You are considering three index funds that follow the three major market indexes: the Dow Jones Industrial Average, the S&P 500, and the NASDAQ Compsite Index.

Q1. Load tidyquant and tidyverse packages.

library(tidyquant)
library(tidyverse)

Q2. Import the Dow Jones Industrial Average, the S&P 500, and the NASDAQ Compsite Index for the last 30 years. Save the imported data under Stocks.

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

from = today() - years(30)
Stocks <- tq_get(c("^GSPC","^IXIC", "^DJI"), get = "stock.prices", from = from) %>%
    group_by(symbol)
Stocks 
## # 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 ^GSPC  1989-04-17  301.  302.  301.  302. 128540000     302.
##  2 ^GSPC  1989-04-18  302.  306.  302.  306. 208650000     306.
##  3 ^GSPC  1989-04-19  306.  308.  305.  307. 191510000     307.
##  4 ^GSPC  1989-04-20  307.  308.  305.  306. 175970000     306.
##  5 ^GSPC  1989-04-21  306.  310.  306.  310. 187310000     310.
##  6 ^GSPC  1989-04-24  310.  310.  308.  309. 142100000     309.
##  7 ^GSPC  1989-04-25  309.  310.  307.  307. 165430000     307.
##  8 ^GSPC  1989-04-26  307.  307.  306.  307. 146090000     307.
##  9 ^GSPC  1989-04-27  307.  310.  307.  310. 191170000     310.
## 10 ^GSPC  1989-04-28  310.  310.  308.  310. 158390000     310.
## # ... with 22,667 more rows

Q3. Calculate yearly returns, and save the result under returns_yearly.

Hint: Take Stocks and pipe it to tidyquant::tq_transmute. Assign the result to returns_yearly.

returns_yearly <-
  Stocks %>%
   tq_transmute(select = adjusted, mutate_fun = periodReturn, period = "yearly")


returns_yearly
## # A tibble: 93 x 3
## # Groups:   symbol [3]
##    symbol date       yearly.returns
##    <chr>  <date>              <dbl>
##  1 ^GSPC  1989-12-29         0.171 
##  2 ^GSPC  1990-12-31        -0.0656
##  3 ^GSPC  1991-12-31         0.263 
##  4 ^GSPC  1992-12-31         0.0446
##  5 ^GSPC  1993-12-31         0.0706
##  6 ^GSPC  1994-12-30        -0.0154
##  7 ^GSPC  1995-12-29         0.341 
##  8 ^GSPC  1996-12-31         0.203 
##  9 ^GSPC  1997-12-31         0.310 
## 10 ^GSPC  1998-12-31         0.267 
## # ... with 83 more rows

Q4. Create a density plot for returns of all considered index funds.

Hint: Refer to the ggplot2 cheatsheet. Look for geom_density under One Variable. Use the fill argument to create the plot per each stock.

returns_yearly%>%
  ggplot(aes(x=yearly.returns,fill=symbol))+geom_density(alpha=0.3)

Q5. Which of the considered index funds has the highest expected yearly return?

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

returns_yearly%>%
  summarise(returns_avg=mean(yearly.returns))
## # A tibble: 3 x 2
##   symbol returns_avg
##   <chr>        <dbl>
## 1 ^DJI        0.0917
## 2 ^GSPC       0.0895
## 3 ^IXIC       0.134

The NASDAQ has a higher expected yearly return, due to it having a higher return average than the other stocks.

Q6. Which of the considered index funds is the riskiest?

Hint: Discuss your answer in terms of standard deviation. Take returns_yearly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute sd (standard deviation).

returns_yearly %>%
    tq_performance(Ra = yearly.returns,
                   Rb = NULL, # Calculataing downside risk measures doesn't require Rb
                   performance_fun = sd)
## # A tibble: 3 x 2
## # Groups:   symbol [3]
##   symbol  sd.1
##   <chr>  <dbl>
## 1 ^GSPC  0.165
## 2 ^IXIC  0.276
## 3 ^DJI   0.146

The NASDAQ would be the riskier stock becasue it has the highest standard deviation of the three.

Q7. Would you consider the standard deviation as an appropriate measure of risk for the considered index funds?

