Analyzing Performance
Matt Ordway
April 16, 2019
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)
stock <- tq_get(c("^GSPC","^IXIC","^DJI"), get = "stock.prices", from = from) %>% group_by(symbol)
stock
## # 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 rowsQ3. 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 <-
stock %>%
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 rowsQ4. 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 0.134After reviewing all of the indexโs the Nasdaq is the highesst expected yearly return.
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,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 0.146Dow Jones would be considered the riskiest index because it has the worst yearly return.
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,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,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 0.750Standard deviation is an appropriate measure of risk.
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,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 would be considered to have the greatest downside risk.
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,performance_fun = SharpeRatio)
## # A tibble: 3 x 4
## # Groups: symbol [3]
## symbol `ESSharpe(Rf=0%,p=95~ `StdDevSharpe(Rf=0%,p=~ `VaRSharpe(Rf=0%,p=~
## <chr> <dbl> <dbl> <dbl>
## 1 ^GSPC 0.297 0.542 0.423
## 2 ^IXIC 0.328 0.486 0.454
## 3 ^DJI 0.355 0.630 0.534