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@mgei
Created Sep 25, 2020
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Calculating the return, standard deviation, and SR for the SPX
library(tidyverse)
library(tidyquant)
library(lubridate)
# get data from Yahoo ----
spx <- tq_get("^GSPC")
# calculate returns ----
ret_daily <- spx %>%
mutate(ret = adjusted/lag(adjusted)-1,
log_ret = log(adjusted/lag(adjusted))) %>%
filter(date <= as.Date("2020-08-31"))
ret_weekly_end <- spx %>%
group_by(d = ceiling_date(date, "weeks")) %>%
filter(date == max(date)) %>%
ungroup() %>%
select(-d) %>%
mutate(ret = adjusted/lag(adjusted)-1,
log_ret = log(adjusted/lag(adjusted)))
ret_monthly_end <- spx %>%
group_by(d = ceiling_date(date, "months")) %>%
filter(date == max(date)) %>%
ungroup() %>%
select(-d) %>%
mutate(ret = adjusted/lag(adjusted)-1,
log_ret = log(adjusted/lag(adjusted)))
ret_quarterly_end <- spx %>%
group_by(d = ceiling_date(date, "quarter")) %>%
filter(date == max(date)) %>%
ungroup() %>%
select(-d) %>%
mutate(ret = adjusted/lag(adjusted)-1,
log_ret = log(adjusted/lag(adjusted)))
ret_yearly_end <- spx %>%
group_by(d = ceiling_date(date, "years")) %>%
filter(date == max(date)) %>%
ungroup() %>%
select(-d) %>%
mutate(ret = adjusted/lag(adjusted)-1,
log_ret = log(adjusted/lag(adjusted)))
ret_weekly_beg <- spx %>%
group_by(d = ceiling_date(date, "weeks")) %>%
filter(date == min(date)) %>%
ungroup() %>%
select(-d) %>%
mutate(ret = adjusted/lag(adjusted)-1,
log_ret = log(adjusted/lag(adjusted)))
ret_monthly_beg <- spx %>%
group_by(d = ceiling_date(date, "months")) %>%
filter(date == min(date)) %>%
ungroup() %>%
select(-d) %>%
mutate(ret = adjusted/lag(adjusted)-1,
log_ret = log(adjusted/lag(adjusted)))
ret_quarterly_beg <- spx %>%
group_by(d = ceiling_date(date, "quarter")) %>%
filter(date == min(date)) %>%
ungroup() %>%
select(-d) %>%
mutate(ret = adjusted/lag(adjusted)-1,
log_ret = log(adjusted/lag(adjusted)))
ret_yearly_beg <- spx %>%
group_by(d = ceiling_date(date, "years")) %>%
filter(date == min(date)) %>%
ungroup() %>%
select(-d) %>%
mutate(ret = adjusted/lag(adjusted)-1,
log_ret = log(adjusted/lag(adjusted)))
out <- tibble()
for (yr in c(3,5,10)) {
# calculate annualized mean return, volatility, SR ----
daily <- ret_daily %>%
filter(date >= Sys.Date()- years(yr)) %>%
summarise(mu = (1+(mean.geometric(1+ret)-1))^252-1,
sigma = sd(ret, na.rm = T)*sqrt(252),
log_mu = mean(log_ret, na.rm = T)*252,
log_sigma = sd(log_ret, na.rm = T)*sqrt(252),
SR = mu/sigma,
log_SR = log_mu/log_sigma)
weekly_end <- ret_weekly_end %>%
filter(date >= Sys.Date()- years(yr)) %>%
summarise(mu = (1+(mean.geometric(1+ret)-1))^52-1,
sigma = sd(ret, na.rm = T)*sqrt(52),
log_mu = mean(log_ret, na.rm = T)*52,
log_sigma = sd(log_ret, na.rm = T)*sqrt(52),
SR = mu/sigma,
log_SR = log_mu/log_sigma)
monthly_end <- ret_monthly_end %>%
filter(date >= Sys.Date()- years(yr)) %>%
summarise(mu = (1+(mean.geometric(1+ret)-1))^12-1,
sigma = sd(ret, na.rm = T)*sqrt(12),
log_mu = mean(log_ret, na.rm = T)*12,
log_sigma = sd(log_ret, na.rm = T)*sqrt(12),
SR = mu/sigma,
log_SR = log_mu/log_sigma)
monthly <- ret_monthly %>%
filter(date >= Sys.Date()- years(yr)) %>%
summarise(mu = (1+(mean.geometric(1+ret)-1))^12-1,
sigma = sd(ret, na.rm = T)*sqrt(12),
