Portfolio Performance Analysis: multiple portfolios

Q1 Get monthly returns of Facebook, Amazon, and Netflix for the last 5 years.

# Load packages  
library(tidyquant)
library(tidyverse)

from <- today() - years(5)
stock_returns_monthly <- c("FB", "NFLX", "AMZN") %>%
    tq_get(get  = "stock.prices",
           from = from) %>%
    group_by(symbol) %>%
    tq_transmute(select     = adjusted, 
                 mutate_fun = periodReturn, 
                 period     = "monthly", 
                 col_rename = "Ra")
stock_returns_monthly

## # A tibble: 183 x 3
## # Groups:   symbol [3]
##    symbol date             Ra
##    <chr>  <date>        <dbl>
##  1 FB     2015-11-30 -0.0328 
##  2 FB     2015-12-31  0.00403
##  3 FB     2016-01-29  0.0721 
##  4 FB     2016-02-29 -0.0471 
##  5 FB     2016-03-31  0.0672 
##  6 FB     2016-04-29  0.0305 
##  7 FB     2016-05-31  0.0105 
##  8 FB     2016-06-30 -0.0381 
##  9 FB     2016-07-29  0.0845 
## 10 FB     2016-08-31  0.0176 
## # ... with 173 more rows

Q2 Get monthly returns of NASDAQ for the same period as the baseline.

baseline_returns_monthly <- "^GSPC" %>%
    tq_get(get  = "stock.prices",
           from = from) %>%
    tq_transmute(select     = adjusted, 
                 mutate_fun = periodReturn, 
                 period     = "monthly", 
                 col_rename = "Rb")
baseline_returns_monthly

## # A tibble: 61 x 2
##    date              Rb
##    <date>         <dbl>
##  1 2015-11-30 -0.00152 
##  2 2015-12-31 -0.0175  
##  3 2016-01-29 -0.0507  
##  4 2016-02-29 -0.00413 
##  5 2016-03-31  0.0660  
##  6 2016-04-29  0.00270 
##  7 2016-05-31  0.0153  
##  8 2016-06-30  0.000911
##  9 2016-07-29  0.0356  
## 10 2016-08-31 -0.00122 
## # ... with 51 more rows

Q3 Aggregate for 10 portfolios with the following weighting schemes.

• Facebook(0.80), Amazon(0.10), Netflix (0.10)
• Facebook(0.10), Amazon(0.80), Netflix (0.10)
• Facebook(0.10), Amazon(0.10), Netflix (0.80)
• Facebook(0.60), Amazon(0.20), Netflix (0.20)
• Facebook(0.20), Amazon(0.60), Netflix (0.20)
• Facebook(0.20), Amazon(0.20), Netflix (0.60)
• Facebook(0.50), Amazon(0.25), Netflix (0.25)
• Facebook(0.25), Amazon(0.50), Netflix (0.25)
• Facebook(0.25), Amazon(0.25), Netflix (0.50)
• Facebook(0.40), Amazon(0.40), Netflix (0.20)

# 
stock_returns_monthly_multi <- stock_returns_monthly %>%
    tq_repeat_df(n = 10)
stock_returns_monthly_multi

## # A tibble: 1,830 x 4
## # Groups:   portfolio [10]
##    portfolio symbol date             Ra
##        <int> <chr>  <date>        <dbl>
##  1         1 FB     2015-11-30 -0.0328 
##  2         1 FB     2015-12-31  0.00403
##  3         1 FB     2016-01-29  0.0721 
##  4         1 FB     2016-02-29 -0.0471 
##  5         1 FB     2016-03-31  0.0672 
##  6         1 FB     2016-04-29  0.0305 
##  7         1 FB     2016-05-31  0.0105 
##  8         1 FB     2016-06-30 -0.0381 
##  9         1 FB     2016-07-29  0.0845 
## 10         1 FB     2016-08-31  0.0176 
## # ... with 1,820 more rows

