Relating Future Volatility with Realized Volatility

RV vs FV

getSymbols("^GSPC", from="1950-01-01")
p = 10
a = na.omit(merge( volatility(GSPC, n=p)*100, lag(volatility(GSPC, n=p), k=-p)*100 ))
names(a) = c("hv", "rv")
medianvalues = c()
meanvalues = c()
maxvalues = c()
minvalues = c()
keys = c()
for ( x in seq( 0, max(a$hv), 2 ) )
{
	x2 = x + 2
	y = median(a[a$hv >= x & a$hv <x2, 2])
	if ( !is.na(y) && y != -Inf && y != Inf )
	{
		y = median(a[a$hv >= x & a$hv <x2, 2])
		medianvalues = c(medianvalues, y)

		y = mean(a[a$hv >= x & a$hv <x2, 2])
		meanvalues = c(meanvalues, y)

		y = min(a[a$hv >= x & a$hv <x2, 2])
		minvalues = c(minvalues, y)


		y = max(a[a$hv >= x & a$hv <x2, 2])
		maxvalues = c(maxvalues, y)

		
		keys = c(keys, x)
	}
}

buckets = c(keys, medianvalues)
bucketm = na.omit(matrix(buckets, nrow=length(keys)))
scatter.smooth(bucketm, xlab=paste(p, "-day Annualized Historical Volatility", sep=""), ylab=paste(p, "-day Annualized Future Volatility", sep=""), pch=16, col="dodgerblue3")
m = lmrob(bucketm[,2] ~ bucketm[,1])
abline(m, col="dodgerblue3")
median_equation = paste("y = ", round(m$coefficients[1], 2), " + x(", round(m$coefficients[2], 2), ")", sep="")

buckets = c(keys, maxvalues)
bucketm = na.omit(matrix(buckets, nrow=length(keys)))
points(bucketm, col="red", pch=13)
m = lmrob(bucketm[,2] ~ bucketm[,1])
abline(m, col="red")
max_equation = paste("y = ", round(m$coefficients[1], 2), " + x(", round(m$coefficients[2], 2), ")", sep="")


buckets = c(keys, minvalues)
bucketm = na.omit(matrix(buckets, nrow=length(keys)))
points(bucketm, col="green", pch=13)
m = lmrob(bucketm[,2] ~ bucketm[,1])
abline(m, col="green")
min_equation = paste("y = ", round(m$coefficients[1], 2), " + x(", round(m$coefficients[2], 2), ")", sep="")


legend("bottomright", 
	c(paste("Median:", median_equation), paste("Max:", max_equation), paste("Min:", min_equation)), 
	col=c("dodgerblue3", "red", "green"), 
	lty=1,
	pch=c(16, 13, 13) ,
	cex=.7)