Calculating Long-Short Portfolio Returns and Sharpe Ratio
Summary
The discussion explains how to aggregate profit and loss across long and short holdings to calculate a portfolio return relative to total starting capital. It also clarifies that a stock’s beta does not become negative merely because the position is short; position direction affects portfolio exposure, not the stock’s beta itself. The standard Sharpe ratio applies to the portfolio’s return series, with the risk-free rate and portfolio volatility used in the usual way.
The answer recommends judging the combined portfolio against a benchmark, while comparing long and short books separately can help diagnose their contributions. It does not provide a method for including margin or borrow costs, and the advice is limited: it does not discuss detailed financing conventions, leverage, or risk attribution. The discussion also refers to an example spreadsheet that is not available in the text.
Key ideas
- Aggregate long and short position P&L, then divide by total starting portfolio value to calculate return.
- A security’s beta does not change sign when the investor takes a short position.
- Calculate Sharpe from the long-short portfolio’s returns, risk-free rate, and return volatility.
- Use a benchmark to assess the combined portfolio, and compare books separately when evaluating their contributions.
- The answer leaves margin and borrowing costs unresolved.
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# Calculation of Returns and Risk Metrics for L/S Portfolio
# Calculation of Returns and Risk Metrics for L/S Portfolio
I am trying to build a test for a long/short portfolio. I am aiming for market neutral and have put together a long portfolio as well as a short portfolio (see below). However, I am not sure if I am doing this correctly. The specific questions I have are:
- Will betas be negative for the short book?
- How would I calculate returns for the L/S portfolio
- How would you factor in margin/borrowing costs in a model like this?
- Is there a different way that I need to calculate sharpe ratio since this is a L/S portfolio
- How should I use the benchmark (I have read elsewhere that the benchmark should be long for the long portfolio, short the same benchmark for the short portfolio, and then long a cash investment)?
- Is there anything else that I should be considering here?
## Answer by Nikos (score 2)
https://quant.stackexchange.com/a/15706
I will try and give some feedback on your questions.
- Will betas be negative for the short book?
Not necessarily, no. The beta of a stock is not related to you having a long or a short position to it.
- How would I calculate returns for the L/S portfolio
Assuming your total portfolio including cash is $V_{0}$, and each line has made $PNL_{i}$, then your long book ($L$) would make $P_{L}=\sum_{i \in L} PNL_{i}$ and your short book ($S$) $P_{S}=\sum_{i \in S} PNL_{i}$. Your total return would be $\frac{V_{0}+P_{L}+P_{S}}{V_{0}}$. In your excel picture, I would devide the column GQ with the total portfolio value (I think it is 1M) and this would be each line's performance contribution. If you sum that, then you end up to your portfolio's return.
- How would you factor in margin/borrowing costs in a model like this?
I do not really know about this.
- Is there a different way that I need to calculate sharpe ratio since this is a L/S portfolio
Well the sharpe ratio is a function of the portfolio returns and its standard deviation, $S=\frac{R_{p}-R}{\sigma}$, where $R_{p}$ is your return, $R$ is the risk free rate, and $\sigma$ is your portfolio's standard deviation. So I don't think you need to change the computation. Most of the L/S hedge funds report on both Sharpe and Sortino ratio.
- How should I use the benchmark (I have read elsewhere that the benchmark should be long for the long portfolio, short the same benchmark for the short portfolio, and then long a cash investment)?
I am a little puzzled with your suggestion. The aim of the benchmark is to compare your portfolio in total with the benchmark. It doesn't really matter if your longs are doing fine, so you are overperforming the benchmark. If your shorts are very bad you might be net negative. But you can certainly consider this to test your longs vs your shorts.
Hope this helps.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.