
    "Companies issue commercial paper (CP) in the public market or through a private placement as a *low-cost source of short-term financing*. Corporations, governments, and supranational agencies all use commercial paper, but **financial institutions are the largest issuers**.\n",
    "\n",
    "Commercial paper obligations are unsecured promissory notes with maturities of less than *three months* on average, but they may be up to one year or as short as overnight. Maturing obligations can be rolled over by issuing new commercial paper. This can be a valuable source of `bridge financing` when borrowers would prefer to wait before issuing long-term debt.\n",
    "#### Credit Quality of Commercial Paper\n",
    "Historical default rates on commercial paper are very low, largely because this source of funding has traditionally been available to only the largest corporations. Over time, investors have become increasingly willing to hold the commercial paper of less creditworthy issuers if they are sufficiently compensated with higher yields.\n",
    "\n",
    "Because commercial paper obligations are `unsecured`, credit rating agencies typically require borrowers to have sufficient `backup lines of credit` to cover 100% of their obligations. This acts as a safeguard against rollover risk as it gives investors assurance that issuers will be able to repurchase their outstanding commercial paper.\n",
    "\n",
    "Commercial paper is attractive to investors with short horizons and a low tolerance for credit risk (e.g., corporate treasury departments, money market mutual funds). Because investors generally hold these short-term securities until maturity, relatively little commercial paper is traded in the secondary market. Yields on corporate commercial paper are higher than those on comparable government securities to reflect greater credit risk exposure and lower market liquidity.\n",
    "#### US Commercial Paper vs. Eurocommercial Paper\n",
    "Many countries have active markets for domestic commercial paper. Of these, the `United States commercial paper (USCP) market` is the largest. The international market for commercial paper is called the `Eurocommercial paper (ECP) market`. In general, ECP transaction sizes are smaller and market liquidity is lower compared to the USCP market.\n",
    "\n",
    "Key differences between the USCP and ECP markets are summarized in the table below. Commercial paper, whether US commercial paper or Eurocommercial paper, is negotiable—that is, investors can buy and sell commercial paper on secondary markets.\n",
    "\n",
    "### Corporate Notes and Bonds\n",
    "#### Maturities\n",
    "Most bonds have maturities between 1 and 30 years, but maturities of 40, 50, or even 100 years are not uncommon. While there is no universal classification system, bonds are often placed in the following maturity categories:\n",
    "- Short-term: Five years or less\n",
    "- Intermediate-term: Longer than 5 years, up to 12 years\n",
    "- Long-term: 12 years or longer\n",
    "- Medium-term notes (`MTNs`) have traditionally been used by companies to bridge the funding gap between commercial paper and long-term bonds. However, MTNs can have maturities as long as 100 years.\n",
    "\n",
    "The distinguishing feature of MTNs is that companies can offer them continuously to investors through an agent (dealer) in a range of maturities. This gives the issuer more flexibility in raising funds compared to bonds and lets investors *customize* their purchases to match their specific cash flow needs. The MTN market can be broken into three segments: \n",
    "- short-term securities that carry floating or fixed rates, \n",
    "- medium- to long-term securities that primarily bear a fixed rate of interest, and \n",
    "- structured notes.\n",
    "\n",
    "**Yields on MTNs are higher compared to equivalent publicly issued bonds due to their relative liquidity**. However, MTNs may still be a lower-cost source of financing for issuers due to lower registration and underwriting costs.\n",
    "#### Coupon Payment Structures\n",
    "Coupons take on a variety of formats, including \n",
    "- fixed, \n",
    "- floating, \n",
    "- linked to inflation or credit risk, \n",
    "- deferred, or \n",
    "- `payment-in-kind` (PIK coupon bonds make periodic coupon payments, but not necessarily in cash; the issuer may pay interest in the form of securities, such as bonds or common shares.)\n",
    "\n",
    "Payment frequencies range from monthly to annual.\n",
    "#### Principal Repayment Structures\n",
    "Maturity structures can be `serial` or `term`. Investors can choose their preferred maturity.\n",
    "- A bond with a term maturity structure repays its *entire* face value at maturity. \n",
    "- A serial maturity structure reduces credit risk by having a certain amount of bonds within an issue mature. \n",
    "\n",
    "`Sinking fund arrangements` can also be used to reduce credit risk by requiring the borrower to repurchase a certain percentage of the issue each year. The bonds to be retired are selected at random. Adding a sinking fund arrangement to a term maturity structure effectively creates a serial maturity structure, except that investors do not know in advance which bonds will be retired.\n",
    "#### Asset or Collateral Backing\n",
    "Collateral, including physical and financial assets, can be pledged to reduce credit risk. Secured lenders have a claim to specific assets. By contrast, unsecured creditors typically experience greater losses in the event of a bankruptcy.\n",
    "#### Contingency Provisions\n",
    "Contingency provisions like calls, puts, and conversions are common. The call provision benefits the issuer, while the put and conversion provisions benefit the investor.\n",
    "#### Issuance, Trading, and Settlement\n",
    "Issuance and settling procedures for bonds are consistent worldwide. New corporate bond issues are initially sold by underwriters in the primary market.\n",
    "\n",
    "Secondary bond market trading is largely done OTC through dealers who carry inventories and \"make a market\" by being willing to take either side of a trade. Dealers quote bid and ask prices in basis point terms and profit from the spread. Settlement usually occurs faster in the secondary market compared to the primary market."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>USCP</th>\n",
       "      <th>ECP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Currency</th>\n",
       "      <td>US dollar</td>\n",
       "      <td>Any currency</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maturity</th>\n",
       "      <td>Overnight to 270 days</td>\n",
       "      <td>Overnight to 364 days</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Interest calculation</th>\n",
       "      <td>Discount basis</td>\n",
       "      <td>Interest-bearing or discount basis</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Settlement</th>\n",
       "      <td>T + 0 (Trade date)</td>\n",
       "      <td>T + 2 (Two days after trade date)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Negotiable</th>\n",
       "      <td>Can be sold to another party</td>\n",
       "      <td>Can be sold to another party</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                              USCP  \\\n",
       "Currency                                 US dollar   \n",
       "Maturity                     Overnight to 270 days   \n",
       "Interest calculation                Discount basis   \n",
       "Settlement                      T + 0 (Trade date)   \n",
       "Negotiable            Can be sold to another party   \n",
       "\n",
       "                                                     ECP  \n",
       "Currency                                    Any currency  \n",
       "Maturity                           Overnight to 364 days  \n",
       "Interest calculation  Interest-bearing or discount basis  \n",
       "Settlement             T + 2 (Two days after trade date)  \n",
       "Negotiable                  Can be sold to another party  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Key differences between the USCP and ECP markets\n",
    "df = pd.read_csv('uscp_ecp.csv', delimiter='\\t')\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Structured Financial Instruments\n",
    "Structured financial instruments represent a broad sector of financial instruments. This sector includes \n",
    "- asset-backed securities (ABS) and \n",
    "- collateralized debt obligations (CDOs). \n",
    "\n",
    "CDOs are securities backed by a diversified pool of one or more debt obligations. The structured financial instruments covered in this section are structured financial instruments apart from ABS and CDOs. These instruments typically have customized structures that often combine a bond and at least one derivative. **A structured instrument's coupons and/or redemption value are linked to the performance of the underlying asset(s).** The use of `derivatives` gives the holder of the structured financial instrument exposure to one or more underlying assets, such as equities, bonds, and commodities.\n",
    "### Capital Protected Instruments\n",
    "A `guarantee certificate` combines a zero-coupon bond with a call option. Consider the example of a 1-year zero-coupon bond yielding 4.17\\%. An investor purchases this bond today for 960 and receives \\\\$1,000 in one year. With a guarantee certificate, the investor pays \\\\$1,000 today for a package that includes the zero-coupon bond that is currently worth \\\\$960 and a \\\\$40 call option on an underlying asset.\n",
    "\n",
    "For the investor, the worse outcome is to receive \\\\$1,000 in one year and have the call option expire worthless. However, the upside potential is unlimited if the price of the underlying asset rises above the call price. Note that the guarantee to receive at least \\\\$1,000 assumes that the financial intermediary selling the certificate does not go bankrupt over the next year.\n",
    "### Yield Enhancement Instruments\n",
    "A `credit-linked note (CLN)` is a type of insurance contract between a party buying credit protection and a credit protection seller. The CLN buyer effectively borrows from the seller, receiving an up-front payment, and agreeing to pay coupons and return the principal at maturity.\n",
