Equity_Investments_I.ipynb

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   "source": [
    "# Market Organization and Structure"
   ]
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   "source": [
    "Investment decisions involve trading *securities, currencies, contracts, commodities, and real assets such as real estate*."
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    "## The Functions of the Financial System\n",
    "Ability to identify the various uses of the financial system will help you avoid confusion that often leads to poor financial decisions. People use the financial system for six main purposes:\n",
    "1. to save money for the future;<br>\n",
    "To move money from the present to the future, savers buy notes, certificates of deposit, bonds, stocks, mutual funds, or real assets such as real estate. \n",
    "2. to borrow money for current use;<br>\n",
    "Lenders may contribute capital in exchange for equity in the projects.\n",
    "3. to raise equity capital;<br>\n",
    "Although these equity instruments legally represent ownership in companies rather than loans to the companies, selling equity to raise capital is simply another mechanism for moving money from the future to the present.\n",
    "4. to manage risks;<br>\n",
    "Risks include default risk and the risk of changes in interest rates, exchange rates, raw material prices, and sale prices, among many other risks. These risks are often managed by trading contracts that serve as hedges for the risks.\n",
    "\n",
    "The financial system facilitates risk management when liquid markets exist in which risk managers can trade instruments that are correlated (or inversely correlated) with the risks that concern them without incurring substantial transaction costs. Investment banks, exchanges, and insurance companies devote substantial resources to designing such contracts and to ensuring that they will trade in liquid markets. \n",
    "5. to exchange assets for immediate and future deliveries (Spot Market Trading); \n",
    "6. to trade on information<br>\n",
    "Information-motivated traders trade to profit from information that they believe allows them to predict future prices. Like all other traders, they hope to buy at low prices and sell at higher prices. Unlike pure investors, however, they expect to earn a return on their information in addition to the normal return expected for bearing risk through time.\n",
    "\n",
    "Active investment managers are information-motivated traders who collect and analyze information to identify securities, contracts, and other assets that their analyses indicate are under- or overvalued (` active portfolio management`) in order to earn a return in excess of the fair rate of return.\n",
    "\n",
    "The characteristic that most distinguishes investors from information-motivated traders is the return that they expect. Although both types of traders hope to obtain extraordinary returns, investors rationally expect to receive only fair returns during the periods of their investments. In contrast, information-motivated traders expect to make returns in excess of required fair rates of return. \n",
    "\n",
    "**The main functions of the financial system are to facilitate:**\n",
    "1. the achievement of the purposes for which people use the financial system;\n",
    "2. the discovery of the rates of return that equate aggregate savings with aggregate borrowings; and\n",
    "3. the allocation of capital to the best uses.\n",
    "\n",
    "### Determining Rates of Return\n",
    "The aggregate amount of money that savers will move from the present to the future is related to the expected rate of return on their investments.\n",
    "\n",
    "Because the total money saved must equal the total money borrowed and received in exchange for equity, the expected rate of return depends on the aggregate supply of funds through savings and the aggregate demand for funds. (If the rate is too high, savers will want to move more money to the future than borrowers and equity issuers will want to move to the present. The expected rate will have to be lower to discourage the savers and to encourage the borrowers and equity issuers.)\n",
    "\n",
    "`Equilibrium interest rate`: Between rates too high and too low, an expected rate of return exists, in theory, in which the aggregate supply of funds for investing (supply of funds saved) and the aggregate demand for funds through borrowing and equity issuing are equal.\n",
    "### Capital Allocation Efficiency\n",
    "`Primary capital markets (primary markets)` are the markets in which companies and governments raise capital (funds). Companies may raise funds by borrowing money or by issuing equity. Governments may raise funds by borrowing money.\n",
    "\n",
    "Economies are said to be `allocationally efficient` when their financial systems allocate capital (funds) to those uses that are most productive. "
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    "## Assets and Contracts\n",
    "Including notes, bonds, stocks, exchange-traded funds, currencies, forward contracts, futures contracts, option contracts, swap contracts, and certain commodities.\n",
    "\n",
    "### Classifications of Assets and Markets\n",
    "Classified by **common characteristics**. \n",
    "`financial assets`:<br>\n",
    "- Securities generally include \n",
    "  - debt instruments, (also called `fixed-income` instruments, e.g. government bonds) \n",
    "  - equities, and (represent ownership in companies)\n",
    "  - shares in pooled investment vehicles. \n",
    "- Currencies are monies issued by national monetary authorities. \n",
    "- Contracts are agreements to exchange securities, currencies, commodities or other contracts in the future. \n",
    "`physical assets`:<br>\n",
    "- Commodities include precious metals, energy products, industrial metals, and agricultural products. \n",
    "- Real assets are tangible properties such as real estate, airplanes, or machinery. \n",
    "\n",
    "Classfied by **immediate delivery or for future** delivery:<br>\n",
    "- Forward or futures markets (Markets that trade contracts that call for delivery in the future)\n",
    "- Spot markets (Those that trade for immediate delivery)\n",
    "- Options markets (Trade contracts that deliver in the future, but delivery takes place only if the holders of the options choose to exercise them)\n",
    "\n",
    "Classified by **money or capital** markets:<br>\n",
    "- Money markets trade debt instruments maturing in one year or less. The most common such instruments are `repurchase agreements`, `negotiable certificates of deposit`, `government bills`, and `commercial paper`. \n",
    "- Capital markets trade instruments of longer duration, such as bonds and equities, whose values depend on the credit-worthiness of the issuers and on payments of interest or dividends that will be made in the future and may be uncertain. \n",
    "\n",
    "Classified by **traditional or alternative** investment markets:<br>\n",
    "- Traditional investment markets: include all publicly traded debts and equities and shares in pooled investment vehicles that hold publicly traded debts and/or equities.\n",
    "- Alternative investment markets: include `hedge funds`, `private equities` (including `venture capital`), `commodities`, `real estate securities` and `real estate properties`, `securitized debts`, `operating leases`, `machinery`, `collectibles`, and `precious gems`.\n",
    "\n",
    "### Securities\n",
    "Securities include bonds, notes, commercial paper, mortgages, common stocks, preferred stocks, warrants, mutual fund shares, unit trusts, and depository receipts. \n",
    "\n",
    "Securities that are sold to the public or that can be resold to the public are called issues. Companies and governments are the most common issuers.\n",
    "\n",
    "Securities are also classified by whether they are **public or private securities**. \n",
    "- Public securities are those registered to trade in public markets, such as on exchanges or through dealers. \n",
    "- Private securities are all other securities. *(Often, only specially qualified investors can purchase private equities and private debt instruments. Venture capital is private equity that investors supply to companies when or shortly after they are founded. Private securities generally are illiquid.)*\n",
    "\n",
    "- `primary market`\n",
    "- `secondary market`\n",
    "\n",
    "#### Fixed Income\n",
    "Fixed-income instruments contractually include `predetermined payment schedules` that usually include interest and principal payments. \n",
    "\n",
    "(Fixed-income instruments generally are promises to repay borrowed money but may include other instruments with payment schedules, such as settlements of legal cases or prizes from lotteries.) \n",
    "\n",
    "The payment amounts may be pre-specified or they may vary according to a fixed formula that depends on the future values of an interest rate or a commodity price. Examples of promises to repay money in the future:\n",
    "- bonds (convertible bonds, which are typically convertible into stock, usually at the option of the holder after some period. If stock prices are high so that conversion is likely, convertibles are valued like stock.)\n",
    "- notes (Corporations and governments issue bonds and notes. Fixed-income securities with shorter maturities are called “notes,” those with longer maturities are called “bonds.”)\n",
    "- bills\n",
    "- certificates of deposit\n",
    "- commercial paper (Bills, certificates of deposit, and commercial paper are respectively issued by governments, banks, and corporations. They usually mature within a year of being issued; certificates of deposit sometimes have longer initial maturities.)\n",
    "- repurchase agreements (repos are short-term lending instruments.)\n",
    "- loan agreements\n",
    "- mortgages\n",
    "#### Equities\n",
    "##### Common Shares\n",
    "Own `residual rights` to the assets of the company. They have the right to \n",
    "- receive any dividends declared by the boards of directors, \n",
    "- in the event of liquidation, any assets remaining after all other claims are paid,\n",
    "- usually can select the managers who run the corporations\n",
    "\n",
    "##### Preferred Shares\n",
    "Preferred shares are equities that have preferred rights (relative to common shares) to the cash flows and assets of the company. Preferred shareholders generally have the right to \n",
    "- receive a specific dividend on a regular basis. (If the preferred share is a cumulative preferred equity, the company must pay the preferred shareholders any previously omitted dividends before it can pay dividends to the common shareholders.) \n",
    "- have higher claims to assets relative to common shareholders in the event of corporate liquidation. \n",
    "\n",
    "*(Note: For valuation purposes, financial analysts generally treat preferred stocks as fixed-income securities when the issuers will clearly be able to pay their promised dividends in the foreseeable future.)*\n",
    "\n",
    "`Warrants` are securities issued by a corporation that allow the warrant holders to buy a security issued by that corporation, if they so desire, usually at any time before the warrants expire or, if not, upon expiration. The security that warrant holders can buy usually is the issuer’s common stock, in which case the warrants are considered equities because the warrant holders can obtain equity in the company by exercising their warrants. The warrant exercise price is the price that the warrant holder must pay to buy the security.\n",
    "#### Pooled Investments\n",
    "Pooled investment vehicles are mutual funds, trusts, depositories, and hedge funds, that issue securities that represent shared ownership in the assets that these entities hold. \n",
    "\n",
    "*(The securities created by mutual funds, trusts, depositories, and hedge fund are respectively called `shares, units, depository receipts, and limited partnership interests` but practitioners often use these terms interchangeably.)*\n",
    "\n",
    "Mutual funds are investment vehicles that pool money from many investors for investment in a portfolio of securities. They are often legally organized as investment trusts or as corporate investment companies. \n",
    "\n",
    "Asset-backed securities are securities whose values and income payments are derived from a pool of assets\n",
    "\n",
    "Hedge funds are investment funds that generally organize as limited partnerships. The hedge fund managers are the general partners. The limited partners are qualified investors who are wealthy enough and well informed enough to tolerate and accept substantial losses, should they occur. The regulatory requirements to participate in a hedge fund and the regulatory restrictions on hedge funds vary by jurisdiction. Most hedge funds follow only one investment strategy, but no single investment strategy characterizes hedge funds as a group. Hedge funds exist that follow almost every imaginable strategy ranging from long–short arbitrage in the stock markets to direct investments in exotic alternative assets. The primary distinguishing characteristic of hedge funds is their management compensation scheme. Almost all funds pay their managers with an annual fee that is proportional to their assets and with an additional performance fee that depends on the wealth that the funds generate for their shareholders. A secondary distinguishing characteristic of many hedge funds is the use of leverage to increase risk exposure and to hopefully increase returns.\n",
    "\n",
    "Pooled investment vehicles may be open-ended or closed-ended. \n",
    "1. Open-ended funds issue new shares and redeem existing shares on demand, usually on a daily basis. The price at which a fund redeems and sells the fund’s shares is based on the net asset value of the fund’s portfolio, which is the difference between the fund’s assets and liabilities, expressed on a per share basis. Investors generally buy and sell open-ended mutual funds by trading with the mutual fund.\n",
    "  - Exchange-traded funds (ETFs) and exchange-traded notes (ETNs) are open-ended funds that investors can trade among themselves in secondary markets. (related: authorized participants (APs))\n",
    "  - Many ETFs permit only in-kind deposits and redemptions. Buyers who buy directly from such a fund pay for their shares with a portfolio of securities rather than with cash.\n",
    "2. Closed-end funds issue shares in `primary market offerings` that the fund or its investment bankers arrange. Once issued, investors cannot sell their shares of the fund back to the fund by demanding redemption. Instead, investors in closed-end funds must sell their shares to other investors in the secondary market. The secondary market prices of closed-end funds may differ—sometimes quite significantly—from their net asset values. Closed-end funds generally trade at a discount to their net asset values. The discount reflects the expenses of running the fund and sometimes investor concerns about the quality of the management. Closed-end funds may also trade at a discount or a premium to net asset value when investors believe that the portfolio securities are overvalued or undervalued. Many financial analysts thus believe that discounts and premiums on closed-end funds measure market sentiment."
