Risk-Free Rates and Long-Short Portfolio Excess Returns
Summary
The document explains how risk-free rates affect long-short portfolio returns. If the long and short legs have equal funding amounts, subtracting the risk-free rate from each leg before combining them gives the same result as calculating the long-short return first: the funding terms cancel. A long-short portfolio can therefore be viewed as zero-cost when short-sale proceeds fund the long position.
It contrasts this with a standalone long investment, whose excess return accounts for the opportunity cost or borrowing cost of capital. The explanation uses factor portfolios as context: market returns are commonly expressed above the risk-free rate, while long-short factors such as size and value are treated as having no net funding cost. The cancellation depends on the portfolio construction and equal funding; the document does not discuss cases with unequal leg financing, transaction costs, or other implementation details.
Key ideas
- For equally funded long and short legs, the risk-free rate cancels when calculating the portfolio return.
- A long-short position can be zero-cost when short-sale proceeds fund the long position.
- Standalone long returns are often measured relative to the risk-free rate to reflect the cost of capital.
- Market factors and long-short factors can require different excess-return conventions.
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Full text
# Long Short excess returns? # Long Short excess returns? When calculating the long-short excess returns for a portfolio. Do I have to first calculate the excess returns of the long and short leg and then add them together or first calculate the average long short return and then subtract the risk free rate? So either - Calculate average returns for both the long and short portfolio. - Calculate excess returns for the long and short portfolio separately. - Calculate the long short return by adding them together. OR - Calculate average returns for both the long and short portfolio. - Calculate the average long short portfolio return - Calculate the excess return for the long short portfolio. Many thanks in Advance! ## Answer by Kevin (score 2) https://quant.stackexchange.com/a/51581 You're right, there is no difference between the long-short (LS) portfolio between two returns or two excess returns, the risk-free rate cancels out. But there is an economic reason why we consider returns, excess returns and long-short returns. A simple raw return does not tell you much as you need to incorporate how much it cost you to obtain that performance. If a stock returns 1% but the risk-free rate is 2%, then your real return -1% after considering that you first need to borrow $1 to invest into the stock. So, the raw stock return really doesn't tell you much if you don't subtract the cost of having this return. The long-short portfolio is different. Here, you gain $1 from selling one portfolio and invest this \$1 into the long portfolio. Hence, people refer to a long-short portfolio as ``zero-cost portfolio'' because you don't need to borrow \$1 at the risk-free rate (the funding cost is covered by the selling of the short portfolio). Equivalently, you can of course gain \$0.5 from selling one portfolio and investing 50 cent in the long portfolio. It doesn't matter. An example is when you run a simple time series regressions using the Fama-French factors. You never regress the raw returns on the factors, you always first subtract the risk-free rate because this is the true performance an investor would have by investing in this particular portfolio. Similarly, that's why Fama & French subtract the risk-free rate from the market portfolio ... one needs to borrow \$1 to be able to obtain the market return. The other factors, SMB and HML (1993) or CMA, RMW (2015) or UMD (1997) etc. are all long-short portfolios and hence do not include the risk-free rate as they have zero funding cost.
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