    "\n",
    "The performance of a CLN is contingent upon a specific event, such as a default on an underlying bond. If that event does not occur, the credit protection seller will receive regular coupon payments and the full repayment of their principal. If the event does occur, the credit protection seller is only required to repay the difference between the par value of the CLN and the nominal value of the reference asset.\n",
    "\n",
    "CLNs effectively transfer specific credit risks to those willing to bear them. These are attractive investments for those willing to accept credit risk because they pay relatively high coupons (i.e., yield enhancement) and can usually be purchased at a discount to par, allowing for potential capital gains.\n",
    "### Participation Instruments\n",
    "Participation instruments pay coupons based on the performance of an underlying asset. Floating-rate notes are participation instruments with a reference rate as their underlying asset. Fixed-income investors seeking equity market exposure can purchase a participation instrument linked to an equity index. These instruments typically do not offer capital protection.\n",
    "### Leveraged Instruments\n",
    "Leveraged instruments are structured financial instruments created to magnify returns and offer the possibility of high payoffs from small investments. `Leverage inverse floaters` pay higher coupons when the underlying reference rate decreases (and vice versa). The coupon rate for an inverse floater is calculated as follows:\n",
    "\n",
    "$$Inverse\\ floater\\ coupon\\ rate=Maxiumum\\ coupon\\ rate−(Leverage\\times Reference\\ rate)$$\n",
    "\n",
    "Consider the example of a leveraged inverse floater with 2× leverage and a maximum rate of 10\\%, which is what the coupon rate would be if the reference rate fell to zero. If the reference rate is 3\\%, the inverse floater's coupon rate will be:\n",
    "\n",
    "$10\\%−(2×3\\%)=4\\%$\n",
    "\n",
    "If the reference rate falls to 2\\%, the inverse floater's coupon rate will increase to 6\\%. Conversely, the coupon rate will fall to 2\\% if the reference rate increases to 4\\%.\n",
    "\n",
    "- `\"pure\" inverse floater` has 1× leverage, meaning that a 1\\% increase in the reference rate will cause a 1\\% decrease in the coupon rate (and vice versa). \n",
    "- `deleveraged inverse floater` has leverage between 0 and 1.\n",
    "\n",
    "Inverse floaters often have a floor that specifies a `minimum coupon rate`; for example, a floor may be set at zero to avoid the possibility of a negative interest rate. \n",
    "### Short-Term Funding Alternatives Available to Banks\n",
    "#### Retail Deposits\n",
    "Retail deposits are a primary source of funding for many banks. This includes demand deposits and savings accounts. However, often banks originate more loans than they can fund with retail deposits.\n",
    "#### Short-Term Wholesale Funds\n",
    "Wholesale funds can come from central banks, interbank funds, and certificates of deposit.\n",
    "\n",
    "Many central banks require deposits from its member banks to ensure sufficient liquidity. Central banks allow borrowing for short-term funding needs. Banks with surplus funds at the central bank are allowed to loan to banks with deficit reserves at the central bank funds rate, which is called the Fed funds rate in the United States.\n",
    "\n",
    "Interbank loans and deposits are made between banks. The term ranges from one day to one year. Since it is unsecured, it relies on the confidence in the banking sector, which can be shaky in times of economic turmoil.\n",
    "\n",
    "Certificates of deposit (CDs) have specified maturity and interest rate. They can be negotiable or non-negotiable. If a certificate of deposit is non-negotiable, investors are not allowed to sell the certificate. They will also pay a withdrawal penalty to access the money early. Negotiable CDs allow investors to sell the certificate on the open market prior to maturity. Large-denomination negotiable CDs are an important source of wholesale funds. Most have maturities less than one year.\n",
    "#### Repurchase and Reverse Repurchase Agreements\n",
    "A repo is an agreement to sell securities and repurchase them later at a higher price. It is effectively a collateralized loan. Repos are needed for active bond markets. It is referred to as a reverse repurchase agreement from the perspective of the lending party.\n",
    "\n",
    "Repo agreement terms vary. A one-day term is called an overnight repo. Government securities dealers use repos to fund purchases of new issues and central banks use repos as part of their open market operations.\n",
    "\n",
    "The interest rate on a repurchase agreement is called the repo rate. It is paid on the repurchase date. The repo rate is affected by the following factors:\n",
    "- Collateral risk: Repo rates increase with the level of credit risk in the collateral.\n",
    "- Term: Repo rates increase with the term.\n",
    "- Delivery requirements: Repo rates are lower when delivery to the lender is required.\n",
    "- Supply and demand conditions of the collateral: Repo rates are lower when the collateral used is in high demand.\n",
    "- Interest rates of alternative financing: Repo rates are lower if alternative financing rates are low.\n",
    "\n",
    "Credit risk is still present even if the collateral is of high quality. The dealer could default and not repurchase the collateral when it has dropped in value. The lender of funds is most vulnerable. The repo margin, or haircut, is the difference between the collateral market value and loan value. The margin is affected by the agreement length, collateral quality, credit quality of counterparty, and supply and demand conditions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Fixed-Income Valuation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bond Prices and the Time Value of Money\n",
    "The general approach to bond valuation is to use a series of spot rates that correspond to the timing of the future cash flows.\n",
    "### Bond Pricing with a Market Discount Rate \n",
    "On traditional fixed-rate bonds, the cash flows are a series of periodic coupon payments and a return of principal at maturity. The price of the bond is the present value of these cash flows, discounted at the market discount rate (or required yield).\n",
    "\n",
    "It depends on the amount of the cash flow, the timing of the cash flow, and the discount rate. If all the cash flows are discounted at the same rate, the present value is the sum of the present values of the individual cash flows.\n",
    "\n",
    "$$PV=\\frac{PMT}{(1+r)^1}+\\frac{PMT}{(1+r)^2}+…+\\frac{PMT + FV}{(1+r)^N}=\\sum{CF_t(1+r)^{−t}}$$\n",
    "<div style=\"text-align: right\"> Equation 1 <div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The relationship of the coupon rate to the market yield dictates the relationship of the bond price relative to its par value. This is summarized in the table below.\n",
    "\n",
    "Bonds that are trading at a discount or a premium will be `\"pulled to par\"` as they approach maturity. Consider the example of two 3-year annual coupon bonds: Bond A pays 7% and Bond B pays 3%. Assuming a 5% discount rate, Bond A will be issued at a price of 105.45 per 100 par. At the end of one year, its price will fall to 103.72. One year after that, the price will fall to 101.94. Bond B's price will be 94.55 initially before rising to 96.28 after one year and 98.10 after two years. The path that a bond's price would follow assuming no change in the yield curve is called the constant-yield price trajectory.\n",
    "\n",
    "Many bonds pay coupons twice per year, or semiannually. For example, if a 5% annual coupon bond pays $50 once a year, a 5\\% semiannual coupon bond pays $25 every 6 months. To calculate the price of a semiannual coupon bond, the discount rate, coupon payments, and compounding periods must be adjusted.\n",
    "### Yield-to-Maturity\n",
    "A bond's yield to maturity (YTM) is the discount rate that makes the present value of its expected future cash flows equal to its current price. It is the `internal rate of return (IRR)` that would be earned by an investor who purchased the bond today and held it until maturity. The YTM measure assumes that all coupon payments received prior to maturity are reinvested at this rate.\n",
    "\n",
    "YTM calculations can be done by `trial and error`, or simply by using a financial calculator.\n",
    "### Relationships between the Bond Price and Bond Characteristics\n",
    "The relationships between bond prices and characteristics allow us to make the following observations:\n",
    "- Inverse effect: A bond's price moves in the opposite direction as its yield. A higher yield causes a lower price and vice versa.\n",
    "- Convexity effect: All else equal, the percentage increase in a bond's price caused by lower yield will be greater in magnitude than the percentage decrease caused by an equivalent increase in its yield. (For the same coupon rate and time-to-maturity, the percentage price change is greater (in absolute value, meaning without regard to the sign of the change) when the market discount rate goes down than when it goes up.)\n",
    "- Coupon effect: Lower coupon bonds experience a greater percentage price change for a given change in the market discount rate than otherwise equivalent bonds with higher coupon rates.\n",
    "- Maturity effect: Generally, longer-term bonds have a greater percentage price change for a given change in the market discount rate. The maturity effect holds for zero-coupon bonds and bonds that are trading at or above par. However, exceptions to this rule can be observed among low-coupon, long-term bonds trading at a deep discount.\n",
    "\n",
    "But bond prices change as time passes even if the market discount rate remains the same. As time passes, the bondholder comes closer to receiving the par value at maturity. The constant-yield price trajectory illustrates the change in the price of a fixed-income bond over time. This trajectory shows the “pull to par” effect on the price of a bond trading at a premium or a discount to par value. If the issuer does not default, the price of a bond approaches par value as its time-to-maturity approaches zero.\n",
