Invesment Portofolio Mid

1.Import data Download ETF daily data from yahoo with ticker names of SPY, QQQ, EEM, IWM, EFA, TLT, IYR andGLD from 2010 to current date (See http://etfdb.com/ for ETF information). (Hint: Use libraryquantmod to help you to download these prices and use adjusted prices for your computation.)

x<-c("quantmod", "tidyquant", "lubridate", "timetk", "purrr","tidyverse", "tibble", "readr", "xts", "performanceanalytics", "magrittr", "dplyr")

lapply(x, require, character.only = TRUE)

## Loading required package: quantmod

## Loading required package: xts

## Loading required package: zoo

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## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
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## Loading required package: TTR

## Registered S3 method overwritten by 'quantmod':
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##   as.zoo.data.frame zoo

## Loading required package: tidyquant

## Warning: package 'tidyquant' was built under R version 4.4.3

## Warning: package 'PerformanceAnalytics' was built under R version 4.4.3

## ── Attaching core tidyquant packages ─────────────────────── tidyquant 1.0.11 ──
## ✔ PerformanceAnalytics 2.0.8

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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
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## Loading required package: timetk

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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsLoading required package: performanceanalytics

## Warning in library(package, lib.loc = lib.loc, character.only = TRUE,
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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)

## [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 85.76846 40.48582 31.08410 51.92011 36.38437 58.68241 27.40289
## 2010-01-05 85.99548 40.48582 31.30972 51.74157 36.41643 59.06135 27.46869
## 2010-01-06 86.05604 40.24161 31.37521 51.69289 36.57036 58.27076 27.45672
## 2010-01-07 86.41930 40.26777 31.19326 52.07430 36.42926 58.36873 27.70199
## 2010-01-08 86.70688 40.59919 31.44071 52.35832 36.71787 58.34260 27.51655
## 2010-01-11 86.82797 40.43347 31.37521 52.14734 37.01932 58.02243 27.64814
##               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
## 2010-01-11 112.85

2. Calculate weekly and monthly returns using discrete returns.

etf_data.xts <- xts(etf_data)
head(etf_data)

##                 SPY      QQQ      EEM      IWM      EFA      TLT      IYR
## 2010-01-04 85.76846 40.48582 31.08410 51.92011 36.38437 58.68241 27.40289
## 2010-01-05 85.99548 40.48582 31.30972 51.74157 36.41643 59.06135 27.46869
## 2010-01-06 86.05604 40.24161 31.37521 51.69289 36.57036 58.27076 27.45672
## 2010-01-07 86.41930 40.26777 31.19326 52.07430 36.42926 58.36873 27.70199
## 2010-01-08 86.70688 40.59919 31.44071 52.35832 36.71787 58.34260 27.51655
## 2010-01-11 86.82797 40.43347 31.37521 52.14734 37.01932 58.02243 27.64814
##               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
## 2010-01-11 112.85

WEEKLY - Only count the last day of the week. exclude na values

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 -0.008117313 -0.015037535 -0.02893523 -0.01301920 -0.003493580
## 2010-01-22 -0.038982871 -0.036859451 -0.05578065 -0.03062164 -0.055740338
## 2010-01-29 -0.016665322 -0.031023326 -0.03357724 -0.02624334 -0.025803083
## 2010-02-05 -0.006797297  0.004440172 -0.02821332 -0.01397428 -0.019054797
## 2010-02-12  0.012938499  0.018147851  0.03333344  0.02952568  0.005244899
## 2010-02-19  0.028692839  0.024451696  0.02445360  0.03343168  0.022995029
##                      TLT          IYR          GLD
## 2010-01-15  2.004732e-02 -0.006304396 -0.004579349
## 2010-01-22  1.010091e-02 -0.041785624 -0.033285246
## 2010-01-29  3.370149e-03 -0.008446762 -0.011290465
## 2010-02-05 -5.502338e-05  0.003223281 -0.012080019
## 2010-02-12 -1.946101e-02 -0.007573715  0.022544905
## 2010-02-19 -8.204916e-03  0.050184404  0.022701796

