Quiz6

# Load packages  
library(tidyquant)
library(tidyverse)

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

from <- today() - years(5)
stock_returns_monthly <- c("TSLA","AAPL", "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: 180 x 3
## # Groups:   symbol [3]
##    symbol date             Ra
##    <chr>  <date>        <dbl>
##  1 TSLA   2016-05-31 -0.0768 
##  2 TSLA   2016-06-30 -0.0491 
##  3 TSLA   2016-07-29  0.106  
##  4 TSLA   2016-08-31 -0.0970 
##  5 TSLA   2016-09-30 -0.0376 
##  6 TSLA   2016-10-31 -0.0309 
##  7 TSLA   2016-11-30 -0.0421 
##  8 TSLA   2016-12-30  0.128  
##  9 TSLA   2017-01-31  0.179  
## 10 TSLA   2017-02-28 -0.00770
## # ... with 170 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: 60 x 2
##    date              Rb
##    <date>         <dbl>
##  1 2016-05-31  0.00746 
##  2 2016-06-30  0.000911
##  3 2016-07-29  0.0356  
##  4 2016-08-31 -0.00122 
##  5 2016-09-30 -0.00123 
##  6 2016-10-31 -0.0194  
##  7 2016-11-30  0.0342  
##  8 2016-12-30  0.0182  
##  9 2017-01-31  0.0179  
## 10 2017-02-28  0.0372  
## # ... with 50 more rows

Q3 Aggregate for 10 portfolios with the following weighting schemes.

• Tesla(0.80), Amazon(0.10), Netflix (0.10)
• Tesla(0.10), Amazon(0.80), Netflix (0.10)
• Tesla(0.10), Amazon(0.10), Netflix (0.80)
• Tesla(0.60), Amazon(0.20), Netflix (0.20)
• Tesla(0.20), Amazon(0.60), Netflix (0.20)
• Tesla(0.20), Amazon(0.20), Netflix (0.60)
• Tesla(0.50), Amazon(0.25), Netflix (0.25)
• Tesla(0.25), Amazon(0.50), Netflix (0.25)
• Tesla(0.25), Amazon(0.25), Netflix (0.50)
• Tesla(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: 1,800 x 4
## # Groups:   portfolio [10]
##    portfolio symbol date             Ra
##        <int> <chr>  <date>        <dbl>
##  1         1 TSLA   2016-05-31 -0.0768 
##  2         1 TSLA   2016-06-30 -0.0491 
##  3         1 TSLA   2016-07-29  0.106  
##  4         1 TSLA   2016-08-31 -0.0970 
##  5         1 TSLA   2016-09-30 -0.0376 
##  6         1 TSLA   2016-10-31 -0.0309 
##  7         1 TSLA   2016-11-30 -0.0421 
##  8         1 TSLA   2016-12-30  0.128  
##  9         1 TSLA   2017-01-31  0.179  
## 10         1 TSLA   2017-02-28 -0.00770
## # ... with 1,790 more rows

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("TSLA","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 TSLA       0.8
##  2         1 AMZN       0.1
##  3         1 NFLX       0.1
##  4         2 TSLA       0.1
##  5         2 AMZN       0.8
##  6         2 NFLX       0.1
##  7         3 TSLA       0.1
##  8         3 AMZN       0.1
##  9         3 NFLX       0.8
## 10         4 TSLA       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")

## Warning in check_weights(weights, assets_col, map, x): The assets in weights
## does not match the assets in data.

## Warning in Return.portfolio.geometric(R = R, weights = weights, wealth.index =
## wealth.index, : The weights for one or more periods do not sum up to 1: assuming
## a return of 0 for the residual weights

## Warning in check_weights(weights, assets_col, map, x): The assets in weights
## does not match the assets in data.

## Warning in Return.portfolio.geometric(R = R, weights = weights, wealth.index =
## wealth.index, : The weights for one or more periods do not sum up to 1: assuming
## a return of 0 for the residual weights

## Warning in check_weights(weights, assets_col, map, x): The assets in weights
## does not match the assets in data.

## Warning in Return.portfolio.geometric(R = R, weights = weights, wealth.index =
## wealth.index, : The weights for one or more periods do not sum up to 1: assuming
## a return of 0 for the residual weights

## Warning in check_weights(weights, assets_col, map, x): The assets in weights
## does not match the assets in data.

## Warning in Return.portfolio.geometric(R = R, weights = weights, wealth.index =
## wealth.index, : The weights for one or more periods do not sum up to 1: assuming
## a return of 0 for the residual weights

## Warning in check_weights(weights, assets_col, map, x): The assets in weights
## does not match the assets in data.

## Warning in Return.portfolio.geometric(R = R, weights = weights, wealth.index =
## wealth.index, : The weights for one or more periods do not sum up to 1: assuming
## a return of 0 for the residual weights

## Warning in check_weights(weights, assets_col, map, x): The assets in weights
## does not match the assets in data.

## Warning in Return.portfolio.geometric(R = R, weights = weights, wealth.index =
## wealth.index, : The weights for one or more periods do not sum up to 1: assuming
## a return of 0 for the residual weights

## Warning in check_weights(weights, assets_col, map, x): The assets in weights
## does not match the assets in data.

## Warning in Return.portfolio.geometric(R = R, weights = weights, wealth.index =
## wealth.index, : The weights for one or more periods do not sum up to 1: assuming
## a return of 0 for the residual weights

