Q1 Import stock prices of NASDAQ Compsite Index, Microsoft and Walmart for the last 30 years.

Hint: Add group_by(symbol) at the end of the code so that calculations below will be done per stock.

## Warning in system("timedatectl", intern = TRUE): running command 'timedatectl'
## had status 1
## # A tibble: 22,677 x 8
## # Groups:   symbol [3]
##    symbol date        open  high   low close   volume adjusted
##    <chr>  <date>     <dbl> <dbl> <dbl> <dbl>    <dbl>    <dbl>
##  1 MSFT   1990-04-23 0.818 0.826 0.795 0.819 64876800    0.526
##  2 MSFT   1990-04-24 0.830 0.830 0.785 0.806 47913600    0.517
##  3 MSFT   1990-04-25 0.809 0.816 0.792 0.806 53868800    0.517
##  4 MSFT   1990-04-26 0.812 0.816 0.795 0.797 46294400    0.511
##  5 MSFT   1990-04-27 0.793 0.795 0.773 0.781 57123200    0.501
##  6 MSFT   1990-04-30 0.781 0.806 0.774 0.806 51449600    0.517
##  7 MSFT   1990-05-01 0.816 0.816 0.788 0.793 52473600    0.509
##  8 MSFT   1990-05-02 0.795 0.812 0.795 0.809 33264000    0.519
##  9 MSFT   1990-05-03 0.812 0.830 0.809 0.819 45891200    0.526
## 10 MSFT   1990-05-04 0.826 0.858 0.819 0.858 47811200    0.550
## # … with 22,667 more rows

Q2 Calculate yearly returns.

Hint: Take the adjusted variable from Stocks, and calculate yearly returns using ***tq_transmute().

## # A tibble: 93 x 3
## # Groups:   symbol [3]
##    symbol date       yearly.returns
##    <chr>  <date>              <dbl>
##  1 MSFT   1990-12-31         0.275 
##  2 MSFT   1991-12-31         1.22  
##  3 MSFT   1992-12-31         0.151 
##  4 MSFT   1993-12-31        -0.0556
##  5 MSFT   1994-12-30         0.516 
##  6 MSFT   1995-12-29         0.436 
##  7 MSFT   1996-12-31         0.883 
##  8 MSFT   1997-12-31         0.564 
##  9 MSFT   1998-12-31         1.15  
## 10 MSFT   1999-12-31         0.684 
## # … with 83 more rows

Q3 Which of the three stocks has the highest expected yearly return?

Hint: Take returns_yearly and pipe it to summarise. Calculate the mean yearly returns.

## # A tibble: 3 x 2
##   symbol returns_avg
##   <chr>        <dbl>
## 1 ^IXIC        0.137
## 2 MSFT         0.275
## 3 WMT          0.160

Microsoft has the highest expected yearly return at 0.275.

Q4 Calculate standard deviation of the yearly returns. Which of the three stocks is the riskiest in terms of standard deviation?

Hint: Take returns_yearly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute sd (standard deviation).

## # A tibble: 3 x 2
## # Groups:   symbol [3]
##   symbol  sd.1
##   <chr>  <dbl>
## 1 MSFT   0.402
## 2 ^IXIC  0.278
## 3 WMT    0.327

Microsoft is the riskiest stock in terms at 0.4022 and the least risky is the Nasdaq at 0.2780

Q5 Is the standard deviation appropriate measure of risk for the three stocks? Calculate skewness and kurtosis, and discuss them in your answer.

Hint: when the return distribution is not normal, the standard deviation is not an appropriate measure of risk. One can use skewness and kurtosis to detect non-normal returns. Take returns_yearly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute skewness. Do the same for kurtosis.

