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”.

# Load packages
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

# Create Vector of Weights
# not all symbols need to be specified. Any symbol not specified by default gets a weight of zero.
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.

Portfolio 1- -2.1% is the first period return.

It’s computed by using the portfolio weights and multiplying them by each portfolio’s return for that period then adding each of them together.

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 [?]
##    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.

If Beta is above 1 it is more volitile than the market, and if it is below 1 it is less volitle than the market. Portfolio 1- Beta = 0.8465 is less than 1 meaning it is less volitile Portfolio 2- Beta = 1.2389 is more than 1 meaning it is more volitile Portfolio 3- Beta = 1.2484 is more than 1 meaning it is more volitile

Q8 Interpret Alpha.

If Alpha is positive it is seen as doing better than the market. Portfolio 1- Alpha = 0.0132 Seen as doing better than the benchmark Portfolio 2- Alpha = 0.0149 Seen as doing better than the benchmark Portfolio 3- Alpha = 0.0275 Seen as doing better than the benchmark

Q9 Interpret AnnualizedAlpha.

If AnnualizedAlpha is positive it is seen as doing better than the market on an annual basis. Portfolio 1- AnnualizedAlpha = 0.1709 Seen as doing better than the benchmark Portfolio 2- AnnualizedAlpha = 0.1937 Seen as doing better than the benchmark Portfolio 3- AnnualizedAlpha = 0.3856 Seen as doing better than the benchmark

Portfolio Analysis, case of multiple portfolios

Nikolas Kellogg

April 30, 2019