Adjusted Realized Volatility

Question

Suppose these are the returns (1000 rows):

1-a
2-b
3-c

I want to calculate adjusted volatility: drop first return calculate realized volatility, then drop the second one and calculate the realized volatility and etc. if you have n returns you will have n realized volatility.

Volatility1 = b*b+c*c
Volatility2 = a*a+c*c
Volatility3 = a*a+b*b

I can handle it with for loop, but is there any other way?

`Volatility3 = a*a+b*b`, no? – Khashaa Feb 26 '15 at 02:06 — Khashaa, Feb 26 '15 at 02:06

score 1 · Accepted Answer · answered Feb 26 '15 at 02:22

1

You can efficiently calculate it by sum(x*x)-x*x

#dummy data
x <- rnorm(1000)
#vectorized
f1 <- function(x) sum(x*x)-x*x
#for loop 
f2 <- function(x){
    n <- length(x)
    rv <- rep(NA, n)
    s <- x*x
    for(i in 1:n)
    {rv[i]=sum(s[-i])}
    rv
}
rbenchmark::benchmark(f1(x), f2(x))[1:3]
   test replications elapsed
1 f1(x)          100    0.0
2 f2(x)          100    3.1

answered Feb 26 '15 at 02:22

Khashaa

7,293
2
21
37

creative solution, but you use the loop. – Soheil Feb 27 '15 at 01:11
`f1` doesn't use any loop. I included `f2` just for comparison. – Khashaa Feb 27 '15 at 01:14

score 0 · Answer 2 · answered Feb 26 '15 at 02:21

0

Does it make sense? Maybe the function is wrong, but the structure seems to work.

Is volatility standard deviation?

            x <- rnorm(1000, sd=2)
            vol <- sapply(2:length(x), function(i) {
                sd(x[0:i])
            })

answered Feb 26 '15 at 02:21

incitatus451

163
1
6

volatility is not the standard deviation – Soheil Feb 27 '15 at 01:10

Adjusted Realized Volatility

2 Answers2