Quiz 5
Joaquin German
- Q1 Create a density plot for the returns of the given stocks.
- Q2 Which stock has higher expected quarterly 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, 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)## Warning: package 'tidyquant' was built under R version 4.0.3library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.0.3# Import stock prices and calculate returns
returns_quarterly <- 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 = quarterlyReturn)
returns_quarterly## # A tibble: 372 x 3
## # Groups: symbol [3]
## symbol date quarterly.returns
## <chr> <date> <dbl>
## 1 ^DJI 1990-03-30 -0.0366
## 2 ^DJI 1990-06-29 0.0641
## 3 ^DJI 1990-09-28 -0.149
## 4 ^DJI 1990-12-31 0.0739
## 5 ^DJI 1991-03-28 0.106
## 6 ^DJI 1991-06-28 -0.00244
## 7 ^DJI 1991-09-30 0.0378
## 8 ^DJI 1991-12-31 0.0504
## 9 ^DJI 1992-03-31 0.0210
## 10 ^DJI 1992-06-30 0.0257
## # ... with 362 more rows# See options for the `performance_fun` argument
tq_performance_fun_options()## $table.funs
## [1] "table.AnnualizedReturns" "table.Arbitrary"
## [3] "table.Autocorrelation" "table.CAPM"
## [5] "table.CaptureRatios" "table.Correlation"
## [7] "table.Distributions" "table.DownsideRisk"
## [9] "table.DownsideRiskRatio" "table.DrawdownsRatio"
## [11] "table.HigherMoments" "table.InformationRatio"
## [13] "table.RollingPeriods" "table.SFM"
## [15] "table.SpecificRisk" "table.Stats"
## [17] "table.TrailingPeriods" "table.UpDownRatios"
## [19] "table.Variability"
##
## $CAPM.funs
## [1] "CAPM.alpha" "CAPM.beta" "CAPM.beta.bear" "CAPM.beta.bull"
## [5] "CAPM.CML" "CAPM.CML.slope" "CAPM.dynamic" "CAPM.epsilon"
## [9] "CAPM.jensenAlpha" "CAPM.RiskPremium" "CAPM.SML.slope" "TimingRatio"
## [13] "MarketTiming"
##
## $SFM.funs
## [1] "SFM.alpha" "SFM.beta" "SFM.CML" "SFM.CML.slope"
## [5] "SFM.dynamic" "SFM.epsilon" "SFM.jensenAlpha"
##
## $descriptive.funs
## [1] "mean" "sd" "min" "max"
## [5] "cor" "mean.geometric" "mean.stderr" "mean.LCL"
## [9] "mean.UCL"
##
## $annualized.funs
## [1] "Return.annualized" "Return.annualized.excess"
## [3] "sd.annualized" "SharpeRatio.annualized"
##
## $VaR.funs
## [1] "VaR" "ES" "ETL" "CDD" "CVaR"
##
## $moment.funs
## [1] "var" "cov" "skewness" "kurtosis"
## [5] "CoVariance" "CoSkewness" "CoSkewnessMatrix" "CoKurtosis"
## [9] "CoKurtosisMatrix" "M3.MM" "M4.MM" "BetaCoVariance"
## [13] "BetaCoSkewness" "BetaCoKurtosis"
##
## $drawdown.funs
## [1] "AverageDrawdown" "AverageLength" "AverageRecovery"
## [4] "DrawdownDeviation" "DrawdownPeak" "maxDrawdown"
##
## $Bacon.risk.funs
## [1] "MeanAbsoluteDeviation" "Frequency" "SharpeRatio"
## [4] "MSquared" "MSquaredExcess" "HurstIndex"
##
## $Bacon.regression.funs
## [1] "CAPM.alpha" "CAPM.beta" "CAPM.epsilon" "CAPM.jensenAlpha"
## [5] "SystematicRisk" "SpecificRisk" "TotalRisk" "TreynorRatio"
## [9] "AppraisalRatio" "FamaBeta" "Selectivity" "NetSelectivity"
##
## $Bacon.relative.risk.funs
## [1] "ActivePremium" "ActiveReturn" "TrackingError" "InformationRatio"
##
## $Bacon.drawdown.funs
## [1] "PainIndex" "PainRatio" "CalmarRatio" "SterlingRatio"
## [5] "BurkeRatio" "MartinRatio" "UlcerIndex"
##
## $Bacon.downside.risk.funs
## [1] "DownsideDeviation" "DownsidePotential" "DownsideFrequency"
## [4] "SemiDeviation" "SemiVariance" "UpsideRisk"
## [7] "UpsidePotentialRatio" "UpsideFrequency" "BernardoLedoitRatio"
## [10] "DRatio" "Omega" "OmegaSharpeRatio"
## [13] "OmegaExcessReturn" "SortinoRatio" "M2Sortino"
## [16] "Kappa" "VolatilitySkewness" "AdjustedSharpeRatio"
## [19] "SkewnessKurtosisRatio" "ProspectRatio"
##
## $misc.funs
## [1] "KellyRatio" "Modigliani" "UpDownRatios"Q1 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_quarterly, aes(x = quarterly.returns, fill = symbol)) +
geom_density(alpha = .3)
Q2 Which stock has higher expected quarterly return?
