Analyzing Performance with tidyquant

Q1 Load tidyquant and tidyverse packages.
Q2 Import stock prices of S&P 500 and NASDAQ Compsite Index for the last 20 years.
Q3 Calculate monthly returns, and save the result under returns_monthly.
Q4 Create a density plot for returns of both stocks.
Q5 Which of the two stocks have higher expected monthly return?
Q6 Which of the two stocks is riskier?
Q7 Are the returns normally distributed?
Q8 Investors use additional risk measures that focus on describing the potential losses because the return distribution is often not normal. List three additional risk measures.
Q9 Calculate the downside risk measures by revising the code below. Which of the two stocks has greater downside risks? Discuss HistoricalES(95%), HistoricalVaR(95%), and SemiDeviation.
Q10 Which of the two stocks would you choose?

Suppose that you consider investing in two stocks: S&P500 and NASDAQ. As a prudent investor, you analyze the historical performance of the stocks for the past 20 years.

Q1 Load tidyquant and tidyverse packages.

library(tidyquant)
library(tidyverse)

Q2 Import stock prices of S&P 500 and NASDAQ Compsite Index for the last 20 years.

Hint: Add group_by(symbol) at the end of the code so that calculations below will be done per stock.

# Import stock prices
from = today() - years(20)
Stocks <- 
  tq_get(c("^GSPC", "^IXIC"), get = "stock.prices", from = from) %>%
  group_by(symbol)
Stocks
## # A tibble: 5,031 x 8
## # Groups:   symbol [1]
##    symbol date        open  high   low close     volume adjusted
##    <chr>  <date>     <dbl> <dbl> <dbl> <dbl>      <dbl>    <dbl>
##  1 ^IXIC  1999-10-29 2919. 2979. 2919. 2966. 1441380000    2966.
##  2 ^IXIC  1999-11-01 2971. 2998. 2968. 2968. 1076080000    2968.
##  3 ^IXIC  1999-11-02 2984. 3015. 2972. 2982. 1248540000    2982.
##  4 ^IXIC  1999-11-03 3022. 3041. 3012. 3029. 1339050000    3029.
##  5 ^IXIC  1999-11-04 3067. 3077. 3030. 3056. 1364610000    3056.
##  6 ^IXIC  1999-11-05 3100. 3118. 3081. 3102. 1346320000    3102.
##  7 ^IXIC  1999-11-08 3072. 3148. 3069. 3144. 1300800000    3144.
##  8 ^IXIC  1999-11-09 3173. 3175. 3099. 3125. 1470420000    3125.
##  9 ^IXIC  1999-11-10 3126. 3187. 3122. 3156. 1433250000    3156.
## 10 ^IXIC  1999-11-11 3186. 3201. 3169. 3197. 1382840000    3197.
## # … with 5,021 more rows

Q3 Calculate monthly returns, and save the result under returns_monthly.

Hint: Take the adjusted variable from Stocks, and calculate monthly returns using ***tq_transmute().

# Calculate returns. 
returns_monthly <- 
  Stocks %>%
    tq_transmute(select = adjusted, mutate_fun = periodReturn, period = "monthly")
returns_monthly
## # A tibble: 241 x 3
## # Groups:   symbol [1]
##    symbol date       monthly.returns
##    <chr>  <date>               <dbl>
##  1 ^IXIC  1999-10-29          0     
##  2 ^IXIC  1999-11-30          0.125 
##  3 ^IXIC  1999-12-31          0.220 
##  4 ^IXIC  2000-01-31         -0.0317
##  5 ^IXIC  2000-02-29          0.192 
##  6 ^IXIC  2000-03-31         -0.0264
##  7 ^IXIC  2000-04-28         -0.156 
##  8 ^IXIC  2000-05-31         -0.119 
##  9 ^IXIC  2000-06-30          0.166 
## 10 ^IXIC  2000-07-31         -0.0502
## # … with 231 more rows

Q4 Create a density plot for returns of both 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.

# density plot
returns_monthly %>%
  ggplot(aes(x = monthly.returns, fill = symbol)) +
  geom_density(alpha = 0.3)

Q5 Which of the two stocks have higher expected monthly return?

Hint: Take returns_monthly and pipe it to summarise. Calculate the mean monthly returns.

^IXIC has a higher return. ^IXIC has a return of .64% where ^GSPC has a return of .42%

returns_monthly %>% 
  summarise(returns_avg = mean(monthly.returns))
## # A tibble: 1 x 2
##   symbol returns_avg
##   <chr>        <dbl>
## 1 ^IXIC      0.00642

Q6 Which of the two stocks is riskier?

Hint: Discuss your answer in terms of standard deviation. Take returns_monthly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute sd (standard deviation).

^IXIC is the riskier of the two stocks. They have a standard deviation of 6.5% where ^GSPC has a standard deviation of 4.2%. ^IXIC has a larger standard deviation than ^GSPC.

