Actuarial Outpost > MFE ASM Practice Exam#1, Problem 4
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#1
05-07-2007, 11:12 PM
 nkt Member Join Date: Feb 2007 Posts: 36
ASM Practice Exam#1, Problem 4

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.
#2
05-08-2007, 07:21 AM
 mingchenckm Member SOA Join Date: Feb 2007 Posts: 97

you have not annualized it right?
If annualized, the term h should be placed outside the square sign.
#3
05-08-2007, 11:03 AM
 CaptainAwesome Member Join Date: Aug 2006 Favorite beer: Stella Artois Posts: 173

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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