    "### Pricing Bonds Using Spot Rates\n",
    "Valuation using spot rates allows for each future cash flow to be discounted at a rate associated with its timing. \n",
    "\n",
    "*(So far in this section, we have calculated bond prices by discounting all future cash flows at the same rate. This assumes that the yield curve is flat (i.e., yields are the same at all maturities). In practice, the yield curve is rarely flat, so it is appropriate to discount each individual cash flow at its relevant spot rate.)*\n",
    "\n",
    "The resulting price is called the “`no-arbitrage value`” because any deviation from this price creates arbitrage opportunities. For example, if a bond is trading above its no-arbitrage price, an investor can earn a risk-free profit by selling it short and purchasing the zero-coupon bonds that are used in the spot curve.\n",
    "\n",
    "formula for calculating a bond price given the sequence of spot rates:\n",
    "$$PV=\\frac{PMT}{(1+Z_1)^1}+\\frac{PMT}{(1+Z_2)^2}+⋯+\\frac{PMT+FV}{(1+Z_N)^N}$$\n",
    "where\n",
    "\n",
    "$Z_1$ = spot rate, or the zero-coupon yield, or zero rate, for Period 1\n",
    "\n",
    "$Z_2$ = spot rate, or the zero-coupon yield, or zero rate, for Period 2\n",
    "\n",
    "$Z_N$ = spot rate, or the zero-coupon yield, or zero rate, for Period N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prices and Yields: Conventions for Quotes and Calculations\n",
    "### Flat Price, Accrued Interest and the Full price\n",
    "When a bond is sold between coupon payments, the next coupon payment must be allocated between the buyer and seller. The seller's portion is called the `accrued interest`. \n",
    "- The full price (or `dirty price`) includes the accrued interest. \n",
    "- The flat price (or `clean price`) excludes the accrued interest.\n",
    "\n",
    "$$PV^{Full}=PV^{Flat}+AI$$\n",
    "\n",
    "Dealers generally quote flat prices to avoid confusion, but the full price is paid on the settlement date. The accrued interest does not depend on the yield-to-maturity, so only the flat price is affected by market rates. The accrued interest is the proportional share of the next coupon payment.\n",
    "\n",
    "$$AI=\\frac{t}{T}(PMT)$$ \n",
    "where $\\frac{t}{T}$ is the fraction of coupon period completed since last payment.\n",
    "\n",
    "Counting days is usually done on an actual/actual basis. Another common approach with corporate bonds is the 30/360 day-count convention.\n",
    "\n",
    "The full price of the bond can be calculated by adjusting the present value for the fraction of time since the last coupon payment.\n",
    "\n",
    "$$PV^{Full}=\\frac{PMT}{(1+r)^{1−t/T}}+\\frac{PMT}{(1+r)^{2−t/T}}+⋯+\\frac{PMT+FV}{(1+r)^{N−t/T}}$$\n",
    "\n",
    "$$PV^{Full}=[\\frac{PMT}{(1+r)^1}+\\frac{PMT}{(1+r)^2}+⋯+\\frac{PMT+FV}{(1+r)^N}]×(1+r)^{t/T}$$\n",
    "\n",
    "$$PV^{Full}=(PV)(1+r)^{\\frac{t}{T}}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example\n",
    "\n",
    "Calculating the Full Price, Accrued Interest, and Flat Price for a Bond\n",
    "A 6% German corporate bond is priced for settlement on 18 June 2019. The bond makes semiannual coupon payments on 19 March and 19 September of each year and matures on 19 September 2030. The corporate bond uses the 30/360 day-count convention for accrued interest. Calculate the full price, the accrued interest, and the flat price per EUR100 of par value for three stated annual yields-to-maturity: (A) 5.80%, (B) 6.00%, and (C) 6.20%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- How to determine the number of days for $t$:\n",
    "\n",
    "Given the 30/360 day-count convention assumption, there are 89 days between the last coupon on 19 March 2019 and the settlement date on 18 June 2019 (11 days between 19 March and 30 March, plus 60 days for the full months of April and May, plus 18 days in June). Therefore, the fraction of the coupon period that has gone by is assumed to be 89/180. \n",
    "\n",
    "- How to determine the number of days for $T$:\n",
    "\n",
    "**At the beginning of the period, there are 11.5 years (and 23 semiannual periods) to maturity.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "89\n"
     ]
    }
   ],
   "source": [
    "# Number of days: t\n",
    "f_date_1 = date(2019, 3, 19)\n",
    "l_date_1 = date(2019, 3, 30)\n",
    "delta_1 = l_date_1 - f_date_1\n",
    "t1 = delta.days \n",
    "\n",
    "f_date_2 = date(2019, 6, 1)\n",
    "l_date_2 = date(2019, 6, 18)\n",
    "delta_2 = l_date_2 - f_date_2\n",
    "t2 = delta_2.days\n",
    "print(t1 + (t2+1) + 60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Matrix Pricing\n",
    "Prices for some bonds must be estimated because they are traded infrequently or not yet issued. This can be done by using quoted prices from similar bonds with a process called matrix pricing.\n",
    "\n",
    "In matrix pricing, the yield-to-maturity for similar bonds is calculated. (Linear) `interpolation` is used to calculate the yield for the desired maturity.\n",
    "$$Yield\\ to\\ maturity$$\n",
    "#### Required Yield Spread\n",
    "A similar process can be completed to estimate the `required yield spread` (yield to maturity less benchmark rate, a.k.a. `spread over the benchmark`), which compensates investors for credit risk, liquidity, and tax status. These are often stated in basis points, which are one-hundredth of a percent.\n",
    "#### Term Structure of Credit Spread\n",
    "The yield spreads reflect the term structure of credit spreads. The `term structure of credit spreads` is the relationship between the spreads over the “risk-free” (or benchmark) rates and times-to-maturity. These term structures are covered in more detail in later readings."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example: Using Matrix Pricing to Estimate Bond Price\n",
    "\n",
    "An analyst needs to assign a value to an illiquid four-year, 4.5% annual coupon payment corporate bond. The analyst identifies two corporate bonds that have similar credit quality: One is a three-year, 5.50% annual coupon payment bond priced at 107.500 per 100 of par value, and the other is a five-year, 4.50% annual coupon payment bond priced at 104.750 per 100 of par value. Using matrix pricing, the estimated price of the illiquid bond per 100 of par value is closest to:\n",
    "\n",
    "103.895.\n",
    "\n",
    "104.991.\n",
    "\n",
    "106.125."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pay attention to how the interpolation works \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Annual Yields for Varying Compounding Periods in the Year\n",
    "There are many ways to calculate the rate of return for bonds. Most yield measures are annualized and compounded because the need for a yield measure that is standardized to allow for comparison between bonds that have different times-to-maturity: thus the `annualized and compounded yield-to-maturity`. \n",
    "\n",
    "*(TBC: Money market rates on instruments maturing in one year or less typically are annualized but not compounded.)*\n",
    "\n",
    "In general, an annualized and compounded yield on a fixed-rate bond depends on the assumed number of periods in the year, which is called the `periodicity` of the annual rate. Typically, the periodicity matches the frequency of coupon payments.\n",
    "- The periodicity for zero-coupon bonds is somewhat arbitrary because there are no coupon payments. \n",
    "- The `effective annual rate` has a periodicity of one because there is just one compounding period in the year.\n",
    "\n",
    "The compounded total return is the same for each expression for the annual rate. They differ in terms of the number of compounding periods per year—that is, in terms of the periodicity of the annual rate. For a given pair of cash flows, the stated annual rate and the periodicity are inversely related. (e.g. In this zero-coupon bond example, 2.2565% compounded two times a year, 1.1220% compounded four times a year, and 0.3726% compounded twelve times a year are all equivalent to an effective annual rate of 4.5640%.)\n",
    "\n",
    "**Semiannual bond basis yield, or semiannual bond equivalent yield** \n",
    "The most common periodicity for USD-denominated bond yields is two because most bonds in the USD market make semiannual coupon payments. Therefore, a semiannual bond basis yield is the yield per semiannual period times two. *(It is important to remember that “semiannual bond basis yield” and “yield per semiannual period” have different meanings.)*\n",
    "\n",
    "An important tool used in fixed-income analysis is to convert an annual yield from one periodicity to another. These are called periodicity, or compounding, conversions. The following formula can be used to convert between an `annual percentage rate (APR)` for $m$ periods per year and one for $n$ periods per year.\n",
    "\n",
    "$$(1+\\frac{APR_m}{m})^m=(1+\\frac{APR_n}{n})^n$$\n",
    "\n",
    "**A general rule for these periodicity conversions is compounding more frequently at a lower annual rate corresponds to compounding less frequently at a higher annual rate. This rule can be used to check periodicity conversion calculations.**\n",
    "\n",
    "The equation also applies to *negative* bond yields. Government bond yields have been negative in in several countries, including Switzerland, Germany, Sweden, and Japan."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Yield Measures for Fixed-Rate Bonds\n",
    "The *timing* of the cash flows must be closely considered when viewing bond yields. \n",
    "1. Yield measures that neglect weekends and holidays are quoted on what is called `street convention`. \n",
    "2. The `true yield` uses the actual date the cash flow will be made. It will be slightly less than the street convention yield if the cash flows are delayed a day or two by holidays or weekends. \n",
