Quiz5
Jordyn Carpenter
- 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)## Loading required package: lubridate##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
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## date, intersect, setdiff, union## Loading required package: PerformanceAnalytics## Loading required package: xts## Loading required package: zoo##
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## legend## Loading required package: quantmod## Loading required package: TTR## Registered S3 method overwritten by 'quantmod':
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## as.zoo.data.frame zoo## Version 0.4-0 included new data defaults. See ?getSymbols.## == Need to Learn tidyquant? =============================================
## Business Science offers a 1-hour course - Learning Lab #9: Performance Analysis & Portfolio Optimization with tidyquant!
## </> Learn more at: https://university.business-science.io/p/learning-labs-pro </>library(tidyverse)## -- Attaching packages -------------------------------- tidyverse 1.3.0 --## v ggplot2 3.3.2 v purrr 0.3.4
## v tibble 3.0.3 v dplyr 1.0.2
## v tidyr 1.1.2 v stringr 1.4.0
## v readr 1.3.1 v forcats 0.5.0## -- Conflicts ----------------------------------- tidyverse_conflicts() --
## x lubridate::as.difftime() masks base::as.difftime()
## x lubridate::date() masks base::date()
## x dplyr::filter() masks stats::filter()
## x dplyr::first() masks xts::first()
## x lubridate::intersect() masks base::intersect()
## x dplyr::lag() masks stats::lag()
## x dplyr::last() masks xts::last()
## x lubridate::setdiff() masks base::setdiff()
## x lubridate::union() masks base::union()# 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.
ggplot(returns_quarterly,
aes(x = quarterly.returns,
fill = symbol)) +
geom_density(alpha = 0.4) +
labs(title = "Stock Return")
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, 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 0.0333^IXIC had a higher expected quartely return with a mean of 0.0333
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, 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 0.122^IXIC is also the riskier investment with a standard deviation of 0.122
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, 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, 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 1.81You do need additional risk measurements because dependent on outliers the graph could be very skewed one way or another as well as observing the kurtosis of a chart can help you to find the degree at which data is clustered in the tails of a density chart.Also, when these problems are present they are very problematic for ratios and cause standard ddeviation to be less effective in calculating risk.
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, performance_fun = table.DownsideRisk)## # A tibble: 3 x 12
## # Groups: symbol [3]
## symbol `DownsideDeviat~ `DownsideDeviat~ `DownsideDeviat~ GainDeviation
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 ^DJI 0.0492 0.0528 0.0492 0.0428
## 2 ^GSPC 0.0512 0.0548 0.0512 0.0463
## 3 ^IXIC 0.0734 0.077 0.0734 0.0814
## # ... with 7 more variables: `HistoricalES(95%)` <dbl>,
## # `HistoricalVaR(95%)` <dbl>, LossDeviation <dbl>, MaximumDrawdown <dbl>,
## # `ModifiedES(95%)` <dbl>, `ModifiedVaR(95%)` <dbl>, SemiDeviation <dbl>Based on the vary high counts for HistoricalES(95%) and HistoricalVaR(95%) for both ^DJI and ^GSPC, ^IXIC is still the stock with the greatest downside risk.
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, performance_fun = SharpeRatio, p = .95)## # 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 0.201Q7 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, performance_fun = SharpeRatio, p = .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 0.108Q8 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.