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    "### Currencies, Commodities, and Real Assets\n",
    "`Reserve currencies` are currencies that national central banks and other monetary authorities hold in significant quantities. The primary reserve currencies are the US dollar and the euro. Secondary reserve currencies include the British pound, the Japanese yen, and the Swiss franc.\n",
    "\n",
    "Commodities include precious metals, energy products, industrial metals, agricultural products, and carbon credits. \n",
    "\n",
    "Commodities also interest information-motivated traders and investment managers because they can use them as hedges against risks that they hold in their portfolios or as vehicles to speculate on future price changes. Information-motivated traders and investment managers also prefer to trade in futures markets because most futures markets are more liquid than their associated spot markets and forward markets. The liquidity allows them to easily close their positions before delivery so that they can avoid handling physical products. \n",
    "\n",
    "Some information-motivated traders and investment managers, however, trade in the spot commodity markets, especially when they can easily contract for low-cost storage. \n",
    "\n",
    "Real assets include such tangible properties as real estate, airplanes, machinery, or lumber stands. Real assets are unique properties in the sense that no two assets are alike. \n",
    "\n",
    "Many financial intermediaries create entities, such as `real estate investment trusts (REITs)` and `master limited partnerships (MLPs)`, to *securitize real assets and to facilitate indirect investment in real assets*. The financial intermediaries manage the assets and pass through the net benefits after management costs to the investors who hold these securities. (Because these securities are much more homogenous and divisible than the real assets that they represent, they tend to trade in much more liquid markets. Thus, they are much more suitable as investments than the real assets themselves.)\n",
    "\n",
    "Investors seeking exposure to real assets can also buy shares in corporations that hold and operate real assets. \n",
    "### Contracts\n",
    "The most common contracts are option, futures, forward, swap, and insurance contracts. The values of most contracts depend on the value of an underlying asset. \n",
    "- Physical\n",
    "- Financial\n",
    "\n",
    "Contracts are `derivative contracts` (e.g., a single stock futures contract) if their values depend on the prices of other underlying assets. Derivative contracts may be classified as physical or financial depending on whether the underlying instruments are physical products or financial securities. \n",
    "- `Equity derivatives` are contracts whose values depend on equities or indexes of equities. \n",
    "- `Fixed-income derivatives` are contracts whose values depend on debt securities or indexes of debt securities.\n",
    "\n",
    "#### Forward Contracts\n",
    "A forward contract is an agreement to trade the underlying asset in the future at a price agreed upon today. \n",
    "\n",
    "hedging (operating) risks\n",
    "- The first problem is counterparty risk. Counterparty risk is the risk that the other party to a contract will fail to honor the terms of the contract.\n",
    "- The second problem is liquidity. Trading out of a forward contract is very difficult because it can only be done with the consent of the other party. The liquidity problem ensures that forward contracts tend to be executed only among participants for whom delivery is economically efficient and quite certain at the time of contracting so that both parties will want to arrange for delivery.\n",
    "\n",
    "#### Futures Contracts\n",
    "A futures contract is a standardized forward contract for which a clearinghouse guarantees the performance of all traders. \n",
    "\n",
    "The buyer of a futures contract is the side that will take physical delivery or its cash equivalent. The seller of a futures contract is the side that is liable for the delivery or its cash equivalent. A clearinghouse is an organization that ensures that no trader is harmed if another trader fails to honor the contract. \n",
    "\n",
    "Because futures contracts are standardized, a buyer can eliminate his obligation to buy by selling his contract to anyone. A seller similarly can eliminate her obligation to deliver by buying a contact from anyone. \n",
    "\n",
    "`Variation margin payments` ensure that the liabilities associated with futures contracts do not grow large:\n",
    "- initial margin: The amount that must be deposited in a clearinghouse account when entering into a futures contract.\n",
    "- maintenance margin: The minimum amount that is required by a futures clearinghouse to maintain a margin account and to protect against default. If a participant does not provide sufficient additional margin when required, the participant’s broker will immediately trade to offset the participant’s position. \n",
    "\n",
    "Hedgers for whom the terms of the standard contract are not ideal generally still use the futures markets because the contracts embody most of the price risk that concerns them. They simply offset (close out) their futures positions, at the same time they enter spot contracts on which they make or take ultimate delivery.\n",
    "#### Swap Contracts\n",
    "A swap contract is an agreement to exchange payments of periodic cash flows that depend on future asset prices or interest rates.\n",
    "- `interest rate swap`: at periodic intervals, one party makes *fixed cash payments* to the counterparty in exchange for *variable cash payments* from the counterparty. \n",
    "  <br> The variable payments are based on a pre-specified variable interest rate such as the London Interbank Offered Rate (Libor).<br>\n",
    "  Use case: Investment managers often enter interest rate swaps when they own a fixed long-term income stream that they want to convert to a cash flow that varies with current short-term interest rates, or vice versa. The conversion may allow them to substantially reduce the total interest rate risk to which they are exposed. Hedgers often use swap contracts to manage risks.\n",
    "- `commodity swap`, one party typically makes fixed payments in exchange for payments that depend on future prices of a commodity such as oil. \n",
    "- In a `currency swap`, the parties exchange payments denominated in different currencies. The payments may be fixed, or they may vary depending on future interest rates in the two countries. \n",
    "- In an `equity swap`, the parties exchange fixed cash payments for payments that depend on the returns to a stock or a stock index.\n",
    "\n",
    "#### Option Contracts\n",
    "- An option to buy is a `call option`\n",
    "- An option to sell is a `put option` \n",
    "- The specified price is called the `strike price` (`exercise price`)\n",
    "- If the holders can exercise their contracts only when they mature, they are `European-style contracts`. \n",
    "- If they can exercise the contracts earlier, they are `American-style contracts`.\n",
    "- The price that traders pay for an option is the `option premium`. \n",
    "- The premium compensates the sellers of options—called `option writers`—for giving the call option holders the right to potentially buy below market prices and put option holders the right to potentially sell above market prices. Because the writers must trade if the holders exercise their options, option contracts may impose substantial liabilities on the writers.\n",
    "\n",
    "Option holders generally will exercise call options if the strike price is below the market price of the underlying instrument, in which case, they will be able to buy at a lower price than the market price. \n",
    "#### Other Contracts\n",
    "- Insurance contracts \n",
    "  - `Credit default swaps (CDS)` are insurance contracts that promise payment of principal in the event that a company defaults on its bonds.\n",
    "  \n",
    "People sometimes also buy insurance contracts as investments, especially in jurisdictions where payouts from insurance contracts are not subject to as much taxation as are payouts to other investment vehicles. "
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   "source": [
    "# EXAMPLE 13\n"
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    "Example: \n",
    "\n",
    "NYMEX’s Light Sweet Crude Oil futures contract specifies the delivery of 1,000 barrels of West Texas Intermediate Crude Oil when the contract finally settles. A broker requires that its clients post an initial overnight margin of \\\\$7,763 per contract and an overnight maintenance margin of \\\\$5,750 per contract. A client buys ten contracts at \\\\$75 per barrel through this broker. On the next day, the contract settles for \\\\$72 per barrel. How much additional margin will the client have to provide to his broker?"