    "3. A `government equivalent yield` uses a 30/360 day-count to calculate the yield-to-maturity. The government equivalent yield on a corporate bond can be used to obtain the spread over the government yield. Doing so keeps the yields stated on the same day-count convention basis.\n",
    "4. The `current yield` (`income or running yield`) is the sum of the coupon payments received over a year divided by the flat price. It ignores the frequency of coupon payments and the accrued interest. It also ignores the gain or loss from purchasing a bond at a discount or premium. \n",
    "$$Current\\ Yield=\\frac{Annual\\ Dollar\\ Coupon\\ Interest}{Flat\\ Price}$$\n",
    "5. The `simple yield` adjusts the current yield calculation by including the amortized gain or loss in the numerator. It is the sum of the coupon payments plus the **straight-line amortized share of the gain or loss**, divided by the flat price. (Simple yields are used mostly to quote Japanese government bonds, known as “JGBs.”)\n",
    "\n",
    "$$Simple\\ Yield=\\frac{Annual\\ Dollar\\ Coupon\\ Interest + Amortized\\ Gain\\ or\\ Loss}{Flat\\ Price}$$\n",
    "\n",
    "**Bond yields with options**\n",
    "Other yield measures are used if the fixed-rate bond has embedded options. \n",
    "6. One example is a `yield-to-nth-call`, which calculates the internal rate of return assuming the bond is called early at the stated call price. (Each calculation is based on Equation 1, whereby the call price (or par value) is used for FV.)\n",
    "7. The `yield-to-worst` is the lowest of the calculated yield-to-calls and yield-to-maturity.\n",
    "\n",
    "The `option-adjusted yield` is a better approach to account for the embedded options. It is the discount rate consistent with the price difference between an option-free bond and a callable bond."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example:\n",
    "\n",
    "A ten-year, 3.50% semiannual coupon payment government bond is priced at 98.\n",
    "\n",
    "Calculate the current yield and simple yield."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03775510204081633"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# current yield\n",
    "3.5 / 98\n",
    "# simple yield\n",
    "(3.5 + (100-98)/10) / 98"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Bond A</th>\n",
       "      <th>Bond B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Annual Coupon Rate</th>\n",
       "      <td>8.00%</td>\n",
       "      <td>12.00%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Coupon Payment Frequency</th>\n",
       "      <td>Semiannually</td>\n",
       "      <td>Quarterly</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Years to Maturity</th>\n",
       "      <td>5 Years</td>\n",
       "      <td>5 Years</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Price (per 100 of par value)</th>\n",
       "      <td>90</td>\n",
       "      <td>105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Current Yield</th>\n",
       "      <td>8.889%</td>\n",
       "      <td>11.429%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Yield-to-Maturity</th>\n",
       "      <td>10.630%</td>\n",
       "      <td>10.696%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                    Bond A     Bond B\n",
       "Annual Coupon Rate                   8.00%     12.00%\n",
       "Coupon Payment Frequency      Semiannually  Quarterly\n",
       "Years to Maturity                  5 Years    5 Years\n",
       "Price (per 100 of par value)            90        105\n",
       "Current Yield                       8.889%    11.429%\n",
       "Yield-to-Maturity                  10.630%    10.696%"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#An analyst observes these reported statistics for two bonds:\n",
    "df = pd.read_csv('comparing_yields.csv', delimiter='\\t')\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The analyst believes that Bond B has a little more risk than Bond A. How much additional compensation, (in terms of a higher yield-to-maturity), does a buyer of Bond B receive for bearing this risk compared with Bond A?\n",
    "\n",
    "The yield-to-maturity on Bond A of 10.630% is an annual rate for compounding semiannually. The yield-to-maturity on Bond B of 10.696% is an annual rate for compounding quarterly. The difference in the yields is not 6.6 bps (0.10696 – 0.10630 = 0.00066). It is essential to compare the yields for the same periodicity to make a statement about relative value.\n",
    "\n",
    "10.630% for a periodicity of two converts to 10.492% for a periodicity of four:\n",
    "\n",
    "$\\displaystyle\\frac{(1+0.10630)^2}{2}=\\frac{(1+APR_4)^4}{4}$,     $APR_4=0.10492$\n",
    "\n",
    "10.696% for a periodicity of four converts to 10.839% for a periodicity of two:\n",
    "\n",
    "$\\displaystyle\\frac{(1+0.10696)^4}{4}=\\frac{(1+APR_2)^2}{2}$,     $APR_2=0.10839$\n",
    "\n",
    "The additional compensation for the greater risk in Bond B is 20.9 bps (0.10839 – 0.10630 = 0.00209) when the yields are stated on a semiannual bond basis. The additional compensation is 20.4 bps (0.10696 – 0.10492 = 0.00204) when both are annualized for quarterly compounding."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Yield Measures for Floating-Rate Notes (FRN or Floater)\n",
    "Floating-rate notes have less market price risk because the coupon payments move up and down with market rates. The principal on the floater typically is `non-amortizing` and is redeemed in full at maturity. Reference rates are usually short-term money market rates such as Libor. The reference rate at the beginning of the period is used to compute the coupon payment at the end, which is an `arrears` payment structure.\n",
    "\n",
    "*(The reference rate is determined at the beginning of the period, and the interest payment is made at the end of the period. This payment structure is called “in arrears.”)*\n",
    "\n",
    "The most common day-count conventions for calculating accrued interest on floaters are `actual/360` and `actual/365`.\n",
    "\n",
    "- The `quoted margin` is the spread over the reference rate. It compensates investors for the credit risk of the issuer. The floater is priced at a premium above par value if the quoted margin (QM) is greater than the discount margin (DM)b.\n",
    "- The `required margin` (or `discount margin`) is the yield spread over the reference rate needed to make the FRN trade at par. It usually differs from the quoted margin due to changes in the issuer’s credit rating. The required margin will increase if the credit quality decreases. Changes in liquidity or tax status also could affect the required margin. \n",
    "\n",
    "The present value of a floating-rate note can be calculated with the following simplified formula:\n",
    "$$PV=\\displaystyle\\frac{\\frac{(Index + QM)(FV)}{m}}{(1+\\frac{(Index + DM)}{m})^1}+\\displaystyle\\frac{\\frac{(Index + QM)(FV)}{m}}{(1+\\frac{(Index + DM)}{m})^2}+…+\\displaystyle\\frac{\\frac{(Index + QM)(FV)}{m}+FV}{(1+\\frac{(Index + DM)}{m})^N}$$\n",
    "where\n",
    "\n",
    "$PV$ = present value, or the price of the floating-rate note\n",
    "\n",
    "$Index$ = reference rate, stated as an annual percentage rate\n",
    "\n",
    "$QM$ = quoted margin, stated as an annual percentage rate\n",
    "\n",
    "$FV$ = future value paid at maturity, or the par value of the bond\n",
    "\n",
    "$m$ = periodicity of the floating-rate note, the number of payment periods per year\n",
    "\n",
    "$DM$ = discount margin, the required margin stated as an annual percentage rate\n",
    "\n",
    "$N$ = number of evenly spaced periods to maturity\n",
    "\n",
    "If the price is known, the above formula can be used to estimate the discount margin.\n",
    "\n",
    "This equation is similar to Equation 1, which is the basic pricing formula for a fixed-rate bond given the market discount rate. \n",
    "- In Equation 1, $PMT$ is the coupon payment per period. Here, annual rates are used. The first interest payment is the annual rate for the period $(Index + QM)$ times the par value ($FV$) and divided by the number of periods in the year ($m$). \n",
    "- In Equation 1, the market discount rate per period ($r$) is used to discount the cash flows. Here, the discount rate per period is the reference rate plus the discount margin $(Index + DM)$ divided by the periodicity ($m$).\n",
    "\n",
    "This is a simplified FRN pricing model for several reasons. \n",
    "- First, PV is for a rate reset date when there are $N$ evenly spaced periods to maturity. There is no accrued interest ($AI$) so that the flat price is the full price. \n",
    "- Second, the model assumes a 30/360 day-count convention so that the periodicity is an integer. \n",
    "- Third, and most important, the same reference rate (Index) is used for all payment periods in both the numerators and denominators. \n",
    "\n",
    "More complex FRN pricing models use projected future rates for Index in the numerators and spot rates in the denominators. Therefore, the calculation for DM depends on the simplifying assumptions in the pricing model.\n",
    "\n",
    "With fixed-rate bonds, the premium or discount arises from a difference in the fixed coupon rate and the required yield-to-maturity. With floating-rate bonds, the premium or discount arises from a difference in the fixed quoted margin and the required margin. However, fixed-rate and floating-rate bonds are very different with respect to changes in benchmark interest rates.\n",
    "### Yield Measures for Money Market Instruments\n",
    "Fixed-income securities are classified as money market instruments if they have maturities of less than one year. Money market mutual funds are a major investor in such securities. These mutual funds can invest only in certain eligible money market securities. They include \n",
    "- repos\n",
    "- bank certificates of deposit\n",
    "- commercial paper\n",
    "- government issues\n",
    "- bankers’ acceptances\n",
    "- time deposits based on such indexes as Libor and Euribor\n",
    "\n",
    "There are key differences between the money market and bond market.\n",
    "- Bond yields-to-maturity are annualized and compounded. **Yield measures in the money market are annualized but not compounded**. Instead, the rate of return on a money market instrument is stated on a `simple interest basis`.\n",
