Portfolio Analysis, case of multiple portfolios

Q1 Import stock prices and calculate monthly returns.

Hint: Import Apple, Google, Netflix, Microsoft and Tesla from “2015-01-01” to “2018-12-31”.

library(tidyquant)
library(tidyverse)

# Asset Period Returns
stock_returns_monthly <- c("AAPL", "GOOG", "NFLX", "MSFT", "TSLA") %>%
    tq_get(get  = "stock.prices",
           from = "2015-01-01",
           to   = "2018-12-31") %>%
    group_by(symbol) %>%
    tq_transmute(select     = adjusted, 
                 mutate_fun = periodReturn, 
                 period     = "monthly", 
                 col_rename = "Ra")
stock_returns_monthly 
## # A tibble: 240 x 3
## # Groups:   symbol [5]
##    symbol date             Ra
##    <chr>  <date>        <dbl>
##  1 AAPL   2015-01-30  0.0716 
##  2 AAPL   2015-02-27  0.101  
##  3 AAPL   2015-03-31 -0.0314 
##  4 AAPL   2015-04-30  0.00579
##  5 AAPL   2015-05-29  0.0453 
##  6 AAPL   2015-06-30 -0.0372 
##  7 AAPL   2015-07-31 -0.0329 
##  8 AAPL   2015-08-31 -0.0662 
##  9 AAPL   2015-09-30 -0.0218 
## 10 AAPL   2015-10-30  0.0834 
## # … with 230 more rows

Q2 Import S&P500 as a baseline index fund and calculate monthly returns.

# Baseline Period Returns
baseline_returns_monthly <- "^GSPC" %>%
    tq_get(get  = "stock.prices",
           from = "2015-01-01",
           to   = "2018-12-31") %>%
    tq_transmute(select     = adjusted, 
                 mutate_fun = periodReturn, 
                 period     = "monthly", 
                 col_rename = "Rb")
baseline_returns_monthly
## # A tibble: 48 x 2
##    date             Rb
##    <date>        <dbl>
##  1 2015-01-30 -0.0307 
##  2 2015-02-27  0.0549 
##  3 2015-03-31 -0.0174 
##  4 2015-04-30  0.00852
##  5 2015-05-29  0.0105 
##  6 2015-06-30 -0.0210 
##  7 2015-07-31  0.0197 
##  8 2015-08-31 -0.0626 
##  9 2015-09-30 -0.0264 
## 10 2015-10-30  0.0830 
## # … with 38 more rows

Q3 Aggregate three Portfolios with the following weighting schemes.

• Portfolio 1: Assign 60% on Tesla and the rest 40% equally on the other four stocks.
• Portfolio 2: Assign 60% on Microsoft and the rest 40% equally on the other four stocks.
• Portfolio 3: Assign 60% on Netflix and the rest 40% equally on the other four stocks.

# scaling a single portfolio to many, 3 in this case
stock_returns_monthly_multi <- stock_returns_monthly %>%
    tq_repeat_df(n = 3)
stock_returns_monthly_multi
## # A tibble: 720 x 4
## # Groups:   portfolio [3]
##    portfolio symbol date             Ra
##        <int> <chr>  <date>        <dbl>
##  1         1 AAPL   2015-01-30  0.0716 
##  2         1 AAPL   2015-02-27  0.101  
##  3         1 AAPL   2015-03-31 -0.0314 
##  4         1 AAPL   2015-04-30  0.00579
##  5         1 AAPL   2015-05-29  0.0453 
##  6         1 AAPL   2015-06-30 -0.0372 
##  7         1 AAPL   2015-07-31 -0.0329 
##  8         1 AAPL   2015-08-31 -0.0662 
##  9         1 AAPL   2015-09-30 -0.0218 
## 10         1 AAPL   2015-10-30  0.0834 
## # … with 710 more rows

weights <- c(
    0.10, 0.10, 0.10, 0.10, 0.60,
    0.10, 0.10, 0.10, 0.60, 0.10,
    0.10, 0.10, 0.60, 0.10, 0.10
)
stocks <- c("AAPL", "GOOG", "NFLX", "MSFT", "TSLA")
weights_table <-  tibble(stocks) %>%
    tq_repeat_df(n = 3) %>%
    bind_cols(tibble(weights)) %>%
    group_by(portfolio)
weights_table
## # A tibble: 15 x 3
## # Groups:   portfolio [3]
##    portfolio stocks weights
##        <int> <chr>    <dbl>
##  1         1 AAPL       0.1
##  2         1 GOOG       0.1
##  3         1 NFLX       0.1
##  4         1 MSFT       0.1
##  5         1 TSLA       0.6
##  6         2 AAPL       0.1
##  7         2 GOOG       0.1
##  8         2 NFLX       0.1
##  9         2 MSFT       0.6
## 10         2 TSLA       0.1
## 11         3 AAPL       0.1
## 12         3 GOOG       0.1
## 13         3 NFLX       0.6
## 14         3 MSFT       0.1
## 15         3 TSLA       0.1