log_mu = mean(log_ret, na.rm = T)*12,
log_sigma = sd(log_ret, na.rm = T)*sqrt(12),
SR = mu/sigma,
log_SR = log_mu/log_sigma)
quarterly_end <- ret_quarterly_end %>%
filter(date >= Sys.Date()- years(yr)) %>%
summarise(mu = (1+(mean.geometric(1+ret)-1))^4-1,
sigma = sd(ret, na.rm = T)*sqrt(4),
log_mu = mean(log_ret, na.rm = T)*4,
log_sigma = sd(log_ret, na.rm = T)*sqrt(4),
SR = mu/sigma,
log_SR = log_mu/log_sigma)
yearly_end <- ret_yearly_end %>%
filter(date >= Sys.Date()- years(yr)) %>%
summarise(mu = mean.geometric(1+ret)-1,
sigma = sd(ret, na.rm = T),
log_mu = mean(log_ret, na.rm = T),
log_sigma = sd(log_ret, na.rm = T),
SR = mu/sigma,
log_SR = log_mu/log_sigma)
weekly_beg <- ret_weekly_beg %>%
filter(date >= Sys.Date()- years(yr)) %>%
summarise(mu = (1+(mean.geometric(1+ret)-1))^52-1,
sigma = sd(ret, na.rm = T)*sqrt(52),
log_mu = mean(log_ret, na.rm = T)*52,
log_sigma = sd(log_ret, na.rm = T)*sqrt(52),
SR = mu/sigma,
log_SR = log_mu/log_sigma)
monthly_beg <- ret_monthly_beg %>%
filter(date >= Sys.Date()- years(yr)) %>%
summarise(mu = (1+(mean.geometric(1+ret)-1))^12-1,
sigma = sd(ret, na.rm = T)*sqrt(12),
log_mu = mean(log_ret, na.rm = T)*12,
log_sigma = sd(log_ret, na.rm = T)*sqrt(12),
SR = mu/sigma,
log_SR = log_mu/log_sigma)
monthly <- ret_monthly %>%
filter(date >= Sys.Date()- years(yr)) %>%
summarise(mu = (1+(mean.geometric(1+ret)-1))^12-1,
sigma = sd(ret, na.rm = T)*sqrt(12),
log_mu = mean(log_ret, na.rm = T)*12,
log_sigma = sd(log_ret, na.rm = T)*sqrt(12),
SR = mu/sigma,
log_SR = log_mu/log_sigma)
quarterly_beg <- ret_quarterly_beg %>%
filter(date >= Sys.Date()- years(yr)) %>%
summarise(mu = (1+(mean.geometric(1+ret)-1))^4-1,
sigma = sd(ret, na.rm = T)*sqrt(4),
log_mu = mean(log_ret, na.rm = T)*4,
log_sigma = sd(log_ret, na.rm = T)*sqrt(4),
SR = mu/sigma,
log_SR = log_mu/log_sigma)
yearly_beg <- ret_yearly_beg %>%
filter(date >= Sys.Date()- years(yr)) %>%
summarise(mu = mean.geometric(1+ret)-1,
sigma = sd(ret, na.rm = T),
log_mu = mean(log_ret, na.rm = T),
log_sigma = sd(log_ret, na.rm = T),
SR = mu/sigma,
log_SR = log_mu/log_sigma)
# create overview table ----
o <- bind_rows(daily %>% mutate(freq = "daily"),
weekly_end %>% mutate(freq = "weekly end"),
monthly_end %>% mutate(freq = "monthy end"),
quarterly_end %>% mutate(freq = "quarterly end"),
yearly_end %>% mutate(freq = "yearly end"),
weekly_beg %>% mutate(freq = "weekly beg"),
monthly_beg %>% mutate(freq = "monthy beg"),
quarterly_beg %>% mutate(freq = "quarterly beg"),
yearly_beg %>% mutate(freq = "yearly beg"))
out <- bind_rows(out, o %>% mutate(risk = yr))
}
simple <- bind_rows(out) %>%
select(mu, sigma, SR, freq, risk) %>% mutate(calc = "simple")
logari <- bind_rows(out) %>%
select(mu = log_mu, sigma = log_sigma, SR = log_SR, freq, risk) %>% mutate(calc = "log")
bind_rows(simple, logari) %>%
# figures we get from https://www.morningstar.com/indexes/spi/spx/risk
mutate(mu_ms = case_when(risk == 10 ~ 0.1115,
risk == 5 ~ 0.108,
risk == 3 ~ 0.0896),
sigma_ms = case_when(risk == 10 ~ 0.1338,
risk == 5 ~ 0.148,
risk == 3 ~ 0.1751),
SR_ms = case_when(risk == 10 ~ 0.92,
risk == 5 ~ 0.77,
risk == 3 ~ 0.66)) %>%
# differences
mutate(delta_mu = mu_ms - mu,
delta_sigma = sigma_ms - sigma,
delta_SR = SR_ms - SR)
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