Quiz 6

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

# Load packages  
library(tidyquant)
library(tidyverse)

from <- today() - years(5)
stock_returns_monthly <- c("TSLA", "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 TSLA   2016-04-29  0     
##  2 TSLA   2016-05-31 -0.0728
##  3 TSLA   2016-06-30 -0.0491
##  4 TSLA   2016-07-29  0.106 
##  5 TSLA   2016-08-31 -0.0970
##  6 TSLA   2016-09-30 -0.0376
##  7 TSLA   2016-10-31 -0.0309
##  8 TSLA   2016-11-30 -0.0421
##  9 TSLA   2016-12-30  0.128 
## 10 TSLA   2017-01-31  0.179 
## # ... 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 2016-04-29  0      
##  2 2016-05-31  0.0362 
##  3 2016-06-30 -0.0213 
##  4 2016-07-29  0.0660 
##  5 2016-08-31  0.00990
##  6 2016-09-30  0.0189 
##  7 2016-10-31 -0.0231 
##  8 2016-11-30  0.0259 
##  9 2016-12-30  0.0112 
## 10 2017-01-31  0.0430 
## # ... with 51 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: 1,830 x 4
## # Groups:   portfolio [10]
##    portfolio symbol date            Ra
##        <int> <chr>  <date>       <dbl>
##  1         1 TSLA   2016-04-29  0     
##  2         1 TSLA   2016-05-31 -0.0728
##  3         1 TSLA   2016-06-30 -0.0491
##  4         1 TSLA   2016-07-29  0.106 
##  5         1 TSLA   2016-08-31 -0.0970
##  6         1 TSLA   2016-09-30 -0.0376
##  7         1 TSLA   2016-10-31 -0.0309
##  8         1 TSLA   2016-11-30 -0.0421
##  9         1 TSLA   2016-12-30  0.128 
## 10         1 TSLA   2017-01-31  0.179 
## # ... 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("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

# 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 2016-04-29  0      
##  2         1 2016-05-31 -0.0347 
##  3         1 2016-06-30 -0.0516 
##  4         1 2016-07-29  0.0886 
##  5         1 2016-08-31 -0.0675 
##  6         1 2016-09-30 -0.0161 
##  7         1 2016-10-31  0.00120
##  8         1 2016-11-30 -0.0463 
##  9         1 2016-12-30  0.101  
## 10         1 2017-01-31  0.163  
## # ... 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 2016-04-29  0        0      
##  2         1 2016-05-31 -0.0347   0.0362 
##  3         1 2016-06-30 -0.0516  -0.0213 
##  4         1 2016-07-29  0.0886   0.0660 
##  5         1 2016-08-31 -0.0675   0.00990
##  6         1 2016-09-30 -0.0161   0.0189 
##  7         1 2016-10-31  0.00120 -0.0231 
##  8         1 2016-11-30 -0.0463   0.0259 
##  9         1 2016-12-30  0.101    0.0112 
## 10         1 2017-01-31  0.163    0.0430 
## # ... 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                           1.25
##  2         2                           1.56
##  3         3                           1.36
##  4         4                           1.42
##  5         5                           1.61
##  6         6                           1.51
##  7         7                           1.49
##  8         8                           1.61
##  9         9                           1.55
## 10        10                           1.55

Q5 Sort the portfolios in descending order of Sharpe Ratio.

Hint: Use dplyr::arrange().

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

arrange(sharpe_ratio, desc(`AnnualizedSharpeRatio(Rf=0%)`))

## # A tibble: 10 x 2
## # Groups:   portfolio [10]
##    portfolio `AnnualizedSharpeRatio(Rf=0%)`
##        <int>                          <dbl>
##  1         5                           1.61
##  2         8                           1.61
##  3         2                           1.56
##  4         9                           1.55
##  5        10                           1.55
##  6         6                           1.51
##  7         7                           1.49
##  8         4                           1.42
##  9         3                           1.36
## 10         1                           1.25

Q6 Which weighting scheme would have performed the best?

Hint: Make your argument using the calculated Sharpe

Both portfolio 5 and 8 have a sharpe ratio of 1.61, making them the top performing portfolios. Portfolio 5 had a weight of 20% TSLA, 60% AMZN, and 20% NFLX. Portfolio 8 had a weight of 25% TSLA, 50% AMZN, and 25% NFLX.

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      0.4102 0.1952 0.2072 0.3612 0.2362 0.2424 0.3342 0.2551
## Alpha              0.0155 0.0086 0.0140 0.0130 0.0097 0.0129 0.0123 0.0104
## AnnualizedAlpha    0.2024 0.1076 0.1816 0.1681 0.1233 0.1659 0.1585 0.1321
## Beta               1.9166 1.3061 1.1156 1.7490 1.3888 1.2725 1.6538 1.4256
## Beta-              0.3888 0.8608 0.8610 0.6543 0.8389 0.8397 0.7291 0.8265
## Beta+              2.7186 1.5075 1.4671 2.4390 1.7220 1.6960 2.2776 1.8217
## Correlation        0.6200 0.7921 0.5728 0.6948 0.7939 0.6722 0.7232 0.7819
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio   0.9436 1.1067 0.7719 1.0994 1.2438 1.0123 1.1661 1.2534
## R-squared          0.3844 0.6274 0.3281 0.4827 0.6303 0.4519 0.5231 0.6114
## TrackingError      0.4348 0.1764 0.2684 0.3285 0.1899 0.2394 0.2866 0.2035
## TreynorRatio       0.3374 0.3306 0.3977 0.3418 0.3404 0.3763 0.3451 0.3448
##                      [,9]   [,10]
## portfolio          9.0000 10.0000
## ActivePremium      0.2587  0.3039
## Alpha              0.0124  0.0111
## AnnualizedAlpha    0.1588  0.1417
## Beta               1.3505  1.5857
## Beta-              0.8277  0.7785
## Beta+              1.8050  2.1088
## Correlation        0.7106  0.7604
## Correlationp-value 0.0000  0.0000
## InformationRatio   1.1161  1.2281
## R-squared          0.5049  0.5782
## TrackingError      0.2318  0.2474
## TreynorRatio       0.3667  0.3408

Based on calculated beta, portfolio 1 is the most volatile with a beta of 1.9166. Since a beta greater than 1 indicates that the security’s price tends to be more volatile than the market, this is the most volatile portfolio out of the others. Its weighting scheme is 80% TSLA, 10% AMZN, and 10% NFLX.

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.