Hint: Discuss your answer in terms of whether the returns are normally distributed. The normality of the distribution may be measured by skewness and kurtosis. To compute the metrics, take returns_yearly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute skewness. Do the same for kurtosis.

returns_yearly %>%
    tq_performance(Ra = yearly.returns,
                   Rb = NULL, # Calculataing downside risk measures doesn't require Rb
                   performance_fun = skewness)
## # A tibble: 3 x 2
## # Groups:   symbol [3]
##   symbol skewness.1
##   <chr>       <dbl>
## 1 ^GSPC      -0.819
## 2 ^IXIC       0.179
## 3 ^DJI       -0.777


returns_yearly %>%
    tq_performance(Ra = yearly.returns,
                   Rb = NULL, # Calculataing downside risk measures doesn't require Rb
                   performance_fun = kurtosis)
## # A tibble: 3 x 2
## # Groups:   symbol [3]
##   symbol kurtosis.1
##   <chr>       <dbl>
## 1 ^GSPC       0.631
## 2 ^IXIC       0.435
## 3 ^DJI        0.750

I do believe that the standard devitation is an appropriate form of measuring risk for stocks that are noramlly distributed. However, these stocks are not noramlly distributed. NASDAQ has both a postiive skewness and positive kurtosis. This means a large positive return is more likely than a large negative return, whereas both the DOW JONES and S&P 500 have a negative skewness and a positive kurtosis, meaning a large negative return is more likely than a large postive return.

Q8. Which of the considered index funds poses the greatest downside risks?

Hint: Discuss your answer in terms of HistoricalES(95%), HistoricalVaR(95%), and SemiDeviation. To compute the metrics, take returns_yearly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute table.DownsideRisk.

returns_yearly %>%
    tq_performance(Ra = yearly.returns,
                   Rb = NULL, # Calculataing downside risk measures doesn't require Rb
                   performance_fun = table.DownsideRisk) %>%
  t()
##                                           [,1]      [,2]      [,3]     
## symbol                                    "^GSPC"   "^IXIC"   "^DJI"   
## DownsideDeviation(0%)                     "0.0877"  "0.1266"  "0.0712" 
## DownsideDeviation(MAR=0.833333333333333%) "0.0908"  "0.1300"  "0.0741" 
## DownsideDeviation(Rf=0%)                  "0.0877"  "0.1266"  "0.0712" 
## GainDeviation                             "0.0928"  "0.2028"  "0.0888" 
## HistoricalES(95%)                         "-0.3093" "-0.3991" "-0.2530"
## HistoricalVaR(95%)                        "-0.1820" "-0.3541" "-0.1193"
## LossDeviation                             "0.1261"  "0.1606"  "0.1092" 
## MaximumDrawdown                           "0.4012"  "0.6718"  "0.3384" 
## ModifiedES(95%)                           "-0.3013" "-0.4083" "-0.2584"
## ModifiedVaR(95%)                          "-0.2116" "-0.2957" "-0.1718"
## SemiDeviation                             "0.1268"  "0.1883"  "0.1105"

NASDAQ appears to present greater downside risk than S&P 500 and DOW JONES. For example, yearly returns are more volatile below the mean for NASDAQ (semideviation of 0.1883) than S&P 500 (semideviation of 0.1268) and DOW JONES (semideviation of 0.1105); the largest loss one could expect with 95% confidence is larger for NASDAQ (VaR of -0.3541 at 5%) than S&P 500 (VaR of -0.1820 at 5%) and the DOW JONES (VaR of -0.1193); and the average of the 5% most negative yearly returns is larger for NAQDAQ (ES of -0.3991 at 5%) than S&P 500 (ES of -0.3093 at 5%) and DOW JONES (ES of -0.2530.

Q9. Which of the considered index funds would you choose if you were a risk-averse investor?

Hint: Discuss your answer in terms of Sharpe Ratio. Take returns_yearly and pipe it to tidyquant:: tq_performance. Use the performance_fun argument to compute SharpeRatio. The function returns Sharpe Ratios adjusted to three different types of risks: 1) standard deviation, 2) expected shortfall (5% worst loss), and 3) value at risk (the largest loss at the 95% confidence level).

returns_yearly %>%
    tq_performance(Ra = yearly.returns,
                   Rb = NULL, # Calculataing downside risk measures doesn't require Rb
                   performance_fun = SharpeRatio)%>%
t()
##                           [,1]        [,2]        [,3]       
## symbol                    "^GSPC"     "^IXIC"     "^DJI"     
## ESSharpe(Rf=0%,p=95%)     "0.2970939" "0.3284609" "0.3549842"
## StdDevSharpe(Rf=0%,p=95%) "0.5417175" "0.4863393" "0.6297887"
## VaRSharpe(Rf=0%,p=95%)    "0.4230432" "0.4535240" "0.5338788"

I would choose the DOW JONES because it has a higher return per unit of risk.

Q10.a. Display both code and the results of the code on the webpage.

Q10.b. Display the title and your name correctly at the top of the webpage.

Q10.c. Use the correct slug.