Get the Stock Data from Yahoo Finance and Clean the Data
rm(list = ls())
# Get the financial data from Yahoo Finance!
# install.packages("quantmod")
library(quantmod)
## Loading required package: xts
## Warning: package 'xts' was built under R version 4.0.2
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: TTR
## Warning: package 'TTR' was built under R version 4.0.2
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
getSymbols("AAPL")
## [1] "AAPL"
getSymbols("BAC")
## [1] "BAC"
getSymbols("AXP")
## [1] "AXP"
getSymbols("KO")
## [1] "KO"
getSymbols("CVX")
## [1] "CVX"
# Calculate the monthly returns
AAPL_m <- monthlyReturn(AAPL[,6], type = 'log')*100
colnames(AAPL_m) <- "AAPL"
BAC_m <- monthlyReturn(BAC[,6], type = 'log')*100
colnames(BAC_m) <- "BAC"
AXP_m <- monthlyReturn(AXP[,6], type = 'log')*100
colnames(AXP_m) <- "AXP"
KO_m <- monthlyReturn(KO[,6], type = 'log')*100
colnames(KO_m) <- "KO"
CVX_m <- monthlyReturn(CVX[,6], type = 'log')*100
colnames(CVX_m) <- "CVX"
MonthlyFactor <- read.csv("/Volumes/GoogleDrive/My Drive/CBS/1 งานสà¸à¸™/704 Summer 2023/Data/MonthlyFactor.csv")
dim(AAPL_m)
## [1] 198 1
dim(BAC_m)
## [1] 198 1
dim(AXP_m)
## [1] 198 1
dim(KO_m)
## [1] 198 1
dim(CVX_m)
## [1] 198 1
dim(MonthlyFactor)
## [1] 196 8
TT <- dim(MonthlyFactor)[1]
AAPL_m <- as.matrix(AAPL_m[1:TT,],TT,1)
BAC_m <- as.matrix(BAC_m[1:TT,],TT,1)
AXP_m <- as.matrix(AXP_m[1:TT,],TT,1)
KO_m <- as.matrix(KO_m[1:TT,],TT,1)
CVX_m <- as.matrix(CVX_m[1:TT,],TT,1)
MonthlyFactor <- as.matrix(MonthlyFactor[,2:8], TT,7)
data <- cbind(AAPL_m, BAC_m, AXP_m, KO_m, CVX_m, MonthlyFactor)
data <- as.data.frame(data)
str(data)
