Quiz 6

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

library(tidyquant)
library(tidyverse)

from <- today() - years(5)
stock_returns_monthly <- c("FB", "AMZN", "NFLX") %>%
  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 -0.0287 
##  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 <- "^IXIC" %>%
  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  0.000735
##  2 2015-12-31 -0.0198  
##  3 2016-01-29 -0.0786  
##  4 2016-02-29 -0.0121  
##  5 2016-03-31  0.0684  
##  6 2016-04-29 -0.0194  
##  7 2016-05-31  0.0362  
##  8 2016-06-30 -0.0213  
##  9 2016-07-29  0.0660  
## 10 2016-08-31  0.00990 
## # ... 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 -0.0287 
##  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

weights <- c(
  0.8, 0.1, 0.1,
  0.1, 0.8, 0.1,
  0.1, 0.1, 0.8,
  0.6, 0.2, 0.2,
  0.2, 0.6, 0.2,
  0.2, 0.2, 0.6,
  0.5, 0.25, 0.25,
  0.25, 0.5, 0.25,
  0.25, 0.25, 0.5,
  0.4, 0.4, 0.2
)
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

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 -0.0239 
##  2         1 2015-12-31 -0.00250
##  3         1 2016-01-29  0.0255 
##  4         1 2016-02-29 -0.0434 
##  5         1 2016-03-31  0.0699 
##  6         1 2016-04-29  0.0254 
##  7         1 2016-05-31  0.0274 
##  8         1 2016-06-30 -0.0407 
##  9         1 2016-07-29  0.0758 
## 10         1 2016-08-31  0.0205 
## # ... with 600 more rows

Q4 Calcualte the Sharpe Ratio per portfolio.

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 -0.0239   0.000735
##  2         1 2015-12-31 -0.00250 -0.0198  
##  3         1 2016-01-29  0.0255  -0.0786  
##  4         1 2016-02-29 -0.0434  -0.0121  
##  5         1 2016-03-31  0.0699   0.0684  
##  6         1 2016-04-29  0.0254  -0.0194  
##  7         1 2016-05-31  0.0274   0.0362  
##  8         1 2016-06-30 -0.0407  -0.0213  
##  9         1 2016-07-29  0.0758   0.0660  
## 10         1 2016-08-31  0.0205   0.00990 
## # ... with 600 more rows

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                          0.909
##  2         2                          1.25 
##  3         3                          0.933
##  4         4                          1.04 
##  5         5                          1.23 
##  6         6                          1.03 
##  7         7                          1.09 
##  8         8                          1.20 
##  9         9                          1.08 
## 10        10                          1.16

Q5 Sort the portfolios in descending order of Sharpe Ratio.

Hint: Use dplyr::arrange().

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                          1.25 
##  2         5                          1.23 
##  3         8                          1.20 
##  4        10                          1.16 
##  5         7                          1.09 
##  6         9                          1.08 
##  7         4                          1.04 
##  8         6                          1.03 
##  9         3                          0.933
## 10         1                          0.909

Q6 Which weighting scheme would have performed the best?

Hint: Make your argument using the calculated Sharpe

The weighting scheme in portfolio 2 is the best, with a sharpe ratio of 1.25. This shows the best risk adjusted return for each portfolio

Q7 Which weighting scheme is most volatile?

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

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      0.0511 0.1557 0.1225 0.0790 0.1380 0.1184 0.0921 0.1288
## Alpha              0.0027 0.0090 0.0093 0.0045 0.0080 0.0081 0.0054 0.0075
## AnnualizedAlpha    0.0328 0.1138 0.1170 0.0557 0.1004 0.1012 0.0668 0.0942
## Beta               1.1484 1.2108 1.1353 1.1452 1.1891 1.1414 1.1474 1.1772
## Beta-              0.6889 1.0701 0.8992 0.7752 0.9917 0.8852 0.8162 0.9516
## Beta+              1.5794 1.3206 1.3370 1.4857 1.3507 1.3588 1.4473 1.3661
## Correlation        0.7716 0.7701 0.5990 0.7893 0.7840 0.6759 0.7865 0.7834
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio   0.3105 0.8846 0.4682 0.5099 0.8366 0.5503 0.5874 0.7886
## R-squared          0.5954 0.5931 0.3588 0.6231 0.6147 0.4569 0.6186 0.6137
## TrackingError      0.1646 0.1760 0.2617 0.1550 0.1649 0.2151 0.1568 0.1633
## TreynorRatio       0.2023 0.2783 0.2676 0.2273 0.2685 0.2625 0.2382 0.2633
##                      [,9]   [,10]
## portfolio          9.0000 10.0000
## ActivePremium      0.1163  0.1099
## Alpha              0.0076  0.0063
## AnnualizedAlpha    0.0945  0.0782
## Beta               1.1458  1.1664
## Beta-              0.8824  0.8876
## Beta+              1.3707  1.4122
## Correlation        0.7134  0.8008
## Correlationp-value 0.0000  0.0000
## InformationRatio   0.5965  0.7205
## R-squared          0.5089  0.6413
## TrackingError      0.1949  0.1525
## TreynorRatio       0.2597  0.2496

Portfolio 2’s weighting scheme is also the most volatile. The beta is 1.2108, higher than 1, which means it is more risky. It also had a higher beta than any of the other portfolios shown

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.