Purpose

The purpose of this script is to show the steps and decisions taken to complete the pre-assignment 2 for FINA 9210.
The data used are downloaded from Dropbox and saved locally in the same folder as this script.

library(dplyr)
library(tidyverse)
library(data.table)
library(ggplot2)
library(kableExtra)
library(xtable)
library(TTR)
library(zoo)
library(MASS)
library(DBI)
library(PerformanceAnalytics)

Data

The data is first downloaded from WRDS and stored locally, which will then used for analysis.
Data between 1990-01-01 and 2023-12-31.

wrds <- dbConnect(Postgres(),
                  host = 'wrds-pgdata.wharton.upenn.edu',
                  port = 9737,
                  user = 'ktl24537',  # replace with your WRDS username
                  password = 'Letuankiet0101@',  # replace with your WRDS password
                  sslmode = 'require',
                  dbname = 'wrds')

# SQL query to get ETF returns
query <- "
          SELECT date, permno, ret, prc
          FROM crsp_a_stock.msf
          WHERE permno IN (SELECT permno FROM crsp.stocknames WHERE ticker IN ('SPY','QQQ','SHY','TLT','VB','VTV','VNQ'))
          AND date BETWEEN '1990-01-01' AND '2023-12-31'
          "

# Execute the query
etf_returns <- dbGetQuery(wrds, query)

# Close the connection
dbDisconnect(wrds)

# View the first few rows of the data
head(etf_returns)

# save as csv

write.csv(etf_returns, "returns.csv", row.names = FALSE)

Loading and cleaning data

stock <- read.csv("returns.csv")
ticker <- read.csv("ticker_permno.csv")

stock$permno <- as.character(stock$permno)
ticker$permno <- as.character(ticker$permno)

# For each ticker, keep observations of the most recent permno

ticker_list <- ticker %>% 
  group_by(ticker) %>% 
  filter(date == max(date)) %>% 
  ungroup() %>%
  dplyr::select(ticker, permno)

stock <- stock %>% 
  left_join(ticker_list, by = "permno") %>% 
  dplyr::select(-permno) 
stock$date <- as.Date(stock$date)
stock %>% count(ticker) %>%  kable(digits = 3, col.names = c("Ticker Symbol", "N")) |>
      kable_styling(bootstrap_options = c("striped", "hover")) |>
      kableExtra::scroll_box( height = "500px")

Ticker Symbol	N
QQQ	299
SHY	259
SPY	372
TLT	259
VB	240
VNQ	233
VTV	240

Problem 1

For this assignment, I use Jonathan’s strategy. Jonathan suggested using the moving strategy. When the 2-mo simple moving average crosses above the 6-mo simple moving average, buy the stock. When the 2-mo simple moving average crosses below the 6-mo simple moving average, sell the stock. Otherwise we will hold the stock.

# filter ticker to SPY and filter date to be between 1994 and 2003

spy_setA <- stock %>% 
  filter(ticker == "SPY") %>% 
  filter(date >= "1994-01-01" & date <= "2003-12-31") %>% 
  dplyr::select(date, ret, prc) %>%
  mutate(SMA_2mo = zoo::rollmean(prc, k = 2, fill = NA, align = "right"),
         SMA_6mo = zoo::rollmean(prc, k = 6, fill = NA, align = "right")) %>%
  mutate(signal = 0) %>%
  mutate(signal = ifelse(SMA_2mo > SMA_6mo, 1, signal)) %>%
  mutate(signal = ifelse(SMA_2mo < SMA_6mo, -1, signal)) %>%
  mutate(position = lag(signal, 1),
         strat_ret = position * ret) %>%
  mutate(cum_strat_ret = cumprod(coalesce(1 + strat_ret, 1)) - 1,
         cum_spy_ret = cumprod(coalesce(1 + ret, 1)) - 1) %>%
  mutate(log_strat_ret = log(1 + cum_strat_ret),
         log_spy_ret = log(1 + cum_spy_ret))



seta <- ggplot(data = spy_setA, aes(x = date)) +
  geom_line(aes(y = log_strat_ret, color = "Strategy Returns"), size = 1) +
  geom_line(aes(y = log_spy_ret, color = "SPY Returns"), size = 1) +
  labs(title = "SMA Crossover Strategy vs SPY Returns",
       x = "Date",
       y = "Log Cumulative Return") +
  scale_color_manual(values = c("Strategy Returns" = "blue", "SPY Returns" = "red")) +
  theme_minimal() +
  theme(legend.title = element_blank())  # Remove legend title

print(seta)

ggsave("seta.png", seta, width = 10, height = 6, dpi = 300)

