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Minimum variance hedge

Market makingMedium

A market maker holds $30$ units of contract A. Price changes of A have a standard deviation of $5$ , those of hedging contract B have a standard deviation of $2$ , and their correlation is $0.8$ . How many units of B should be sold to minimize the variance of the combined position?

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Hint

The best hedge per unit is correlation times the ratio of the standard deviations.

Solution

The hedge ratio per unit of A is $0.8 \times 5 \div 2 = 2$ .
The position holds $30$ units of A.
The hedge is $30 \times 2 = 60$ units of B.

Answer: $60$

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