Quiz 5
Hailey Botelho
- Q1 Create a density plot for the returns of the given stocks.
- Q2 Which stock has higher expected yearly return?
- Q3 Which stock is riskier?
- Q4 Is the standard deviation enough as a risk measure? Or do you need additional downside risk measurements? Why? Or why not?
- Q5 Calculate the downside risk measures. Which stock has the greatest downside risk? Discuss HistoricalES(95%), HistoricalVaR(95%), and SemiDeviation.
- Q6 Which stock would you choose? Calculate and interpret the Sharpe Ratio.
- Q7 Redo Q6 at the 99% confidence level instead of the 95% confidence level. Which stock would you choose now? Is your answer different from Q6? Why? Or why not?
- Q8 Hide the messages and warnings, but display the code and its results on the webpage.
- Q9 Display the title and your name correctly at the top of the webpage.
- Q10 Use the correct slug.
# Load packages
library(tidyquant)
library(tidyverse)
# Import stock prices and calculate returns
returns_yearly <- c("^DJI", "^GSPC", "^IXIC") %>%
tq_get(get = "stock.prices",
from = "1990-01-01",
to = "2020-11-01") %>%
group_by(symbol) %>%
tq_transmute(select = adjusted,
mutate_fun = yearlyReturn)
returns_yearly## # A tibble: 91 x 3
## # Groups: symbol [3]
## symbol date yearly.returns
## <chr> <date> <dbl>
## 1 ^DJI 1992-12-31 0.0406
## 2 ^DJI 1993-12-31 0.137
## 3 ^DJI 1994-12-30 0.0214
## 4 ^DJI 1995-12-29 0.335
## 5 ^DJI 1996-12-31 0.260
## 6 ^DJI 1997-12-31 0.226
## 7 ^DJI 1998-12-31 0.161
## 8 ^DJI 1999-12-31 0.252
## 9 ^DJI 2000-12-29 -0.0617
## 10 ^DJI 2001-12-31 -0.0710
## # … with 81 more rowsQ1 Create a density plot for the returns of the given stocks.
Hint: Refer to the ggplot2 cheatsheet. Look for geom_density under One Variable. Use the fill argument to create the plot per each stock.
ggplot(returns_yearly, aes(x = yearly.returns, fill = symbol)) +
geom_density(alpha = 0.3)
Q2 Which stock has higher expected yearly return?
Hint: Discuss your answer in terms of the mean. Take returns_yearly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute the mean.
returns_yearly %>%
tq_performance(
Ra = yearly.returns,
Rb = NULL,
performance_fun = mean)## # A tibble: 3 x 2
## # Groups: symbol [3]
## symbol mean.1
## <chr> <dbl>
## 1 ^DJI 0.0871
## 2 ^GSPC 0.0880
## 3 ^IXIC 0.143Q3 Which stock is riskier?
Hint: Discuss your answer in terms of the 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,
performance_fun = sd)## # A tibble: 3 x 2
## # Groups: symbol [3]
## symbol sd.1
## <chr> <dbl>
## 1 ^DJI 0.151
## 2 ^GSPC 0.169
## 3 ^IXIC 0.279Q4 Is the standard deviation enough as a risk measure? Or do you need additional downside risk measurements? Why? Or why not?
Hint: Discuss your answer in terms of the skewness and the kurtosis. Take returns_yearly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute the skewness. Do the same for the kurtosis.
returns_yearly %>%
tq_performance(
Ra = yearly.returns,
Rb = NULL,
performance_fun = skewness)## # A tibble: 3 x 2
## # Groups: symbol [3]
## symbol skewness.1
## <chr> <dbl>
## 1 ^DJI -0.669
## 2 ^GSPC -0.700
## 3 ^IXIC 0.0914returns_yearly %>%
tq_performance(
Ra = yearly.returns,
Rb = NULL,
performance_fun = kurtosis)## # A tibble: 3 x 2
## # Groups: symbol [3]
## symbol kurtosis.1
## <chr> <dbl>
## 1 ^DJI 0.410
## 2 ^GSPC 0.357
## 3 ^IXIC 0.289Q5 Calculate the downside risk measures. Which stock has the greatest downside risk? Discuss HistoricalES(95%), HistoricalVaR(95%), and SemiDeviation.