# filter ticker to SPY and filter date to be between 2004 and 2023

spy_setB <- stock %>% 
  filter(ticker == "SPY") %>% 
  filter(date >= "2004-01-01" & date <= "2023-12-31") %>% 
  dplyr::select(date, ret, prc) %>%
  mutate(SMA_2mo = zoo::rollmean(prc, k = 2, fill = NA, align = "right"),
         SMA_6mo = zoo::rollmean(prc, k = 6, fill = NA, align = "right"))  %>%
  mutate(signal = 0) %>%
  mutate(signal = ifelse(SMA_2mo > SMA_6mo, 1, signal)) %>%
  mutate(signal = ifelse(SMA_2mo < SMA_6mo, -1, signal)) %>%
  mutate(position = lag(signal, 1),
         strat_ret = position * ret) %>%
  mutate(cum_strat_ret = cumprod(coalesce(1 + strat_ret, 1)) - 1,
         cum_spy_ret = cumprod(coalesce(1 + ret, 1)) - 1) %>%
  mutate(log_strat_ret = log(1 + cum_strat_ret),
         log_spy_ret = log(1 + cum_spy_ret))



# Plot cumulative returns by month

setb <- ggplot(data = spy_setB, aes(x = date)) +
  geom_line(aes(y = log_strat_ret, color = "Strategy Returns"), size = 1) +
  geom_line(aes(y = log_spy_ret, color = "SPY Returns"), size = 1) +
  labs(title = "SMA Crossover Strategy vs SPY Returns",
       x = "Date",
       y = "Log Cumulative Return") +
  scale_color_manual(values = c("Strategy Returns" = "blue", "SPY Returns" = "red")) +
  theme_minimal() +
  theme(legend.title = element_blank())  # Remove legend title


print(setb)

ggsave("setb.png", setb, width = 10, height = 6, dpi = 300)

# Looking at the whole period from 1994 to 2023

spy_setC <- stock %>% 
  filter(ticker == "SPY") %>% 
  filter(date >= "1994-01-01" & date <= "2023-12-31") %>% 
  dplyr::select(date, ret, prc) %>%
  mutate(SMA_2mo = zoo::rollmean(prc, k = 2, fill = NA, align = "right"),
         SMA_6mo = zoo::rollmean(prc, k = 6, fill = NA, align = "right")) %>%
  mutate(signal = 0) %>%
  mutate(signal = ifelse(SMA_2mo > SMA_6mo, 1, signal)) %>%
  mutate(signal = ifelse(SMA_2mo < SMA_6mo, -1, signal)) %>%
  mutate(position = lag(signal, 1),
         strat_ret = position * ret) %>%
  mutate(cum_strat_ret = cumprod(coalesce(1 + strat_ret, 1)) - 1,
         cum_spy_ret = cumprod(coalesce(1 + ret, 1)) - 1) %>%
  mutate(log_strat_ret = log(1 + cum_strat_ret),
         log_spy_ret = log(1 + cum_spy_ret))

# Plot

set_c<- ggplot(data = spy_setC, aes(x = date)) +
  geom_line(aes(y = log_strat_ret, color = "Strategy Returns"), size = 1) +
  geom_line(aes(y = log_spy_ret, color = "SPY Returns"), size = 1) +
  labs(title = "SMA Crossover Strategy vs SPY Returns",
       x = "Date",
       y = "Log Cumulative Return") +
  scale_color_manual(values = c("Strategy Returns" = "blue", "SPY Returns" = "red")) +
  theme_minimal() +
  theme(legend.title = element_blank())  # Remove legend title

print(set_c)

ggsave("setc.png", set_c, width = 10, height = 6, dpi = 300)

sum_setA <- spy_setA %>% 
  dplyr::select(strat_ret) %>%
  mutate(set = "1994_2003")

sum_setB <- spy_setB %>% 
  dplyr::select(strat_ret) %>%
  mutate(set = "2004_2023")

combine <- rbind(sum_setA, sum_setB)

combine_sum <- combine  %>%
  group_by(set) %>%
  summarise(
    mean = mean(strat_ret, na.rm = TRUE),
    max = max(strat_ret, na.rm = TRUE),
    min = min(strat_ret, na.rm = TRUE),
    median = median(strat_ret, na.rm = TRUE),
    sd = sd(strat_ret, na.rm = TRUE)) 


combine_sum %>% 
  kable(digits = 3, col.names = c("Date Range", "Mean", "Max", "Min", "Median", "SD")) |>
      kable_styling(bootstrap_options = c("striped", "hover")) |>
      kableExtra::scroll_box( height = "500px")