    "- Bond yields-to-maturity can be calculated using standard time-value-of-money analysis and with formulas programmed into a financial calculator. Money market instruments often are quoted using `nonstandard interest rates` and require different pricing equations than those used for bonds.\n",
    "- Bond yields-to-maturity usually are stated for a common periodicity for all times-to-maturity. Money market instruments having different times-to-maturity have different periodicities for the annual rate.\n",
    "\n",
    "#### Discount Rate (DR) Basis\n",
    "It is important to understand that “discount rate” has a unique meaning in the money market. In general, discount rate means “interest rate used to calculate a present value”—for instance, “market discount rate” as used in this reading. In the money market, however, discount rate is a specific type of quoted rate. \n",
    "\n",
    "Usually, `commercial paper`, `Treasury bills`, and `bankers’ acceptances` are quoted on a `discount rate (DR)` basis. \n",
    "\n",
    "This method understates the rate of return to the investor because it is based on the `maturity value (FV)` rather than the `investment amount (PV)`.\n",
    "\n",
    "Pricing formula for money market instruments quoted on a discount rate basis\n",
    "$$PV=(FV)(1−\\frac{Days}{Year}×DR)$$\n",
    "where\n",
    "\n",
    "$PV$\t=\tpresent value, or the price of the money market instrument\n",
    "\n",
    "$FV$\t=\tfuture value paid at maturity, or the face value of the money market instrument\n",
    "\n",
    "$Days$\t=\tnumber of days between settlement and maturity\n",
    "\n",
    "$Year$\t=\tnumber of days in the year\n",
    "\n",
    "$DR$\t=\tdiscount rate, stated as an annual percentage rate\n",
    "\n",
    "The unique characteristics of a money market discount rate can be examined with:\n",
    "$$DR=(\\frac{Year}{Days})(\\frac{FV−PV}{FV})$$\n",
    "The first term, $\\frac{Year}{Days}$, is the periodicity of the annual rate.\n",
    "\n",
    "The second term reveals the odd character of a money market discount rate. The numerator, $FV – PV$, is the interest earned on the T-bill over the (n days) to maturity. H\n",
    "\n",
    "owever, the denominator is $FV$, not $PV$. In theory, an interest rate is the amount earned divided by the investment amount ($PV$)—not divided by the total return at maturity, which includes the earnings ($FV$). Therefore, by design, a money market discount rate understates the rate of return to the investor, and it understates the cost of borrowed funds to the issuer. That is because $PV$ is less than $FV$ (as long as DR is greater than zero).\n",
    "#### Add-on Rate (AOR) Basis\n",
    "- `Bank certificates of deposit`\n",
    "- `repos` (repurchase agreements) \n",
    "- such indexes as Libor and Euribor\n",
    "\n",
    "Pricing formula for money market instruments quoted on an add-on rate basis\n",
    "$$PV=\\frac{FV}{(1+\\frac{Days}{Year}×AOR)}$$\n",
    "where\n",
    "\n",
    "$PV$\t=\tpresent value, principal amount, or the price of the money market instrument\n",
    "\n",
    "$FV$\t=\tfuture value, or the redemption amount paid at maturity including interest\n",
    "\n",
    "$Days$\t=\tnumber of days between settlement and maturity\n",
    "\n",
    "$Year$\t=\tnumber of days in the year\n",
    "\n",
    "$AOR$\t=\tadd-on rate, stated as an annual percentage rate\n",
    "\n",
    "The interest is calculated as the principal times the fraction of the year times the annual add-on rate. It is added to the principal to determine the redemption amount.\n",
    "\n",
    "The characteristics of an add-on rate can be examined with:\n",
    "$$AOR=(\\frac{Year}{Days})(\\frac{FV−PV}{PV})$$\n",
    "\n",
    "This equation indicates that an add-on rate is a reasonable yield measure for a money market investment. The first term, $Year/Days$, is the periodicity of the annual rate. The second term is the interest earned, FV – PV, divided by PV, the amount invested.\n",
    "\n",
    "#### Bond Equivalent Yield\n",
    "When comparing money market securities, it is important to use consistent methods. This is often done using a `bond equivalent yield`, which is a 365-day add-on rate basis. (definition: A calculation of yield that is annualized using the ratio of 365 to the number of days to maturity. Bond equivalent yield allows for the restatement and comparison of securities with different compounding periods.)\n",
    "\n",
    "Although these money market instruments might have been issued and traded on a discount rate basis, they typically are reported as bond equivalent yields. It is important for the analyst to know whether they have been converted to the same periodicity as the longer-term government bonds. If not, the observed yield curve can be misleading because the number of periods in the year is not the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# EXAMPLE 9\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# EXAMPLE 10\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Maturity Structure of Interest Rates\n",
    "### The Maturity Structure of Interest Rates (1)\n",
    "There are many reasons the yields on two bonds would be different, including \n",
    "- currency\n",
    "- credit risk\n",
    "- liquidity\n",
    "- tax status\n",
    "- periodicity\n",
    "- maturity\n",
    "\n",
    "Yields vary by maturity, i.e. `maturity structure of interest rates` or `term structure of interest rates`. It involves the analysis of yield curves, which are relationships between yields-to-maturity and times-to-maturity. There are different types of yield curves, depending on the characteristics of the underlying bonds.\n",
    "#### Spot Curve \n",
    "The `spot curve` (the zero or “strip” curve) is the yield on zero-coupon government bonds. These are thought of as risk-free because there is no credit risk. Normally, the spot curve has a positive slope, which means longer maturity bonds earn a higher yield than shorter maturity bonds. A downward sloping spot curve is called an `inverted yield curve`.\n",
    "\n",
    "*However, most actively traded government and corporate bonds make coupon payments. Therefore, analysis of maturity structure usually is based on price data on government bonds that make coupon payments.*\n",
    "\n",
    "**The most recently issued government bonds are normally used to construct the spot curve because they are most similar in liquidity and have fewer tax effects.** But this limits the observable maturities (there are limited data for the full range of maturities), so `interpolation` is necessary. Usually, this is done with `straight-line interpolation`. \n",
    "\n",
    "#### Par Curve\n",
    "The par curve is obtained from a spot curve. On a coupon payment date, the following equation can be used to calculate a `par rate` given the sequence of spot rates.\n",
    "\n",
    "$$100=\\frac{PMT}{(1+z_1)^1}+\\frac{PMT}{(1+z_2)^2}+⋯+\\frac{PMT+100}{(1+z_N)^N}$$\n",
    "This equation is very similar to Equation 2 whereby $PV = FV = 100$. The problem is to solve for PMT algebraically. Then, $\\frac{PMT}{100}$ is equal to the par rate per period."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example\n",
    "\n",
    "The spot rates on government bonds are 5.2% for one year, 5.6% for two years, and 6.4% for three years.\n",
    "\n",
    "Derive the par curve from these rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# par rate of Y1\n",
    "\n",
    "# par rate of Y2\n",
    "\n",
    "# par rate of Y3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Yield curves\n",
    "Image(filename='yield_curve.png') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An example illustrates the calculation of the par curve given a spot curve. Suppose the spot rates on government bonds are 5.263% for one year, 5.616% for two years, 6.359% for three years, and 7.008% for four years. These are effective annual rates. The one-year par rate is 5.263%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Maturity Structure of Interest Rates (2)\n",
    "Money market securities are often settled on a `cash basis` (the same day). Other bonds may have a *delay* between the trade date and settlement date (like T+1 or T+3).\n",
    "#### Forward Curve\n",
    "`Forward rates` are the interest rates on bonds traded in the forward market. The notation can be confusing, but normally the first number is the length of the forward period and the second number is the tenor of the underlying bond. For example, the “3y5y” is the five-year yield three years into the future.\n",
    "\n",
    "Implied forward rates can be calculated from spot rates. Returns on shorter-term bonds are linked to match the total return on a longer-term bond. This makes the implied forward rate a breakeven reinvestment rate. The following formula can be used to construct a forward curve:\n",
    "\n",
    "$$(1+z_A)^A×(1+IFR_{A, B−A})^{B−A}=(1+z_B)^B$$\n",
    "where\n",
    "\n",
    "$z_A$ is the zero-coupon spot yield for Time A\n",
    "\n",
    "$z_B$ is the zero-coupon spot yield for Time B\n",
    "\n",
    "$IFR_{A, B−A}$ is the implied forward rate for a security start at Time A and maturity at Time B\n",
    "\n",
    "A `forward curve` is a series of forward rates, each having the same time frame. In an upward-sloping spot rate environment, forward rates will be higher than spot rates for the same maturities. Thus, if the yield curve is upward sloping, the forward curve must be located above the spot curve.\n",
    "\n",
    "Forward rates can also be used to calculate the present value of fixed income securities because spot rates are just the *geometric averages* of forward rates.\n",
    "\n",
    "$$(1+z_1)×(1+IFR_{1,1})×(1+IFR_{2,1})×…×(1+IFR_{n−1,1})=(1+z_n)^n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Yield Spreads\n",
    "Yield spreads are measures of how much additional yield over the benchmark security (usually a government bond) investors expect for bearing additional risk. \n",
    "### Yield Spreads over Benchmark Rates\n",
    "In fixed-income security analysis, it is important to understand why bond prices and yields-to-maturity change. To do this, it is useful to separate a `yield-to-maturity` into two components: \n",