Hint: 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,
performance_fun = table.DownsideRisk) %>% t()## [,1] [,2] [,3]
## symbol "^DJI" "^GSPC" "^IXIC"
## DownsideDeviation(0%) "0.0743" "0.0882" "0.1270"
## DownsideDeviation(MAR=0.833333333333333%) "0.0775" "0.0913" "0.1304"
## DownsideDeviation(Rf=0%) "0.0743" "0.0882" "0.1270"
## GainDeviation "0.0935" "0.1023" "0.2005"
## HistoricalES(95%) "-0.2530" "-0.3093" "-0.3991"
## HistoricalVaR(95%) "-0.1291" "-0.1820" "-0.3541"
## LossDeviation "0.1078" "0.1254" "0.1605"
## MaximumDrawdown "0.3384" "0.4012" "0.6718"
## ModifiedES(95%) "-0.2632" "-0.3017" "-0.4179"
## ModifiedVaR(95%) "-0.1831" "-0.2161" "-0.2995"
## SemiDeviation "0.1131" "0.1275" "0.1931"returns_yearly %>%
tq_performance(
Ra = yearly.returns,
Rb = NULL,
performance_fun = table.DownsideRisk, p = 0.99) %>% t()## [,1] [,2] [,3]
## symbol "^DJI" "^GSPC" "^IXIC"
## DownsideDeviation(0%) "0.0743" "0.0882" "0.1270"
## DownsideDeviation(MAR=0.833333333333333%) "0.0775" "0.0913" "0.1304"
## DownsideDeviation(Rf=0%) "0.0743" "0.0882" "0.1270"
## GainDeviation "0.0935" "0.1023" "0.2005"
## HistoricalES(99%) "-0.3384" "-0.3849" "-0.4054"
## HistoricalVaR(99%) "-0.2906" "-0.3395" "-0.4017"
## LossDeviation "0.1078" "0.1254" "0.1605"
## MaximumDrawdown "0.3384" "0.4012" "0.6718"
## ModifiedES(99%) "-0.4500" "-0.5196" "-0.6014"
## ModifiedVaR(99%) "-0.3208" "-0.3679" "-0.4944"
## SemiDeviation "0.1131" "0.1275" "0.1931"Q6 Which stock would you choose? Calculate and interpret the Sharpe Ratio.
Hint: Assume that the risk free rate is zero and 95% confidence level. Note that the Sharpe Ratios are calculated using different risk measures: ES, VaR and semideviation. Make your argument based on all three Sharpe Ratios.
returns_yearly %>%
tq_performance(
Ra = yearly.returns,
Rb = NULL,
performance_fun = SharpeRatio)## # A tibble: 3 x 4
## # Groups: symbol [3]
## symbol `ESSharpe(Rf=0%,p=95%… `StdDevSharpe(Rf=0%,p=95… `VaRSharpe(Rf=0%,p=95…
## <chr> <dbl> <dbl> <dbl>
## 1 ^DJI 0.331 0.576 0.476
## 2 ^GSPC 0.292 0.520 0.407
## 3 ^IXIC 0.342 0.512 0.477Q7 Redo Q6 at the 99% confidence level instead of the 95% confidence level. Which stock would you choose now? Is your answer different from Q6? Why? Or why not?
Hint: Google tq_performance(). Discuss in terms of ES, VaR and semideviation and their differences between 95% and 99%.
returns_yearly %>%
tq_performance(
Ra = yearly.returns,
Rb = NULL,
performance_fun = SharpeRatio,
Rf = 0.01 / 12)## # A tibble: 3 x 4
## # Groups: symbol [3]
## symbol `ESSharpe(Rf=0.1%,p=9… `StdDevSharpe(Rf=0.1%,p=… `VaRSharpe(Rf=0.1%,p=…
## <chr> <dbl> <dbl> <dbl>
## 1 ^DJI 0.328 0.570 0.471
## 2 ^GSPC 0.289 0.515 0.404
## 3 ^IXIC 0.340 0.509 0.474Q8 Hide the messages and warnings, but display the code and its results on the webpage.
Hint: Use message, warning, echo and results in the chunk options. Refer to the RMarkdown Reference Guide.