monthly_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  0.03119478  0.04603912  0.017763624  0.04475112  0.002667681
## 2010-03-31  0.06088000  0.07710873  0.081108750  0.08230691  0.063854219
## 2010-04-30  0.01546970  0.02242557 -0.001661597  0.05678457 -0.028045505
## 2010-05-28 -0.07945428 -0.07392414 -0.093936049 -0.07536604 -0.111927979
## 2010-06-30 -0.05174062 -0.05975628 -0.013986487 -0.07743426 -0.020619751
## 2010-07-30  0.06830001  0.07258186  0.109324931  0.06730951  0.116104407
##                     TLT         IYR          GLD
## 2010-02-26 -0.003424668  0.05457001  0.032748219
## 2010-03-31 -0.020573878  0.09748536 -0.004386396
## 2010-04-30  0.033218425  0.06388063  0.058834363
## 2010-05-28  0.051083026 -0.05683542  0.030513147
## 2010-06-30  0.057978818 -0.04670140  0.023553189
## 2010-07-30 -0.009464197  0.09404822 -0.050871157

3.Download Fama French 3 factors data and change to digit numbers (not inpercentage): •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).

fama <- read_csv("C:/Users/ramera/Downloads/F-F_Research_Data_Factors.csv")

## New names:
## Rows: 1288 Columns: 5
## ── Column specification
## ──────────────────────────────────────────────────────── Delimiter: "," chr
## (5): This file was created by CMPT_ME_BEME_RETS using the 202412 CRSP da...
## 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.
## • `` -> `...2`
## • `` -> `...3`
## • `` -> `...4`
## • `` -> `...5`

head(fama)

## # A tibble: 6 × 5
##   This file was created by CMPT_ME_BEME_RETS using the…¹ ...2  ...3  ...4  ...5 
##   <chr>                                                  <chr> <chr> <chr> <chr>
## 1 The 1-month TBill rate data until 202405 are from Ibb… the … <NA>  <NA>  <NA> 
## 2 <NA>                                                   <NA>  <NA>  <NA>  <NA> 
## 3 <NA>                                                   Mkt-… SMB   HML   RF   
## 4 192607                                                 2.96  -2.56 -2.43 0.22 
## 5 192608                                                 2.64  -1.17 3.82  0.25 
## 6 192609                                                 0.36  -1.4  0.13  0.23 
## # ℹ abbreviated name:
## #   ¹`This file was created by CMPT_ME_BEME_RETS using the 202412 CRSP database.`

Format the data frame

colnames(fama) <- paste(c("date","MKT-RF","SMB","HML","RF")) fama.digit <- fama %>% 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: ## ! 101 parsing failures. ## row col expected actual ## 1 -- date like %Y%m The 1-month TBill rate data until 202405 are from Ibbotson Associates. Starting from 202406 ## 1187 -- date like %Y%m Annual Factors: January-December ## 1189 -- date like %Y%m 1927 ## 1190 -- date like %Y%m 1928 ## 1191 -- date like %Y%m 1929 ## .... ... .............. ........................................................................................... ## See problems(...) for more details.

head(fama.digit)

## # A tibble: 6 × 5 ## date `MKT-RF` SMB HML RF ## <date> <chr> <chr> <chr> <chr> ## 1 NA the 1-month TBill rate is from ICE BofA US 1-Mon… <NA> <NA> <NA> ## 2 NA <NA> <NA> <NA> <NA> ## 3 NA Mkt-RF SMB HML RF ## 4 1926-06-30 2.96 -2.56 -2.43 0.22 ## 5 1926-07-31 2.64 -1.17 3.82 0.25 ## 6 1926-08-31 0.36 -1.4 0.13 0.23

fama.digit <- fama.digit[!is.na(fama.digit$date) & !is.infinite(as.numeric(fama.digit$date)), ] fama.digit.xts <- xts(fama.digit[, -1], order.by = as.Date(fama.digit$date)) head(fama.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 -1.4 0.13 0.23 ## 1926-09-30 -3.24 -0.09 0.7 0.32 ## 1926-10-31 2.53 -0.1 -0.51 0.31 ## 1926-11-30 2.62 -0.03 -0.05 0.28

fama.digit.xts <- xts(fama.digit[,-1],order.by=as.Date(fama.digit$date)) head(fama.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 -1.4 0.13 0.23 ## 1926-09-30 -3.24 -0.09 0.7 0.32 ## 1926-10-31 2.53 -0.1 -0.51 0.31 ## 1926-11-30 2.62 -0.03 -0.05 0.28

4. Merge with ETF Monthly returns

merge_data <- merge(fama.digit, etf_monthly_returns) tail(merge_data)

