Mid Term Investment Portfolio Analysis
Emmanuel Ferdinand Anggawirja
2024-04-15
Investment Portfolio Analysis Mid Term
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library(readr)
library(xts)
library(PerformanceAnalytics)
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## set_nameslibrary(dplyr)Question 1
Download ETF daily data from yahoo with ticker names of SPY, QQQ, EEM, IWM, EFA, TLT, IYR and GLD from 2010 to current date (See http://etfdb.com/ for ETF information). (Hint: Use library quantmod to help you to download these prices and use adjusted prices for your computation.)
tickers <- c("SPY", "QQQ", "EEM", "IWM", "EFA", "TLT", "IYR", "GLD")
data = new.env()
getSymbols(tickers, src = 'yahoo', from = '2010-01-01', to = '2021-04-14', auto.assign = TRUE)## pausing 1 second between requests for more than 5 symbols
## pausing 1 second between requests for more than 5 symbols
## pausing 1 second between requests for more than 5 symbols
## pausing 1 second between requests for more than 5 symbols## [1] "SPY" "QQQ" "EEM" "IWM" "EFA" "TLT" "IYR" "GLD"ETF_Data<- merge(Ad(SPY), Ad(QQQ),Ad(EEM), Ad(IWM),Ad(EFA),Ad(TLT),Ad(IYR),Ad(GLD))
colnames(ETF_Data) <- c("SPY", "QQQ", "EEM", "IWM", "EFA", "TLT", "IYR", "GLD")
head(ETF_Data)## SPY QQQ EEM IWM EFA TLT IYR
## 2010-01-04 86.86007 40.73329 31.82711 52.51540 37.52378 61.13187 28.10298
## 2010-01-05 87.08998 40.73329 32.05812 52.33483 37.55686 61.52665 28.17048
## 2010-01-06 87.15130 40.48757 32.12519 52.28557 37.71560 60.70303 28.15819
## 2010-01-07 87.51920 40.51389 31.93890 52.67136 37.57008 60.80515 28.40971
## 2010-01-08 87.81046 40.84735 32.19225 52.95864 37.86773 60.77791 28.21953
## 2010-01-11 87.93309 40.68064 32.12519 52.74524 38.17862 60.44436 28.35450
## GLD
## 2010-01-04 109.80
## 2010-01-05 109.70
## 2010-01-06 111.51
## 2010-01-07 110.82
## 2010-01-08 111.37
## 2010-01-11 112.85ETF_Data.xts <- xts(ETF_Data)
head(ETF_Data.xts)## SPY QQQ EEM IWM EFA TLT IYR
## 2010-01-04 86.86007 40.73329 31.82711 52.51540 37.52378 61.13187 28.10298
## 2010-01-05 87.08998 40.73329 32.05812 52.33483 37.55686 61.52665 28.17048
## 2010-01-06 87.15130 40.48757 32.12519 52.28557 37.71560 60.70303 28.15819
## 2010-01-07 87.51920 40.51389 31.93890 52.67136 37.57008 60.80515 28.40971
## 2010-01-08 87.81046 40.84735 32.19225 52.95864 37.86773 60.77791 28.21953
## 2010-01-11 87.93309 40.68064 32.12519 52.74524 38.17862 60.44436 28.35450
## GLD
## 2010-01-04 109.80
## 2010-01-05 109.70
## 2010-01-06 111.51
## 2010-01-07 110.82
## 2010-01-08 111.37
## 2010-01-11 112.85Question 2
Calculate weekly and monthly returns using discrete returns
weekly_returns <- to.weekly(ETF_Data.xts, indexAt = "last", OHLC = FALSE)
ETF_weekly_returns <- na.omit(Return.calculate(weekly_returns, method = "discrete"))
head(ETF_weekly_returns)## SPY QQQ EEM IWM EFA