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   "source": [
    "# "
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    "## Financial Intermediaries\n",
    "### Brokers, Exchanges, and Alternative Trading Systems\n",
    "**Brokers** are agents who fill orders for their clients. They do not trade with their clients. Instead, they search for traders who are willing to take the other side of their clients’ orders. Brokers help their clients trade by reducing the costs of finding counterparties for their trades.\n",
    "\n",
    "**Block brokers** provide brokerage service to large traders.\n",
    "\n",
    "**Investment banks** provide advice to their mostly corporate clients and help them arrange transactions such as initial and seasoned securities offerings. Their corporate finance divisions help corporations finance their business by issuing securities or identify and acquire other companies. \n",
    "\n",
    "**Exchanges** provide places where traders can meet to arrange their trades. Historically, brokers and dealers met on an exchange floor to negotiate trades. Increasingly, exchanges arrange trades for traders based on orders that brokers and dealers submit to them. Such exchanges essentially act as brokers.\n",
    "\n",
    "  - *(Alternative trading systems (ATSs), also known as electronic communications networks (ECNs) or multilateral trading facilities (MTFs) are trading venues that function like exchanges but that do not exercise regulatory authority over their subscribers except with respect to the conduct of their trading in their trading systems.)*\n",
    "  - Many ATSs are known as dark pools because they do not display the orders that their clients send to them. Large investment managers especially like these systems because market prices often move to their disadvantage when other traders know about their large orders. \n",
    "  \n",
    "### Dealers\n",
    "Dealers fill their clients’ orders by trading with them. When their clients want to sell securities or contracts, dealers buy the instruments for their own accounts. If their clients want to buy securities, dealers sell securities that they own or have borrowed. After completing a transaction, dealers hope to reverse the transaction by trading with another client on the other side of the market. \n",
    "\n",
    "The service that dealers provide is liquidity. Liquidity is the ability to buy or sell with low transactions costs when you want to trade. By allowing their clients to trade when they want to trade, dealers provide liquidity to them. In over-the-counter markets, dealers offer liquidity when their clients ask them to trade with them. In exchange markets, dealers offer liquidity to anyone who is willing to trade at the prices that the dealers offer at the exchange.\n",
    "\n",
    "Dealers may organize their operations within proprietary trading houses, investment banks, and hedge funds, or as sole proprietorships. Almost all investment banks have large dealing operations.\n",
    "\n",
    "*(Most dealers also broker orders, and many brokers deal to their customers. Accordingly, practitioners often use the term broker–dealer to refer to dealers and brokers. Broker–dealers have a conflict of interest with respect to how they fill their customers’ orders. The problem is most serious when the customer allows the broker–dealer to decide whether to trade the order with another trader or to fill it as a dealer.)*\n",
    "\n",
    "`Primary dealers` are dealers with whom central banks trade when conducting monetary policy. They buy bills, notes, and bonds when the central banks sell them to decrease the money supply. The dealers then sell these instruments to their clients. Similarly, when the central banks want to increase the money supply, the primary dealers buy these instruments from their clients and sell them to the central banks.\n",
    "### Arbitrageurs\n",
    "Arbitrageurs trade when they can identify opportunities to buy and sell identical or essentially similar instruments at different prices in different markets. They profit when they can buy in one market for less than they sell in another market. \n",
    "- The purest form of arbitrage involves buying and selling the same instrument in two different markets. \n",
    "\n",
    "Buying and selling instruments, whose values are closely related, at different prices in different markets.\n",
    "### Securitizers\n",
    "The process of buying assets, placing them in a pool, and then selling securities that represent ownership of the pool is called `securitization`.\n",
    "\n",
    "Because investors value liquidity—the ability to sell when they want to—they will pay more for securitized mortgages than for individual mortgages. \n",
    "\n",
    "In many securitizations, the financial intermediary avoids placing the assets and liabilities on its balance sheet by setting up a special `corporation or trust` that buys the assets and issues the securities. That corporation or trust is called a `special purpose vehicle (SPV)` or alternatively a `special purpose entity (SPE)`. Conducting a securitization through a special purpose vehicle is advantageous to investors because their interests in the asset pool are better protected in an SPV than they would be on the balance sheet of the financial intermediary if the financial intermediary were to go bankrupt.\n",
    "\n",
    "When financial intermediaries securitize assets, they often create several classes of securities, called `tranches`, that have different rights to the cash flows from the asset pool. The tranches are structured so that some produce more predictable cash flows than do others. The senior tranches have first rights to the cash flow from the asset pool. Because the overall risk of a given asset pool cannot be changed, the more junior tranches bear a disproportionate share of the risk of the pool. Practitioners often call the most junior tranche toxic waste because it is so risky.\n",
    "\n",
    "Investment companies also create `pass-through securities` based on investment pools. \n",
    "### Depository Institutions\n",
    "Depository institutions include commercial banks, savings and loan banks, credit unions, and similar institutions that raise funds from depositors and other investors and lend it to borrowers. The banks give their depositors interest and transaction services, such as check writing and check cashing, in exchange for using their money. They may also raise funds by selling bonds or equity in the bank.\n",
    "### Insurance Companies\n",
    "### Settlement and Custodial Services\n",
    "In addition to connecting buyers to sellers through a variety of direct and indirect means, financial intermediaries also help their customers settle their trades and ensure that the resulting positions are not stolen or pledged more than once as collateral.\n",
    "\n",
    "Clearinghouses arrange for final settlement of trades.\n",
    "\n",
    "Brokers and dealers similarly monitor the trades made by their retail and institutional customers, and regulate their customers to ensure that they do not arrange trades that they cannot settle.\n",
    "\n",
    "This hierarchical system of responsibility generally ensures that traders settle their trades. The brokers and dealers guarantee settlement of the trades they arrange for their retail and institutional customers. The clearinghouse members guarantee settlement of the trades that their customers present to them, and clearinghouses guarantee settlement of all trades presented to them by their members. \n",
    "\n",
    "Depositories or custodians hold securities on behalf of their clients. These services, which are often offered by banks, help prevent the loss of securities through fraud, oversight, or natural disaster. Broker–dealers also often hold securities on behalf of their customers so that the customers do not have to hold the securities in certificate form. To avoid problems with lost certificates, securities increasingly are issued only in electronic form."
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    "### Positions \n",
    "People generally solve their financial and risk management problems by taking positions in various assets or contracts. A position in an asset is the quantity of the instrument that an entity owns or owes. A portfolio consists of a set of positions.\n",
    "- Long positions: when they own assets or contracts. \n",
    "- Short positions: when they have sold assets that they do not own, or when they write and sell contracts. Short positions benefit from a decrease in the prices of the assets or contracts sold.\n",
    "\n",
    "In an option contract, the long side `holds` the option and the short side `writes` the option, (holders and writers). The put contract holder has the right to sell the underlying to the writer. **The holder is long the put contract and has an indirect short position in the underlying instrument. Analysts call the indirect short position short exposure to the underlying. The put contract holders have long exposure to their option contract and short exposure to the underlying instrument.**\n",
    "\n",
    "The identification of the long side in a swap contract is often arbitrary because swap contracts call for the exchange of contractually determined cash flows rather than for the purchase (or the cash equivalent) of some underlying instrument. In general, the side that benefits from an increase in the quoted price is the long side.\n",
    "\n",
    "The buyer of one currency is the seller of the other currency, and vice versa for the seller. Thus, a long forward position in one currency is a short forward position in the other currency. When practitioners describe a position, they generally will say, “I’m long the dollar against the yen,” which means they have bought dollars and sold yen.\n",
    "\n",
    "#### Short Positions\n",
    "A short position is created by selling something you do not own. Short sellers do this by borrowing and selling securities that must eventually be replaced. The short seller hopes to repurchase the securities after a drop in value. Gains from a short sale are limited to the initial sales prices, while losses are theoretically unlimited.\n",
    "\n",
    "The proceeds from selling the borrowed securities must be deposited with the lender, who invests these funds and rebates any interest to the short seller. Short rebate rates may be low or even negative if the collateral is sufficiently high quality. Lenders profit from the spread between the earned interest earned on the collateral and rebate rate paid to the short seller. Although the lender technically no longer owns the borrowed shares, the short seller agrees to pass along any dividend payments or interest received during the term of the loan.\n",
    "### Leveraged Positions\n",
