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Choosing a Risk-Free Rate That Matches the Return Interval

Article Quant Q&A · Author: ThereGoesMyMoney
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Summary

The document addresses a common CAPM input question: whether the S&P 500 or a Treasury yield should serve as the risk-free rate. Its answer distinguishes the market portfolio, often represented by a broad equity index, from the risk-free asset used in the model. It recommends government bond rates as a practical proxy and says the bond maturity should correspond to the interval over which returns are measured.

For example, a quarterly Security Characteristic Line would call for a three-month government rate rather than automatically using a ten-year yield. This gives a useful rule for aligning the financing benchmark with the model’s time index. The response is brief and does not discuss differences among government instruments, credit or liquidity risks, or alternative conventions for matching rates to periods. It also does not establish that any government yield is perfectly risk-free; the recommendation is a modeling choice for CAPM analysis.

Key ideas

  • The S&P 500 represents the market portfolio in a typical CAPM setup, not the risk-free asset.
  • Government bond yields can serve as practical proxies for the risk-free rate.
  • The chosen bond maturity should match the return interval used in the model.
  • A quarterly return analysis can use a three-month government rate rather than defaulting to a ten-year yield.

Tags

EquitiesFixed incomeRisk managementStatistics
Full text
# What is considered the risk free rate?


# What is considered the risk free rate?












I see some place reference the S&P 500 index (SPY) as the risk-free rate and other place reference the 10-year Treasury yield as the risk-free rate. Which one is the correct one?

## Answer by Bernd (score 1)

https://quant.stackexchange.com/a/40441

I assume you want to use CAPM that ralates e.g. a single stock to "the market" (often take to be the S&P500). In this model you need a "risk free rate". I think you do not make a mistake if you take government bonds as the risk free rate. But do not simply use 10Y. The maturity should depend on the time index t in the Security Characteristic Line. If it is a quarterly index use the 3M government bond rate.

See this link for the equation I am refering to:

https://en.wikipedia.org/wiki/Security_characteristic_line

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.