## 2010-01-15 -0.008117291 -0.015037230 -0.02893497 -0.01301907 -0.003493581
## 2010-01-22 -0.038982959 -0.036859359 -0.05578071 -0.03062199 -0.055740123
## 2010-01-29 -0.016665160 -0.031023671 -0.03357730 -0.02624317 -0.025803223
## 2010-02-05 -0.006797515 0.004439813 -0.02821308 -0.01397438 -0.019054673
## 2010-02-12 0.012938098 0.018148474 0.03333336 0.02952581 0.005244720
## 2010-02-19 0.028692959 0.024451765 0.02445335 0.03343146 0.022995204
## TLT IYR GLD
## 2010-01-15 2.004649e-02 -0.006304073 -0.004579348
## 2010-01-22 1.010162e-02 -0.041785190 -0.033285251
## 2010-01-29 3.369057e-03 -0.008447703 -0.011290464
## 2010-02-05 -5.349054e-05 0.003223858 -0.012080021
## 2010-02-12 -1.946114e-02 -0.007573999 0.022544908
## 2010-02-19 -8.205260e-03 0.050184743 0.022701794monthly_returns <- to.monthly(ETF_Data.xts, indexAt = "last", OHLC = FALSE)
ETF_monthly_returns <- na.omit(Return.calculate(monthly_returns, method = "discrete"))
head(ETF_monthly_returns)## SPY QQQ EEM IWM EFA
## 2010-02-26 0.03119473 0.04603872 0.017763809 0.04475079 0.00266776
## 2010-03-31 0.06087965 0.07710921 0.081108579 0.08230713 0.06385434
## 2010-04-30 0.01547025 0.02242522 -0.001661556 0.05678459 -0.02804589
## 2010-05-28 -0.07945456 -0.07392379 -0.093935991 -0.07536625 -0.11192786
## 2010-06-30 -0.05174144 -0.05975656 -0.013986406 -0.07743382 -0.02061989
## 2010-07-30 0.06830093 0.07258253 0.109324720 0.06730879 0.11610458
## TLT IYR GLD
## 2010-02-26 -0.003424477 0.05457082 0.032748217
## 2010-03-31 -0.020573453 0.09748493 -0.004386393
## 2010-04-30 0.033218409 0.06388087 0.058834366
## 2010-05-28 0.051083793 -0.05683502 0.030513141
## 2010-06-30 0.057978401 -0.04670136 0.023553189
## 2010-07-30 -0.009464147 0.09404774 -0.050871154Question 3
Download Fama French 3 factors data and change to digit numbers (not in percentage): •Go to http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html •Download Fama/French 3 factor returns’ monthly data (Mkt-RF, SMB and HML).
famafrench <- read_csv("C:\\Users\\emman\\Downloads\\F-F_Research_Data_Factors_CSV\\F-F_Research_Data_Factors.csv")## Warning: One or more parsing issues, call `problems()` on your data frame for details,
## e.g.:
## dat <- vroom(...)
## problems(dat)## Rows: 1272 Columns: 5
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): DATE
## dbl (4): Mkt-RF, SMB, HML, RF
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.head(famafrench)## # A tibble: 6 × 5
## DATE `Mkt-RF` SMB HML RF
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 192607 2.96 -2.56 -2.43 0.22
## 2 192608 2.64 -1.17 3.82 0.25
## 3 192609 0.36 -1.4 0.13 0.23
## 4 192610 -3.24 -0.09 0.7 0.32
## 5 192611 2.53 -0.1 -0.51 0.31
## 6 192612 2.62 -0.03 -0.05 0.28colnames(famafrench) <- paste(c("date","Mkt-RF","SMB","HML","RF"))
famafrench.digit <- famafrench %>% mutate(date = as.character(date))%>%
mutate(date=ymd(parse_date(date,format="%Y%m"))) %>%
mutate(date=rollback(date))## Warning: There was 1 warning in `mutate()`.
