Quantitative Finance: Compare Portfolio Performance using Backtesting

R Finance Series

R Codes and Results

#==============================
#    Portfolio Backtesting
#==============================

#--------------------
#    Prepare data
#--------------------

# Clear workspace: 
rm(list = ls())


# Collect price data from Yahoo: 
symbols <- c("FB", "AMZN", "NFLX", "GOOG", "^IXIC") # Note that ^IXIC is NASDAQ Composite.  
tidyquant::tq_get(x = symbols, from = "2016-01-01", to = "2021-05-30") -> data_raw

# Convert to wide form: 

library(tidyverse)

data_raw %>% 
  select(date, symbol, adjusted) %>% 
  pivot_wider(names_from = symbol, values_from = adjusted) -> data_wide_price


date_ymd <- data_wide_price$date # Date time series. 

market_data <- data_wide_price$`^IXIC` # Assume that IXIC is market indicator. 

stocks_data <- data_wide_price %>% select(symbols[1:4]) # Historical price data for FB, AMZN NFLX and GOOG. 

n <- ncol(stocks_data) # Number of stocks. 

# Convert to xts object: 

library(xts)

xts(stocks_data, order.by = date_ymd) -> stocks_data_xts
xts(market_data, order.by = date_ymd) -> market_data_xts

# Prepare data for backtesting: 
data_for_backtesting <- list(list(adjusted = stocks_data_xts, index = market_data_xts))

#----------------------------------------------------------------------------
#  Compare two portfolios by Portfolio Backtesting Process (Naive approach)
#----------------------------------------------------------------------------

# Equal-weighted portfolio: 

portfolio1 <- function(...) {
  
  equal_weights <- rep(1 / n, n)
  
  return(equal_weights)
}

# Portfolio contains 40% FB, 10% AMZN, 25% NFLX, 25% GOOG: 

portfolio2 <- function(...) {
  
  weights <- c(0.4, 0.1, 0.25, 0.25)
  
  return(weights)
  
}

# Back-testing process for comparing: 

portfolios <- list("Portfolio1" = portfolio1, "Portfolio2" = portfolio2)

library(portfolioBacktest)

bt <- portfolioBacktest(portfolio_funs = portfolios, 
                        data = data_for_backtesting, 
                        benchmark = c("index"), 
                        T_rolling_window = 252*4, 
                        show_progress_bar = TRUE)

res_sum <- backtestSummary(bt)

res_sum$performance_summary[1:9, 1:2] %>% 
  data.frame() %>% 
  mutate(Metric = row.names(.)) %>% 
  mutate_if(is.numeric, function(x) {round(x, 3)}) %>% 
  select(Metric, everything()) -> df_compare

rownames(df_compare) <- NULL

library(kableExtra) # For presenting table. 

# Cpmpare performance: 

df_compare %>% 
  kbl(caption = "Table 1: Portfolio Performance", escape = TRUE) %>%
  kable_classic(full_width = FALSE, html_font = "Cambria")

Table 1: Portfolio Performance

Metric	Portfolio1	Portfolio2
Sharpe ratio	1.360	1.270
max drawdown	0.267	0.283
annual return	0.460	0.446
annual volatility	0.338	0.352
Sterling ratio	1.725	1.576
Omega ratio	1.252	1.240
ROT (bps)	1931.357	1947.215
VaR (0.95)	0.034	0.034
CVaR (0.95)	0.047	0.050

# Cumulative weath: 

library(lubridate)

bt$Portfolio1$data1$wealth %>% 
  as.data.frame() %>% 
  mutate(Date = row.names(.)) %>% 
  mutate(Date = ymd(Date)) %>% 
  rename(Weath = `portfolio wealth`) %>% 
  mutate(Approach = "Portfolio1") -> df1

bt$Portfolio2$data1$wealth %>% 
  as.data.frame() %>% 
  mutate(Date = row.names(.)) %>% 
  mutate(Date = ymd(Date)) %>% 
  rename(Weath = `portfolio wealth`) %>% 
  mutate(Approach = "Portfolio2") -> df2

bt$index$data1$wealth %>% 
  as.data.frame() %>% 
  mutate(Date = row.names(.)) %>% 
  mutate(Date = ymd(Date)) %>% 
  rename(Weath = V1) %>% 
  mutate(Approach = "Portfolio3") -> df3

bind_rows(df1, df2, df3) -> df

df %>% 
  mutate(Weath = round(Weath, 3)) %>% 
  ggplot(aes(Date, Weath, color = Approach)) + 
  geom_line() + 
  theme(legend.title = element_blank()) + 
  labs(title = "Compare Daily-Portfolio Cumulative Return") -> p

# https://rstudio.github.io/dygraphs/
library(dygraphs)

df %>% 
  mutate(Weath = round(100*Weath, 2)) %>% 
  pivot_wider(names_from = Approach, values_from = Weath) -> df_wider

xts(df_wider %>% select(2:4), order.by = df_wider$Date) -> df_wider_xts  

df_wider_xts %>% 
  dygraph(main = "Daily Portfolio Weath") %>%
  dyAxis(name = "y", 
         # label = "Weath ($)", 
         axisLabelFormatter = 'function(d){return Math.round(d) + "$"}') %>% 
  dyRangeSelector(dateWindow = c("2020-01-03", "2020-12-31"))

References

1. Financial Risk Forecasting, Chapter 8
2. Machine Learning for Factor Investing: R Version, Chapter 12
3. Numerical Methods and Optimization in Finance, Chapter 15
4. Backtesting Optimal Portfolios based on Forecasting Models
5. The Essential Guide to Backtesting Trading Strategies