## date MKT-RF SMB HML RF SPY QQQ EEM ## 159565 2024-06-30 1.24 6.8 5.74 0.45 0.04170751 0.06727652 0.002062213 ## 159566 2024-07-31 1.61 -3.55 -1.13 0.48 0.04170751 0.06727652 0.002062213 ## 159567 2024-08-31 1.74 -0.17 -2.59 0.4 0.04170751 0.06727652 0.002062213 ## 159568 2024-09-30 -0.97 -1.01 0.89 0.39 0.04170751 0.06727652 0.002062213 ## 159569 2024-10-31 6.51 4.63 -0.05 0.4 0.04170751 0.06727652 0.002062213 ## 159570 2024-11-30 -3.17 -2.73 -2.95 0.37 0.04170751 0.06727652 0.002062213 ## IWM EFA TLT IYR GLD ## 159565 0.0009053014 0.02820602 0.02376814 0.03371773 0.02169283 ## 159566 0.0009053014 0.02820602 0.02376814 0.03371773 0.02169283 ## 159567 0.0009053014 0.02820602 0.02376814 0.03371773 0.02169283 ## 159568 0.0009053014 0.02820602 0.02376814 0.03371773 0.02169283 ## 159569 0.0009053014 0.02820602 0.02376814 0.03371773 0.02169283 ## 159570 0.0009053014 0.02820602 0.02376814 0.03371773 0.02169283

merge_data_tibble <- as_tibble(merge_data) head(merge_data_tibble)

## # A tibble: 6 × 13 ## date `MKT-RF` SMB HML RF SPY QQQ EEM IWM EFA ## <date> <chr> <chr> <chr> <chr> <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 ## # ℹ 3 more variables: TLT <dbl>, IYR <dbl>, GLD <dbl>

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.

calc_data <- merge_data_tibble[merge_data_tibble$date>="2019-03-01"&merge_data_tibble$date<="2024-02-01",] head(calc_data)

## # A tibble: 6 × 13 ## date `MKT-RF` SMB HML RF SPY QQQ EEM IWM EFA ## <date> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 2019-03-31 3.97 -1.72 2.16 0.21 0.0312 0.0460 0.0178 0.0448 0.00267 ## 2 2019-04-30 -6.94 -1.31 -2.37 0.21 0.0312 0.0460 0.0178 0.0448 0.00267 ## 3 2019-05-31 6.93 0.28 -0.7 0.18 0.0312 0.0460 0.0178 0.0448 0.00267 ## 4 2019-06-30 1.19 -1.93 0.47 0.19 0.0312 0.0460 0.0178 0.0448 0.00267 ## 5 2019-07-31 -2.58 -2.39 -4.79 0.16 0.0312 0.0460 0.0178 0.0448 0.00267 ## 6 2019-08-31 1.43 -0.97 6.77 0.18 0.0312 0.0460 0.0178 0.0448 0.00267 ## # ℹ 3 more variables: TLT <dbl>, IYR <dbl>, GLD <dbl>

merge_data_tibble <- merge_data_tibble %>% mutate(across(c(SPY, QQQ, EEM, IWM, EFA, TLT, IYR, GLD, RF, `MKT-RF`), as.numeric)) spy_rf <- merge_data_tibble$SPY - merge_data_tibble$RF qqq_rf <- merge_data_tibble$QQQ - merge_data_tibble$RF eem_rf <- merge_data_tibble$EEM - merge_data_tibble$RF iwm_rf <- merge_data_tibble$IWM - merge_data_tibble$RF efa_rf <- merge_data_tibble$EFA - merge_data_tibble$RF tlt_rf <- merge_data_tibble$TLT - merge_data_tibble$RF iyr_rf <- merge_data_tibble$IYR - merge_data_tibble$RF gld_rf <- merge_data_tibble$GLD - merge_data_tibble$RF x <- cbind(spy_rf, qqq_rf, eem_rf, iwm_rf, efa_rf, tlt_rf, iyr_rf, gld_rf) n <- nrow(x) one.vec <- rep(1, n) y <- cbind(one.vec, merge_data_tibble$`MKT-RF`) x.mat <- as.matrix(x) beta <- solve(t(x.mat) %*% x.mat) %*% t(x.mat) %*% y beta

## one.vec ## spy_rf -2.4581205 -1.46855191 ## qqq_rf 7.3647591 7.26912431 ## eem_rf -0.3171686 -0.38399533 ## iwm_rf -0.1165191 -0.05946168 ## efa_rf -5.5125163 -5.55411091 ## tlt_rf -1.3974355 -0.72564361 ## iyr_rf 1.4466707 1.15965650 ## gld_rf -0.8563238 -0.79763376

sapply(merge_data_tibble, class)