## ℹ In argument: `date = ymd(parse_date(date, format = "%Y%m"))`.
## Caused by warning:
## ! 99 parsing failures.
## row col expected actual
## 1173 -- date like %Y%m Annual Factors: January-December
## 1175 -- date like %Y%m 1927
## 1176 -- date like %Y%m 1928
## 1177 -- date like %Y%m 1929
## 1178 -- date like %Y%m 1930
## .... ... .............. ................................
## See problems(...) for more details.head(famafrench.digit)## # A tibble: 6 × 5
## date `Mkt-RF` SMB HML RF
## <date> <dbl> <dbl> <dbl> <dbl>
## 1 1926-06-30 2.96 -2.56 -2.43 0.22
## 2 1926-07-31 2.64 -1.17 3.82 0.25
## 3 1926-08-31 0.36 -1.4 0.13 0.23
## 4 1926-09-30 -3.24 -0.09 0.7 0.32
## 5 1926-10-31 2.53 -0.1 -0.51 0.31
## 6 1926-11-30 2.62 -0.03 -0.05 0.28famafrench.digit <- famafrench.digit[complete.cases(famafrench.digit), ]
famafrench.digit.xts <- xts(famafrench.digit[,-1],order.by=as.Date(famafrench.digit$date))
head(famafrench.digit.xts)## Mkt-RF SMB HML RF
## 1926-06-30 2.96 -2.56 -2.43 0.22
## 1926-07-31 2.64 -1.17 3.82 0.25
## 1926-08-31 0.36 -1.40 0.13 0.23
## 1926-09-30 -3.24 -0.09 0.70 0.32
## 1926-10-31 2.53 -0.10 -0.51 0.31
## 1926-11-30 2.62 -0.03 -0.05 0.28Question 4
Merge monthly return data in question 2 and 3.
merged_data <- merge(famafrench.digit,ETF_monthly_returns)
tail(merged_data)## date Mkt-RF SMB HML RF SPY QQQ EEM
## 158215 2023-08-31 -5.24 -2.51 1.52 0.43 0.04170778 0.06727648 0.002062358
## 158216 2023-09-30 -3.19 -3.87 0.19 0.47 0.04170778 0.06727648 0.002062358
## 158217 2023-10-31 8.84 -0.02 1.64 0.44 0.04170778 0.06727648 0.002062358
## 158218 2023-11-30 4.87 6.34 4.93 0.43 0.04170778 0.06727648 0.002062358
## 158219 2023-12-31 0.71 -5.09 -2.38 0.47 0.04170778 0.06727648 0.002062358
## 158220 2024-01-31 5.06 -0.24 -3.48 0.42 0.04170778 0.06727648 0.002062358
## IWM EFA TLT IYR GLD
## 158215 0.000905095 0.02820616 0.02376805 0.03371777 0.02169283
## 158216 0.000905095 0.02820616 0.02376805 0.03371777 0.02169283
## 158217 0.000905095 0.02820616 0.02376805 0.03371777 0.02169283
## 158218 0.000905095 0.02820616 0.02376805 0.03371777 0.02169283
## 158219 0.000905095 0.02820616 0.02376805 0.03371777 0.02169283
## 158220 0.000905095 0.02820616 0.02376805 0.03371777 0.02169283final_data_as_tibble <- as_tibble(merged_data)
head(final_data_as_tibble)## # A tibble: 6 × 13
## date `Mkt-RF` SMB HML RF SPY QQQ EEM IWM EFA
## <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1926-06-30 2.96 -2.56 -2.43 0.22 0.0312 0.0460 0.0178 0.0448 0.00267
## 2 1926-07-31 2.64 -1.17 3.82 0.25 0.0312 0.0460 0.0178 0.0448 0.00267
## 3 1926-08-31 0.36 -1.4 0.13 0.23 0.0312 0.0460 0.0178 0.0448 0.00267
## 4 1926-09-30 -3.24 -0.09 0.7 0.32 0.0312 0.0460 0.0178 0.0448 0.00267
## 5 1926-10-31 2.53 -0.1 -0.51 0.31 0.0312 0.0460 0.0178 0.0448 0.00267
## 6 1926-11-30 2.62 -0.03 -0.05 0.28 0.0312 0.0460 0.0178 0.0448 0.00267
## # … with 3 more variables: TLT <dbl>, IYR <dbl>, GLD <dbl>Question 5
Based on CAPM model, compute MVP monthly returns based on estimated covariance matrix for the 8-asset portfolio by using past 60-month returns from 2019/03 - 2024/02.