## 'data.frame': 196 obs. of 12 variables:
## $ AAPL : num 2.28 -1.32 9.36 7.15 19.42 ...
## $ BAC : num -1.416 -2.276 0.373 -0.235 0.726 ...
## $ AXP : num -3.61 -2.35 -0.83 7.57 6.86 ...
## $ KO : num -1.45 -2.54 3.5 8.37 1.52 ...
## $ CVX : num 2.66 -5.45 7.64 5.05 5.37 ...
## $ Mkt.RF: num 1.4 -1.96 0.68 3.49 3.24 -1.96 -3.73 0.92 3.22 1.8 ...
## $ SMB : num 0.08 1.28 0.19 -2.03 0.4 0.75 -2.98 -0.37 -2.43 -0.03 ...
## $ HML : num -0.69 -0.13 -0.96 -1.46 -0.65 -1.07 -3.72 -1.86 -2.23 -3.05 ...
## $ RMW : num 0.25 -0.51 0.64 1.15 1.58 0.53 0.2 -1.21 -0.52 -0.3 ...
## $ CMA : num 0.38 -0.71 -0.65 1.04 -1.36 0.08 -1.13 -0.53 -3.02 -0.09 ...
## $ MOM : num 0.24 -1.35 2.56 -0.24 -0.34 0.51 2.94 0.1 4.63 5.02 ...
## $ RF : num 0.44 0.38 0.43 0.44 0.41 0.4 0.4 0.42 0.32 0.32 ...
# Data Exploration
psych::describe(data)
## vars n mean sd median trimmed mad min max range skew
## AAPL 1 196 2.14 9.11 2.88 2.59 7.95 -39.98 21.33 61.31 -0.97
## BAC 2 196 -0.15 13.17 0.41 0.45 9.42 -76.07 54.89 130.96 -1.12
## AXP 3 196 0.63 9.34 0.90 0.99 5.84 -32.73 62.87 95.60 0.87
## KO 4 196 0.75 4.75 1.10 0.97 4.42 -18.25 13.27 31.52 -0.72
## CVX 5 196 0.76 7.02 1.14 0.72 5.63 -25.32 24.13 49.45 0.07
## Mkt.RF 6 196 0.76 4.73 1.28 0.98 3.81 -17.23 13.65 30.88 -0.53
## SMB 7 196 0.01 2.62 0.14 -0.05 2.56 -8.30 7.13 15.43 0.15
## HML 8 196 -0.20 3.37 -0.45 -0.30 2.40 -13.95 12.75 26.70 0.13
## RMW 9 196 0.37 1.91 0.39 0.29 1.59 -4.78 7.22 12.00 0.51
## CMA 10 196 0.11 1.98 -0.04 0.01 1.84 -6.92 7.74 14.66 0.49
## MOM 11 196 0.05 4.72 0.44 0.39 3.63 -34.30 12.75 47.05 -2.28
## RF 12 196 0.07 0.11 0.01 0.05 0.01 0.00 0.44 0.44 1.65
## kurtosis se
## AAPL 2.91 0.65
## BAC 7.37 0.94
## AXP 10.34 0.67
## KO 1.77 0.34
## CVX 1.68 0.50
## Mkt.RF 0.97 0.34
## SMB 0.34 0.19
## HML 2.53 0.24
## RMW 1.06 0.14
## CMA 1.60 0.14
## MOM 13.81 0.34
## RF 1.85 0.01
# Data Visualization
# install.packages("scatterPlotMatrix")
library(scatterPlotMatrix)
scatterPlotMatrix(data)
scatterPlotMatrix(data, regressionType = 1)
Factor Models of a Single Stock
# Model Estimation
# Single Factor Model: Capital Asset Pricing Model
# Ref:
AAPL_1f <- lm(AAPL-RF ~ Mkt.RF, data = data)
summary(AAPL_1f)
##
## Call:
## lm(formula = AAPL - RF ~ Mkt.RF, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -31.966 -3.359 0.304 4.564 17.708
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.1769 0.5221 2.254 0.0253 *
## Mkt.RF 1.1784 0.1092 10.794 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.218 on 194 degrees of freedom
## Multiple R-squared: 0.3752, Adjusted R-squared: 0.372
## F-statistic: 116.5 on 1 and 194 DF, p-value: < 2.2e-16
# Three-Factor Model
# Ref:
AAPL_3f <- lm(AAPL-RF ~ Mkt.RF + SMB + HML, data = data)
summary(AAPL_3f)
##
## Call:
## lm(formula = AAPL - RF ~ Mkt.RF + SMB + HML, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28.283 -3.353 -0.032 4.366 16.290
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.9338 0.4909 1.902 0.0586 .
## Mkt.RF 1.3283 0.1099 12.083 < 2e-16 ***
## SMB -0.3410 0.2067 -1.650 0.1006
## HML -0.6811 0.1518 -4.486 1.25e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.757 on 192 degrees of freedom
## Multiple R-squared: 0.458, Adjusted R-squared: 0.4496
## F-statistic: 54.09 on 3 and 192 DF, p-value: < 2.2e-16
# Four-Factor Model
# Ref:
AAPL_4f <- lm(AAPL-RF ~ Mkt.RF + SMB + HML + MOM, data = data)
summary(AAPL_4f)
##
## Call:
## lm(formula = AAPL - RF ~ Mkt.RF + SMB + HML + MOM, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.9873 -3.4547 -0.0483 4.3781 16.3360
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.92628 0.49274 1.880 0.0617 .
