Quiz 5

Q1 Import stock prices of NASDAQ Compsite Index, Microsoft and Walmart for the last 30 years.
Q2 Calculate yearly returns.
Q3 Which of the three stocks has the highest expected yearly return?
Q4 Calculate standard deviation of the yearly returns. Which of the three stocks is the riskiest in terms of standard deviation?
Q5 Is the standard deviation appropriate measure of risk for the three stocks? Calculate skewness and kurtosis, and discuss them in your answer.
Q6 Which of the three stocks poses greater downside risk? Calculate HistoricalES(95%), HistoricalVaR(95%), and SemiDeviation, and discuss them in your answer.
Q7 Which of the three stocks would you choose? Calculate the Sharpe ratios with an annualized risk-free rate of 2% and a default confidence interval of 0.95.
Q7.a Repeat Q7 but at a confidence interval of 0.99. Does it change your answer in Q7?
Q8 Hide the messages and the code, but display results of the code from the webpage.
Q9 Display the title and your name correctly at the top of the webpage.
Q10 Use the correct slug.

library(tidyverse)
library(tidyquant)

Q1 Import stock prices of NASDAQ Compsite Index, Microsoft and Walmart for the last 30 years.

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

from = today() - years(30)
Stocks <- 
  tq_get(c("^IXIC", "WMT", "MSFT"), get = "stock.prices", from = from) %>%
  group_by(symbol)
Stocks
## # A tibble: 22,674 x 8
## # Groups:   symbol [3]
##    symbol date        open  high   low close    volume adjusted
##    <chr>  <date>     <dbl> <dbl> <dbl> <dbl>     <dbl>    <dbl>
##  1 ^IXIC  1990-05-07  429.  432.  429.  431. 122690000     431.
##  2 ^IXIC  1990-05-08  431.  432.  431.  432. 133840000     432.
##  3 ^IXIC  1990-05-09  431.  432.  430.  431. 146630000     431.
##  4 ^IXIC  1990-05-10  432.  434.  431.  433. 142490000     433.
##  5 ^IXIC  1990-05-11  434.  438.  434.  438. 167560000     438.
##  6 ^IXIC  1990-05-14  440.  443.  439.  442. 177170000     442.
##  7 ^IXIC  1990-05-15  441   443.  440   442. 162330000     442.
##  8 ^IXIC  1990-05-16  442.  443.  440.  443. 152490000     443.
##  9 ^IXIC  1990-05-17  445   446.  443.  446. 171410000     446.
## 10 ^IXIC  1990-05-18  446   448.  445   448. 191410000     448.
## # … with 22,664 more rows

Q2 Calculate yearly returns.

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

returns_yearly <- 
  Stocks %>%
    tq_transmute(select = adjusted, mutate_fun = periodReturn, period = "yearly")
returns_yearly
## # A tibble: 93 x 3
## # Groups:   symbol [3]
##    symbol date       yearly.returns
##    <chr>  <date>              <dbl>
##  1 ^IXIC  1990-12-31        -0.133 
##  2 ^IXIC  1991-12-31         0.569 
##  3 ^IXIC  1992-12-31         0.155 
##  4 ^IXIC  1993-12-31         0.147 
##  5 ^IXIC  1994-12-30        -0.0320
##  6 ^IXIC  1995-12-29         0.399 
##  7 ^IXIC  1996-12-31         0.227 
##  8 ^IXIC  1997-12-31         0.216 
##  9 ^IXIC  1998-12-31         0.396 
## 10 ^IXIC  1999-12-31         0.856 
## # … with 83 more rows

Q3 Which of the three stocks has the highest expected yearly return?

