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Risk left after the best hedge

Market makingMedium

Inventory has a daily P&L standard deviation of $50$ . A hedge instrument has correlation $0.8$ with it, and you size the hedge to minimise variance. What is the standard deviation of the hedged P&L? Give a number.

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Hint

The best hedge leaves the share $1 - ρ^{2}$ of the variance.

Solution

The share of variance left is $1 - 0. 8^{2} = 0.36$ .
The standard deviation scales by its square root, $0.6$ .
The hedged figure is $50 \times 0.6 = 30$ .

Answer: $30$

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