## Mkt.RF 1.33904 0.11626 11.518 < 2e-16 ***
## SMB -0.33438 0.20842 -1.604 0.1103
## HML -0.66880 0.15809 -4.231 3.61e-05 ***
## MOM 0.03418 0.11826 0.289 0.7729
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.774 on 191 degrees of freedom
## Multiple R-squared: 0.4583, Adjusted R-squared: 0.4469
## F-statistic: 40.4 on 4 and 191 DF, p-value: < 2.2e-16
# Five-Factor Model
# Ref:
AAPL_5f <- lm(AAPL-RF ~ Mkt.RF + SMB + HML + RMW + CMA, data = data)
summary(AAPL_5f)
##
## Call:
## lm(formula = AAPL - RF ~ Mkt.RF + SMB + HML + RMW + CMA, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28.9811 -3.5060 -0.0402 4.2576 16.0626
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.7651 0.5056 1.513 0.1319
## Mkt.RF 1.3176 0.1132 11.638 <2e-16 ***
## SMB -0.1999 0.2207 -0.906 0.3663
## HML -0.6381 0.1968 -3.243 0.0014 **
## RMW 0.5513 0.2738 2.014 0.0455 *
## CMA -0.2148 0.3222 -0.667 0.5058
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.717 on 190 degrees of freedom
## Multiple R-squared: 0.4701, Adjusted R-squared: 0.4561
## F-statistic: 33.71 on 5 and 190 DF, p-value: < 2.2e-16
# Five-Factor Model + Momentum Factor
# Ref:
AAPL_6f <- lm(AAPL-RF ~ Mkt.RF + SMB + HML + RMW + CMA + MOM, data = data)
summary(AAPL_6f)
##
## Call:
## lm(formula = AAPL - RF ~ Mkt.RF + SMB + HML + RMW + CMA + MOM,
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28.5319 -3.5468 0.2156 4.2713 15.8681
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.76042 0.50681 1.500 0.1352
## Mkt.RF 1.33144 0.11770 11.312 <2e-16 ***
## SMB -0.19148 0.22204 -0.862 0.3896
## HML -0.60690 0.20942 -2.898 0.0042 **
## RMW 0.55341 0.27440 2.017 0.0451 *
## CMA -0.24585 0.33041 -0.744 0.4578
## MOM 0.05329 0.12025 0.443 0.6582
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.731 on 189 degrees of freedom
## Multiple R-squared: 0.4706, Adjusted R-squared: 0.4538
## F-statistic: 28.01 on 6 and 189 DF, p-value: < 2.2e-16
# Expected Return, Variance and SD Implied by the Models
# Example: Single Factor Model
model <- AAPL_1f
alpha <- model[["coefficients"]][["(Intercept)"]]
beta1 <- model[["coefficients"]][["Mkt.RF"]]
ave_F1 <- mean(data$Mkt.RF)
var_F1 <- var(data$Mkt.RF)
EX_AAPL <- alpha + beta1 * ave_F1
VX_AAPL <- beta1^2 * var_F1
SD_AAPL <- sqrt(VX_AAPL)
print(c(EX_AAPL, SD_AAPL))
## [1] 2.067393 5.579100
# Example: Three-Factor Model
model <- AAPL_3f
alpha <- model[["coefficients"]][["(Intercept)"]]
beta1 <- model[["coefficients"]][["Mkt.RF"]]
beta2 <- model[["coefficients"]][["SMB"]]
beta3 <- model[["coefficients"]][["HML"]]
ave_F1 <- mean(data$Mkt.RF)
ave_F2 <- mean(data$SMB)
ave_F3 <- mean(data$HML)
var_F1 <- var(data$Mkt.RF)
var_F2 <- var(data$SMB)
var_F3 <- var(data$HML)
EX_AAPL <- alpha + beta1 * ave_F1 + beta2 * ave_F2 + beta3 * ave_F3
VX_AAPL <- beta1^2 * var_F1 + beta2^2 * var_F2 + beta3^2 * var_F3
SD_AAPL <- sqrt(VX_AAPL)
print(c(EX_AAPL, SD_AAPL))