Date Range	Mean	Max	Min	Median	SD
1994_2003	0.004	0.105	-0.141	0.008	0.047
2004_2023	0.006	0.165	-0.127	0.009	0.044

#print LaTex

print(xtable(combine_sum, digits = 3, caption = "Summary Statistics", label = "tab:summary"), type = "latex")

## % latex table generated in R 4.3.3 by xtable 1.8-4 package
## % Sat Aug 24 23:48:49 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{rlrrrrr}
##   \hline
##  & set & mean & max & min & median & sd \\ 
##   \hline
## 1 & 1994\_2003 & 0.004 & 0.105 & -0.141 & 0.008 & 0.047 \\ 
##   2 & 2004\_2023 & 0.006 & 0.165 & -0.127 & 0.009 & 0.044 \\ 
##    \hline
## \end{tabular}
## \caption{Summary Statistics} 
## \label{tab:summary}
## \end{table}

Maximum drawdown

max_drawdown_setA <- -maxDrawdown(spy_setA$strat_ret)
max_drawdown_setB <- -maxDrawdown(spy_setB$strat_ret)

# rounding

max_drawdown_setA <- round(max_drawdown_setA, 3)
max_drawdown_setB <- round(max_drawdown_setB, 3)

# set as character 

max_drawdown_setA <- as.character(max_drawdown_setA)
max_drawdown_setB <- as.character(max_drawdown_setB)

During period 1994-2003, the maximum drawdown is -0.312. During period 2004-2023, the maximum drawdown is -0.255.

Evaluate performance consistency

sum_setA <- spy_setA %>% 
  dplyr::select(date, cum_strat_ret, cum_spy_ret, log_strat_ret, log_spy_ret) %>%
  mutate(set = "1994_2003")

sum_setB <- spy_setB %>%
  dplyr::select(date, cum_strat_ret, cum_spy_ret, log_strat_ret, log_spy_ret) %>%
  mutate(set = "2004_2023")

combine <- rbind(sum_setA, sum_setB)

combine <- combine %>% 
  mutate(diff_cum_ret = cum_strat_ret - cum_spy_ret,
         diff_log_ret = log_strat_ret - log_spy_ret)

# Plot diff in log returns

log_diff <- ggplot(data = combine, aes(x = date, y = diff_log_ret)) +
  geom_line(aes(color = set), size = 1) +
  labs(title = "Difference in Log Cumulative Returns (Strategy - SPY)",
       x = "Date",
       y = "Difference in Log Cumulative Returns") +
  scale_color_manual(values = c("1994_2003" = "brown", "2004_2023" = "violet")) +
  theme_minimal() +
  theme(legend.title = element_blank())  # Remove legend title


print(log_diff)

ggsave("log_diff.png", log_diff, width = 10, height = 6, dpi = 300)

# Plot diff in cumulative returns

cum_diff <- ggplot(data = combine, aes(x = date, y = diff_cum_ret)) +
  geom_line(aes(color = set), size = 1) +
  labs(title = "Difference in Cumulative Returns (Strategy - SPY)",
       x = "Date",
       y = "Difference in Cumulative Returns %") +
  scale_color_manual(values = c("1994_2003" = "brown", "2004_2023" = "violet")) +
  theme_minimal() +
  theme(legend.title = element_blank())  # Remove legend title

print(cum_diff)

ggsave("cum_diff.png", cum_diff, width = 10, height = 6, dpi = 300)

Problem 2

wrds <- dbConnect(Postgres(),
                  host = 'wrds-pgdata.wharton.upenn.edu',
                  port = 9737,
                  user = 'ktl24537',  # replace with your WRDS username
                  password = 'Letuankiet0101@',  # replace with your WRDS password
                  sslmode = 'require',
                  dbname = 'wrds')


# Query to get PERMNOs for U.S. common stocks (shrcd = 10, 11) with end-of-month prices < $5
permnos_query <- "
SELECT DISTINCT permno
FROM crsp.msf
WHERE shrcd IN (10, 11)
AND prc < 5
AND date BETWEEN '1999-01-01' AND '2003-12-31'
AND date = (SELECT MAX(date) FROM crsp.msf WHERE date BETWEEN '1999-01-01' AND '2003-12-31')
"