    "Traders can buy securities by borrowing some of the purchase price. (They usually borrow the money from their brokers.) The borrowed money is called the `margin loan`, and they are said to `buy on margin`. The interest rate that the buyers pay for their margin loan is called the `call money rate`. \n",
    "\n",
    "Trader’s equity is that portion of the security price that the buyer must supply. Traders who buy securities on margin are subject to `minimum margin requirements`, the minimum fraction of the purchase price that must be trader’s equity. (the initial margin requirement is the percentage of the purchase price the buyer must supply.) \n",
    "\n",
    "  - *(Many markets allow brokers to lend their clients more money if the brokers use risk models to measure and control the overall risk of their clients’ portfolios. This system is called `portfolio margining`.*)\n",
    "\n",
    "The relation between risk and borrowing is called `financial leverage` (often simply called `leverage`). Traders leverage their positions when they borrow to buy more securities. \n",
    "\n",
    "#### Total Return to Equity Investments in a Leveraged Position\n",
    "The total return depends on \n",
    "- the price change of the purchased security, \n",
    "- the dividends or interest paid by the security, \n",
    "- the interest paid on the margin loan, and \n",
    "- the commissions paid to buy and sell the security. \n",
    "\n",
    "This financial leverage allows the trader to increase `upside potential`, though `downside risk` also increases.\n",
    "$$Leverage\\ Ratio=\\frac{Position}{Equity}$$\n",
    "The leverage ratio indicates how many times larger a position is than the equity that supports it. \n",
    "\n",
    "$$Maximum\\ Initial\\ Leverage\\ Ratio=\\frac{1}{Initial\\ Margin\\ Requirement}$$\n",
    "The maximum leverage ratio associated with a position financed by the `minimum margin requirement`. If the requirement is 40 percent, then the maximum leverage ratio is 2.5 = 100% position ÷ 40% equity.\n",
    "\n",
    "**The leverage ratio indicates how much more risky a leveraged position is relative to an unleveraged position.** \n",
    "\n",
    "For example, if a stock bought on 40 percent margin rises 10 percent, the buyer will experience a 25 percent (2.5 × 10%) return on the equity investment in her leveraged position. But if the stock falls by 10 percent, the return on the equity investment will be −25 percent (before the interest on the margin loan and before payment of commissions)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example: \n",
    "\n",
    "A trader has purchased 200 shares of a non-dividend-paying firm on margin at a price of \\\\$50 per share. The leverage ratio is 2.5. Six months later, the trader sells these shares at \\\\$60 per share. Ignoring the interest paid on the borrowed amount and the transaction costs, what was the return to the trader during the six-month period?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50.0"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In percentage\n",
    "((60 - 50) / 50) * 100 * 2.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example: A buyer buys stock on margin and holds the position for exactly one year, during which time the stock pays a dividend. For simplicity, assume that the interest on the loan and the dividend are both paid at the end of the year.\n",
    "- Purchase price\t\\\\$20/share\n",
    "- Sale price\t\\\\$15/share\n",
    "- Shares purchased\t1,000\n",
    "- Leverage ratio\t2.5\n",
    "- Call money rate\t5%\n",
    "- Dividend\t\\\\$0.10/share\n",
    "- Commission\t\\\\$0.01/share"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8000.0 12000.0 8010.0 2400.1000000000004 14400.1 74.90948813982524\n"
     ]
    }
   ],
   "source": [
    "# know that \n",
    "call_money_rate = 0.05\n",
    "p_buy = 20\n",
    "p_sell = 15\n",
    "shares = 1000\n",
    "leverage = 2.5\n",
    "dividend = 0.10 # per share\n",
    "commission = 0.01 # per share\n",
    "# The leverage ratio of 2.5 indicates that the buyer’s equity financed 40 percent = (1 ÷ 2.5) of the purchase price. \n",
    "buyer_equity = shares * p_buy * (1/leverage)\n",
    "# What is the total return on this investment? \n",
    "dividends = dividend * shares \n",
    "commissions = commission * shares\n",
    "borrowed = shares * p_buy - buyer_equity\n",
    "interest = borrowed * call_money_rate\n",
    "# Initial investment \n",
    "initial_investment = buyer_equity + commissions\n",
    "# Returns\n",
    "sales_proceeds = shares * p_sell\n",
    "gain = sales_proceeds + dividend - interest # ?\n",
    "remaining_equity = gain - borrowed # ?\n",
    "# Total returns\n",
    "returns = remaining_equity / initial_investment * 100 * leverage # ?\n",
    "\n",
    "print(buyer_equity, borrowed, initial_investment, remaining_equity, gain, returns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Orders and Execution Instructions\n",
    "Orders are used by buyers and sellers to communicate with brokers and exchanges. An order will specify the following information:\n",
    "- What instrument to trade\n",
    "- Whether to buy or sell\n",
    "- How much to trade\n",
    "\n",
    "Additional instruction may include:\n",
    "1. Execution instructions: How to fill the order\n",
    "2. Validity instructions: When the order may be filled\n",
    "3. Clearing instructions: How to settle the trade\n",
    "\n",
    "Dealers are willing to buy at bid prices and sell at ask prices (or offer prices). Traders may specify bid or ask sizes – the amount they are willing to trade at that price. The market bid-ask spread is the difference between the best bid and best offer.\n",
    "\n",
    "Those who offer a trade are said to `make the market`, while those who accept those offers are said to `take the market`.\n",
    "### Execution Instructions\n",
    "Execution instructions specify how to fill the order.\n",
    "\n",
    "- A `market order` trades immediately at the best price, which can be costly in illiquid markets because price concessions are needed to attract traders.\n",
    "- A `limit order` specifies either the maximum price that a buyer is willing to pay or the minimum price that a seller is willing to accept. If the limit price is greater than the best offer, the order is described as a marketable limit order because it will be filled immediately (at least partially) as if it were a market order.\n",
    "  - `Buy orders` placed below the best bid are described as being behind the market and will only execute if the best offer price drops. Limit orders waiting to trade are called standing limit orders. A limit order makes a new market if it is between the best bid and offer prices.\n",
    "- `All-or-nothing (AON) orders` will only be executed if the entire quantity can be filled.\n",
    "- `Hidden orders` can only be seen by brokers or exchanges, not by other traders.\n",
    "- `Iceberg orders` only display a fraction of the amount the trader is really willing to transact.\n",
    "\n",
    "### Validity Instructions\n",
    "Validity instructions indicate when an order may be filled.\n",
    "- `Day orders` are the most common. They expire at the end of the business day if not filled.\n",
    "- `Good-till-cancelled (GTC) orders` are valid until executed; however, some brokers will automatically cancel them after a few months.\n",
    "- `Immediate or cancel orders` (aka. fill or kill) expire if they are not filled (at least partly) immediately upon being received.\n",
    "- `Good-on-close orders` are filled at close of trading. They are also called market-on-close.\n",
    "- `Stop orders` cannot be filled until the stop price condition has been met.\n",
    "- `Stop-loss orders` are often used to limit losses. For example, the order will be automatically filled if the price falls below a trigger point. If the price is falling rapidly, there is no guarantee that the order will be executed at the specified price. In such circumstances, a put option may be preferable to a stop-loss order.\n",
    "- `Stop-buy orders` can be used to limit losses on short positions or to ensure that an\n",
    "\n",
    "### Clearing Instructions\n",
    "Clearing instructions are usually given as standing instructions rather than being specified as part of individual orders. They specify the final settlement terms, such as which party is responsible for clearing and settling the trade. This will be a broker for retail trades and either a broker or a custodian for institutional trades.\n",
    "\n",
    "The party representing a sell order must specify if it is a long sale or short sale and confirm that the seller will be able to deliver the securities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Primary Security Markets\n",
    "Primary markets are where issuers sell securities directly to investors. These sales can be initial public offerings (IPOs) or seasoned offerings, which are also called secondary offerings.\n",
    "\n",
    "Secondary markets are where investors trade with each other.\n",
    "### Public Offerings\n",
    "Investment banks line up subscribers in a process called book building. In Europe, accelerated book builds can be arranged over just one or two days, but issuers typically receive discounted prices in these transactions.\n",
    "\n",
    "An investment bank executes an underwritten offering if it commits to pay the offering price for any shares that go unsubscribed. If the issue is an IPO, the underwriter typically agrees to act as a market maker for a minimum period. Investment banks charge underwriting fees of approximately 7% of the value of the issue. In a best efforts offering, the investment bank does not agree to act as a buyer if the issue is undersubscribed; rather, it simply acts as a broker.\n",
    "\n",
    "Offering prices are typically the result of negotiations between the issuer and the investment bank. A low price is attractive to investors, but the issuer raises less capital. If the price is set too high, the issue is at risk of being undersubscribed. Concern about the message that would be sent by undersubscribed IPOs often leads first-time issuers to accept discounted offering prices.\n",
    "\n",
    "While investment banks have an interest in helping the issuer achieve the highest offering price, they also have an interest in setting a low price that will allow them to allocate undervalued securities to their other clients. This conflict of interest is particularly evident in the case of IPOs, but less so for secondary offerings.\n",
    "### Private Placements and Other Primary Market Transactions\n",
    "In private placements, securities are sold to a small group of qualified investors. Compared to public offerings, disclosure requirements are lower because it is assumed that qualified investors are capable of performing adequate risk analysis.\n",