## [1] 2.067393 6.753934
Factor Models of a Portfolio
# Let's choose a portfolio weight. This is up to you how you would do the portfolio allocation.
w1 <- 0.2 #AAPL
w2 <- 0.2 #BAC
w3 <- 0.2 #AXP
w4 <- 0.2 #KO
w5 <- 0.2 #CVX
data$PORT <- w1*data$AAPL + w2*data$BAC + w3*data$AXP + w4*data$KO + w5*data$KO
hist(data$PORT)
plot(data$PORT)
# Model Estimation
# Single Factor Model: Capital Asset Pricing Model
# Ref:
PORT_1f <- lm(PORT-RF ~ Mkt.RF, data = data)
summary(PORT_1f)
##
## Call:
## lm(formula = PORT - RF ~ Mkt.RF, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.8391 -1.5833 0.1316 1.5966 10.4050
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.06956 0.22473 -0.31 0.757
## Mkt.RF 1.08563 0.04699 23.10 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.107 on 194 degrees of freedom
## Multiple R-squared: 0.7334, Adjusted R-squared: 0.732
## F-statistic: 533.7 on 1 and 194 DF, p-value: < 2.2e-16
# Three-Factor Model
# Ref:
PORT_3f <- lm(PORT-RF ~ Mkt.RF + SMB + HML, data = data)
summary(PORT_3f)
##
## Call:
## lm(formula = PORT - RF ~ Mkt.RF + SMB + HML, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.8818 -1.6646 0.1348 1.6307 9.6572
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.003546 0.201839 0.018 0.986
## Mkt.RF 1.104350 0.045201 24.432 < 2e-16 ***
## SMB -0.342317 0.084977 -4.028 8.09e-05 ***
## HML 0.421827 0.062438 6.756 1.65e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.779 on 192 degrees of freedom
## Multiple R-squared: 0.789, Adjusted R-squared: 0.7857
## F-statistic: 239.3 on 3 and 192 DF, p-value: < 2.2e-16
# Four-Factor Model
# Ref:
PORT_4f <- lm(PORT-RF ~ Mkt.RF + SMB + HML + MOM, data = data)
summary(PORT_4f)
##
## Call:
## lm(formula = PORT - RF ~ Mkt.RF + SMB + HML + MOM, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.4068 -1.5627 0.1103 1.8343 7.8714
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.03196 0.19889 0.161 0.87252
## Mkt.RF 1.06396 0.04693 22.673 < 2e-16 ***
## SMB -0.36728 0.08413 -4.366 2.07e-05 ***
## HML 0.37531 0.06381 5.882 1.79e-08 ***
## MOM -0.12888 0.04773 -2.700 0.00756 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.734 on 191 degrees of freedom
## Multiple R-squared: 0.7967, Adjusted R-squared: 0.7925
## F-statistic: 187.2 on 4 and 191 DF, p-value: < 2.2e-16
# Five-Factor Model
# Ref:
PORT_5f <- lm(PORT-RF ~ Mkt.RF + SMB + HML + RMW + CMA, data = data)
summary(PORT_5f)
##
## Call:
## lm(formula = PORT - RF ~ Mkt.RF + SMB + HML + RMW + CMA, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.2840 -1.6244 0.2145 1.7008 9.6228
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.11524 0.20661 0.558 0.5777
## Mkt.RF 1.07337 0.04626 23.202 < 2e-16 ***
## SMB -0.38911 0.09020 -4.314 2.58e-05 ***
## HML 0.55415 0.08041 6.892 7.89e-11 ***
## RMW -0.07276 0.11187 -0.650 0.5162
## CMA -0.32408 0.13166 -2.461 0.0147 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.745 on 190 degrees of freedom
## Multiple R-squared: 0.7962, Adjusted R-squared: 0.7909
## F-statistic: 148.5 on 5 and 190 DF, p-value: < 2.2e-16
# Five-Factor Model + Momentum Factor
# Ref:
PORT_6f <- lm(PORT-RF ~ Mkt.RF + SMB + HML + RMW + CMA + MOM, data = data)
summary(PORT_6f)
##
## Call:
## lm(formula = PORT - RF ~ Mkt.RF + SMB + HML + RMW + CMA + MOM,
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.637 -1.615 0.244 1.750 7.035
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.12487 0.20450 0.611 0.5422
## Mkt.RF 1.04503 0.04749 22.004 < 2e-16 ***
## SMB -0.40635 0.08959 -4.536 1.02e-05 ***
## HML 0.49038 0.08450 5.803 2.70e-08 ***
## RMW -0.07704 0.11072 -0.696 0.4874
## CMA -0.26069 0.13332 -1.955 0.0520 .
## MOM -0.10879 0.04852 -2.242 0.0261 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.716 on 189 degrees of freedom
## Multiple R-squared: 0.8015, Adjusted R-squared: 0.7952
## F-statistic: 127.2 on 6 and 189 DF, p-value: < 2.2e-16
# You can also calculate the expected returns and the variance and the SD of this portfolio