Goal

Measure portfolio risk using kurtosis. It describes the fatness of the tails in probability distributions. In other words, it measures whether a distribution has more or less returns in its tails than the normal distribution. It matters to investors because a distribution with excess kurtosis (kurtosis > 3) means our portfolio might be at risk of a rare but huge downside event. Kurtosis less than 3 means the portfolio is less risky because it has fewer returns in the tails.

five stocks: “SPY”, “EFA”, “IJS”, “EEM”, “AGG”

from 2012-12-31 to 2017-12-31

1 Import stock prices

2 Convert prices to returns

3 Assign a weight to each asset

## [1] "AGG" "EEM" "EFA" "IJS" "SPY"
## [1] 0.25 0.25 0.20 0.20 0.10
## # A tibble: 5 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 AGG        0.25
## 2 EEM        0.25
## 3 EFA        0.2 
## 4 IJS        0.2 
## 5 SPY        0.1

4 Build a portfolio

## # A tibble: 60 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.0204 
##  2 2013-02-28 -0.00239
##  3 2013-03-28  0.0121 
##  4 2013-04-30  0.0174 
##  5 2013-05-31 -0.0128 
##  6 2013-06-28 -0.0247 
##  7 2013-07-31  0.0321 
##  8 2013-08-30 -0.0224 
##  9 2013-09-30  0.0511 
## 10 2013-10-31  0.0301 
## # ℹ 50 more rows

5 Calculate Sharpe Ratio

## # A tibble: 1 × 1
##   `StdDevSharpe(Rf=0%,p=95%)`
##                         <dbl>
## 1                       0.239

6 Plot

Returns Histogram with Risk-Free Rate

Scatter Returns around Risk Free Rate

Rolling Sharpe

## # A tibble: 37 × 3
##    date        returns sharpeRatio
##    <date>        <dbl>       <dbl>
##  1 2014-12-31 -0.0131       0.230 
##  2 2015-01-30 -0.00933      0.178 
##  3 2015-02-27  0.0377       0.240 
##  4 2015-03-31 -0.00527      0.210 
##  5 2015-04-30  0.0202       0.214 
##  6 2015-05-29 -0.00840      0.222 
##  7 2015-06-30 -0.0177       0.238 
##  8 2015-07-31 -0.0134       0.162 
##  9 2015-08-31 -0.0551       0.0950
## 10 2015-09-30 -0.0253      -0.0279
## # ℹ 27 more rows