# Query to get PERMNOs for U.S. common stocks (shrcd = 10, 11) with end-of-month prices < $5
permnos_query <- "
SELECT DISTINCT msf.permno
FROM crsp.msf AS msf
JOIN crsp.stocknames AS sn ON msf.permno = sn.permno
WHERE sn.shrcd IN (10, 11)
AND msf.prc < 5
AND msf.date BETWEEN '1999-01-01' AND '2003-12-31'
AND msf.date = (SELECT MAX(date) FROM crsp.msf WHERE date BETWEEN '1999-01-01' AND '2003-12-31')
"

# Fetch the PERMNOs
permnos <- dbGetQuery(wrds, permnos_query)

# Convert permnos to a vector
permno_vector <- permnos$permno

# Query to get daily returns for the selected PERMNOs
daily_returns_query <- sprintf("
SELECT date, permno, ret, prc, shrout
FROM crsp.dsf
WHERE permno IN (%s)
AND date BETWEEN '1999-01-01' AND '2003-12-31'
", paste(permno_vector, collapse = ","))

# Fetch the daily returns data
daily_returns <- dbGetQuery(wrds, daily_returns_query)

# Close the WRDS connection
dbDisconnect(wrds)

# View the first few rows of the data
head(daily_returns)

# Save locally

write.csv(daily_returns, "permno_returns.csv", row.names = FALSE)

Load data locally

permno_returns <- read.csv("permno_returns.csv")

# value weighted 

vw_returns <- permno_returns %>% 
  mutate(market_cap = prc * shrout) %>% 
  group_by(date) %>% 
  mutate(total_market_cap = sum(market_cap, na.rm = TRUE)) %>% 
  ungroup() %>% 
  mutate(weight = market_cap / total_market_cap) %>% 
  group_by(date) %>% 
  summarise(ret = sum(weight * ret, na.rm = TRUE)) %>% 
  ungroup() %>% 
  mutate(date = as.Date(date)) %>% 
  mutate(set = "Value Weighted")

# equal weighted

ew_returns <- permno_returns %>% 
  group_by(date) %>% 
  summarise(ret = mean(ret, na.rm = TRUE)) %>% 
  ungroup() %>% 
  mutate(date = as.Date(date)) %>% 
  mutate(set = "Equal Weighted")

# combine

combine_returns <- rbind(vw_returns, ew_returns)

# summary statistics 

combine_sum <- combine_returns %>% 
  group_by(set) %>% 
  summarise(
    mean = mean(ret, na.rm = TRUE),
    max = max(ret, na.rm = TRUE),
    min = min(ret, na.rm = TRUE),
    median = median(ret, na.rm = TRUE),
    sd = sd(ret, na.rm = TRUE),
    annualized_mean = mean * 252,
    annualized_sd = sd * sqrt(252))

combine_sum %>%
  kable(digits = 3, col.names = c("Set", "Mean", "Max", "Min", "Median", "SD", "Annualized Daily Mean", "Annualized Daily SD")) |>
      kable_styling(bootstrap_options = c("striped", "hover")) |>
      kableExtra::scroll_box( height = "500px")

Set	Mean	Max	Min	Median	SD	Annualized Daily Mean	Annualized Daily SD
Equal Weighted	0.001	0.078	-0.091	0.002	0.012	0.373	0.192
Value Weighted	0.001	0.180	-0.088	0.002	0.027	0.328	0.436

# print LaTex

print(xtable(combine_sum, digits = 3, caption = "Summary Statistics", label = "tab:summary"), type = "latex")

## % latex table generated in R 4.3.3 by xtable 1.8-4 package
## % Sat Aug 24 23:49:09 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{rlrrrrrrr}
##   \hline
##  & set & mean & max & min & median & sd & annualized\_mean & annualized\_sd \\ 
##   \hline
## 1 & Equal Weighted & 0.001 & 0.078 & -0.091 & 0.002 & 0.012 & 0.373 & 0.192 \\ 
##   2 & Value Weighted & 0.001 & 0.180 & -0.088 & 0.002 & 0.027 & 0.328 & 0.436 \\ 
##    \hline
## \end{tabular}
## \caption{Summary Statistics} 
## \label{tab:summary}
## \end{table}

