Equity Index Standard Deviation

Summary

Equity Index (Hang Seng Index of Hong Kong) and Standard Deviation Relationship

R Libraries

library(tidyverse)
library(quantmod)
library(ggplot2)

Preparation of data

Direct download by getSymbols

tickers <- c("^HSI","^GSPC")
getSymbols(Symbols = tickers,
           src = "yahoo",
           index.class = "POSIXct",
           from = "1997-01-01")

## [1] "^HSI"  "^GSPC"

Drop the NA and add daily return column, daily standard deviation (SD) and annualised SD

GSPC.new <- na.omit(GSPC)
GSPC.new <- merge(GSPC.new, dailyReturn(GSPC.new$GSPC.Adjusted))
colnames(GSPC.new)[7] <- "GSPC.adj.ret"
GSPC.new <- merge(GSPC.new,rollapply(GSPC.new$GSPC.adj.ret, 252, sd))
colnames(GSPC.new)[8] <- "GSPC.adj.std"
GSPC.new <- merge(GSPC.new, GSPC.new$GSPC.adj.std*sqrt(252))
colnames(GSPC.new)[9] <- "GSPC.adj.std.annualised"

HSI.new <- na.omit(HSI)
HSI.new <- merge(HSI.new, dailyReturn(HSI.new$HSI.Adjusted))
colnames(HSI.new)[7] <- "HSI.adj.ret"
HSI.new <- merge(HSI.new,rollapply(HSI.new$HSI.adj.ret, 252, sd))
colnames(HSI.new)[8] <- "HSI.adj.std"
HSI.new <- merge(HSI.new, HSI.new$HSI.adj.std*sqrt(252))
colnames(HSI.new)[9] <- "HSI.adj.std.annualised"

Convert to tibble for easier plotting

HSI.new.tbl <- as_tibble(fortify(HSI.new)) #fortify to keep the datetime index

Plot

p <- ggplot(HSI.new.tbl, aes(x=Index,y=HSI.adj.std.annualised))
p+geom_line()

avg10yr <- mean(HSI.new$HSI.adj.std.annualised["2011/2022"])
avg15yr <- mean(HSI.new$HSI.adj.std.annualised["2006/2022"])
avg20yr <- mean(HSI.new$HSI.adj.std.annualised["2001/2022"])
avg25yr <- mean(na.omit(HSI.new$HSI.adj.std.annualised["1997/2022"]))
p+geom_line()+
  geom_hline(yintercept = avg10yr, color = "red")+
  geom_hline(yintercept = avg15yr, color = "blue")+
  geom_hline(yintercept = avg20yr, color = "green")+
  geom_hline(yintercept = avg25yr, color = "black")

HSI.new2.tbl <- HSI.new.tbl %>% 
  pivot_longer(cols = c("HSI.Adjusted","HSI.adj.std.annualised"), 
               names_to ="Series", 
               values_to = "Values") %>% 
  select(c(Index,Series,Values))

p1 <- ggplot(HSI.new2.tbl, aes(x=Index,y=Values))
p1 + geom_line() +
  facet_grid(Series ~ ., scales = "free") +
  scale_x_datetime(name = "Date", date_breaks = "1 year", date_labels = "%Y")