## date MKT-RF SMB HML RF SPY ## "Date" "numeric" "character" "character" "numeric" "numeric" ## QQQ EEM IWM EFA TLT IYR ## "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" ## GLD ## "numeric"

summary(merge_data_tibble)

## date MKT-RF SMB HML ## Min. :1926-06-30 Min. :-29.1300 Length:159570 Length:159570 ## 1st Qu.:1951-01-31 1st Qu.: -2.0200 Class :character Class :character ## Median :1975-09-15 Median : 1.0650 Mode :character Mode :character ## Mean :1975-09-15 Mean : 0.6865 ## 3rd Qu.:2000-04-30 3rd Qu.: 3.6500 ## Max. :2024-11-30 Max. : 38.8500 ## RF SPY QQQ EEM ## Min. :-0.0600 Min. :-0.12487 Min. :-0.08661 Min. :-0.178947 ## 1st Qu.: 0.0300 1st Qu.:-0.01019 1st Qu.:-0.01457 1st Qu.:-0.029055 ## Median : 0.2300 Median : 0.01773 Median : 0.02074 Median : 0.004088 ## Mean : 0.2693 Mean : 0.01248 Mean : 0.01738 Mean : 0.005588 ## 3rd Qu.: 0.4200 3rd Qu.: 0.03647 3rd Qu.: 0.04757 3rd Qu.: 0.037615 ## Max. : 1.3500 Max. : 0.12698 Max. : 0.14974 Max. : 0.162678 ## IWM EFA TLT IYR ## Min. :-0.21477 Min. :-0.141067 Min. :-0.082137 Min. :-0.196324 ## 1st Qu.:-0.01794 1st Qu.:-0.021764 1st Qu.:-0.021123 1st Qu.:-0.012972 ## Median : 0.01770 Median : 0.009208 Median : 0.002565 Median : 0.010133 ## Mean : 0.01242 Mean : 0.006369 Mean : 0.005973 Mean : 0.009888 ## 3rd Qu.: 0.04659 3rd Qu.: 0.032912 3rd Qu.: 0.028185 3rd Qu.: 0.037719 ## Max. : 0.18244 Max. : 0.142694 Max. : 0.132061 Max. : 0.131896 ## GLD ## Min. :-0.110623 ## 1st Qu.:-0.029437 ## Median :-0.001480 ## Mean : 0.004297 ## 3rd Qu.: 0.032748 ## Max. : 0.122749

e.hat <- y - x%*%beta res.var <- diag(t(e.hat)%*%e.hat)/(n-2) d <- diag(res.var);d

## [,1] [,2] ## [1,] 0.4414904 0.0000 ## [2,] 0.0000000 28.7215

cov.mat <- var(merge_data_tibble$`MKT-RF`)*t(beta)%*%beta + d cov.mat

## one.vec ## one.vec 2710.212 2587.919 ## 2587.919 2538.315

one.vec2 <- matrix(rep(1, 2), ncol = 1) top <- solve(cov.mat) %*% one.vec2 bot <- t(one.vec2) %*% top mvp_capm <- top / as.numeric(bot) mvp_capm

## [,1] ## one.vec -0.6824291 ## 1.6824291

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(calc_data)[1] markets <- calc_data[,c(2,3,4)] FM <- calc_data[,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 0.0327

str(FM)

## tibble [7,965 × 8] (S3: tbl_df/tbl/data.frame) ## $ SPY: num [1:7965] 0.0312 0.0312 0.0312 0.0312 0.0312 ... ## $ QQQ: num [1:7965] 0.046 0.046 0.046 0.046 0.046 ... ## $ EEM: num [1:7965] 0.0178 0.0178 0.0178 0.0178 0.0178 ... ## $ IWM: num [1:7965] 0.0448 0.0448 0.0448 0.0448 0.0448 ... ## $ EFA: num [1:7965] 0.00267 0.00267 0.00267 0.00267 0.00267 ... ## $ TLT: num [1:7965] -0.00342 -0.00342 -0.00342 -0.00342 -0.00342 ... ## $ IYR: num [1:7965] 0.0546 0.0546 0.0546 0.0546 0.0546 ... ## $ GLD: num [1:7965] 0.0327 0.0327 0.0327 0.0327 0.0327 ...

dim(FM)

## [1] 7965 8

str(markets)

