Calculating Returns and Factor Regressions for Long-Short Portfolios
Summary
The discussion describes how to calculate periodic returns for a long-short portfolio formed from high- and low-ranked asset groups. With equal allocations to the long and short sides, combine the two leg returns using their portfolio weights, reversing the sign of the short leg’s return exposure. This calculation should be repeated for each period before estimating average return and volatility or calculating a Sharpe ratio. The answer also says to annualize monthly return and volatility when reporting an annual Sharpe ratio.
For factor analysis, regress the long-short return series on contemporaneous factor returns from matching periods. The question concerns portfolios formed by ranking assets, including an ESG score example, but the answer does not resolve how to handle every weighting convention or clarify the poster’s numerical setup. The stated calculation assumes a particular allocation between portfolio legs; results depend on the strategy’s actual weights and return construction.
Key ideas
- Calculate each period’s long-short return from the weighted returns of the long and short legs.
- The short leg’s return contributes with the opposite sign to the portfolio return.
- Compute Sharpe ratios from the resulting return series and annualize consistently when reporting annualized measures.
- Regress portfolio returns against factor returns from the same time periods.
- The example assumes a specified allocation across the long and short sides.
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Full text
# How to create a long-short portfolio on an academic basis # How to create a long-short portfolio on an academic basis This question may have been asked before, but unfortunately the answers didn't help me very much. It's about how to create long short portfolios. In the papers you often read that they have created portfolios based on indicators depending on their quantiles. Often a portfolio is like top-bottom. I have done something similar. I have 4 portfolios (each equally weighted and market value weighted) and want to build a long-short portfolio from the best 10% and the worst 10% (based on their esg score). But I'm not sure how to determine the returns correctly. My current procedure is that I subtract the monthly portfolio return " top" from my monthly portfolio return "bottom". I then calculate my Sharpe ratio from these monthly returns and regress these on my FF factors. Is this correct? Or would I still have to include the individual weightings of the portfolios? E.g. portfolio a 31.12. Initial portfolio value: 1 31.01. Portfolio value: 1.2, return = 20% 28.02. Portfolio value: 1.6, return = 33% E.g. portfolio b 31.12. Initial portfolio value: 1 31.01. Portfolio value: 1.5, return = 50% 28.02. Portfolio value: 1.8, return = 20% My approach would be to determine the return of my long short portfolio as follows: 31.01: r = 20% - 50%= -30%. 28.02. r = 33% - 20 % = 13% Is this correct if you do the same for the following months? Thank you very much in advance for your answers Best regards Hi Kai, thank you very much for your answer. I posted a picture with me procedure. Let's assume, that i invest 1 dollar in my long (top) portfolio and 1 dollar in my short (bottom) portfolio as initial starting capital. So my return of my LS-Portfolio is just?: 31.01.: r = 0,5 * 0,15 - 0,5 * 0,05 31.02.: r = 0,5 * 0,1 - 0,5 * 0,13 ## Answer by KaiSqDist (score 1, accepted) https://quant.stackexchange.com/a/79245 > My current procedure is that I subtract the monthly portfolio return " top" from my monthly portfolio return "bottom". I then calculate my Sharpe ratio from these monthly returns and regress these on my FF factors. Is this correct? Or would I still have to include the individual weightings of the portfolios? From what I know about long-short decile portfolios, they are equal-weighted to compute their overall returns. For example, if you are short (long) top (bottom) 10% percentiles of that asset universe, with returns of -10% (15%), then the overall portfolio return is just $$ 0.5 * 15\% - 0.5 * (-10\%) = 12.5\% $$ This calculation has to be done for all periods before computing an average monthly return and monthly volatility, annualized before computing a Sharpe ratio (which by then would be an annual Sharpe ratio). For the FF factors, the returns should be regressed against these factors across time, but take note that these are contemporaneous regressions and that the factors should be at the same time as the returns themselves (as compared to lead-lag regressions used in predictions). I could not really understand how you represented your numbers, maybe you can organize them into a table for better illustration?
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