# Getting monthly return

monthly_returns <- permno_returns %>% 
  mutate(date = as.Date(date)) %>% 
  mutate(year = year(date),
         month = month(date)) %>% 
  group_by(year, month) %>% 
  summarise(ret = mean(ret, na.rm = TRUE)) %>% 
  ungroup() %>% 
  mutate(date = as.Date(paste(year, month, "01", sep = "-")))

Fama French data on monthly risk-free rate and market excess return from 1999-01-01 to 2003-12-31 was downloaded and stored locally.

fama <- read.csv("fama.csv")
daily_rf <- read.csv("daily_rf.csv")

fama_2 <- fama %>% 
  mutate(market = mktrf + rf) %>% 
  mutate(date = as.Date(dateff)) %>% 
  summarise(mean = mean(market, na.rm = TRUE),
    max = max(market, na.rm = TRUE),
    min = min(market, na.rm = TRUE),
    median = median(market, na.rm = TRUE),
    sd = sd(market, na.rm = TRUE),
    annualized_mean = mean * 12,
    annualized_sd = sd * sqrt(12)) 

fama_2 %>%
  kable(digits = 3, col.names = c("Mean", "Max", "Min", "Median", "SD", "Annualized Mean", "Annualized SD")) |>
      kable_styling(bootstrap_options = c("striped", "hover")) |>
      kableExtra::scroll_box( height = "500px")

Mean	Max	Min	Median	SD	Annualized Mean	Annualized SD
0.009	0.136	-0.172	0.014	0.045	0.109	0.157

# print LaTex

print(xtable(fama_2, digits = 3, caption = "Summary Statistics for Market Portfolio", label = "tab:summary"), type = "latex")

## % latex table generated in R 4.3.3 by xtable 1.8-4 package
## % Sat Aug 24 23:49:38 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrrrrr}
##   \hline
##  & mean & max & min & median & sd & annualized\_mean & annualized\_sd \\ 
##   \hline
## 1 & 0.009 & 0.137 & -0.172 & 0.014 & 0.045 & 0.109 & 0.157 \\ 
##    \hline
## \end{tabular}
## \caption{Summary Statistics for Market Portfolio} 
## \label{tab:summary}
## \end{table}

Getting daily risk free to find Sharpe ratio

daily_rf <- daily_rf %>% 
  mutate(date = as.Date(date))

# merge to vw return using date

vw_returns <- merge(vw_returns, daily_rf, by = "date")
ew_returns <- merge(ew_returns, daily_rf, by = "date")

vw_returns <- vw_returns %>% 
  mutate(rt_minus_rf = ret - rf)

ew_returns <- ew_returns %>%
  mutate(rt_minus_rf = ret - rf)

# sharpe ratio 

vw_sharpe <- mean(vw_returns$rt_minus_rf, na.rm = TRUE) / sd(vw_returns$rt_minus_rf, na.rm = TRUE) * sqrt(252)
ew_sharpe <- mean(ew_returns$rt_minus_rf, na.rm = TRUE) / sd(ew_returns$rt_minus_rf, na.rm = TRUE) * sqrt(252)

vw_sharpe <- round(vw_sharpe, 3)
ew_sharpe <- round(ew_sharpe, 3)

vw_sharpe <- as.character(vw_sharpe)
ew_sharpe <- as.character(ew_sharpe)

The Sharpe ratio for the value-weighted portfolio is 0.676, and the Sharpe ratio for the equal-weighted portfolio is 1.765.

# Extract year and month from the date
daily_returns <- permno_returns %>%
  mutate(date = as.Date(date)) %>%
  mutate(year = format(date, "%Y"),
         month = format(date, "%m"))

# Calculate the standard deviation of daily returns for each stock in each month
monthly_sd <- daily_returns %>%
  group_by(permno, year, month) %>%
  summarise(sd = sd(ret, na.rm = TRUE)) %>%
  ungroup()

# Calculate the cross-sectional median of the standard deviations for each month
monthly_sd <- monthly_sd %>%
  group_by(year, month) %>%
  mutate(median_sd = median(sd, na.rm = TRUE),
         sd_group = ifelse(sd > median_sd, "high", "low")) %>%
        filter (!is.na(sd_group)) %>%
  ungroup()

# Merge the SD classification back with daily returns
daily_returns <- merge(daily_returns, monthly_sd, by = c("permno", "year", "month"))

# Calculate portfolio returns for each subsample
portfolio_returns <- daily_returns %>%
  mutate(market_cap = prc * shrout) %>%
  group_by(year, month, date, sd_group) %>%
  summarise(
    ew_return = mean(ret, na.rm = TRUE),  # Equally-weighted
    vw_return = sum(ret * market_cap, na.rm = TRUE) / sum(market_cap, na.rm = TRUE)  # Value-weighted
  ) %>%
  ungroup()