Hint: Take returns_yearly and pipe it to summarise. Calculate the mean yearly returns.

returns_yearly %>% 
  summarise(returns_avg = mean(yearly.returns))
## # A tibble: 3 x 2
##   symbol returns_avg
##   <chr>        <dbl>
## 1 ^IXIC        0.137
## 2 MSFT         0.273
## 3 WMT          0.156
returns_yearly
## # A tibble: 93 x 3
## # Groups:   symbol [3]
##    symbol date       yearly.returns
##    <chr>  <date>              <dbl>
##  1 ^IXIC  1990-12-31        -0.133 
##  2 ^IXIC  1991-12-31         0.569 
##  3 ^IXIC  1992-12-31         0.155 
##  4 ^IXIC  1993-12-31         0.147 
##  5 ^IXIC  1994-12-30        -0.0320
##  6 ^IXIC  1995-12-29         0.399 
##  7 ^IXIC  1996-12-31         0.227 
##  8 ^IXIC  1997-12-31         0.216 
##  9 ^IXIC  1998-12-31         0.396 
## 10 ^IXIC  1999-12-31         0.856 
## # … with 83 more rows

Q4 Calculate standard deviation of the yearly returns. Which of the three stocks is the riskiest in terms of standard deviation?

Hint: 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 ^IXIC  0.278
## 2 WMT    0.327
## 3 MSFT   0.402

Q5 Is the standard deviation appropriate measure of risk for the three stocks? Calculate skewness and kurtosis, and discuss them in your answer.

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_yearly and pipe it to tidyquant::tq_performance. Use the performance_fun argument to compute skewness. Do the same for kurtosis.

yearly_skewness <- returns_yearly %>%
  tq_performance(Ra = yearly.returns,
                   Rb = NULL,
                   performance_fun = skewness)


yearly_kurtosis <- returns_yearly %>%
  tq_performance(Ra = yearly.returns,
                   Rb = NULL,
                   performance_fun = kurtosis)

Q6 Which of the three stocks poses greater downside risk? Calculate HistoricalES(95%), HistoricalVaR(95%), and SemiDeviation, and discuss them in your answer.

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

Downside_risk <- returns_yearly %>%
  tq_performance(Ra = yearly.returns,
                   Rb = NULL,
                   performance_fun = table.DownsideRisk) %>%
  t()

Q7 Which of the three stocks would you choose? Calculate the Sharpe ratios with an annualized risk-free rate of 2% and a default confidence interval of 0.95.

Hint: Make your argument based on the three Sharpe Ratios.

returns_yearly %>%
  tq_performance(Ra = yearly.returns,
                   Rb = NULL,
                   performance_fun = SharpeRatio, Rf = .02) %>%
  t()
##                           [,1]        [,2]        [,3]       
## symbol                    "^IXIC"     "WMT"       "MSFT"     
## ESSharpe(Rf=2%,p=95%)     "0.2867333" "0.2501061" "0.5185779"
## StdDevSharpe(Rf=2%,p=95%) "0.4206751" "0.4160441" "0.6288367"
## VaRSharpe(Rf=2%,p=95%)    "0.3928930" "0.6271157" "0.7412996"

Q7.a Repeat Q7 but at a confidence interval of 0.99. Does it change your answer in Q7?

Hint: Make your argument based on the three Sharpe Ratios.

returns_yearly %>%
  tq_performance(Ra = yearly.returns,
                   Rb = NULL,
                   performance_fun = SharpeRatio, p= .01, Rf = .02) %>%
  t()
##                          [,1]        [,2]        [,3]       
## symbol                   "^IXIC"     "WMT"       "MSFT"     
## ESSharpe(Rf=2%,p=1%)     "0.2040602" "0.1361574" "0.3671338"
## StdDevSharpe(Rf=2%,p=1%) "0.4206751" "0.4160441" "0.6288367"
## VaRSharpe(Rf=2%,p=1%)    "0.2430265" "1.2119986" "0.4274725"

Q8 Hide the messages and the code, but display results of the code from the webpage.

Hint: Use message, echo and results in the chunk options. Refer to the RMarkdown Reference Guide.