# Load packages

# Core
library(tidyverse)
library(tidyquant)

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: “AMZN”, “INTC”, “TSLA”, “GME”, “AAPL”

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

1 Import stock prices

symbols <- c("LULU", "NFLX", "TSLA")

prices <- tq_get(x    = symbols,
                 get  = "stock.prices",    
                 from = "2012-12-31",
                 to   = "2017-12-31")

2 Convert prices to returns

asset_returns_tbl <- prices %>%
    
    group_by(symbol) %>%
    
    tq_transmute(select     = adjusted, 
                 mutate_fun = periodReturn, 
                 period     = "monthly",
                 type       = "log") %>%
    
    slice(-1) %>%
    
    ungroup() %>%
    
    set_names(c("asset", "date", "returns"))

3 Assign a weight to each asset

# symbols
symbols <- asset_returns_tbl %>% distinct(asset) %>% pull()
symbols
## [1] "LULU" "NFLX" "TSLA"
# weights
weights <- c(0.30, 0.35, 0.35)
weights
## [1] 0.30 0.35 0.35
w_tbl <- tibble(symbols, weights)
w_tbl
## # A tibble: 3 × 2
##   symbols weights
##   <chr>     <dbl>
## 1 LULU       0.3 
## 2 NFLX       0.35
## 3 TSLA       0.35

4 Build a portfolio

# ?tq_portfolio

portfolio_returns_tbl <- asset_returns_tbl %>%
    
    tq_portfolio(assets_col = asset, 
                 returns_col = returns, 
                 weights = w_tbl, 
                 rebalance_on = "months", 
                 col_rename = "returns")

portfolio_returns_tbl
## # A tibble: 60 × 2
##    date        returns
##    <date>        <dbl>
##  1 2013-01-31  0.209  
##  2 2013-02-28  0.0108 
##  3 2013-03-28  0.00990
##  4 2013-04-30  0.230  
##  5 2013-05-31  0.230  
##  6 2013-06-28 -0.0432 
##  7 2013-07-31  0.148  
##  8 2013-08-30  0.138  
##  9 2013-09-30  0.0866 
## 10 2013-10-31 -0.0688 
## # … with 50 more rows

5 Calculate Sharpe Ratio

# Define risk free rate
rfr <- 0.0003

portfolio_SharpeRatio_tbl <- portfolio_returns_tbl %>%
    
    tq_performance(Ra = returns, 
                   performance_fun = SharpeRatio,
                   Rf              =  rfr,
                   FUN             =  "StdDev")
portfolio_SharpeRatio_tbl
## # A tibble: 1 × 1
##   `StdDevSharpe(Rf=0%,p=95%)`
##                         <dbl>
## 1                       0.348

6 Plot

Histogram of Returns with risk free rate

portfolio_returns_tbl %>%
    
    ggplot(aes(x = returns)) + 
    geom_histogram(binwidth = 0.01, fill = "cornflowerblue", alpha = 0.5) +
    
    geom_vline(xintercept = rfr, color = "green", size = 1) + 
    
    annotate(geom = "text", 
                x = rfr, + 0.002,
                y = 13,
                label = "risk free rate",
                angle = 90 ) +
    labs(y = "count")

Scatterplot of Returns around Risk Free Rate

portfolio_returns_tbl %>%
    
    # Add a new variable 
    mutate(excess_returns = if_else(returns > rfr, "rfr_above",
                                                    "rfr_below")) %>%
    # Plot
    ggplot(aes(x = date, y = returns)) +
    geom_point(aes(color = excess_returns)) +
    geom_hline(yintercept = rfr, color = "cornflowerblue", 
               linetype = 3, size = 1) +
    geom_vline(xintercept = as.Date("2016-11-01"), 
               color = "cornflowerblue", size = 1, alpha = 0.5) +
    
    theme(legend.position = "none") +
    
    annotate(geom = "text", 
             x = as.Date("2016-12-01"), y = -0.04, 
             label = "Election", size = 5, angle = 90) +
    
    annotate(geom = "text", 
             x = as.Date("2017-05-01"), y = -0.01,
             label = str_glue("No returns below RFR after the 2016 election."),
             
             color = "green") +
    
        labs(y = "monthly returns", x = NULL)

Rolling Sharpe Ratio

# Create a custom function to calculate rolling SR

Calculate_rolling_SharpeRatio <- function(data) {
    
    
    
   rolling_SR <- SharpeRatio(R = data,
                Rf = rfr,
                FUN = "StdDev")
    return(rolling_SR)
}  
# Define window
window <- 24

# Transform date: calculate rolling Sharpe ratio
rolling_sr_tbl <- portfolio_returns_tbl %>%
    
    tq_mutate(select = returns, 
              mutate_fun = rollapply,
              width = window,
              FUN = Calculate_rolling_SharpeRatio,
              col_rename = "rolling_sr") %>%
    
        select(-returns) %>%
        na.omit()
    
rolling_sr_tbl
## # A tibble: 37 × 2
##    date       rolling_sr
##    <date>          <dbl>
##  1 2014-12-31      0.413
##  2 2015-01-30      0.392
##  3 2015-02-27      0.403
##  4 2015-03-31      0.347
##  5 2015-04-30      0.335
##  6 2015-05-29      0.289
##  7 2015-06-30      0.346
##  8 2015-07-31      0.314
##  9 2015-08-31      0.245
## 10 2015-09-30      0.137
## # … with 27 more rows
rolling_sr_tbl %>%
    
    ggplot(aes(x = date, y = rolling_sr)) +
    geom_line(color = "cornflowerblue") +
    
    # Labeling
    labs(x = NULL, y = "Rolling Sharpe Ratio") +
    
    annotate(geom = "text", 
             x = as.Date("2016-06-01"), y = 0.5,
             label = "This portfolio has done quite well since 2016",
             color = "red", size = 4)