# Compute standard deviation
returns_monthly %>%
    tq_performance(Ra = monthly.returns,
                   Rb = NULL, # Calculataing downside risk measures doesn't require Rb
                   performance_fun = sd)
## # A tibble: 1 x 2
## # Groups:   symbol [1]
##   symbol   sd.1
##   <chr>   <dbl>
## 1 ^IXIC  0.0648

# See options for the `performance_fun` argument
#tq_performance_fun_options()

Q7 Are the returns normally distributed?

Hint: when the return distribution is not normal, the standard deviation is not an appropriate measure of risk. One can use skewness and kurtosis to detect non-normal returns. Take returns_monthly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute skewness. Do the same for kurtosis.

Skewness (is it symmetric?)
- Zero: symmetric
- Negative: extreme negative returns are likelier than extreme positive returns
- Positive: extreme positive returns are likelier than extreme negative returns
Excess kurtosis (does it have fat-tails?)
- Zero: normal distribution
- Greater than zero: extreme returns of both positive and negative occur more often

Both S&P500 and NASDAQ have a negative skewness, long tail to the left, and a positive kurtusis, meaning thick tails, indicating a large negative return is likelier than a large positive return.

# Compute skewness
returns_monthly %>%
    tq_performance(Ra = monthly.returns,
                   Rb = NULL, # Calculataing downside risk measures doesn't require Rb
                   performance_fun = skewness)
## # A tibble: 1 x 2
## # Groups:   symbol [1]
##   symbol skewness.1
##   <chr>       <dbl>
## 1 ^IXIC      -0.365

# Compute kurtosis
returns_monthly %>%
    tq_performance(Ra = monthly.returns,
                   Rb = NULL, # Calculataing downside risk measures doesn't require Rb
                   performance_fun = kurtosis)
## # A tibble: 1 x 2
## # Groups:   symbol [1]
##   symbol kurtosis.1
##   <chr>       <dbl>
## 1 ^IXIC        1.56

Q8 Investors use additional risk measures that focus on describing the potential losses because the return distribution is often not normal. List three additional risk measures.

The return distribution is often not normal. Three additional risk measures are historical ES, expected shortfall, historical VaR, and Semi-deviation. Semi-deviation of .0218 means that the standard deviation of returns below the mean return is .0318. VaR of -.0748 means that -7.48% is the largest loss one could expect with 95% confidence. There is a 5% odd that you could lose more than 7.48%. VaR tells the you the largest loss you expect but there is 5% error that your loss could be larger than posted. ES of -.0949 means that -9.49 is the average of the 5% most negative returns. It shows the worst 5% returns. Var is the skew to the left shows the negative point. ES is to the left of VaR. ES will always be greater than VaR. if VaR is larger than ES you did something wrong.

Q9 Calculate the downside risk measures by revising the code below. Which of the two stocks has greater downside risks? Discuss HistoricalES(95%), HistoricalVaR(95%), and SemiDeviation.

Hint: Take returns_monthly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute table.DownsideRisk.

Semi-Deviation of 0.0318 means that the standard deviation of returns below the mean return is 0.0318.
VaR (p = 0.05) of -0.0748 means that - 7.48% is the largest loss one could expect with 95% confidence. Is it possible that you could lose more than - 7.48%? Yes. What’s the odd? 5%. In other word, a more negative return can only happen with a probability of 5%.
ES (p = 0.05) of -0.0949 means that - 9.49% is the average of the 5% (p = 0.05) most negative returns.
NASDAQ appears to present greater downside risk than S&P500. For example, NASDAQ has more volatile monthly returns below the mean (semideviation of 0.0480) than S&P500 (semideviation of 0.0318); the largest loss one could expect with 95% confidence is larger for NASDAQ (VaR of -0.1047 at 5%) than S&P 500 (VaR of -0.0748 at 5%); and the average of the 5% most negative monthly returns is larger for NASDAQ (ES of -0.1456 at 5%) than S&P 500 (ES of -0.0949 at 5%).

# Retrieve performance metrics
returns_monthly %>%
    tq_performance(Ra = monthly.returns,
                   Rb = NULL, # Calculataing downside risk measures doesn't require Rb
                   performance_fun = table.DownsideRisk) %>%
  t()
##                            [,1]     
## symbol                     "^IXIC"  
## DownsideDeviation(0%)      "0.0449" 
## DownsideDeviation(MAR=10%) "0.0489" 
## DownsideDeviation(Rf=0%)   "0.0449" 
## GainDeviation              "0.0396" 
## HistoricalES(95%)          "-0.1456"
## HistoricalVaR(95%)         "-0.1047"
## LossDeviation              "0.0482" 
## MaximumDrawdown            "0.7504" 
## ModifiedES(95%)            "-0.1571"
## ModifiedVaR(95%)           "-0.1044"
## SemiDeviation              "0.048"

Q10 Which of the two stocks would you choose?

Hint: Discuss your answer in terms of risk and reward.

Based on the return ^IXIC came out on top but when we calculated risk ^GSPC came on top. Since they both came out on top for two different sections. Per unit of risk, the sharpe ratio, measures resturns per unit of risk. Main return divided by standard deviation. Youre underestimating downside risk.