    "1. the benchmark (`risk-free rate of return`)\n",
    "  - the base rate, often an on-the-run government bond yield; \n",
    "  - capture `expected real rate` and the macroeconomic factors that affect bond yields:\n",
    "    - expected rate of *inflation* in the currency in which the bond is denominated\n",
    "    - general economic growth and the business cycle\n",
    "    - foreign exchange rates\n",
    "    - the impact of monetary and fiscal policy \n",
    "  - includes the expected real rate plus the expected inflation rate.\n",
    "2. the spread (`risk premium`): the difference between the yield-to-maturity and the benchmark\n",
    "  - capture the microeconomic factors:\n",
    "    - taxation status of the bond\n",
    "    - credit risk of the issuer and changes in the quality rating on the bond\n",
    "    - liquidity and trading in comparable securities\n",
    "  - *note that the general yield spreads across issuers can widen and narrow with changes in macroeconomic factors.*\n",
    "\n",
    "*(An on-the-run government bond are the most actively traded issues with prices close to par. Off-the-run bonds are not as liquid. `Libor` is a frequent benchmark for floating-rate notes, although it is not risk-free.)* Seasoned government bonds are called off-the-run. **On-the-run bonds typically trade at slightly lower yields-to-maturity than off-the-run bonds having the same or similar times-to-maturity because of differences in demand for the securities and, sometimes, differences in the cost of financing the government security in the repo market.**\n",
    "\n",
    "Benchmark spreads are usually measured in basis points. \n",
    "- If the spread is computed over a government bond yield, it is known as a `G-spread`. \n",
    "- Euro-denominated corporate bonds are priced over a EUR `interest rate swap benchmark`. *(Note that the government bond yield or swap rate used as the benchmark for a specific corporate bond will change over time as the remaining time-to-maturity changes.)*\n",
    "- The `I-spread` (or `interpolated spread`) is the yield spread over a swap curve (`standard swap rate`).\n",
    "\n",
    "This yield spread over Libor allows comparison of bonds with differing credit and liquidity risks against an interbank lending benchmark. \n",
    "- Issuers often use the Libor spread to determine the relative cost of fixed-rate bonds versus floating-rate alternatives, such as an FRN or commercial paper. \n",
    "- Investors use the Libor spread as a measure of a bond’s credit risk. <br>\n",
    "Whereas a `standard interest rate swap` involves an exchange of fixed for floating cash flows based on a floating index, an `asset swap` converts the periodic fixed coupon of a specific bond to a Libor plus or minus a spread. If the bond is priced close to par, this conversion approximates the price of a bond’s credit risk over the Libor index. \n",
    "\n",
    "### Yield Spreads over the Benchmark Yield Curve\n",
    "A yield curve shows the relationship between yields-to-maturity and times-to-maturity for securities with the same risk profile. (e.g. The swap yield curve shows the relationship between fixed Libor swap rates and their times-to-maturity.) Each of these yield curves represents the term structure of benchmark interest rates, whether for “risk-free” government yields or “risky” fixed swap rates.\n",
    "\n",
    "Benchmark yield curves are typically upward-sloping because investors demand a premium to hold longer-term securities. The term structure of interest rates is dynamic, with short-term rates driven by central bank policy and longer-term rates affected by long-term growth and inflation expectations.\n",
    "\n",
    "Isolating credit risk over varying times-to-maturity gives rise to a term structure of credit spreads that is distinct for each borrower:\n",
    "- The G-spread and I-spread approaches use the same discount rate for each cash flow. \n",
    "- Another approach is to calculate a constant yield spread over a government (or interest rate swap) spot curve instead. This spread is known as the `zero volatility spread` (`Z-spread`, a.k.a. `static spread`) of a bond over the benchmark rate. (To fine tune the calculation, a `Z-spread` can be used, which is the spread over the spot curve.) The following equation can be used:\n",
    "$$PV=\\frac{PMT}{(1+z_1+Z)}^1+\\frac{PMT}{(1+z_2+Z)^2}+…+\\frac{PMT+FV}{(1+z_N+Z)^N}$$\n",
    "where \n",
    "$z_1, z_2, …, z_N$ are benchmark spot rates— they are derived from the government yield curve (or from fixed rates on interest rate swaps)\n",
    "\n",
    "$Z$ is the Z-spread per period and is the same for all time periods. \n",
    "\n",
    "$N$ is an integer, so the calculation is on a coupon date when the accrued interest is zero. \n",
    "\n",
    "In practice, the Z-spread is usually calculated in a spreadsheet using a goal seek function or similar solver function.\n",
    "\n",
    "The Z-spread can also be used to calculate the `option-adjusted spread (OAS)` on a `callable bond`.\n",
    "$$OAS=Zspread−Option\\ value\\ (in\\ basis\\ points)$$\n",
    "(In particular, the value of the embedded call option is subtracted from the Z-spread)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example\n",
    "\n",
    "A 6% annual coupon corporate bond with two years remaining to maturity is trading at a price of 100.125. The two-year, 4% annual payment government benchmark bond is trading at a price of 100.750. The one-year and two-year government spot rates are 2.10% and 3.635%, respectively, stated as effective annual rates.\n",
    "\n",
    "Calculate the G-spread, the spread between the yields-to-maturity on the corporate bond and the government bond having the same maturity.\n",
    "\n",
    "Demonstrate that the Z-spread is 234.22 bps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Answer 1: 0.02327"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Asset-Backed Securities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Securitization\n",
    "### Benefits of Securitization\n",
    "For lenders (e.g., banks), loans are assets that provide a stream of incoming cash flows. `Securitization` is the process of transferring ownership of these assets to a special legal entity and creating `asset-backed securities (ABS)` that allow investors to purchase **direct claims to their cash flows**. The pool of securitized assets from which the ABS’s cash flows are generated is called the `collateral`. Assets that are used to create ABS are called `securitized assets`, they are typically: \n",
    "- loans: residential mortgage loans (mortgages), commercial mortgages, automobile (auto) loans, student loans, bank loans\n",
    "- receivables: accounts receivables, and credit card receivables\n",
    "\n",
    "Securitization offers the following benefits:\n",
    "- Banks can originate more loans than they would be able to finance with customer deposits alone\n",
    "- More funds are available to borrowers at a lower cost\n",
    "- ABS is more liquid (tradable) than unsecuritized loans, which makes markets more efficient\n",
    "- Investors can choose the securities that match their risk and return objectives\n",
    "- Governments can use securitization to privatize public assets\n",
    "\n",
    "The risks of securitization include:\n",
    "- Borrowers may default on the underlying loans (credit risk)\n",
    "- The underlying cash flows may be received sooner or later than expected (`contraction risk` and `extension risk`, respectively)"
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    "## How Securitization Works\n",
    "### Parties to a Securitization and Their Roles\n",
    "There are three key parties to a securitization:\n",
    "1. The seller (or `depositor`) originates the assets that are used as collateral\n",
    "2. The issuer is the legally distinct `special purpose vehicle (SPV)` that is established to create the asset-backed securities\n",
    "3. The `servicer` collects payments on the underlying loans: the servicer may be the seller or a third party appointed by the SPV. (responsible for collecting payments from borrowers, notifying borrowers who may be delinquent, and if necessary, recovering and disposing of the automobile - as an example, if the borrower defaults.)\n",
    "\n",
    "Other third parties that are involved in a securitization include:\n",
    "- Lawyers to draft the sale agreements as well as the prospectus for the security issue\n",
    "- Investment banks to underwrite the securities\n",
    "- Monoline insurance companies to guarantee to performance of the underlying assets, although such guarantees have been less common since the credit crisis of 2007 - 2009\n",
    "- Rating agencies to assess the credit risk of the securities\n",
    "- Trustees, typically financial institutions, to safeguard the assets that have been transferred to the SPV and hold funds that are due to be transferred to investors\n",
    "\n",
    "An important legal document is the `prospectus`, which describes the structure of the securitization, including the priority and amount of payments to be made to the servicer, administrators, and the ABS holders.\n",
    "\n",
    "Securitizations often use several forms of `credit enhancements`, which are documented in the prospectus. Credit enhancements are provisions that are used to reduce the credit risk of a bond issue. They include \n",
    "- internal credit enhancements\n",
    "  - subordination (a.k.a. `credit tranching`)\n",
    "  - overcollateralization \n",
    "  - reserve accounts\n",
    "- external credit enhancements\n",
    "  - financial guarantees by banks or insurance companies\n",
    "  - letters of credit\n",
    "  - cash collateral accounts\n",
    "\n",
    "### Structure of a Securitization - Credit Tranching and Time Tranching\n",
    "Securitizations are typically structured with **multiple classes of bonds, called tranches**. Senior tranches have the lowest credit risk because the first losses are absorbed by subordinated tranches.\n",
    "\n",