final_data2 <- final_data_as_tibble[final_data_as_tibble$date>="2019-03-01"&final_data_as_tibble$date<="2024-02-01",]
head(final_data2)## # A tibble: 6 × 13
## date `Mkt-RF` SMB HML RF SPY QQQ EEM IWM EFA
## <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2019-03-31 3.97 -1.74 2.15 0.21 0.0312 0.0460 0.0178 0.0448 0.00267
## 2 2019-04-30 -6.94 -1.32 -2.37 0.21 0.0312 0.0460 0.0178 0.0448 0.00267
## 3 2019-05-31 6.93 0.29 -0.71 0.18 0.0312 0.0460 0.0178 0.0448 0.00267
## 4 2019-06-30 1.19 -1.93 0.48 0.19 0.0312 0.0460 0.0178 0.0448 0.00267
## 5 2019-07-31 -2.58 -2.38 -4.78 0.16 0.0312 0.0460 0.0178 0.0448 0.00267
## 6 2019-08-31 1.43 -0.96 6.75 0.18 0.0312 0.0460 0.0178 0.0448 0.00267
## # … with 3 more variables: TLT <dbl>, IYR <dbl>, GLD <dbl>spy_rf <- final_data_as_tibble$SPY-final_data_as_tibble$RF
qqq_rf <- final_data_as_tibble$QQQ-final_data_as_tibble$RF
eem_rf <- final_data_as_tibble$EEM-final_data_as_tibble$RF
iwm_rf <- final_data_as_tibble$IWM-final_data_as_tibble$RF
efa_rf <- final_data_as_tibble$EFA-final_data_as_tibble$RF
tlt_rf <- final_data_as_tibble$TLT-final_data_as_tibble$RF
iyr_rf <- final_data_as_tibble$IYR-final_data_as_tibble$RF
gld_rf <- final_data_as_tibble$GLD-final_data_as_tibble$RF
y <- cbind(spy_rf,qqq_rf,eem_rf,iwm_rf,efa_rf,tlt_rf,iyr_rf,gld_rf)
n <- nrow(y)
one.vec <- rep(1,n)
x <- cbind(one.vec,final_data_as_tibble$`Mkt-RF`)
x.mat <- as.matrix(x)
beta <- solve(t(x)%*%x)%*%t(x)%*%y
beta## spy_rf qqq_rf eem_rf iwm_rf efa_rf
## one.vec -0.257580973 -0.252687282 -0.264474097 -0.257645508 -0.263693113
## 0.003069948 0.003069948 0.003069948 0.003069948 0.003069948
## tlt_rf iyr_rf gld_rf
## one.vec -0.264089533 -0.260174432 -0.265765506
## 0.003069948 0.003069948 0.003069948e.hat <- y - x%*%beta
res.var <- diag(t(e.hat)%*%e.hat)/(n-2)
d <- diag(res.var);d## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.06407155 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
## [2,] 0.00000000 0.06461115 0.00000000 0.00000000 0.00000000 0.00000000
## [3,] 0.00000000 0.00000000 0.06534369 0.00000000 0.00000000 0.00000000
## [4,] 0.00000000 0.00000000 0.00000000 0.06552049 0.00000000 0.00000000
## [5,] 0.00000000 0.00000000 0.00000000 0.00000000 0.06450559 0.00000000
## [6,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.06388393
## [7,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
## [8,] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
## [,7] [,8]
## [1,] 0.00000000 0.00000000
## [2,] 0.00000000 0.00000000
## [3,] 0.00000000 0.00000000
## [4,] 0.00000000 0.00000000
## [5,] 0.00000000 0.00000000
## [6,] 0.00000000 0.00000000
## [7,] 0.06447875 0.00000000
## [8,] 0.00000000 0.06465395cov.mat <- var(final_data_as_tibble$`Mkt-RF`)*t(beta)%*%beta + d
cov.mat## spy_rf qqq_rf eem_rf iwm_rf efa_rf tlt_rf iyr_rf gld_rf
## spy_rf 1.955798 1.855791 1.942343 1.892200 1.936609 1.939520 1.910770 1.951826
## qqq_rf 1.855791 1.885150 1.905447 1.856256 1.899821 1.902676 1.874473 1.914750
## eem_rf 1.942343 1.905447 2.059659 1.942830 1.988427 1.991416 1.961897 2.004052
## iwm_rf 1.892200 1.856256 1.942830 1.958195 1.937094 1.940005 1.911249 1.952315
## efa_rf 1.936609 1.899821 1.988427 1.937094 2.047062 1.985536 1.956105 1.998135
## tlt_rf 1.939520 1.902676 1.991416 1.940005 1.985536 2.052405 1.959045 2.001138
## iyr_rf 1.910770 1.874473 1.961897 1.911249 1.956105 1.959045 1.994485 1.971476
## gld_rf 1.951826 1.914750 2.004052 1.952315 1.998135 2.001138 1.971476 2.078490one.vec2 <- rep(1,8)
top <- solve(cov.mat)%*%one.vec2
bot <- t(one.vec2)%*%top
mvp_capm <- top/as.numeric(bot)
mvp_capm## [,1]
## spy_rf 0.4735263
## qqq_rf 0.9990351
## eem_rf -0.2731200
## iwm_rf 0.4561692
## efa_rf -0.1920332
## tlt_rf -0.2372801
## iyr_rf 0.1893654
## gld_rf -0.4156627Question 6
Based on FF 3-factor model, compute MVP monthly returns covariance matrix for the 8-asset portfolio by using past 60-month returns from 2019/03 -2024/02.
