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Hedge ratio for a long position

Market makingEasy

You are long $100$ lots of $A$ . Per lot, daily changes have $Var (A) = 36$ , $Var (B) = 25$ and $Cov (A, B) = 15$ . How many lots of $B$ should you sell to make the variance of the position as low as possible? Give a whole number of lots.

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Hint

The best hedge per lot is the covariance over the variance of the hedge.

Solution

The hedge per lot is $\frac{15}{25} = 0.6$ .
For the whole position that is $100 \times 0.6 = 60$ .

Answer: $60$

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