    "\n",
    "`Private placement securities` are illiquid because they cannot be traded in the secondary market. Issuers are forced to accept lower prices than they would receive for an equivalent public offering.\n",
    "\n",
    "A `shelf registration` is used by issuers to sell securities directly to secondary market investors on a piecemeal basis rather than in a single large offering. This gives the issuer the flexibility to raise capital as needed.\n",
    "\n",
    "`Dividend reinvestment plans (DRIPs)` allow investors to purchase new shares with dividends, sometimes at a discount. The company must issue new shares for DRIPs rather than purchasing existing shares in the secondary market.\n",
    "\n",
    "`Rights offerings` grant existing shareholders the option to purchase additional shares at a below-market price. These are effectively warrants that dilute the value of existing shares.\n",
    "### Importance of Secondary Markets to Primary Markets\n",
    "Having a liquid secondary market *reduces the cost of capital* for issuers because investors are willing to pay higher offering prices in the primary market if they are confident that they will be able to sell their shares to other investors quickly and without having to accept a discount."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Secondary Security Market and Contract Market Structures\n",
    "### Trading Sessions\n",
    "Markets can be organized as `call markets` or `continuous trading markets`. \n",
    "- `Call market` trades only take place when the market is called at a particular time and place. They are very liquid markets when called, but completely illiquid otherwise. Most use a single price auction in which the price chosen maximizes the total trading volume. They are usually called once a day.\n",
    "- In `continuous trading markets`, trades can take place anytime the market is open. It may be difficult if other buyers and sellers are not present. Many continuous trading markets use call market auctions at the beginning and/or end of the trading day.\n",
    "\n",
    "### Execution Mechanisms\n",
    "Market structures can be quote-driven, order-driven, or brokered.\n",
    "#### Quote-Driven Markets\n",
    "In quote-driven markets, customers trade with dealers. Most trading is done in this type of market. These are also called over-the-counter (OTC) markets.\n",
    "#### Order-Driven Markets\n",
    "Order-driven markets are based on a matching system run by an exchange or broker to match traders. Orders can be submitted by customers or dealers. Exchanges use this type of market structure. Often people are trading with strangers, so there is a need to ensure performance.\n",
    "\n",
    "**`Order Precedence Hierarchy`: In order-driven markets, there are order matching rules. Price is the top priority (`price priority`) – the highest buy orders and lowest sell orders are executed first. Among orders with the same price, a `secondary precedence rule` prioritizes those that were placed earliest.**\n",
    "\n",
    "**If markets where hidden orders are permitted, orders with `displayed quantities` are usually given priority over those with undisplayed quantities. In these markets, orders are prioritized according to price first, display status second, and time of arrival third.**\n",
    "\n",
    "There are also trade pricing rules in order-driven markets:\n",
    "- Uniform pricing rules are used by call markets. All trades are executed at the same price. The market chooses the price to maximize the total quantity traded.\n",
    "- Discriminatory pricing rules are used by continuous trading markets. They fill orders incrementally, starting with the most aggressively priced orders on the other side of the book. This allows investors to submit a single large order rather than breaking it up into many smaller orders.\n",
    "- Derivative pricing rules are used by crossing networks that match buyers and sellers are must be willing to trade at prices that are determined in other markets. Crossing network trades typically execute at the midpoint of the best bid and ask quotes from the exchange where the security is primarily traded.\n",
    "\n",
    "#### Brokered Markets\n",
    "In brokered markets, the brokers arrange trades between customers. They are ideal for trading unique assets, (e.g., real estate) that dealers would be unwilling to carry in inventory.\n",
    "### Market Information Systems\n",
    "A market is pre-trade transparent if it publishes information about quotes and orders in real-time. It is post-trade transparent if execution prices and trade sizes are published soon after trades are completed. Buy-side traders like transparency, while dealers prefer opaque markets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Well-functioning Financial Systems\n",
    "A well-functioning financial system has the following characteristics:\n",
    "- Investors can easily move money from the present to future\n",
    "- Creditworthy borrowers can easily obtain funds\n",
    "- Risk exposures can be easily hedged\n",
    "- Currencies can be easily exchanged for other currencies or commodities\n",
    "\n",
    "A financial system that offers the assets or contracts necessary to meet the above conditions is called a `complete market`.\n",
    "\n",
    "It is `operationally efficient` if trading costs are low.\n",
    "\n",
    "It is `informationally efficient` if prices reflect all available information.\n",
    "\n",
    "An ideal financial system is complete, operationally efficient, and informationally efficient.\n",
    "\n",
    "Financial intermediaries can work toward this ideal by:\n",
    "- Establishing organizing exchanges that match buyers and sellers\n",
    "- Operating clearinghouses to ensure settlement of trades and contracts\n",
    "- Maintaining a banking system that matches borrowers and lenders\n",
    "- Providing liquidity on demand\n",
    "- Securitizing assets to created attractive investment vehicles\n",
    "- Offering insurance products that pool risk\n",
    "- Having a well-functioning financial system makes an economy more allocationally efficient.\n",
    "\n",
    "### Market Regulation\n",
    "To meet their financial needs, consumers rely on specialists, such as bankers, brokers, money managers, financial advisors, and insurance agents. Because these specialists are more knowledgeable about their segment of the financial system (i.e., information is asymmetric), they are in a position to act against the interests of their clients.\n",
    "\n",
    "Regulation is used to give consumers confidence that the financial system has a level playing field. For example, governments create and enforce laws against insider trading. Minimum capital requirements can be used to give consumers confidence that banks, insurance companies, and pension plans will be able to meet their obligations.\n",
    "\n",
    "Non-government entities that act as regulators include self-regulating organizations such as securities exchanges and accounting standards boards. Professional organizations (e.g., CFA Institute) set minimum standards of competence and ethics.\n",
    "\n",
    "As a general objective, regulators seek to maintain fair and orderly markets that allow prices to reflect fundamental values. More specific regulatory objectives include:\n",
    "1. Preventing fraud\n",
    "2. Managing agency problems\n",
    "3. Promoting fairness\n",
    "4. Establishing mutually beneficial standards\n",
    "5. Discouraging excessive risk\n",
    "6. Ensuring that long-term liabilities are funded\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Security Market Indexes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Index Definition and Calculations of Value and Returns\n",
    "A security market index represents a given security market, market segment, or asset class. Most indexes are constructed as portfolios of marketable securities.\n",
    "\n",
    "The value of an index is calculated on a regular basis using either the actual or estimated market prices of the individual securities, known as `constituent securities`, within the index.\n",
    "\n",
    "- A `price return index`, also known as a `price index`, reflects only the prices of the constituent securities within the index. \n",
    "- A `total return index`, reflects not only the prices of the constituent securities but also the reinvestment of all income received since inception.\n",
    "\n",
    "**At inception, the values of the price and total return versions of an index are equal.** As time passes, however, the value of the total return index, which includes the reinvestment of all dividends and/or interest received, will exceed the value of the price return index by an increasing amount. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The value of a price return index is calculated as:\n",
    "$$V_{PRI}=\\frac{\\sum_{i=1}^N{n_iP_i}}{D}$$\n",
    "<div style=\"text-align: right\"> Equation 1 </div>\n",
    "where\n",
    "\n",
    "$V_{PRI}$\t=\tthe value of the price return index\n",
    "    \n",
    "$n_i$\t=\tthe number of units of constituent security i held in the index portfolio\n",
    "    \n",
    "$N$\t=\tthe number of constituent securities in the index\n",
    "    \n",
    "$P_i$\t=\tthe unit price of constituent security i\n",
    "    \n",
    "$D$\t=\tthe value of the divisor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculation of Single-Period Returns\n",
    "For a security market index, price return can be calculated in two ways: either the percentage change in value of the price return index, or the weighted average of price returns of the constituent securities. \n",
    "\n",
    "#### Price Return\n",
    "$$PR_I=\\frac{V_{PRI1−}V_{PRI0}}{V_{PRI0}}$$\n",
    "<div style=\"text-align: right\"> Equation 2 </div>\n",
    "where\n",
    "\n",
    "$PR_I$\t=\tthe price return of the index portfolio (as a decimal number, i.e., 12 percent is 0.12)\n",
    "\n",
    "$V_{PRI1}$\t=\tthe value of the price return index at the end of the period\n",
    "\n",
    "$V_{PRI0}$\t=\tthe value of the price return index at the beginning of the period\n",
    "\n",
    "\n",
    "Similarly, the price return of each constituent security can be expressed as:\n",
    "\n",
    "$$PR_i=\\frac{P_{i1}−P_{i0}}{P_{i0}}$$\n",
    "<div style=\"text-align: right\"> Equation 3 </div>\n",
    "\n",
    "where\n",
    "\n",
    "$PR_i$\t=\tthe price return of constituent security i (as a decimal number)\n",
    "\n",
    "$P_{i1}$\t=\tthe price of constituent security i at the end of the period\n",
    "\n",
    "$P_{i0}$\t=\tthe price of constituent security i at the beginning of the period\n",
    "\n",
    "\n",
    "Because the price return of the index equals the weighted average of price returns of the individual securities, we can write:\n",