# Assign weights to individual stocks
weights <- c(
0.80, 0.10, 0.10,
0.10, 0.80, 0.10,
0.10, 0.10, 0.80,
0.60, 0.20, 0.20,
0.20, 0.60, 0.20,
0.20, 0.20, 0.60,
0.50, 0.25, 0.25,
0.25, 0.50, 0.25,
0.25, 0.25, 0.50,
0.40, 0.40, 0.20
)
stocks <- c("FB", "AMZN", "NFLX")
weights_table <-  tibble(stocks) %>%
    tq_repeat_df(n = 10) %>%
    bind_cols(tibble(weights)) %>%
    group_by(portfolio)
weights_table

## # A tibble: 30 x 3
## # Groups:   portfolio [10]
##    portfolio stocks weights
##        <int> <chr>    <dbl>
##  1         1 FB         0.8
##  2         1 AMZN       0.1
##  3         1 NFLX       0.1
##  4         2 FB         0.1
##  5         2 AMZN       0.8
##  6         2 NFLX       0.1
##  7         3 FB         0.1
##  8         3 AMZN       0.1
##  9         3 NFLX       0.8
## 10         4 FB         0.6
## # ... with 20 more rows

# Aggregate a Portfolio using Vector of Weights
portfolio_returns_monthly  <-
  stock_returns_monthly_multi %>%
    tq_portfolio(assets_col  = symbol, 
                 returns_col = Ra, 
                 weights     = weights_table, 
                 col_rename  = "Ra")
portfolio_returns_monthly 

## # A tibble: 610 x 3
## # Groups:   portfolio [10]
##    portfolio date             Ra
##        <int> <date>        <dbl>
##  1         1 2015-11-30 -0.0238 
##  2         1 2015-12-31 -0.00269
##  3         1 2016-01-29  0.0246 
##  4         1 2016-02-29 -0.0433 
##  5         1 2016-03-31  0.0700 
##  6         1 2016-04-29  0.0251 
##  7         1 2016-05-31  0.0278 
##  8         1 2016-06-30 -0.0408 
##  9         1 2016-07-29  0.0756 
## 10         1 2016-08-31  0.0206 
## # ... with 600 more rows

Q4 Calcualte the Sharpe Ratio per portfolio.

# Merging Ra and Rb
RaRb_multi_portfolio <- left_join(portfolio_returns_monthly , 
                                   baseline_returns_monthly,
                                   by = "date")
RaRb_multi_portfolio

## # A tibble: 610 x 4
## # Groups:   portfolio [10]
##    portfolio date             Ra        Rb
##        <int> <date>        <dbl>     <dbl>
##  1         1 2015-11-30 -0.0238  -0.00152 
##  2         1 2015-12-31 -0.00269 -0.0175  
##  3         1 2016-01-29  0.0246  -0.0507  
##  4         1 2016-02-29 -0.0433  -0.00413 
##  5         1 2016-03-31  0.0700   0.0660  
##  6         1 2016-04-29  0.0251   0.00270 
##  7         1 2016-05-31  0.0278   0.0153  
##  8         1 2016-06-30 -0.0408   0.000911
##  9         1 2016-07-29  0.0756   0.0356  
## 10         1 2016-08-31  0.0206  -0.00122 
## # ... with 600 more rows

# Sharpe Ratio
RaRb_multi_portfolio %>%
  tq_performance(Ra = Ra, Rb = NULL, performance_fun = SharpeRatio.annualized, scale = 12) 

## # A tibble: 10 x 2
## # Groups:   portfolio [10]
##    portfolio `AnnualizedSharpeRatio(Rf=0%)`
##        <int>                          <dbl>
##  1         1                          0.916
##  2         2                          1.26 
##  3         3                          0.945
##  4         4                          1.05 
##  5         5                          1.24 
##  6         6                          1.04 
##  7         7                          1.10 
##  8         8                          1.21 
##  9         9                          1.09 
## 10        10                          1.18

Q5 Sort the portfolios in descending order of Sharpe Ratio.