## # A tibble: 3 x 2
## # Groups:   symbol [3]
##   symbol skewness.1
##   <chr>       <dbl>
## 1 MSFT        0.275
## 2 ^IXIC       0.179
## 3 WMT         1.42
## # A tibble: 3 x 2
## # Groups:   symbol [3]
##   symbol kurtosis.1
##   <chr>       <dbl>
## 1 MSFT        0.431
## 2 ^IXIC       0.302
## 3 WMT         1.52

The standard deviation does not take into account risk. Both Microsoft and Nasdaq are more balanced in terms of skewness (MSFT 0.2749, ^IXIC 0.1787). However Walmart is more likely to have extreme positive returns. The Nasdaq has the lowest kurtosis number meaning it is close to normal distribution but Walmart has a 1.5222 kurtosis meaning that it is likely to have extreme positive and negative returns.

Q6 Which of the three stocks poses greater downside risk? Calculate HistoricalES(95%), HistoricalVaR(95%), and SemiDeviation, and discuss them in your answer.

Hint: Take returns_yearly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute table.DownsideRisk.

##                                           [,1]      [,2]      [,3]     
## symbol                                    "MSFT"    "^IXIC"   "WMT"    
## DownsideDeviation(0%)                     "0.1448"  "0.1245"  "0.0829" 
## DownsideDeviation(MAR=0.833333333333333%) "0.1475"  "0.1279"  "0.0866" 
## DownsideDeviation(Rf=0%)                  "0.1448"  "0.1245"  "0.0829" 
## GainDeviation                             "0.3226"  "0.2050"  "0.3151" 
## HistoricalES(95%)                         "-0.5362" "-0.3991" "-0.2471"
## HistoricalVaR(95%)                        "-0.3317" "-0.3541" "-0.2197"
## LossDeviation                             "0.2388"  "0.1598"  "0.0885" 
## MaximumDrawdown                           "0.6285"  "0.6718"  "0.3206" 
## ModifiedES(95%)                           "-0.4899" "-0.4069" "-0.5204"
## ModifiedVaR(95%)                          "-0.3414" "-0.2976" "-0.2176"
## SemiDeviation                             "0.2659"  "0.1892"  "0.1707"

In terms of the Var the Nasdaq has the greatest downside of risk at -0.3541 this means that the largest loss you can expect is 35.41% with 95% confidence. The HistoricalES of Microsoft has a value of -0.5362 meaning that -53.62% is the average return for 5% of 95%. The SemiDeviation of Microsoft is 0.2659 meaning that the mean return is 0.2659 below the standard deviation.

Q7 Which of the three stocks would you choose? Calculate the Sharpe ratios with an annualized risk-free rate of 2% and a default confidence interval of 0.95.

Hint: Make your argument based on the three Sharpe Ratios.

## # A tibble: 3 x 4
## # Groups:   symbol [3]
##   symbol `ESSharpe(Rf=2%,p=95%… `StdDevSharpe(Rf=2%,p=95… `VaRSharpe(Rf=2%,p=95…
##   <chr>                   <dbl>                     <dbl>                  <dbl>
## 1 MSFT                    0.520                     0.633                  0.746
## 2 ^IXIC                   0.286                     0.419                  0.392
## 3 WMT                     0.269                     0.428                  0.644

I would chose Microsoft because they have the highest Sharp ratio of 0.5197 meaning they have the greatest average return.

Q7.a Repeat Q7 but at a confidence interval of 0.99. Does it change your answer in Q7?

Hint: Make your argument based on the three Sharpe Ratios.

## # A tibble: 3 x 4
## # Groups:   symbol [3]
##   symbol `ESSharpe(Rf=2%,p=99%… `StdDevSharpe(Rf=2%,p=99… `VaRSharpe(Rf=2%,p=99…
##   <chr>                   <dbl>                     <dbl>                  <dbl>
## 1 MSFT                    0.364                     0.633                  0.428
## 2 ^IXIC                   0.205                     0.419                  0.243
## 3 WMT                     0.140                     0.428                  1.13

I would still chose microsoft because Microsoft still has the highest Sharpe ratio of 0.3644 with Nasdaq at 0.2046 and Walmart at 0.1401.

Q8 Hide the messages and the code, but display results of the code from 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.