    "\n",
    "$$PR_I=\\sum_{i=1}^N{w_iPR_i}=\\sum_{i=1}^N{w_i\\big(\\frac{P_{i1}−P_{i0}}{P_{i0}}\\big)}$$\n",
    "<div style=\"text-align: right\"> Equation 4 </div>\n",
    "\n",
    "Equation 4 can be rewritten simply as:\n",
    "\n",
    "$$PR_I = w_1PR_1 + w_2PR_2 + … + w_NPR_N$$  \n",
    "<div style=\"text-align: right\"> Equation 5 </div>\n",
    "\n",
    "#### Total Return\n",
    "Total return measures price appreciation plus interest, dividends, and other distributions. Thus, the total return of an index is the price appreciation, or change in the value of the price return index, plus income (dividends and/or interest) over the period, expressed as a percentage of the beginning value of the price return index. The total return of an index can be expressed as:\n",
    "\n",
    "$$TR_I=\\frac{V_{PRI1}−V_{PRI0}+Inc_I}{V_{PRI0}}$$\n",
    "<div style=\"text-align: right\"> Equation 6 </div>\n",
    "where\n",
    "\n",
    "$TR_I$\t=\tthe total return of the index portfolio (as a decimal number)\n",
    "\n",
    "$V_{PRI1}$\t=\tthe value of the price return index at the end of the period\n",
    "\n",
    "$V_{PRI0}$\t=\tthe value of the price return index at the beginning of the period\n",
    "\n",
    "$Inc_I$\t=\tthe total income (dividends and/or interest) from all securities in the index held over the period\n",
    "\n",
    "The total return of an index can also be calculated as the weighted average of total returns of the constituent securities. The total return of each constituent security in the index is calculated as:\n",
    "$$TR_i=\\frac{P_{1i}−P_{0i}+Inc_i}{P_{0i}}$$\n",
    "<div style=\"text-align: right\"> Equation 7 </div>\n",
    "\n",
    "Because the total return of an index can be calculated as the weighted average of total returns of the constituent securities, we can express total return as:\n",
    "\n",
    "$$TR_I=\\sum_{i=1}^N{w_iTR_i}=\\sum_{i=1}^N{w_i\\big(\\frac{P_{1i}−P_{0i}+Inc_i}{P_{0i}}\\big)}$$\n",
    "<div style=\"text-align: right\"> Equation 8 </div>\n",
    "\n",
    "Equation 8 can be rewritten simply as\n",
    "$$TR_I = w_1TR_1 + w_2TR_2 + … + w_NTR_N$$\n",
    "<div style=\"text-align: right\"> Equation 9 </div>\n",
    "\n",
    "### Calculation of Index Values over Multiple Time Periods\n",
    "The calculation of index values over multiple time periods requires geometrically linking the series of index returns. With a series of price returns for an index, we can calculate the value of the price return index with the following equation:\n",
    "$$V_{PRIT} = V_{PRI0}(1 + PR_{I 1})(1 + PR_{I 2})…(1 + PR_{IT})$$ \n",
    "<div style=\"text-align: right\"> Equation 10 </div>\n",
    "where\n",
    "\n",
    "$V_{PRI 0}$\t=\tthe value of the price return index at inception\n",
    "\n",
    "$V_{PRIT}$\t=\tthe value of the price return index at time t\n",
    "\n",
    "$PR_IT$\t=\tthe price return (as a decimal number) on the index over period t, t = 1, 2, …, T\n",
    "\n",
    "Similarly, the series of total returns for an index is used to calculate the value of the total return index with the following equation:\n",
    "\n",
    "$$V_{TRIT} = V_{TRI 0}(1 + TR_{I 1})(1 + TR_{I 2})…(1 + TR_{IT})$$  \n",
    "<div style=\"text-align: right\"> Equation 11 </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Index Construction and Management\n",
    "Index providers must decide the following:\n",
    "- Which target market should the index represent?\n",
    "- Which securities should be selected from that target market?\n",
    "- How much weight should be allocated to each security in the index?\n",
    "- When should the index be rebalanced?\n",
    "- When should the security selection and weighting decision be re-examined?\n",
    "\n",
    "### Target Market and Security Selection\n",
    "The constituent securities could be nearly all those in the target market or a representative sample of the target market.\n",
    "### Index Weighting\n",
    "The weighting decision determines how much of each security to include in the index. \n",
    "#### Price Weighting\n",
    "In price weighting, the weight on each constituent security is determined by dividing its price by the sum of all the prices of the constituent securities. \n",
    "$$w^P_i=\\frac{P_i}{\\sum_{i=1}^N{P_i}}$$\n",
    "<div style=\"text-align: right\"> Equation 12 </div>\n",
    "\n",
    "A property unique to price-weighted indexes is that a `stock split` on one constituent security changes the weights on all the securities in the index.1 To prevent the stock split and the resulting new weights from changing the value of the index, the index provider must *adjust the value of the divisor*. \n",
    "\n",
    "- The primary advantage of price weighting is its simplicity. \n",
    "- The main disadvantage of price weighting is that it results in arbitrary weights for each security. In particular, a stock split in any one security causes arbitrary changes in the weights of all the constituents’ securities.\n",
    "\n",
    "#### Equal Weighting\n",
    "This method assigns an equal weight to each constituent security at inception. Dividing the value allocated to each security by each security’s individual share price determines the number of shares of each security to include in the index. The weights are calculated as:\n",
    "$$w^E_i=\\frac{1}{N}$$\n",
    "<div style=\"text-align: right\"> Equation 13 </div>\n",
    "where\n",
    "\n",
    "$w_i$ = fraction of the portfolio that is allocated to security i or weight of security i\n",
    "\n",
    "$N$ = number of securities in the index\n",
    "\n",
    "Disadvantages:\n",
    "- First, securities that constitute the largest fraction of the target market value are underrepresented, and securities that constitute a small fraction of the target market value are overrepresented. \n",
    "- Second, after the index is constructed and the prices of constituent securities change, the index is no longer equally weighted. Therefore, maintaining equal weights requires frequent adjustments (rebalancing) to the index.\n",
    "#### Market-Capitalization Weighting (Value Weighting)\n",
    "Market capitalization or value is calculated by multiplying the number of shares outstanding by the market price per share.\n",
    "\n",
    "The market-capitalization weight of security i is:\n",
    "$$w^M_i=\\frac{Q_iP_i}{\\sum_{j=1}^N{Q_jP_j}}$$\n",
    "<div style=\"text-align: right\"> Equation 14 </div>\n",
    "where\n",
    "\n",
    "$w_i$ = fraction of the portfolio that is allocated to security i or weight of security i\n",
    "\n",
    "$Q_i$ = number of shares outstanding of security i\n",
    "\n",
    "$P_i$ = share price of security i\n",
    "\n",
    "$N$ = number of securities in the index\n",
    "\n",
    "**To understand the source and magnitude of the difference, compare the weights and returns of each security under each of the weighting methods. **\n",
    "\n",
    "FLOAT-ADJUSTED MARKET-CAPITALIZATION WEIGHTING: the weight on each constituent security is determined by adjusting its market capitalization for its `market float` (The number of shares that are available to the investing public).\n",
    "\n",
    "In addition to excluding shares held by controlling shareholders, most float-adjusted market-capitalization-weighted indexes also exclude shares held by other corporations and governments. \n",
    "\n",
    "Some providers of indexes that are designed to represent the investment opportunities of global investors further reduce the number of shares included in the index by excluding shares that are not available to foreigner investors. The index providers may refer to these indexes as “free-float-adjusted market-capitalization-weighted indexes.”\n",
    "\n",
    "The float-adjusted market-capitalization weight of security i is calculated as:\n",
    "$$w^M_i=\\frac{f_iQ_iP_i}{\\sum_{j=1}^N{f_jQ_jP_j}}$$\n",
    "<div style=\"text-align: right\"> Equation 15 </div>\n",
    "where\n",
    "\n",
    "$f_i$ = fraction of shares outstanding in the market float\n",
    "\n",
    "$w_i$ = fraction of the portfolio that is allocated to security i or weight of security i\n",
    "\n",
    "$Q_i$ = number of shares outstanding of security i\n",
    "\n",
    "$P_i$ = share price of security i\n",
    "\n",
    "$N$ = number of securities in the index\n",
    "\n",
    "- The advantage of market-capitalization weighting schemes is that each constituent's contribution to index performance is proportionate to its value in the target market. \n",
    "- The disadvantage is it leads to overweighting securities that rise in value and underweighting those that fall in value. This is akin to a momentum investment strategy.\n",
    "\n",
    "#### Fundamental Weighting\n",
    "Fundamental weighting attempts to address the disadvantages of market-capitalization weighting by using measures of a company’s size that are independent of its security price to determine the weight on each constituent security (e.g. Fundamental weighting attempts to address the disadvantages of market-capitalization weighting by using measures of a company’s size that are independent of its security price to determine the weight on each constituent security). This leads to indices with value tilt (e.g. ratio of book value to market value is greater than average). This method also tends to have a contrarian bent rather than a momentum approach.\n",
    "\n",
    "Letting Fi denote a given fundamental size measure of company i, the fundamental weight on security i is:\n",
    "\n",
    "$$w^F_i=\\frac{F_i}{\\sum_{j=1}^N{F_j}}$$\n",
    "<div style=\"text-align: right\"> Equation 16 </div>"
   ]
  },
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   "metadata": {},
   "source": [
    "### Index Management: Rebalancing and Reconstitution\n",
    "#### Rebalancing\n",
    "Rebalancing refers to adjusting the weights of the constituent securities in the index. To maintain the weight of each security consistent with the index’s weighting method, the index provider rebalances the index by adjusting the weights of the constituent securities on a regularly scheduled basis (rebalancing dates)—usually quarterly. \n",
    "\n",
    "Indexes are rebalanced at regularly scheduled intervals. This is necessary because the weights change as security prices change. Price-weighted indices do not need rebalancing for price changes since the price is the weight. \n",
    "\n",
    "Market-capitalization weights rebalance themselves, except for activities such as mergers and acquisitions.\n",
    "#### Reconstitution\n",
    "Reconstitution is a process in which the manager reviews and makes changes to the constituent securities. Some indices reconstitute annually. Security prices will frequently increase in value when the market thinks it is likely the security will be added to a major index."
