Sizing a position to hit a volatility target

Question

You want your portfolio to run at a target volatility of $10\%$ per year. You want to hold an asset whose own volatility is $40\%$ per year.

What fraction of capital do you allocate? What if instead the asset's vol were only $5\%$ ?

Accepted Answer

Portfolio volatility from a single position is (its weight) 	imes (the asset's volatility). Set that equal to your target and solve for the weight w: w 	imes \sigma{	ext{asset}} = \sigma{	ext{target}} \;\Longrightarrow\; w = \frac{\sigma{	ext{target}}}{\sigma{	ext{asset}}}. For the 40\%-vol asset: w = \frac{10\%}{40\%} = 0.25. Put 25\% of capital in it (the rest in cash); the position then contributes exactly 10\% vol. With \1{,}000{,}000, that is a \250{,}000 position. If instead the asset's vol were only 5\%: w = \frac{10\%}{5\%} = 2.0, meaning you'd need 2	imes leverage, borrow to h…

Sizing a position to hit a volatility target

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