Analyzing Performance with tidyquant
Ashley Lester
- Q1. Load tidyquant and tidyverse packages.
- 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.
- Q3. Calculate yearly returns, and save the result under returns_yearly.
- Q4. Create a density plot for returns of all considered index funds.
- Q5. Which of the considered index funds has the highest expected yearly return?
- Q6. Which of the considered index funds is the riskiest?
- Q9. Which of the considered index funds would you choose if you were a risk-averse investor?
- 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.
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 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 <-
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 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. 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 0.134Q6. 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 0.146The riskiest stock would be IXIC because it has the greatest Standard Deviation. ## 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 0.750The Skewness of GSPC and DJI are negitive meaning large negative returns occur more ofte, and IXIC is positive skewness meaning large positive returns occur more often.With Kartosis all GSPC,IXIC,and DJI are positive, this means large returns of both positive and negative occur more often. The Standard deviation is not an appropriate measure of risk for the considered index funds, because you have to have to have a standard deviattion of zero for it to be normally distributed. ## 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"The semi deviations of returns below the means is GSPC: 0.1268 IXIC:0.1883 DJI: 0.1105
IXIC poses the greatest downside risks because it has the highest semideviation and the lowest negitives for HistoricalES(95%) and HistoricalVaR(95%) at“-0.3541” and “-0.3991”
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"DJI would be the the fund to choose if you were a risk-averse investor because it has the highest VarSharpe, which is the higher return.