# Aggregate a Portfolio using Vector of Weights
portfolio_returns_monthly_multi  <-
  stock_returns_monthly_multi %>%
    tq_portfolio(assets_col  = symbol, 
                 returns_col = Ra, 
                 weights     = weights_table, 
                 col_rename  = "Ra")
portfolio_returns_monthly_multi 
## # A tibble: 144 x 3
## # Groups:   portfolio [3]
##    portfolio date            Ra
##        <int> <date>       <dbl>
##  1         1 2015-01-30 -0.0210
##  2         1 2015-02-27  0.0329
##  3         1 2015-03-31 -0.0683
##  4         1 2015-04-30  0.168 
##  5         1 2015-05-29  0.0801
##  6         1 2015-06-30  0.0375
##  7         1 2015-07-31  0.0463
##  8         1 2015-08-31 -0.0468
##  9         1 2015-09-30 -0.0227
## 10         1 2015-10-30 -0.0472
## # … with 134 more rows

Q4 What is the portfolio’s return on the first period? Explain how it’s computed.

The portfolio’s return on the first period -0.02095757371, This is computed with =(0.10 x 0.07)+(0.10 x 0.02)+(0.10+0.26)+(0.10x -0.10)+(0.60 x -.07)

Q5 Merge Ra and Rb

# Merging Ra and Rb
RaRb_single_portfolio <- left_join(portfolio_returns_monthly_multi , 
                                   baseline_returns_monthly,
                                   by = "date")
RaRb_single_portfolio
## # A tibble: 144 x 4
## # Groups:   portfolio [3]
##    portfolio date            Ra       Rb
##        <int> <date>       <dbl>    <dbl>
##  1         1 2015-01-30 -0.0210 -0.0307 
##  2         1 2015-02-27  0.0329  0.0549 
##  3         1 2015-03-31 -0.0683 -0.0174 
##  4         1 2015-04-30  0.168   0.00852
##  5         1 2015-05-29  0.0801  0.0105 
##  6         1 2015-06-30  0.0375 -0.0210 
##  7         1 2015-07-31  0.0463  0.0197 
##  8         1 2015-08-31 -0.0468 -0.0626 
##  9         1 2015-09-30 -0.0227 -0.0264 
## 10         1 2015-10-30 -0.0472  0.0830 
## # … with 134 more rows

Q6 Compute the CAPM Table

RaRb_single_portfolio %>%
    tq_performance(Ra = Ra, Rb = Rb, performance_fun = table.CAPM) %>%
  t()
##                      [,1]   [,2]   [,3]
## portfolio          1.0000 2.0000 3.0000
## ActivePremium      0.1431 0.2005 0.3499
## Alpha              0.0132 0.0149 0.0275
## AnnualizedAlpha    0.1709 0.1937 0.3856
## Beta               0.8465 1.2389 1.2484
## Beta-              0.8137 1.0441 1.6631
## Beta+              0.0575 1.2787 0.9734
## Correlation        0.4093 0.6901 0.4150
## Correlationp-value 0.0039 0.0000 0.0034
## InformationRatio   0.6457 1.2965 1.0878
## R-squared          0.1675 0.4763 0.1722
## TrackingError      0.2216 0.1546 0.3217
## TreynorRatio       0.2261 0.2008 0.3190

Q7 Interpret Beta.

The beta in portfolio 1 is 0.8465, this is the lowest beta. Since portfolio 1 has the lowest beta it means its the least risky portfolio out of the three portfolios. Portfolio 2 has a beta of 1.23 which makes it risker than portfolio 1. portfolio 3 has the highest beta and at 1.24 which makes it the most risky.

Q8 Interpret Alpha.

All of these 3 are beforming better than our benchmark, but the one that did the best is portfolio 3

Q9 Interpret AnnualizedAlpha.

Portfolio 1 did 17.09% better than the bechmark, 2 did 19.37% better, and 3 did 38.56% better than the benchmark.

Q10.a Display both code and the results of the code on the webpage.

Q10.b Display the title and your name correctly at the top of the webpage.

Q10.c Use the correct slug.