ASM Practice Exam#1, Problem 4

nkt · #1 05-07-2007, 11:12 PM

For a delta-hedged portfolio, the stock price is 40, the stock's volatility is .2 and the option's gamma is .02. Estimate the annual variance of the portfolio if it's rehedged every half-month. The answer is given to be 0.0341.

I don't understand why the answer is not
Var(R[1/24, 1]) = .5*[(40^2)*(.2^2)*.02*(1/24)]^2=.001422

I am looking at the textbook and that seems to be the formula. Any comments will be much appreciated. Thanks.

mingchenckm · #2 05-08-2007, 07:21 AM

you have not annualized it right?
If annualized, the term h should be placed outside the square sign.

CaptainAwesome · #3 05-08-2007, 11:03 AM

On page 431 in the example where they compute the variance for rehedging daily, the daily variance is given by $\frac{1}{2}(S^{2}\sigma^{2}\Gamma \frac{1}{365})^{2}$ . The yearly variance is $\frac{1}{2}(S^{2}\sigma^{2}\Gamma \frac{1}{365})^{2}365 = \frac{1}{2}(S^{2}\sigma^{2}\Gamma)^{2}\frac{1}{365 }$ . So your answer is the half-month variance.

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