   ]
  },
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   "cell_type": "markdown",
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    "## Uses of Market Indexes\n",
    "#### Gauges of Market Sentiment\n",
    "As indicators of the collective opinion of market participants, indexes reflect investor attitudes and behavior. \n",
    "#### Proxies for Measuring and Modeling Returns, Systematic Risk, and Risk-Adjusted Performance\n",
    "Often a broad index is used as a proxy for the market in the capital asset pricing model (CAPM). If we know a stock's beta relative to an index, we can calculate its systematic risk-adjusted required return.\n",
    "#### Proxies for Asset Classes in Asset Allocation Models\n",
    "Historical index data an ideal basis for estimates of risk and expected returns that are used as inputs in asset allocation models, such as mean-variance optimization.\n",
    "#### Benchmarks for Actively Managed Portfolios\n",
    "An active manager's returns should be benchmarked against an investable market index so that investors can evaluate them relative to a low-cost passive alternative.\n",
    "#### Model Portfolios for Investment Products\n",
    "Many investors prefer passive exposure to active management. To meet this demand, investment firms have developed many popular low-cost investment vehicles (e.g., ETFs), which are often based on market indexes.\n",
    "\n",
    "Investment management firms initially developed and managed index portfolios for institutional investors. Eventually, mutual fund companies introduced index funds for individual investors. Subsequently, investment management firms introduced `exchange-traded funds`, which are managed the same way as index mutual funds but trade like stocks."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Types of Indices\n",
    "### Equity indexes\n",
    "#### Broad Market Indexes\n",
    "An index is considered to be broadly representative if it includes 90% or more of a market's equities.\n",
    "#### Multi-Market Indexes\n",
    "These usually seek to represent multiple national markets in aggregate. For example, a representative sample of stocks from Canada, the United States, and Mexico could be used as a multi-market index for North American equities.\n",
    "\n",
    "Multi-market indexes do not need to be based on geography. \n",
    "##### Fundamental Weighting in Multi-Market Indexes\n",
    "Including national markets proportionately to their GDP in a multi-market index is a form of fundamental weighting.\n",
    "\n",
    "They are important to global investors. Multi-market indices could be based on a geographic basis or level of economic development. Some indices weight by market capitalization within the country and by GDP between countries.\n",
    "#### Sector Indexes\n",
    "A pure sector index includes only stocks from a specific sector, such as energy, finance, or health care. Sector indexes may be global in scope or limited to companies from a specific country.\n",
    "\n",
    "**An aggregation of pure sector indexes will resemble a broad market index.**\n",
    "\n",
    "Sector indexes are used in the performance evaluation process to determine whether a manager has added value through stock selection or sector allocation.\n",
    "#### Style Indexes\n",
    "##### Market Capitalization\n",
    "- Small-cap\n",
    "- Large-cap\n",
    "\n",
    "##### Value/Growth Classification (Investment Style)\n",
    "- Value (e.g., high dividend yield, low P/B)\n",
    "- Growth (e.g., high P/E)\n",
    "\n",
    "##### Market Capitalization and Value/Growth Classification\n",
    "- Small-cap Value\n",
    "- Small-cap Growth\n",
    "- Large-cap Value\n",
    "- Large-cap Growth\n",
    "\n",
    "### Fixed-income indexes\n",
    "#### Construction\n",
    "The fixed-income universe includes securities issued by governments, government agencies, and corporations. Each of these entities may issue a variety of fixed-income securities with different characteristics. As a result, the number of fixed-income securities is many times larger than the number of equity securities. \n",
    "\n",
    "Maintaining fixed-income indexes is challenging due to the nature of this asset class.\n",
    "\n",
    "An equity index can include a corporation's common stock, but fixed-income indexes must choose from among several different debt issues. In order to be representative of an asset class, fixed-income indexes may need to include several thousand constituents.\n",
    "\n",
    "Fixed-income markets are also relatively illiquid, leaving index providers to rely on dealers for updated prices of thinly-traded issues.  \n",
    "#### Types of Fixed-Income Indexes\n",
    "The wide variety of fixed-income securities, ranging from zero-coupon bonds to bonds with embedded options (i.e., callable or putable bonds), results in a number of different types of fixed-income indexes. \n",
    "\n",
    "Fixed-income securities can also be classified along the following dimensions:\n",
    "- type of issuer (government, government agency, corporation);\n",
    "- type of financing (general obligation, collateralized);\n",
    "- currency of payments;\n",
    "- maturity;\n",
    "- credit quality (investment grade, high yield, credit agency ratings); and\n",
    "- absence or presence of inflation protection.\n",
    "\n",
    "Fixed-income indexes fall into many of the same categories as equities indexes:\n",
    "- Aggregate or broad market indexes\n",
    "- Sector indexes (e.g., government, corporate)\n",
    "- Style indexes (e.g., high-yield)\n",
    "- economic sector indexes; and\n",
    "- specialized indexes such as high-yield, inflation-linked, and emerging market indexes\n",
    "\n",
    "### Indexes for Alternative Investments\n",
    "#### Commodity Indexes\n",
    "Commodity indices consist of `futures contracts` on commodities such as agriculture, livestock, metals, or energy. Indexes are based on `futures contracts` rather than the underlying commodity prices. As such, index values will reflect unrelated factors such as the risk-free rate.\n",
    "\n",
    "There are no obvious weighting scheme indexes that include multiple commodities. `Equal weighting` schemes or `fixed weights` are common for multi-commodity indexes.\n",
    "#### Real Estate Investment Trust Indexes\n",
    "Direct real estate investments trade infrequently is an illiquid market. Real estate indexes may be based on `appraisals` or `repeat sales`.\n",
    "\n",
    "By contrast, REITs trade on public exchanges, allowing the value of REIT indexes to be calculated continuously.\n",
    "#### Hedge Fund Indexes\n",
    "Hedge funds are private investments that often use leverage and long/short strategies. Because reporting is voluntary, hedge fund managers may not provide complete and accurate performance data. Therefore, each hedge fund decides to which database(s) it will report its performance. Thus, for a hedge fund index, constituents determine the index rather than index providers determining the constituents. This creates the potential for survivorship bias."
   ]
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   "source": [
    "# Market Efficiency"
   ]
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    "## The Concept of Market Efficiency\n",
    "### Description of Efficient Markets\n",
    "An efficient market is a market in which asset prices reflect all past and present information.\n",
    "\n",
    "The extent to which a market is efficient affects how many profitable trading opportunities (market inefficiencies) exist. Consistent, superior, risk-adjusted returns (net of all expenses) are not achievable in an efficient market.\n",
    "\n",
    "In an efficient market, a `passive investment strategy` (i.e., buying and holding a broad market portfolio) that does not seek superior risk-adjusted returns can be preferred to an active investment strategy because of lower costs (for example, transaction and information-seeking costs). \n",
    "\n",
    "Understanding the characteristics of an efficient market and being able to evaluate the efficiency of a particular market are important topics for investment analysts and portfolio managers.\n",
    "\n",
    "*HOW QUICKLY is efficient?*<br>\n",
    "Trades are the mechanism by which information can be incorporated into asset transaction prices. The time needed to execute trades to exploit an inefficiency may provide a baseline for judging speed of adjustment.\n",
    "\n",
    "Prices can incorporate new information only as fast as trading mechanisms allow, which could be less than one minute in developed equity markets. If a market is efficient, prices will reflect current consensus expectations and should only react to unexpected information such as surprise earnings announcements.\n",
    "### Market Value versus Intrinsic Value\n",
    "Market value is the price at which an asset currently trades. It represents the intersection of supply and demand. Intrinsic value (or fundamental value) is the theoretical value of an asset that would be calculated by investors if they possessed (and accurately processed) all relevant information. Intrinsic value cannot be known with certainty, it can only be estimated.\n",
    "\n",
    "An asset is described as mispriced if it is trading at a market value that deviates from its intrinsic value. In an efficient market, asset prices are assumed to be reasonably accurate reflections of intrinsic value. If a market is inefficient, there should be opportunities for active investors to profit from trading mispriced assets."
   ]
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    "### Factors Affecting Market Efficiency Including Trading Costs\n",
    "#### Market Participants\n",
    "There should be a positive correlation between the number of market participants and market efficiency. If more investors and analysts are monitoring prices, it is more likely that mispricings will be noticed and acted on until market prices are reflective of intrinsic values. Any restrictions that limit opportunities for investors to trade can be expected to reduce market efficiency.\n",
    "#### Information Availability and Financial Disclosure\n",
    "Markets will be more efficient if investors have more and better information. The most efficient stock markets (e.g., NYSE) have stringent disclosure requirements. By contrast, over-the-counter (OTC) markets are less efficient because there can be significant variation in the quality and quantity of information provided by different dealers.\n",
    "\n",
    "Requiring companies to disclose relevant information to all investors at the same time and penalizing insiders for trading on material nonpublic information makes markets fairer and more efficient.\n",
    "#### Limits to Trading\n",
    "Arbitrageurs contribute to market efficiency by observing mispriced securities and acting quickly to exploit the opportunities. Operational inefficiencies, such as restrictions on short selling, and high trading costs decrease market efficiency by making it more difficult for arbitrageurs to trade.\n",
    "\n",
    "- Arbitrage is a set of transactions that produces riskless profits. Arbitrageurs are traders who engage in such trades to benefit from pricing discrepancies (inefficiencies) in markets. Such trading activity contributes to market efficiency.\n",
    "- Short selling is the transaction whereby an investor sells shares that he or she does not own by borrowing them from a broker and agreeing to replace them at a future date. Short selling allows investors to sell securities they believe to be overvalued, much in the same way they can buy those they believe to be undervalued.\n",
    "\n",
    "#### Transaction Costs and Information-Acquisition Costs\n",
    "The concept of market efficiency must be considered in the context of costs.\n",
    "\n",
    "`Transaction costs`: **A market can still be considered efficient if mispricings are less than transaction costs.** For example, if two identical assets are trading at different prices, investors will not act to eliminate this mispricing unless if the costs that would be incurred to execute the necessary trades are greater than the potential profit.\n",
    "\n",
    "`Information-acquisition costs`: Investors should be able to earn a fair gross return as compensation for the risks and costs incurred to acquire new information. *A market is only considered inefficient if active investors can outperform a passive approach after deducting information-acquisition costs.*"
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    "### Forms of Market Efficiency\n",
    "#### Weak Form\n",
    "Security prices fully reflect all past market trading data (swhich refers to all *historical price* and *trading volume info*). Investors can test this form of efficiency by looking for patterns in past prices. If patterns exist that are pronounced enough to allow for arbitrage profits, then the market is not weak-form efficient.\n",
    "\n",
    "`Technical analysis` is based on the assumption that markets are weak-form inefficient, the purpose is to identify recurring patterns in the trading data that can be used to guide investment decisions. Technicians believe that price movements are heavily influenced by the psychology of market participants, which can be understood by analyzing past price and trading volume data.\n",
    "\n",
    "If markets are weak-form efficient, past trading data are already reflected in current prices and investors *cannot* predict future price changes by extrapolating prices or patterns of prices from the past.\n",
    "\n",
    "The preponderance of empirical evidence supports the view that weak-form inefficiency can be observed in certain developing economies, but not in developed markets. (Overall, the evidence indicates that investors cannot consistently earn abnormal profits using past prices or other technical analysis strategies in developed markets.)\n",
    "#### Semi-Strong Form\n",
    "In this form of market efficiency, prices reflect past market trading data (i.e., they are weak-form efficient) as well as all other publicly available information, such as financial statement data. If a market is semi-strong-form efficient, prices adjust quickly to account for new information and it is not possible to earn superior returns by analyzing public reports.\n",
    "\n",
    "Analyzing earnings announcements of companies to identify underpriced or overpriced securities is pointless because the prices of these securities already reflect all publicly available information.\n",
    "\n",
    "The hypothesis that markets are semi-strong-form efficient can be tested with event studies that measure the speed at which prices respond to company announcements and other significant events. If a market is semi-strong-form efficient, prices will react quickly and fully to the new information. If not, investors will have the opportunity to earn abnormal returns as prices take time to adequately adjust.\n",
    "\n",
    "Most studies indicate that markets in developed economies are semi-strong-form efficient.\n",
    "#### Strong Form\n",
    "Security prices fully reflect all public and private information, meaning that a strong-form efficient market is also semi-strong-form and weak-form efficient.\n",
    "\n",
    "In a strong-form efficient market, insider trading would not be possible because prices have already incorporated all nonpublic information. In reality, insider trading has been shown to be profitable (albeit illegal) in both developed and developing markets.\n",
    "### Implications of the Efficient Market Hypothesis\n",
    "Several implications can be drawn from the evidence on efficient markets for `developed markets`:\n",
    "- Securities markets are weak-form efficient, and therefore, investors cannot earn abnormal returns by trading on the basis of past trends in price.\n",
    "- Securities markets are semi-strong efficient, and therefore, analysts who collect and analyze information must consider whether that information is already reflected in security prices and how any new information affects a security’s value.\n",
    "- Securities markets are not strong-form efficient because securities laws are intended to prevent exploitation of private information.\n",
    "\n",
    "#### Fundamental Analysis\n",
    "Fundamental analysis involves the estimation of an asset’s value using company data, such as earnings and sales forecasts, and risk estimates as well as industry and economic data, such as economic growth, inflation, and interest rates. \n",
    "\n",
    "Analyzing public disclosures (e.g., financial statements) should not generate excess returns in a semi-strong-form efficient market because prices should already reflect this information. However, fundamental analysis is needed to support a semi-strong-form efficient market and investors can still generate abnormal returns if they are able to develop a comparative advantage in analyzing public information.\n",
    "#### Technical Analysis\n",
    "If markets are `weak-form efficient`, technicians may be able to generate abnormal profits occasionally, but not on a consistent basis. By continuing to exploit prices based on their analysis of historical trading data, technicians help markets remain weak-form efficient.\n",
    "#### Portfolio Management\n",
    "Many studies have shown active portfolio managers do not beat the market on average. When fees are considered, investors would be better off using passive strategies. However, even if they do not outperform the market, portfolio managers can still add value by designing investment strategies that are consistent with their clients' objectives and constraints."