t <- dim(final_data2)[1]
markets <- final_data2[,c(2,3,4)]
FM <- final_data2[,c(-1,-2,-3,-4,-5)]
head(FM)## # A tibble: 6 × 8
## SPY QQQ EEM IWM EFA TLT IYR GLD
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.0312 0.0460 0.0178 0.0448 0.00267 -0.00342 0.0546 0.0327
## 2 0.0312 0.0460 0.0178 0.0448 0.00267 -0.00342 0.0546 0.0327
## 3 0.0312 0.0460 0.0178 0.0448 0.00267 -0.00342 0.0546 0.0327
## 4 0.0312 0.0460 0.0178 0.0448 0.00267 -0.00342 0.0546 0.0327
## 5 0.0312 0.0460 0.0178 0.0448 0.00267 -0.00342 0.0546 0.0327
## 6 0.0312 0.0460 0.0178 0.0448 0.00267 -0.00342 0.0546 0.0327FM <- as.matrix(FM)
n <- dim(FM)[2]
one_vec <- rep(1,t)
p <- cbind(one_vec,markets)
p <- as.matrix(p)
b.hat <- solve(t(p)%*%p)%*%t(p)%*%FM
res <- FM-p%*%b.hat
diag.d <- diag(t(res)%*%res)/(t-6)
diag.d## SPY QQQ EEM IWM EFA TLT
## 0.001593373 0.002133371 0.002866460 0.003043388 0.002027735 0.001405613
## IYR GLD
## 0.002000875 0.002176211retvar <- apply(FM,2,var)
rsq <- 1-diag(t(res)%*%res)/((t-1)/retvar)
res.stdev <- sqrt(diag.d)
factor.cov <- var(FM)*t(b.hat)%*%b.hat+diag(diag.d)
stdev <- sqrt(diag(factor.cov))
factor.cor <- factor.cov/(stdev%*%t(stdev))
factor.cor## SPY QQQ EEM IWM EFA
## SPY 1.000000e+00 1.992778e-04 5.234299e-05 1.386861e-04 6.929616e-05
## QQQ 1.992778e-04 1.000000e+00 6.726480e-05 1.682160e-04 8.864295e-05
## EEM 5.234299e-05 6.726480e-05 1.000000e+00 4.901045e-05 3.008275e-05
## IWM 1.386861e-04 1.682160e-04 4.901045e-05 1.000000e+00 6.201341e-05
## EFA 6.929616e-05 8.864295e-05 3.008275e-05 6.201341e-05 1.000000e+00
## TLT -3.402736e-05 -3.774208e-05 -1.225265e-05 -3.743786e-05 -1.678536e-05
## IYR 8.859360e-05 1.040039e-04 3.366757e-05 8.384221e-05 4.182007e-05
## GLD 2.949977e-06 7.882589e-06 6.345593e-06 1.220868e-06 2.116499e-06
## TLT IYR GLD
## SPY -3.402736e-05 8.859360e-05 2.949977e-06
## QQQ -3.774208e-05 1.040039e-04 7.882589e-06
## EEM -1.225265e-05 3.366757e-05 6.345593e-06
## IWM -3.743786e-05 8.384221e-05 1.220868e-06
## EFA -1.678536e-05 4.182007e-05 2.116499e-06
## TLT 1.000000e+00 -3.000744e-06 6.488119e-06
## IYR -3.000744e-06 1.000000e+00 6.547089e-06
## GLD 6.488119e-06 6.547089e-06 1.000000e+00sample.cov <- cov(FM)
sample.cor <- cor(FM)
sample.cov## SPY QQQ EEM IWM EFA
## SPY 0.0015923727 0.0016945338 0.0016038794 0.0019708392 0.0015669222
## QQQ 0.0016945338 0.0021320317 0.0017133455 0.0019871446 0.0016661971
## EEM 0.0016038794 0.0017133455 0.0028646601 0.0020862809 0.0020376119
## IWM 0.0019708392 0.0019871446 0.0020862809 0.0030414775 0.0019480259
## EFA 0.0015669222 0.0016661971 0.0020376119 0.0019480259 0.0020264619
## TLT -0.0006831249 -0.0006298565 -0.0007368303 -0.0010441279 -0.0007448921
