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 Import stock prices of Dow Jones Industrial Avarege and NASDAQ Compsite Index for the last 20 years.

## # A tibble: 10,064 x 8
## # Groups:   symbol [2]
##    symbol date         open   high    low  close    volume adjusted
##    <chr>  <date>      <dbl>  <dbl>  <dbl>  <dbl>     <dbl>    <dbl>
##  1 ^DJI   1999-11-01 10731. 10746. 10649. 10649. 150060000   10649.
##  2 ^DJI   1999-11-02 10654. 10752. 10573. 10582. 143460000   10582.
##  3 ^DJI   1999-11-03 10583. 10650. 10563. 10609. 153890000   10609.
##  4 ^DJI   1999-11-04 10612. 10712. 10603. 10640. 195700000   10640.
##  5 ^DJI   1999-11-05 10640. 10843. 10638. 10704. 171660000   10704.
##  6 ^DJI   1999-11-08 10668. 10776. 10650. 10719. 213120000   10719.
##  7 ^DJI   1999-11-09 10715. 10766. 10585. 10617. 168950000   10617.
##  8 ^DJI   1999-11-10 10612. 10655. 10536. 10598. 148240000   10598.
##  9 ^DJI   1999-11-11 10603. 10644. 10544. 10595. 130060000   10595.
## 10 ^DJI   1999-11-12 10594. 10772. 10542. 10769. 158320000   10769.
## # … with 10,054 more rows

Q2 Calculate monthly returns, and save the result under returns_monthly.

## # A tibble: 480 x 3
## # Groups:   symbol [2]
##    symbol date       monthly.returns
##    <chr>  <date>               <dbl>
##  1 ^DJI   1999-11-30         0.0215 
##  2 ^DJI   1999-12-31         0.0569 
##  3 ^DJI   2000-01-31        -0.0484 
##  4 ^DJI   2000-02-29        -0.0742 
##  5 ^DJI   2000-03-31         0.0784 
##  6 ^DJI   2000-04-28        -0.0172 
##  7 ^DJI   2000-05-31        -0.0197 
##  8 ^DJI   2000-06-30        -0.00707
##  9 ^DJI   2000-07-31         0.00709
## 10 ^DJI   2000-08-31         0.0659 
## # … with 470 more rows

Q3 Which of the two stocks have higher expected monthly return?

## # A tibble: 2 x 2
##   symbol returns_avg
##   <chr>        <dbl>
## 1 ^DJI       0.00474
## 2 ^IXIC      0.00643

^IXIC has the higher expected monthly return because it is 0.0064 and ^DJI is only 0.0047.

Q4 Which of the two stocks is riskier?

Hint: Calculate standard diviation

## # A tibble: 2 x 2
## # Groups:   symbol [2]
##   symbol   sd.1
##   <chr>   <dbl>
## 1 ^DJI   0.0406
## 2 ^IXIC  0.0649

^IXIC is also riskier because its standard diviation is 0.065, which is higher than ^DJI with a standard diviation of 0.041.

Q5 Are the returns normally distributed?

## # A tibble: 2 x 2
## # Groups:   symbol [2]
##   symbol skewness.1
##   <chr>       <dbl>
## 1 ^DJI       -0.515
## 2 ^IXIC      -0.365
## # A tibble: 2 x 2
## # Groups:   symbol [2]
##   symbol kurtosis.1
##   <chr>       <dbl>
## 1 ^DJI        0.912
## 2 ^IXIC       1.55

Q6 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.

##                            [,1]      [,2]     
## symbol                     "^DJI"    "^IXIC"  
## DownsideDeviation(0%)      "0.0282"  "0.0450" 
## DownsideDeviation(MAR=10%) "0.0323"  "0.0490" 
## DownsideDeviation(Rf=0%)   "0.0282"  "0.0450" 
## GainDeviation              "0.0237"  "0.0396" 
## HistoricalES(95%)          "-0.0937" "-0.1491"
## HistoricalVaR(95%)         "-0.0625" "-0.1049"
## LossDeviation              "0.0301"  "0.0482" 
## MaximumDrawdown            "0.4930"  "0.7504" 
## ModifiedES(95%)            "-0.0950" "-0.1572"
## ModifiedVaR(95%)           "-0.0668" "-0.1046"
## SemiDeviation              "0.0305"  "0.0481"

Looking at HistoricalES(95%), ^DJI equals -0.0937 and ^IXIC equals -0.1491. Lookihg at HistoricalVaR(95%) ^DJI equals -0.0625 and ^IXIC equals -0.1049. Lookihg at SemiDeviation ^DJI equals 0.0305 and ^IXIC equals 0.0481. ^IXIC has the greater downside risk becasue its HistoricalES(95%), HistoricalVaR(95%), and SemiDeviation risks are all higher than ^DJI.

Q7 Which of the two stocks would you choose?

Hint: Calculate Sharep Ratio and discuss your answer based on calculated Sharp Ratios.

## # A tibble: 2 x 4
## # Groups:   symbol [2]
##   symbol `ESSharpe(Rf=0%,p=95… `StdDevSharpe(Rf=0%,p=… `VaRSharpe(Rf=0%,p=…
##   <chr>                  <dbl>                   <dbl>                <dbl>
## 1 ^DJI                  0.0499                  0.117                0.0710
## 2 ^IXIC                 0.0409                  0.0991               0.0615

I would choose ^DJI because it has the greater sharp ratio so it’ll have the greater expected return per unit of risk.

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.

Q9 Display the title and your name correctly at the top of the webpage.

Q10 Use the correct slug.