Calculating Volatility and Sharpe Ratio for Long-Short Portfolios

Summary

The document explains that a long-short portfolio’s volatility and Sharpe ratio can be computed from its excess-return or profit-and-loss stream, as for other portfolios. First account for financing, including the difference between cash borrowing and lending rates and any instrument-specific shorting fees, then scale P&L by the chosen risk capital. Volatility is the standard deviation of those excess returns, annualized with the appropriate factor; the Sharpe ratio is annualized average return divided by annualized volatility.

A second answer distinguishes calculations based on gross exposure from those based on net asset value. Gross-based volatility can be translated into NAV volatility using leverage. Leverage does not change the Sharpe ratio when return and volatility are measured on the same basis, because the scaling cancels. The document offers general calculation guidance but does not specify a return frequency, annualization convention, risk-capital definition, or a particular estimator for a portfolio’s P&L series.

Key ideas

• Calculate excess returns after including financing costs and shorting fees.
• Scale portfolio P&L by the selected risk capital before estimating return volatility.
• Annualize the standard deviation of excess returns using a factor appropriate to the observation frequency.
• Compute the Sharpe ratio from annualized average return and annualized volatility.
• Use the same gross or NAV basis for returns and volatility so leverage scaling cancels in the Sharpe ratio.

Tags

# volatilty and Sharpe Ratio of long-short portfolio


# volatilty and Sharpe Ratio of long-short portfolio












What is the proper way to calculate volatility for the long short portfolio?

if calculated in a standard way the offsetting positions are driving it down. How about Sharpe Ratio? that has an impact on the SR either

## Answer by Chris Taylor (score 1, accepted)

https://quant.stackexchange.com/a/30254

You calculate them the same way that you would for any other pnl stream. First calculate the excess returns, i.e. the P&L after accounting for financing (for a long-short portfolio, your financing includes the difference between the rates at which you can borrow and lend cash, as well as any fees for shorting particular instruments) divided by your risk capital.

Then the volatility is the standard deviation of your excess returns, multiplied by the appropriate annualizing factor.

Your Sharpe ratio is the average annualized return, divided by the annualized volatility.

## Answer by user18489 (score 1)

https://quant.stackexchange.com/a/30255

You can either estimate volatility based on gross exposure or NAV. Usually you estimate it on gross and then use your leverage to estimate NAV volatility. Sharpe ratio is not impacted by leverage - returns and volatility should both be estimated on the same basis (NAV/gross) so they cancel out.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.