## Warning in check_weights(weights, assets_col, map, x): The assets in weights
## does not match the assets in data.

## Warning in Return.portfolio.geometric(R = R, weights = weights, wealth.index =
## wealth.index, : The weights for one or more periods do not sum up to 1: assuming
## a return of 0 for the residual weights

## Warning in check_weights(weights, assets_col, map, x): The assets in weights
## does not match the assets in data.

## Warning in Return.portfolio.geometric(R = R, weights = weights, wealth.index =
## wealth.index, : The weights for one or more periods do not sum up to 1: assuming
## a return of 0 for the residual weights

## Warning in check_weights(weights, assets_col, map, x): The assets in weights
## does not match the assets in data.

## Warning in Return.portfolio.geometric(R = R, weights = weights, wealth.index =
## wealth.index, : The weights for one or more periods do not sum up to 1: assuming
## a return of 0 for the residual weights

portfolio_returns_monthly 

## # A tibble: 600 x 3
## # Groups:   portfolio [10]
##    portfolio date             Ra
##        <int> <date>        <dbl>
##  1         1 2016-05-31 -0.0513 
##  2         1 2016-06-30 -0.0507 
##  3         1 2016-07-29  0.0824 
##  4         1 2016-08-31 -0.0705 
##  5         1 2016-09-30 -0.0278 
##  6         1 2016-10-31  0.00843
##  7         1 2016-11-30 -0.0405 
##  8         1 2016-12-30  0.103  
##  9         1 2017-01-31  0.154  
## 10         1 2017-02-28 -0.00451
## # ... with 590 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: 600 x 4
## # Groups:   portfolio [10]
##    portfolio date             Ra        Rb
##        <int> <date>        <dbl>     <dbl>
##  1         1 2016-05-31 -0.0513   0.00746 
##  2         1 2016-06-30 -0.0507   0.000911
##  3         1 2016-07-29  0.0824   0.0356  
##  4         1 2016-08-31 -0.0705  -0.00122 
##  5         1 2016-09-30 -0.0278  -0.00123 
##  6         1 2016-10-31  0.00843 -0.0194  
##  7         1 2016-11-30 -0.0405   0.0342  
##  8         1 2016-12-30  0.103    0.0182  
##  9         1 2017-01-31  0.154    0.0179  
## 10         1 2017-02-28 -0.00451  0.0372  
## # ... with 590 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                           1.16
##  2         2                           1.14
##  3         3                           1.30
##  4         4                           1.27
##  5         5                           1.26
##  6         6                           1.40
##  7         7                           1.31
##  8         8                           1.31
##  9         9                           1.41
## 10        10                           1.27

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         9                           1.41
##  2         6                           1.40
##  3         7                           1.31
##  4         8                           1.31
##  5         3                           1.30
##  6        10                           1.27
##  7         4                           1.27
##  8         5                           1.26
##  9         1                           1.16
## 10         2                           1.14

Q6 Which weighting scheme would have performed the best?

Hint: Make your argument using the calculated Sharpe

The 9th weighting scheme Tesla(0.25), Amazon(0.25), Netflix (0.50), performs the best because it has the highest ratio.

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      0.4881 0.0726 0.2735 0.4237 0.1992 0.2927 0.3870 0.2480
## Alpha              0.0298 0.0097 0.0230 0.0258 0.0156 0.0221 0.0241 0.0179
## AnnualizedAlpha    0.4232 0.1234 0.3136 0.3577 0.2041 0.2994 0.3301 0.2375
## Beta               1.7847 0.6827 0.8692 1.5768 0.9921 1.0146 1.4571 1.0958
## Beta-              1.4853 0.4632 0.7936 1.2809 0.7291 0.8503 1.1681 0.8290
## Beta+              3.0843 1.2512 1.3755 2.7402 1.7623 1.6803 2.5348 1.9249
## Correlation        0.4883 0.5235 0.3998 0.5216 0.5375 0.4800 0.5329 0.5394
## Correlationp-value 0.0001 0.0000 0.0016 0.0000 0.0000 0.0001 0.0000 0.0000
## InformationRatio   0.9891 0.4179 0.9114 1.0667 0.8517 1.0504 1.0920 0.9632
## R-squared          0.2385 0.2741 0.1598 0.2721 0.2890 0.2304 0.2840 0.2909
## TrackingError      0.4935 0.1736 0.3001 0.3972 0.2339 0.2786 0.3544 0.2575
## TreynorRatio       0.3583 0.3280 0.4888 0.3647 0.3533 0.4377 0.3695 0.3645
##                      [,9]   [,10]
## portfolio          9.0000 10.0000
## ActivePremium      0.3019  0.3283
## Alpha              0.0217  0.0213
## AnnualizedAlpha    0.2935  0.2875
## Beta               1.0920  1.3404
## Beta-              0.8871  1.0465
## Beta+              1.8412  2.3688
## Correlation        0.5114  0.5318
## Correlationp-value 0.0000  0.0000
## InformationRatio   1.0937  1.0107
## R-squared          0.2616  0.2828
## TrackingError      0.2761  0.3248
## TreynorRatio       0.4151  0.3579

The most volatile scheme is the first because it has the largest gap in it’s min and max beta of 1.6.

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.