Hint: Use dplyr::arrange().

# Calculate Sharpe Ratio for hundreds of portfolios
RaRb_multi_portfolio %>%
  tq_performance(Ra = Ra, Rb = NULL, performance_fun = SharpeRatio.annualized, scale = 12) %>%
  arrange(desc(`AnnualizedSharpeRatio(Rf=0%)`))

## # A tibble: 10 x 2
## # Groups:   portfolio [10]
##    portfolio `AnnualizedSharpeRatio(Rf=0%)`
##        <int>                          <dbl>
##  1         2                          1.26 
##  2         5                          1.24 
##  3         8                          1.21 
##  4        10                          1.18 
##  5         7                          1.10 
##  6         9                          1.09 
##  7         4                          1.05 
##  8         6                          1.04 
##  9         3                          0.945
## 10         1                          0.916

Q6 Which weighting scheme would have performed the best?

Hint: Make your argument using the calculated Sharpe

Weighting scheme #2 worked the best because the sharpe ratio is the highest.

Q7 Which weighting scheme is most volatile?

Hint: Calculate Beta from the Capital Asset Pricing Model. Make your argument based on the calculated Beta.

# Beta and Alpha
RaRb_multi_portfolio %>%
  tq_performance(Ra = Ra, Rb = Rb, performance_fun = table.CAPM) %>%
  t()

##                      [,1]   [,2]   [,3]   [,4]   [,5]   [,6]   [,7]   [,8]
## portfolio          1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000
## ActivePremium      0.1199 0.2263 0.1938 0.1485 0.2085 0.1893 0.1619 0.1992
## Alpha              0.0089 0.0160 0.0172 0.0111 0.0150 0.0156 0.0121 0.0145
## AnnualizedAlpha    0.1116 0.2094 0.2269 0.1411 0.1955 0.2043 0.1556 0.1891
## Beta               1.1402 1.1666 0.9612 1.1029 1.1296 1.0062 1.0900 1.1099
## Beta-              0.8342 0.8820 0.7865 0.8135 0.8541 0.7856 0.8094 0.8386
## Beta+              1.4721 1.2683 1.2967 1.3855 1.2883 1.2953 1.3536 1.2979
## Correlation        0.6732 0.6520 0.4446 0.6677 0.6541 0.5221 0.6559 0.6485
## Correlationp-value 0.0000 0.0000 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio   0.6306 1.0974 0.6636 0.7980 1.0528 0.7635 0.8537 1.0098
## R-squared          0.4531 0.4251 0.1977 0.4458 0.4279 0.2726 0.4302 0.4205
## TrackingError      0.1901 0.2062 0.2921 0.1861 0.1980 0.2479 0.1897 0.1972
## TreynorRatio       0.2053 0.2918 0.3204 0.2382 0.2856 0.3016 0.2533 0.2823
##                      [,9]   [,10]
## portfolio          9.0000 10.0000
## ActivePremium      0.1870  0.1799
## Alpha              0.0149  0.0131
## AnnualizedAlpha    0.1942  0.1685
## Beta               1.0306  1.1149
## Beta-              0.7915  0.8333
## Beta+              1.2992  1.3318
## Correlation        0.5624  0.6721
## Correlationp-value 0.0000  0.0000
## InformationRatio   0.8178  0.9668
## R-squared          0.3163  0.4517
## TrackingError      0.2286  0.1861
## TreynorRatio       0.2922  0.2638

Scheme #4 is the most volatile because its maximum and minimum betas are have the largest difference.

Q8 Hide the messages, but display the code and its results on the webpage.

Hint: Use message, echo and results in the chunk options. Refer to the RMarkdown Reference Guide.

Q9 Display the title and your name correctly at the top of the webpage.

Q10 Use the correct slug.