Financial Analytics with R

Credit Risk Bootstrapped libor curve.R

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+### Bootstrap Curve ###
+
+rm(list=ls())
+
+raw.data <- read.csv('C:/Users/Shinhyunjin/Dropbox/data1(creditrisk hw1).csv', header=T, fileEncoding="UTF-8-BOM")
+#nrow(raw.data)
+raw.data <- raw.data[1:12,5:6]
+#raw.data
+
+term <- raw.data[,1]
+rate <- raw.data[,2]/100
+
+# discount factor bootstrap
+
+tenor.set <- seq(0,12)
+#df <- NULL
+z <- NULL
+z[1] <- 1/((1+term[1]*rate[1])*(1+(term[2]-term[1])*rate[2]))
+libor <- NULL
+
+for(i in 2:length(tenor.set)){
+  if (i==1) z[1] <- 1/((1+term[1]*rate[1])*(1+(term[2]-term[1])*rate[2]))
+  else z[i]  <- z[1] / (1+(term[i] - term[i-1])*rate[i])
+ # df[i] <- z[i]
+  libor[i] <- rate[i] * z[i]
+}
+
+#source('test.r')
+plot(tenor.set, libor, type = "s", xlab= "years", ylab = "rate(%)",main ="bootstrapped Libor Curve")

