Erratum to ON the variance of the error associated to the squared return as proxy of volatility: [Applied Financial Economics Letters, 2007, 3, 255–7]

In the above publication, we derive, under two different stochastic volatility models, the expression of the variance of the error associate to the use of the squared return as proxy of daily volatility.

On the very last line of p. 256 we have an expression for the expectation of the the square of z_t

This is correct if z_t had not been standardized. Given that z_t is standardized as we describe at the end of Section II, this expectation should be unity (this mistake has been found by Prof. David Giles). On p. 257 it then follows that the expection of e_t is zero and we have unbiasedness. This, of course, then affects and simplifies the calculation for the variance that follows. In particular, we have that, if SV-t model (M2) holds, the correct formula for the variance of e_t , is

We note that a typical value for the parameter p is 7. With this value we have

We can conclude that heavier tails for the returns worse the performance of squared return as proxy of volatility. So, we can confirm the original message of the article.