## tibble [7,965 × 3] (S3: tbl_df/tbl/data.frame) ## $ MKT-RF: chr [1:7965] "3.97" "-6.94" "6.93" "1.19" ... ## $ SMB : chr [1:7965] "-1.72" "-1.31" "0.28" "-1.93" ... ## $ HML : chr [1:7965] "2.16" "-2.37" "-0.7" "0.47" ...

dim(markets)

## [1] 7965 3

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 0.0327

head(markets)

## # A tibble: 6 × 3 ## `MKT-RF` SMB HML ## <chr> <chr> <chr> ## 1 3.97 -1.72 2.16 ## 2 -6.94 -1.31 -2.37 ## 3 6.93 0.28 -0.7 ## 4 1.19 -1.93 0.47 ## 5 -2.58 -2.39 -4.79 ## 6 1.43 -0.97 6.77

FM <- as.matrix(FM) n <- nrow(FM) p <- ncol(FM) one_vec <- rep(1, n) markets <- as.matrix(markets) m <- ncol(markets) p <- cbind(one_vec, markets)

sample.cov <- cov(FM) sample.cor <- cor(FM) sample.cov

## SPY QQQ EEM IWM EFA ## SPY 0.0015923654 0.0016945299 0.0016038756 1.970835e-03 0.0015669173 ## QQQ 0.0016945299 0.0021320310 0.0017133474 1.987147e-03 0.0016661944 ## EEM 0.0016038756 0.0017133474 0.0028646586 2.086282e-03 0.0020376104 ## IWM 0.0019708352 0.0019871471 0.0020862823 3.041479e-03 0.0019480242 ## EFA 0.0015669173 0.0016661944 0.0020376104 1.948024e-03 0.0020264573 ## TLT -0.0006831270 -0.0006298588 -0.0007368332 -1.044132e-03 -0.0007448935 ## IYR 0.0012818696 0.0012509388 0.0014592186 1.685294e-03 0.0013375725 ## GLD 0.0001024301 0.0002275234 0.0006600062 5.889005e-05 0.0001624475 ## TLT IYR GLD ## SPY -6.831270e-04 1.281870e-03 1.024301e-04 ## QQQ -6.298588e-04 1.250939e-03 2.275234e-04 ## EEM -7.368332e-04 1.459219e-03 6.600062e-04 ## IWM -1.044132e-03 1.685294e-03 5.889005e-05 ## EFA -7.448935e-04 1.337572e-03 1.624475e-04 ## TLT 1.404729e-03 -8.521549e-05 4.421315e-04 ## IYR -8.521549e-05 1.999622e-03 3.215517e-04 ## GLD 4.421315e-04 3.215517e-04 2.174845e-03

7.You can invest in the 8-asset portfolio in 2024/03 based on the optimal weightsof MVP from question 5 and 6. What are the realized portfolio returns in theMarch of 2024 using the weights from question 5 and 6?2

calc_data2 <- tail(merge_data_tibble, n=1) head(calc_data2)

## # A tibble: 1 × 13 ## date `MKT-RF` SMB HML RF SPY QQQ EEM IWM EFA ## <date> <dbl> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 2024-11-30 -3.17 -2.73 -2.95 0.37 0.0417 0.0673 0.00206 0.000905 0.0282 ## # ℹ 3 more variables: TLT <dbl>, IYR <dbl>, GLD <dbl>

calc_data2 <- calc_data2[c(-1,-2,-3,-4,-5)] calc_data2

## # 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 0.0217

With Weights

returns_q5 <- rowSums(calc_data2*mvp_capm) returns_q5

## [1] 0.1190676

Invesment Portofolio Mid

Hector Romero

2025-04-18

1.Import data Download ETF daily data from yahoo with ticker names of SPY, QQQ, EEM, IWM, EFA, TLT, IYR andGLD from 2010 to current date (See http://etfdb.com/ for ETF information). (Hint: Use libraryquantmod to help you to download these prices and use adjusted prices for your computation.)

2. Calculate weekly and monthly returns using discrete returns.

WEEKLY - Only count the last day of the week. exclude na values

3.Download Fama French 3 factors data and change to digit numbers (not inpercentage): •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).

Format the data frame

4. Merge with ETF Monthly returns

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.

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.

7.You can invest in the 8-asset portfolio in 2024/03 based on the optimal weightsof MVP from question 5 and 6. What are the realized portfolio returns in theMarch of 2024 using the weights from question 5 and 6?2

With Weights