# Calculate summary statistics for each subsample
summary_stats <- portfolio_returns %>%
  group_by(sd_group) %>%
  summarise(
    max_ew_return = max(ew_return, na.rm = TRUE),
    min_ew_return = min(ew_return, na.rm = TRUE),
    mean_ew_return = mean(ew_return, na.rm = TRUE),
    median_ew_return = median(ew_return, na.rm = TRUE),
    sd_ew_return = sd(ew_return, na.rm = TRUE),
    annualized_mean_ew = mean(ew_return, na.rm = TRUE) * 252,
    annualized_sd_ew = sd(ew_return, na.rm = TRUE) * sqrt(252),
    sharpe_ratio_ew = (mean(ew_return, na.rm = TRUE) * 252) / (sd(ew_return, na.rm = TRUE) * sqrt(252)),
    
    max_vw_return = max(vw_return, na.rm = TRUE),
    min_vw_return = min(vw_return, na.rm = TRUE),
    mean_vw_return = mean(vw_return, na.rm = TRUE),
    median_vw_return = median(vw_return, na.rm = TRUE),
    sd_vw_return = sd(vw_return, na.rm = TRUE),
    annualized_mean_vw = mean(vw_return, na.rm = TRUE) * 252,
    annualized_sd_vw = sd(vw_return, na.rm = TRUE) * sqrt(252),
    sharpe_ratio_vw = (mean(vw_return, na.rm = TRUE) * 252) / (sd(vw_return, na.rm = TRUE) * sqrt(252))
  )


# Calculate the difference between EW and VW portfolios for both high and low SD groups
summary_stats <- summary_stats %>%
  mutate(difference_ew_vw = mean_ew_return - mean_vw_return)

# View the summary statistics
print(summary_stats)

## # A tibble: 2 × 18
##   sd_group max_ew_return min_ew_return mean_ew_return median_ew_return
##   <chr>            <dbl>         <dbl>          <dbl>            <dbl>
## 1 high            0.134        -0.138        0.00366          0.00440 
## 2 low             0.0224       -0.0435      -0.000701        -0.000285
## # ℹ 13 more variables: sd_ew_return <dbl>, annualized_mean_ew <dbl>,
## #   annualized_sd_ew <dbl>, sharpe_ratio_ew <dbl>, max_vw_return <dbl>,
## #   min_vw_return <dbl>, mean_vw_return <dbl>, median_vw_return <dbl>,
## #   sd_vw_return <dbl>, annualized_mean_vw <dbl>, annualized_sd_vw <dbl>,
## #   sharpe_ratio_vw <dbl>, difference_ew_vw <dbl>

# print Latex

print(xtable(summary_stats, digits = 3, caption = "Summary Statistics for High and Low SD Groups", label = "tab:summary"), type = "latex")

## % latex table generated in R 4.3.3 by xtable 1.8-4 package
## % Sat Aug 24 23:51:01 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{rlrrrrrrrrrrrrrrrrr}
##   \hline
##  & sd\_group & max\_ew\_return & min\_ew\_return & mean\_ew\_return & median\_ew\_return & sd\_ew\_return & annualized\_mean\_ew & annualized\_sd\_ew & sharpe\_ratio\_ew & max\_vw\_return & min\_vw\_return & mean\_vw\_return & median\_vw\_return & sd\_vw\_return & annualized\_mean\_vw & annualized\_sd\_vw & sharpe\_ratio\_vw & difference\_ew\_vw \\ 
##   \hline
## 1 & high & 0.134 & -0.138 & 0.004 & 0.004 & 0.019 & 0.923 & 0.294 & 3.136 & 0.253 & -0.149 & 0.004 & 0.004 & 0.039 & 1.030 & 0.618 & 1.667 & -0.000 \\ 
##   2 & low & 0.022 & -0.043 & -0.001 & -0.000 & 0.006 & -0.177 & 0.099 & -1.787 & 0.100 & -0.100 & 0.000 & 0.000 & 0.022 & 0.052 & 0.350 & 0.148 & -0.001 \\ 
##    \hline
## \end{tabular}
## \caption{Summary Statistics for High and Low SD Groups} 
## \label{tab:summary}
## \end{table}

FINA 9210 - Pre-Assignment 2

Kiet Le

2024-08-17