    "Creating multiple tranches to absorb losses sequentially (also called `credit tranching`) allows investors to choose their preferred level of exposure to credit risk. Less senior tranches will appeal to investors who are willing to accept more credit risk in exchange for higher expected returns.\n",
    "\n",
    "As noted earlier, securitizations create uncertainty with respect to credit risk as well as the timing of payments. `Prepayment risk` is a concern for investors if borrowers are able to retire their loan obligations early in a low interest rate environment. This risk can be mitigated with `time tranching`, which is like credit tranching in that certain classes of bonds will absorb prepayments before other classes are affected.\n",
    "### Key Role of the Special Purpose Entity\n",
    "Because an SPV is recognized as a legally distinct entity, its assets are `bankruptcy remote`. *(If the original issuer files for bankruptcy, its creditors have no claim to any assets that have been transferred to an SPV.)* If a bank securitizes a pool of loans, investors who purchase the securities are only exposed to the risk that the borrowers are unable to repay their loans.\n",
    "\n",
    "Because the risk associated with securitizations is completely separate from the issuer's credit risk, investors usually require **lower yields** for more senior tranches than they would for debt issued by the seller, even if the same assets are pledged as collateral, related concept: `credit spread`.\n",
    "\n",
    "According to the `absolute priority rule`, senior creditors must be made whole before subordinated creditors receive anything in the event of a liquidation. However, if the bankrupt company is restructured, there is no guarantee that secured bondholders will receive the assets that have been pledged as collateral. By contrast, **the absolute priority rule is applied strictly when allocating cash flows (and losses) among different tranches of a securitization.**"
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    "## Residential Mortgage Loans\n",
    "A mortgage loan is simply a loan with real estate as collateral. If a borrower is unable to make payments, the lender can take ownership of the property and sell it. This process, known as `foreclosure`, allows lenders to recover the value of their investments.\n",
    "\n",
    "The `loan-to-value ratio (LTV)` is the ratio of the mortgage amount to the property’s purchase price. Borrowers with lower LTV ratios are less likely to default.\n",
    "$$\\frac{mortgage\\ amount}{purchase\\ price}$$\n",
    "#### Maturity\n",
    "The term of a mortgage is the number of years until maturity. In the United States, mortgage terms are typically 15 to 30 years. Maturities tend to be longer in Europe and maybe as long as 100 years in Japan.\n",
    "\n",
    "As a general rule, residential mortgage lenders tend to avoid terms that exceed the amount of time remaining until the borrower's expected retirement.\n",
    "#### Interest Rate Determination\n",
    "Like all loans, mortgages require the borrower to make interest payments. The interest rate for a mortgage can be specified in several ways, including:\n",
    "- Fixed rate: The rate is fixed for the life of the mortgage. This structure is commonly used in the United States and France.\n",
    "- Adjustable (variable) rate: The rate is reset periodically based on an index or at the lender’s discretion. The terms of an `adjustable-rate mortgage (ARM)` typically limit the amount that the rate may change at each reset date and establish a minimum rate over the life of the mortgage.\n",
    "- Initial period fixed rate: The mortgage rate is fixed for a period of time and then reset. \n",
    "  - `Rollover mortgages` reset to another fixed rate, while \n",
    "  - `hybrid mortgages` convert to an ARM\n",
    "- Convertible: At some point during the mortgage term, the borrower has the option to convert from a fixed rate to a variable rate (or vice versa). This structure is common in Japan.\n",
    "\n",
    "#### Amortization Schedule （分期偿还）\n",
    "Most residential mortgages are `amortizing loans`, meaning **a portion of each payment by the borrower reduces the outstanding principal**. Most US mortgage loans amortize the full amount of principal over the term. Partially amortizing loans require a large `balloon payment` at maturity for the amount of outstanding principal.\n",
    "\n",
    "`Interest-only mortgages` have no scheduled principal repayment for a certain number of years. \n",
    "\n",
    "A `bullet mortgage` is an extreme type of interest-only mortgage that requires the full face value of the loan to be repaid at maturity.\n",
    "#### Prepayment Options and Prepayment Penalties\n",
    "Borrowers often have the right to pay more than the scheduled amount of principal. A `prepayment option` allows a borrower to repay some or all of the outstanding principal.\n",
    "\n",
    "Provisions that allow for excess principal repayments create `prepayment risk` for investors. Lenders try to mitigate this risk by imposing penalties on prepayments.\n",
    "#### Rights of the Lender in a Foreclosure\n",
    "A mortgage is described as being \"`underwater`\" if the value of the property is less than the amount of outstanding principal (i.e., the **LTV ratio is greater than 1**). If a borrower defaults on an underwater mortgage, the lender may not be able to recoup the full amount of the outstanding loan from a foreclosure sale.\n",
    "\n",
    "If a mortgage is a `recourse loan`, the lender can require the borrower to make up the difference between the outstanding loan and the sale price. With non-recourse loans, lenders have no claim beyond the proceeds of a foreclosure sale.\n",
    "\n",
    "Borrowers with underwater non-recourse loans have an incentive to strategically default rather than continuing to make payments on a mortgage that is more than the value of their home. However, `strategically defaulting` will have a negative effect on a borrower's creditworthiness and ability to access funds in the future."
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    "## Residential Mortgage-Backed Securities\n",
    "Some residential mortgages are backed by the `government or quasi-government entities` (such as Fannie Mae or Freddie Mac in the United States). This sector is referred to as `agency RMBS` in the United States. *Those issued by `private entities` are in the non-agency RMBS sector.*\n",
    "\n",
    "Government agencies have certain criteria for mortgages to be included in a pool of securitized loans. These include\n",
    "- maximum loan size\n",
    "- loan documentation\n",
    "- maximum LTV ratio\n",
    "- insurance. \n",
    "\n",
    "Loans that meet these standards are called `conforming mortgages`. `Non-conforming loans` may be packaged into non-agency RMBS. (A `non-conforming mortgage` is one that does not satisfy the underwriting standards for inclusion as collateral for an agency RMBS.)\n",
    "### Mortgage Pass-Through Securities\n",
    "#### Characteristics\n",
    "`Mortgage pass-through securities` are shares that represent a claim to the cash flows from an underlying pool of mortgages. Investors receive cash flows in the form of interest, scheduled principal payments, and prepayments.\n",
    "\n",
    "The amount of cash flow received by investors is reduced by the *servicing and administrative fees* that issuers and third parties charge for activities such as collecting payments, sending payment notices, maintaining records, and providing tax information. The `pass-through rate` earned by investors is less than the interest rate on the underlying mortgages by the amount of these fees.\n",
    "\n",
    "Because the underlying mortgages in the pool are not identical, a `weighted average coupon rate (WAC)` and `weighted average maturity (WAM)` are calculated based on the outstanding value of each mortgage.\n",
    "#### Prepayment Risk\n",
    "Prepayment risk includes both `contraction risk` and `extension risk`.\n",
    "\n",
    "**Contraction risk** is the possibility that homeowners will prepay their mortgages and refinance in a low interest rate environment. Investors will receive more cash at a time when expected returns have fallen. Additionally, if the security is callable, it will not appreciate as much as an otherwise identical option-free bond.\n",
    "\n",
    "**Extension risk** is the opposite of contraction risk. If interest rates increase, homeowners will not be motivated to prepay mortgages with relatively low rates. Investors will receive less cash that can be reinvested in this higher interest rate environment.\n",
    "#### Prepayment Risk Measures\n",
    "Prepayment speed is commonly measured with the `single monthly mortality (SMM) rate`, which is calculated as follows:\n",
    "\n",
    "$$SMM=\\frac{Prepayment}{Beginning\\ mortgage\\ balance−Scheduled\\ principal\\ repayment}$$\n",
    "\n",
    "The SMM measure is expressed as a percentage. The SMM stated in annual terms is called the `conditional prepayment rate (CPR)`. For example, a 5% CPR implies that 5% of the outstanding principal at the beginning of the year is expected to be prepaid during the year.\n",
    "\n",
    "A key factor in the valuation of a mortgage pass-through security and other products derived from a pool of mortgages is forecasting the future prepayment rate.\n",
    "\n",
    "Prepayment speeds in the United States are also described as a multiple of the `Public Securities Association (PSA) prepayment benchmark`. The PSA is expressed as a series of monthly prepayment rates. Under this convention, 100 PSA refers to the `baseline prepayment rate`. Prepayment speeds greater than 100 PSA are prepaying faster than the benchmark. The PSA prepayment benchmark assumes that prepayment rates are low for newly originated mortgages and then speed up as the mortgages become seasoned.\n",
    "#### Cash Flow Construction\n",
    "(Example)\n",
    "#### Weighted Average Life\n",
    "Bonds typically pay back all the principal at maturity. However, mortgages usually pay back principal over the life of the security. The `weighted average life` is used by investors to indicate the amount of time before an MBS will be repaid, assuming constant interest rates and prepayment rates. MBS with higher PSA assumptions has shorter averages lives."
