Quiz5
Christopher Roberts
- 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)
library(tidyverse)
# 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 = 0.3)
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) 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 returned higher expected quarterly 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) 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 most risky stock becasue the standard deviation is larger.
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) 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 -0.106returns_quarterly %>%
tq_performance(
Ra = quarterly.returns,
Rb = NULL, #baseline returns (Rb) 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 1.81All the stocks are negatively skewed, meaning that they get large negative sums more often.
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) 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"NASDAQ has the greatest downside risk with higher amounts in HistoricalES, HistoricalVaR, and SemiDeviation.
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) 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 stock that more people should choose is NASDAQ, as it is the highest in all categories except semideviation.
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) 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 0.108The change to 99% confidence level has the DOW be more than NASDAQ in two categories, but by a very small number.There is one category where teh NASDAQ is still significantly higher, so the answer would not change from question 6, but it is a much harder decision now.
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.