## IYR 0.0012818711 0.0012509378 0.0014592159 0.0016852937 0.0013375734
## GLD 0.0001024304 0.0002275218 0.0006600064 0.0000588911 0.0001624498
## TLT IYR GLD
## SPY -6.831249e-04 1.281871e-03 0.0001024304
## QQQ -6.298565e-04 1.250938e-03 0.0002275218
## EEM -7.368303e-04 1.459216e-03 0.0006600064
## IWM -1.044128e-03 1.685294e-03 0.0000588911
## EFA -7.448921e-04 1.337573e-03 0.0001624498
## TLT 1.404730e-03 -8.521095e-05 0.0004421335
## IYR -8.521095e-05 1.999619e-03 0.0003215533
## GLD 4.421335e-04 3.215533e-04 0.0021748446sample.cor## SPY QQQ EEM IWM EFA TLT
## SPY 1.00000000 0.9196679 0.7509531 0.89554317 0.87227983 -0.45675284
## QQQ 0.91966794 1.0000000 0.6932846 0.78035164 0.80160484 -0.36395550
## EEM 0.75095306 0.6932846 1.0000000 0.70679574 0.84569878 -0.36731144
## IWM 0.89554317 0.7803516 0.7067957 1.00000000 0.78466305 -0.50514369
## EFA 0.87227983 0.8016048 0.8456988 0.78466305 1.00000000 -0.44149692
## TLT -0.45675284 -0.3639555 -0.3673114 -0.50514369 -0.44149692 1.00000000
## IYR 0.71837036 0.6058503 0.6096905 0.68337599 0.66446916 -0.05084232
## GLD 0.05504176 0.1056604 0.2644219 0.02289777 0.07738125 0.25295475
## IYR GLD
## SPY 0.71837036 0.05504176
## QQQ 0.60585026 0.10566035
## EEM 0.60969050 0.26442195
## IWM 0.68337599 0.02289777
## EFA 0.66446916 0.07738125
## TLT -0.05084232 0.25295475
## IYR 1.00000000 0.15419324
## GLD 0.15419324 1.00000000one <- rep(1,8)
top.mat <- solve(factor.cov)%*%one
bot.mat <- t(one)%*%top.mat
MVP_FF3 <- top.mat/as.numeric(bot.mat)
MVP_FF3## [,1]
## SPY 0.15935085
## QQQ 0.11897834
## EEM 0.08860295
## IWM 0.08341610
## EFA 0.12524994
## TLT 0.18075352
## IYR 0.12691443
## GLD 0.11673388#Question 7 You can invest in the 8-asset portfolio in 2024/03 based on the optimal weights of MVP from question 5 and 6. What are the realized portfolio returns in the March of 2024 using the weights from question 5 and 6?
final_data3 <- tail(final_data_as_tibble, n=1)
final_data3## # A tibble: 1 × 13
## date `Mkt-RF` SMB HML RF SPY QQQ EEM IWM EFA
## <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2024-01-31 5.06 -0.24 -3.48 0.42 0.0417 0.0673 0.00206 0.000905 0.0282
## # … with 3 more variables: TLT <dbl>, IYR <dbl>, GLD <dbl>final_data3 <- final_data3[,c(-1,-2,-3,-4,-5)]
final_data3## # A tibble: 1 × 8
## SPY QQQ EEM IWM EFA TLT IYR GLD
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.0417 0.0673 0.00206 0.000905 0.0282 0.0238 0.0337 0.0217returnsQ5 <- rowSums(final_data3 * mvp_capm) #QUESTION 5
returnsQ5## [1] 0.07312278returnsQ6 <- rowSums(final_data3 * MVP_FF3) #QUESTION 6
returnsQ6## [1] 0.02954938R Markdown
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