# Load packages
 
# Core
library(tidyverse)
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library(tidyquant)
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library(ggrepel)

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

symbols <- c("SPY", "EFA", "IJS", "EEM", "AGG")
 
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] "AGG" "EEM" "EFA" "IJS" "SPY"
# weights
weights <- c(0.25, 0.25, 0.2, 0.2, 0.1)
weights
## [1] 0.25 0.25 0.20 0.20 0.10
w_tbl <- tibble(symbols, weights)
w_tbl
## # 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

# ?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")
## Warning in check_weights(weights, assets_col, map, x): Sum of weights does not
## equal 1.
portfolio_returns_tbl
## # 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

# Risk free rate
rfr <- 0.0003
 
portfolio_sharpe_tbl <- portfolio_returns_tbl %>%
 
    tq_performance(Ra = returns,
                   Rf = rfr,
                   performance_fun = SharpeRatio,
                   FUN = "StdDev")
 
portfolio_sharpe_tbl
## # A tibble: 1 × 1
##   `StdDevSharpe(Rf=0%,p=95%)`
##                         <dbl>
## 1                       0.239

6 Plot

Returns Histogram with Risk-Free Rate

# Figure 7.2 Returns Histogram with Risk-Free Rate ggplot ----
 
portfolio_returns_tbl %>%
 
    ggplot(aes(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, size = 5) +
    labs(y = "count")
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

Scatter Returns around Risk Free Rate

# Figure 7.1 Scatter Returns around Risk Free Rate ----
 
portfolio_returns_tbl %>%
 
    # Transform data
    mutate(returns_excess = if_else(returns > rfr, "above_rfr", "below_rfr")) %>%
 
    ggplot(aes(date, returns, color = returns_excess)) +
    geom_point(show.legend = FALSE) +
 
    # risk free rate
    geom_hline(yintercept = rfr, linetype = "dotted", size = 1, color = "cornflowerblue") +
 
    # election date
    geom_vline(xintercept = as.Date("2016-11-30"), size = 1, color = "cornflowerblue") +
 
    # formatting
    scale_x_date(breaks = scales::pretty_breaks(n = 7)) +
 
    # labeling
    annotate(geom = "text",
             x = as.Date("2017-01-01"), y = -0.04,
             label = "Election", angle = 90, size = 5) +
    annotate(geom = "text",
             x = as.Date("2017-06-01"), y = -0.01,
             label = str_glue("No returns below the RFR
                              after the 2016 election"),
             color = "red", size = 4) +
    labs(y = "percent monthly returns",
         x = NULL)

Rolling Sharpe

# Custom function
# necessary because we would not be able to specify FUN = "StdDev" otherwise
 
calculate_rolling_sharpeRatio <- function(df) {
 
    SharpeRatio(df,
                Rf = rfr,
                FUN = "StdDev")
 
}
 
# dump(list = "calculate_rolling_sharpeRatio",
#      file = "00_scripts/calculate_rolling_sharpeRatio.R")
 
# Set the length of periods for rolling calculation
window <- 24
 
# Calculate rolling sharpe ratios
rolling_sharpe_tbl <- portfolio_returns_tbl %>%
 
    tq_mutate(select = returns,
              mutate_fun = rollapply,
              width = window,
              align = "right",
              FUN = calculate_rolling_sharpeRatio,
              col_rename = "sharpeRatio") %>%
    na.omit()
 
rolling_sharpe_tbl
## # 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
# Figure 7.5 Rolling Sharpe ggplot ----
 
rolling_sharpe_tbl %>%
 
    ggplot(aes(date, sharpeRatio)) +
    geom_line(color = "cornflowerblue") +
 
    labs(title = paste0("Rolling ", window, "-Month Sharpe Ratio"),
         y = "rolling Sharpe Ratio",
         x = NULL) +
    theme(plot.title = element_text(hjust = 0.5)) +
 
    annotate(geom = "text",
             x = as.Date("2016-06-01"), y = 0.5,
             label = "This portfolio has done quite well since 2016.",
             size = 5, color = "red")