Hint: Discuss your answer in terms of the mean. Take returns_quarterly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute the mean.
returns_quarterly %>%
tq_performance(
Ra = quarterly.returns,
Rb = NULL, #baseline returns (Rb) is not required for this calculation
performance_fun = mean
)## # A tibble: 3 x 2
## # Groups: symbol [3]
## symbol mean.1
## <chr> <dbl>
## 1 ^DJI 0.0212
## 2 ^GSPC 0.0212
## 3 ^IXIC 0.0333NASDAQ has the larger returns on average and also the highest returns.
Q3 Which stock is riskier?
Hint: Discuss your answer in terms of the standard deviation. Take returns_quarterly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute sd (standard deviation).
returns_quarterly %>%
tq_performance(
Ra = quarterly.returns,
Rb = NULL, #baseline returns (Rb) is not required for this calculation
performance_fun = sd
)## # A tibble: 3 x 2
## # Groups: symbol [3]
## symbol sd.1
## <chr> <dbl>
## 1 ^DJI 0.0762
## 2 ^GSPC 0.0794
## 3 ^IXIC 0.122NASDAQ is the riskiest stock because it tends to undergo the most change.
Q4 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_quarterly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute the skewness. Do the same for the kurtosis.
returns_quarterly %>%
tq_performance(
Ra = quarterly.returns,
Rb = NULL, #baseline returns (Rb) is not required for this calculation
performance_fun = skewness
)## # A tibble: 3 x 2
## # Groups: symbol [3]
## symbol skewness.1
## <chr> <dbl>
## 1 ^DJI -0.734
## 2 ^GSPC -0.601
## 3 ^IXIC -0.106if you are to account for skewness you are more likely to have large losses rather than large gains.
returns_quarterly %>%
tq_performance(
Ra = quarterly.returns,
Rb = NULL, #baseline returns (Rb) is not required for this calculation
performance_fun = kurtosis
)## # A tibble: 3 x 2
## # Groups: symbol [3]
## symbol kurtosis.1
## <chr> <dbl>
## 1 ^DJI 0.811
## 2 ^GSPC 0.770
## 3 ^IXIC 1.81NasDAQ has the larger tail because its total is bigger than 1.
Q5 Calculate the downside risk measures. Which stock has the greatest downside risk? Discuss HistoricalES(95%), HistoricalVaR(95%), and SemiDeviation.
Hint: Take returns_quarterly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute table.DownsideRisk.
returns_quarterly %>%
tq_performance(
Ra = quarterly.returns,
Rb = NULL, #baseline returns (Rb) is not required for this calculation
performance_fun = table.DownsideRisk
) %>%
t()## [,1] [,2] [,3]
## symbol "^DJI" "^GSPC" "^IXIC"
## DownsideDeviation(0%) "0.0492" "0.0512" "0.0734"
## DownsideDeviation(MAR=3.33333333333333%) "0.0528" "0.0548" "0.0770"
## DownsideDeviation(Rf=0%) "0.0492" "0.0512" "0.0734"
## GainDeviation "0.0428" "0.0463" "0.0814"
## HistoricalES(95%) "-0.1664" "-0.1686" "-0.2565"
## HistoricalVaR(95%) "-0.1235" "-0.1394" "-0.1954"
## LossDeviation "0.0596" "0.0621" "0.0882"
## MaximumDrawdown "0.4524" "0.4774" "0.7437"
## ModifiedES(95%) "-0.1658" "-0.1724" "-0.2550"
## ModifiedVaR(95%) "-0.1175" "-0.1207" "-0.1658"
## SemiDeviation "0.0587" "0.0607" "0.0885"Because of expected shortfall NASDAQ is the greatest downside risk, this is the highest of the three.
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_quarterly %>%
tq_performance(
Ra = quarterly.returns,
Rb = NULL, #baseline returns (Rb) is not required for this calculation
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 0.128 0.278 0.181
## 2 ^GSPC 0.123 0.266 0.175
## 3 ^IXIC 0.131 0.273 0.201The highest Sharpe Ratio is also held by NASDAQ, but it has the lowest if you use standard deviation
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?
Hint: Google tq_performance(). Discuss in terms of ES, VaR and semideviation and their differences between 95% and 99%.
returns_quarterly %>%
tq_performance(
Ra = quarterly.returns,
Rb = NULL, #baseline returns (Rb) is not required for this calculation
performance_fun = SharpeRatio,
p = 0.99
)## # A tibble: 3 x 4
## # Groups: symbol [3]
## symbol `ESSharpe(Rf=0%,p=99%~ `StdDevSharpe(Rf=0%,p=99~ `VaRSharpe(Rf=0%,p=99~
## <chr> <dbl> <dbl> <dbl>
## 1 ^DJI 0.0784 0.278 0.109
## 2 ^GSPC 0.0799 0.266 0.105
## 3 ^IXIC 0.0814 0.273 0.108NASDAQ is still number 1. The smartest bet is to go for another stock because there is less of a risk and still come out with profit.
Q8 Hide the messages, but display the code and its results on the webpage.
Hint: Use message, echo and results in the chunk options. Refer to the RMarkdown Reference Guide.