Single Index Model Active and Passive Strategy.R

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+rm(list=ls())
+
+# Loading raw data -------------------------------------------------------------
+# Index : KOSPI200 수익률 환산 
+# Stock : 현대제철 NC소프트 현대건설 
+# Risk free rate : CD금리 (3개월) 5년 평ㄱ
+# Prior Authour : Eunsoo Park
+# revisr : Hyunjin Shin균
+
+raw.data <- read.csv('C:/Users/Shinhyunjin/Dropbox/total52.csv', header=T, fileEncoding="UTF-8-BOM")
+#nrow(raw.data)
+raw.data <- raw.data[1:61,-1]
+#raw.data
+
+# Monthly retrun, excess return, risk free rate --------------------------------
+return.m <- raw.data$KOSPI200
+return.v <- var(raw.data$KOSPI200)
+# INDEX & Stocks
+r.free   <- 0.018             # risk free rate (CD금리 평균) 
+excess.return.m <- return.m - r.free    # excess return of INDEX & Stocks
+
+# least square
+out.HCONST    <- lm(HCONST~KOSPI200, data=raw.data)
+out.NCSOFT <- lm(NCSOFT~KOSPI200, data=raw.data)
+out.HSTEEL     <- lm(HSTEEL~KOSPI200, data=raw.data)
+
+# alpha, beta & variance of each stock
+alpha <- c(coef(out.HCONST)[1],
+           coef(out.NCSOFT)[1],
+           coef(out.HSTEEL)[1])
+beta  <- c(coef(out.HCONST)[2],
+           coef(out.NCSOFT)[2],
+           coef(out.HSTEEL)[2])
+variance <- c(deviance(out.HCONST),
+              deviance(out.NCSOFT),
+              deviance(out.HSTEEL))
+resivar <- c((deviance(out.HCONST)-coef(out.HCONST)[2]**2*return.v), 
+             (deviance(out.NCSOFT)-coef(out.NCSOFT)[2]**2*return.v),
+             (deviance(out.HSTEEL)-coef(out.HSTEEL)[2]**2*return.v))
+
+out.m <- cbind(alpha, beta, variance, resivar) # monthly
+rownames(out.m) <- c('현대제철', '엔씨소프트', '현대건설')
+colnames(out.m) <- c('alpha', 'beta', 'total variance', 'residual variance')
+
+out.a <- out.m%*%diag(c(12,1,12,12))     # annualized
+rownames(out.a) <- c('현대제철', '엔씨소프트', '현대건설')
+colnames(out.a) <- c('alpha', 'beta', 'total variance', 'residual variance')
+
+# 알파와 마켓리스크프리미엄 입력 #
+RP.M.a  <- 0.06 # risk premium of the index(6%)
+vol.M.a <- 0.20 # standard deviation of risk preminum(20%)
+
+# risk premiume of stocks using beta estimated & market premium(6%)
+RP.Stock.a <- out.a[,'beta']*RP.M.a
+
+# assumed alpha #
+alpha.a.1 <- 0.03
+alpha.a.2 <- 0.07
+alpha.a.3 <- 0.1
+
+# expected return for each stock #
+ER.Stock.a.1 <- alpha.a.1 + RP.Stock.a
+ER.Stock.a.2 <- alpha.a.2 + RP.Stock.a
+ER.Stock.a.3 <- alpha.a.3 + RP.Stock.a
+
+# function for Sharpe Ratio
+Sharpe.ratio <- function(w, RP, V){
+  w <- c(w, 1-sum(w)) # short sale allowed
+  RP.p <- w %*% RP
+  s.p  <- sqrt(w%*%V%*%w)
+  return(RP.p/s.p)
+}
+
+w <- c(0.1, 0.1, 0.1) # initial weight
+
+# risk premium of stocks & market index
+RP.1 <- c(alpha.a.1 + RP.Stock.a, RP.M.a) # for alpha = 0.03
+RP.2 <- c(alpha.a.2 + RP.Stock.a, RP.M.a) # for alpha = 0.05
+RP.3 <- c(alpha.a.3 + RP.Stock.a, RP.M.a) # for alpha = 0.7
+
+# covariance matrix
+beta.p <- matrix(c(out.a[,'beta'], 1), 4,1)
+V <- beta.p %*% t(beta.p) * vol.M.a^2
+V <- V + diag(4) * c(out.a[,'variance'], 0)
+
+# max Sharpe ratio
+out.1 <- optim(w, Sharpe.ratio, control = list(fnscale=-1), RP=RP.1, V=V)
+out.2 <- optim(w, Sharpe.ratio, control = list(fnscale=-1), RP=RP.2, V=V)
+out.3 <- optim(w, Sharpe.ratio, control = list(fnscale=-1), RP=RP.3, V=V)
+
+# max Sharpe ratio에서 market - Passive Strategy 비중 
+out.1.m <- 1-sum(out.1$par)
+out.2.m <- 1-sum(out.2$par)
+out.3.m <- 1-sum(out.3$par)
+
+# short sale안되면 constOptim : input / constraint : 선형에서 쓴다.
+#value가 sharpe지수고, par미터가 1,2,3가 주식의 비중. 인덱스는 1-parmeterㅎ
+# constriant 에서 shorsale 이 안되면 제곱성질을 이용 #
+
+# Sharpe ration of index 기준점 #
+RP.M.a/vol.M.a
+
+
+#### 참고 : Active & passive 비중  #### 
+# security
+ws1.1 <- (alpha.a.1)/resivar[1]
+ws2.1 <- (alpha.a.1)/resivar[2]
+ws3.1 <- (alpha.a.1)/resivar[3]
+
+ws1.2 <- (alpha.a.2)/resivar[1]
+ws2.2 <- (alpha.a.2)/resivar[2]
+ws3.2 <- (alpha.a.2)/resivar[3]
+
+ws1.3 <- (alpha.a.3)/resivar[1]
+ws2.3 <- (alpha.a.3)/resivar[2]
+ws3.3 <- (alpha.a.3)/resivar[3]
+
+# security normal
+wa1.1 <- ws1.1/(ws1.1 + ws2.1 + ws3.1)
+wa2.1 <- ws2.1/(ws1.1 + ws2.1 + ws3.1)
+wa3.1 <- ws3.1/(ws1.1 + ws2.1 + ws3.1)
+
+wa1.2 <- ws1.2/(ws1.2 + ws2.2 + ws3.2)
+wa2.2 <- ws2.2/(ws1.2 + ws2.2 + ws3.2)
+wa3.2 <- ws3.2/(ws1.2 + ws2.2 + ws3.2)
+
+wa1.3 <- ws1.3/(ws1.3 + ws2.3 + ws3.3)
+wa2.3 <- ws2.3/(ws1.3 + ws2.3 + ws3.3)
+wa3.3 <- ws3.3/(ws1.3 + ws2.3 + ws3.3)
+
+#active
+
+was.1 <- ((wa1.1*alpha.a.1+wa2.1 * alpha.a.1 + wa3.1 * alpha.a.1)/(wa1.1**2*resivar[1]+wa2.1**2*resivar[2]+wa3.1**2*resivar[3]))/((excess.return.m)/return.v)
+was.2 <- ((wa1.2*alpha.a.2+wa2.2 * alpha.a.2 + wa3.2 * alpha.a.2)/(wa1.2**2*resivar[1]+wa2.2**2*resivar[2]+wa3.2**2*resivar[3]))/((excess.return.m)/return.v)
+was.2 <- ((wa1.3*alpha.a.3+wa2.3 * alpha.a.3 + wa3.3 * alpha.a.3)/(wa1.3**2*resivar[1]+wa2.3**2*resivar[2]+wa3.3**2*resivar[3]))/((excess.return.m)/return.v)
+
+
+#Beta -> active weight #
+pfbeta1 <- wa1.1 * beta[1] + wa2.1 * beta[2] + wa3.1 * beta[3]
+pfbeta2 <- wa1.2 * beta[1] + wa2.2 * beta[2] + wa3.2 * beta[3]
+pfbeta3 <- wa1.3 * beta[1] + wa2.3 * beta[2] + wa3.3 * beta[3]
+
+wasb.1 <- was.1 / ((1+(1-pfbeta1)*was.1))
+wasb.2 <- was.2 / ((1+(1-pfbeta2)*was.2))
+wasb.3 <- was.3 / ((1+(1-pfbeta3)*was.3))
+
+#market - passive weight #
+
+wm.1 <- 1-wasb.1
+wm.2 <- 1-wasb.2
+wm.3 <- 1-wasb.3