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Calculating Sharpe Ratios for Long-Short Portfolios

Article Quant Q&A · Author: dydydy
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Summary

The document explains how to calculate returns and risk for a long-short portfolio using asset weights. Portfolio return is the weighted sum of component returns, with short positions represented by negative weights and long positions by positive weights. Portfolio volatility depends on the assets’ individual volatilities and their correlations, rather than on a simple average of the long and short returns.

It illustrates the calculation with a two-stock example, using a short position in one stock and a larger long position in another, then computes Sharpe as excess portfolio return over the risk-free rate divided by portfolio standard deviation. For daily observations, it gives the common approximate annualization convention of multiplying daily Sharpe by the square root of the number of trading days in a year. The example assumes stated weights and inputs; actual results also depend on financing, transaction costs, borrow costs, rebalancing, and consistent return and risk-free-rate frequencies.

Key ideas

  • Portfolio return is computed by multiplying each asset return by its signed portfolio weight and summing the results.
  • Portfolio volatility depends on asset volatilities and correlations as well as position weights.
  • Sharpe ratio divides portfolio excess return over the risk-free rate by portfolio standard deviation.
  • Daily Sharpe is commonly annualized by multiplying by the square root of trading days per year.

Tags

EquitiesPortfolio constructionRisk managementStatistics
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# long short portfolio sharpe ratio


# long short portfolio sharpe ratio












What is the proper way to caluclate sharpe ratio for the long short portfolio? When I calculate daily return with no cost, I use this formula: (return for long k.mean()+ (-1)*(return for short k.mean())/2 So can I use this formula to get daily sharpe ratio?: all daily return with no cost/all daily return's std If this is wrong, what is the right formula? And how can I get the annualized sharpe ratio of long short portfolio? I tried this: one daily return/all daily return's std for each date and divide by date number

## Answer by Quant_in_becoming (score 1)

https://quant.stackexchange.com/a/70920

Let's assume stock "A" yields a 5% return and stock "B" yields a 6% return, they both have standard deviations of 10% (per annum) and a correlation factor of 0.5. You decide to short stock "A" and long stock "B", let's assume you short "A" for an equivalent of 50% of your portfolio's value and use the proceeds (including your portfolio's value) to buy "B" for an equivalent of 150% of your initial margin. You have weights -50% in A and 150% in B.

By doing -50% * 5% + 150% * 6%, you will find your portfolio's return. Your standard deviation for only two stocks can be simply calculated by finding the square root of the "portfolio variance formula", keep in mind that you must know your correlation factor.

return : 6.5%

std : 3.5%

risk free rate: (let's say 2%)

Then, Sharpe = (6.5% - 2%) / 3.5% = 1.29

If your values are daily, then the sharpe ratio can be roughly annualized by multiplying with the square root of 252 (number of trading days).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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