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    "## Market Pricing Anomalies \n",
    "A market anomaly is a change in a security's price that cannot be attributed to new information. Anomalies may be observed in efficient markets. For a market to be considered inefficient, anomalies must persist over long periods.\n",
    "\n",
    "Apparent anomalies may simply be the product of `data mining` (data snooping), which is the practice of analyzing data first and developing a hypothesis based on observed patterns. **Proper research methodology calls for the development of a hypothesis based on economic rationale before any data are analyzed.**\n",
    "\n",
    "**Patterns that are observed in historical data have no value if they cannot be repeated.** A certain strategy may have been successful due to random chance. In reality, it is extremely difficult to develop a strategy that consistently generates excess risk-adjusted returns net of all costs.\n",
    "### Time Series \n",
    "#### Calendar Anomalies\n",
    "Returns in the first few trading days of January are abnormally high, especially for small-cap stocks. This January effect has been observed since the 1980s and it cannot be attributed to the release of new information, which would suggest that these markets are inefficient.\n",
    "\n",
    "One explanation is that investors selling their \"losing\" stocks in December to capture capital losses for tax purposes. Others have proposed portfolio managers sell riskier securities at the end of December to make their holdings appear safer in end-of-year reports. More recent evidence indicates this anomaly has not persisted.\n",
    "\n",
    "Other calendar anomalies include:\n",
    "- Turn-of-the-month effect: Higher returns at the beginning and end of months\n",
    "- Day-of-the-week effect: Monday returns are negative on average\n",
    "- Weekend effect: Weekend returns are lower than weekday returns\n",
    "- Holiday effect: Higher returns on the day before a market holiday\n",
    "\n",
    "#### Momentum and Overreaction Anomalies\n",
    "Some studies have shown markets overreact to good and bad news. This could be exploited by purchasing past losers and selling past winners, which is a `contrarian investment approach`.\n",
    "\n",
    "A contradiction to weak-form efficiency occurs when securities that have experienced high returns in the short term tend to continue to generate higher returns in subsequent periods.\n",
    "\n",
    "Studies have also shown security prices tend to go up and down in runs over short-term periods. This momentum would appear to indicate weak-form inefficiency, although it could simply be a rational reflection of adjustments to market consensus growth rates.\n",
    "### Cross-Sectional\n",
    "#### Size Effect\n",
    "A study published in 1981 showed that small-cap stocks outperformed relative to large-cap stocks on a risk-adjusted basis. However, the size effect has not been observed in subsequent studies, which suggests that the relationship was due to chance.\n",
    "#### Value Effect\n",
    "Value stocks, those with **below-average price-to-earnings and market-to-book ratios,** have consistently outperformed growth stocks over time. This persistent outperformance would indicate that markets are not semi-strong-form efficient. However, if the value effect is simply a reward for accepting additional risk, then investors are not able to earn excess returns on a risk-adjusted basis.\n",
    "\n",
    "value stocks:<br>\n",
    "- Higher than average dividend yield \n",
    "- low price-to-earnings \n",
    "- low market-to-book ratios. \n",
    "\n",
    "Growth stocks are characterized by low dividend yields and high price-to-earnings and high market-to-book ratios.\n",
    "### Other Anomalies\n",
    "#### Closed-End Investment Fund Discounts\n",
    "A closed-end investment fund issues a fixed number of shares at inception and does not sell any additional shares after the initial offering. Therefore, the fund capitalization is fixed unless a secondary public offering is made.\n",
    "\n",
    "Shares of closed-end funds trade on stock markets like other equity securities. Most trade at a sizable discount to their net asset value (NAV). Researchers have proposed this is due to projected management fees or performance, hidden tax liabilities, or illiquidity. However, none of the explanations seem to fully explain the discount.\n",
    "\n",
    "It is important to note that this anomaly cannot be exploited because the transaction costs required to buy and liquidate the fund would eliminate any profits. Additionally, these discounts tend to revert to zero over time.\n",
    "#### Earnings Surprise\n",
    "Many studies have shown companies with positive surprise earnings announcements experience a prolonged period of abnormal positive security returns. In an efficient market, prices should react immediately to this new information. However, these apparently abnormal returns may not adequately account for transaction costs and risks.\n",
    "#### Initial Public Offerings (IPOs)\n",
    "Under pressure from investment banks, companies that issue IPOs tend to set low offering prices. This creates opportunities to earn excess returns by purchasing IPO shares at the offering price. However, investors are often overly optimistic about issuers that subsequently underperform. This apparent anomaly may simply be a reflection of the research methods used in studies.\n",
    "#### Predictability of Returns Based on Prior Information\n",
    "Many researchers have documented equity returns are linked to factors including interest rates, inflation rates, volatility, and dividend yields. However, it is not possible to generate abnormal returns because these relationships tend to change significantly over time.\n",
    "### Implications of Market Pricing Anomalies\n",
    "Any investment strategy that is based on exploiting market inefficiencies must account for trading costs. Even if markets overreact and subsequently correct, it is difficult to exploit price reversals that are smaller than the bid-ask spread. Additionally, a market that underreacts as much as it overreacts is still efficient on average.\n",
    "\n",
    "Most importantly, investors should be skeptical about strategies that lack a compelling economic rationale. Even if the Monday effect is a genuine anomaly, investors are unlikely to have confidence in a manager whose investment strategy is to take short positions on Mondays and long positions for the rest of the week."
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    "## Behavioral Finance\n",
    "Asset pricing models that are grounded in traditional financial theory assume that, on average, individuals are perfectly rational and have access to perfect information. Although individual investors often make sub-optimal decisions, investors collectively learn from these mistakes and make markets more efficient with prices that reflect intrinsic value.\n",
    "\n",
    "The field of behavioral finance seeks to understand how people make investment decisions (individually and collectively) by observing their actions. There is a major focus on cognitive biases that affect decision making. According to the behavioral finance perspective, cognitive biases may explain the existence of market pricing anomalies.\n",
    "\n",
    "Some of the more prominent behavioral biases are summarized below:\n",
    "\n",
    "### Loss Aversion\n",
    "Traditional finance assumes that investors are risk-averse, meaning that they will only take on risk if they expect additional compensation. Behavioralists claim that investors really just dislike losses, which could explain market overreactions. However, evidence indicates that markets underreact as often as they overreact.\n",
    "### Herding\n",
    "Investors exhibit a herd mentality when they take the same side as the market even if this is inconsistent with their own private information. Herding behavior can explain both overreactions and underreactions in markets.\n",
    "### Overconfidence\n",
    "Investors are often overconfident in their own abilities. If enough investors are overconfident, prices will temporarily deviate from intrinsic values before eventually correcting. There is some evidence that overconfidence bias has led to mispricings of growth stocks in developed markets.\n",
    "### Information Cascades\n",
    "With information cascades, those who act first will convey information that influences others. This could explain short-term serial correlations in stock returns (i.e., overreactions). Information cascades can enhance the information available to traders, but they are not always correct.\n",
    "### Other Behavioral Biases\n",
    "- Representativeness: Relying too much on current state when assessing probabilities\n",
    "- Mental accounting: Keeping track of gains in losses separately for different investments\n",
    "- Conservatism: Failing to incorporate new information in a timely manner\n",
    "- Narrow framing: Focusing on certain issues in isolation\n",
    "- The disposition effect relates to the behavioral bias in which investors tend to avoid realizing losses but, rather, seek to realize gains. "
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