# 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?

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

• Not an answer, just a heads up: log-returns are not additive across assets but are additive over time, while percentage returns are additive across assets but not over time. So here you would be considering percentage returns. Commented May 3 at 19:58
• Hi, both edits seem fine. Yes, when there are positive returns on a short portfolio, they are deducted from your positive return components. Also, what is the difference between 28.02 and 31.02? Commented May 4 at 9:21
• Hi, okay that helps me a lot. These should illiustrate different months, so january 31 and february 28. Commented May 4 at 10:13
• I missed this out, but you don't actually need capital to invest in a long short, because usually the cashflows from the short are used to finance the longs. Commented May 4 at 11:15
• Like for example, if you short 0.5\$ worth of stock, you can use that same amount to pay for the long. Commented May 4 at 11:16

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?

• Do you happen to know which paper we should cite for using "long-short portfolio"? Commented May 28 at 10:22
• @Aqqqq there are many papers on equity long-short you can cite. You can do a search on papers that are published in peer-reviewed journals from the Big 3 - JF, JFE and RFS. Commented May 28 at 10:38