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    "### Collateralized Mortgage Obligations & Non-Agency RMBS\n",
    "The key difference between `collateralized mortgage obligations (CMOs)` and mortgage pass-through securities is that CMOs redistribute cash flows among multiple tranches with various levels of exposure to prepayment risk and credit risk.\n",
    "\n",
    "Mortgage securities can redistribute interest and principal payments to various classes through collateralized mortgage obligations (CMOs). This is primarily done to concentrate the prepayment risk in specific classes. There are many CMO structures, including:\n",
    "#### Sequential-Pay CMO Structures\n",
    "In this structure, each class (or tranche) is retired sequentially, which allows investors to choose the class that corresponds to their desired maturity. In a basic sequential-pay CMO structure, each tranche receives the same coupon rate, but all scheduled principal payments and prepayments are directed to one tranche until its full par value is repaid. After that, principal payments are directed to the next tranche. This is done until all tranches are completely paid off.\n",
    "\n",
    "Investors who hold tranches that are filled later are protected against contraction risk as long as there are higher priority tranches to absorb prepayments. Similarly, the first tranches to be filled are protected against extension risk because they will receive principal payments from all of the underlying mortgages until they are repaid.\n",
    "\n",
    "However, having several sequential-pay tranches does not eliminate all uncertainty about the timing of cash flows. The average life of each tranche will vary depending on the actual prepayment rate.\n",
    "#### CMO Structures Including Planned Amortization Class (PAC) and Support Tranches\n",
    "CMOs with planned amortization classes give investors even more protection against prepayment risk than sequential-pay CMOs. This is accomplished by having a `support tranche` to absorb all principal payments in excess of what is required to satisfy the schedule of the `PAC tranches`.\n",
    "\n",
    "If the actual prepayment rate stays within an expected range (e.g., 100 PSA - 200 PSA), each PAC tranche will be repaid on schedule. PAC tranches will only absorb prepayments after the support tranche has been repaid. Of course, the average life of the support tranche is highly volatile, even if the prepayment rate remains within the defined range.\n",
    "#### Other CMO Structures\n",
    "Some CMOs have floating rate tranches, even though they are based on a pool of fixed-rate mortgages. This is accomplished by creating an `inverse floating-rate tranche` to offset the floating rate tranche. When interest rates increase, the floating rate tranche will pay more and the inverse floating tranche will pay less (and vice versa when interest rates fall).\n",
    "### Non-agency Residential Mortgage-Backed Securities\n",
    "Mortgages that do not meet the criteria for inclusion in agency RMBS (`non-conforming mortgages`) may be pooled into privately issued pass-throughs securities call `non-agency RMBS`. The securities are issued by *financial intermediaries (e.g., commercial banks)*.\n",
    "\n",
    "Credit risk is a significant concern for non-agency RMBS, which are not guaranteed by any government or agency. In the event of defaults on underlying mortgages, some of the losses may be recouped via foreclosure sales. **Non-agency RMBS investors must consider the recovery rate, not just the default rate.**\n",
    "\n",
    "- Internal and external credit enhancement measures can be used to mitigate the credit risk of non-agency RMBS. \n",
    "- Subordination is used to allow investors to choose tranches that provide the optimal trade-off between risk and return given their particular investment objectives. \n",
    "- A `shifting interest mechanism` is used to ensure that the level of credit enhancement does not deteriorate for the most senior tranches. \n",
    "\n",
    "Since the credit crisis of 2007 - 2009, RMBS investors have demanded more credit enhancement measures, such as `over-collateralization` and `reserve accounts`."
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    "## Commercial Mortgage-Backed Securities (CMBS)\n",
    "Commercial mortgage-backed securities redistribute cash flows from a pool of mortgages on commercial properties (e.g., apartment buildings, offices, warehouses).\n",
    "### Credit Risk\n",
    "Credit risk is a significant consideration for CMBS investors, particularly in jurisdictions where commercial mortgages are `non-recourse loans`.\n",
    "\n",
    "As with residential mortgages, the `loan-to-value (LTV)` ratio is an important measure of credit risk. For commercial properties, investors can also use the `debt-to-service coverage (DSC) ratio`, which is calculated as follows:\n",
    "\n",
    "$$\\frac{Net\\ annual\\ operating\\ income}{Annual\\ interest\\ payments+Annual\\ principal\\ repayment}$$\n",
    "\n",
    "Lower LTV ratios and higher DSC ratios indicate lower credit risk.\n",
    "### CMBS Structure\n",
    "Like residential CMOs, CMBS are structured in tranches. A `residual tranche` (a.k.a. `equity tranche`) absorbs the first default losses from the underlying pool of mortgages. Using a subordinated structure reduces the credit risk of more senior tranches.\n",
    "#### Call Protection\n",
    "As noted earlier, prepayment risk is a significant concern for RMBS investors. Repaying mortgage principal ahead of schedule is equivalent to exercising a call option. Compared to RMBS, CMBS offers greater call protection, both at the structural level and the loan level.\n",
    "\n",
    "- **Structural call protection** is achieved with sequential payments based on each tranche's credit rating. The highest-rated tranches are repaid before those with lower ratings and default losses are absorbed by the lowest-rated tranches.\n",
    "- **Loan-level call protection** comes from the following mechanisms:\n",
    "  - Lockouts periods during which prepayments are prohibited.\n",
    "  - Prepayment penalty points, such as 1% of the outstanding loan balance to refinance.\n",
    "  - Yield maintenance charges that make lenders whole if the borrower chooses to refinance.\n",
    "  - `Defeasance`: defeasing future cash flows that the lender would receive in the absence of prepayments with a portfolio of government securities funded by the borrower.\n",
    "\n",
    "*(Defeasance is a call protection at the loan level that requires the borrower to provide sufficient funds for the servicer to invest in a portfolio of government securities that replicates the cash flows that would exist in the absence of prepayments.)*\n",
    "#### Balloon Maturity Provision\n",
    "Many CMBS require large principal payments at maturity. Failure to make this \"balloon payment\" triggers a default. Lenders can mitigate this risk by extending the loan for a `workout period` during which the borrower pays a higher mortgage rate. It follows that `balloon risk` is a form of extension risk."
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    "## Non-Mortgage Asset-Backed Securities\n",
    "In addition to mortgages, there are many types of assets that can be pooled and securitized. The two most common types of non-mortgage ABS are based on pools of auto loans and credit card receivables.\n",
    "#### Auto Loan ABS\n",
    "Like mortgages, auto loans follow an amortization schedule. The buyer makes a series of equal payments that are part interest, part principal. Over time, the interest portion of the payment decreases, and the principal component increases. Auto loan ABS investors will also receive cash flows from prepayments when vehicles are traded in or repossessed, as well as when insurance proceeds are paid after loss or destruction. Over time, the par value of the underlying pool decreases as loan payments are made.\n",
    "\n",
    "All auto loan-backed securities have credit enhancements. At a minimum, `subordinated tranches` are used to protect more senior tranches from defaults. `Reserve accounts` and `over-collateralization` may also be used as additional forms of credit enhancement.\n",
    "#### Credit Card Receivable ABS\n",
    "Unlike mortgages and auto loans, credit card receivables are `non-amortizing assets`. Credit card debts are not paid according to a defined schedule, so the underlying obligations may be paid off before the maturity of the ABS. To deal with this, `credit card receivable ABS` have `lockout periods` during which any principal repayments are reinvested in new receivables. Principal repayments received after the lockout period are distributed among the various tranches.\n",
    "\n",
    "`Early amortization provisions` are used to ensure that they protect the credit quality of the ABS if specific events occur (e.g., high default rates)."
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    "## Collateralized Debt Obligations\n",
    "`Collateralized debt obligation (CDO)` is a broad term for securities that are backed by a diversified pool of debt obligations. Examples of CDOs include:\n",
    "- Collateralized bond obligations (CBOs): Backed by corporate and emerging market bonds\n",
    "- Collateralized loan obligations (CLOs): Backed by bank loans\n",
    "- Structured finance CDOs: Backed by ABS, RMBS, CMBS, and other CDOs\n",
    "- Synthetic CDOs: Backed by credit default swaps and other structured securities\n",
    "\n",
    "#### CDO Structure\n",
    "A CDO is technically not an ABS. Rather, a collateral manager issues debt and uses the proceeds to purchase a portfolio of assets that provide cash flows for CDO bondholders. CDO tranches have different levels of risk, with equity tranches offering the highest expected returns.\n",
    "\n",
    "CDOs are effectively highly-leveraged portfolios. The manager's objective is to generate returns in excess of the coupon rate paid to bondholders. Mezzanine tranches fall between the senior and equity tranches in terms of riskiness and expected return. Equity investors receive the residual return in excess of payments to more senior tranches and the CDO manager's fees. Of course, they risk the possibility of less-than-expected returns or even the loss of their entire investment."
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