Choosing a Risk-Free Rate for Monthly Fund Performance Metrics

# How should I calculate monthly Risk free rate?


# How should I calculate monthly Risk free rate?












I'm doing an analysis of ETFs and mutual funds that track the same index (US funds only). Everything is calculated on monthly returns for the period 2019-2023 (5Y).

Currently, I have calculated beta (COVAR/VAR). Now I want to calculate beta and Sharpe etc.

However, I don't know what risk free rate to calculate for further calculations. I've seen a lot of different ways to do it.

My idea now is to take, for example, 5 years treasury bonds monthly data and calculate an average of that - and have it in a single cell for calculations.

Is that the right way to do it? Or should it be done differently?

## Answer by AKdemy (score 7)

https://quant.stackexchange.com/a/82140

In finance, government bond yields are generally not the preferred risk-free rate, especially in modern textbooks and practical applications. This is particularly true in contexts such as pricing (e.g., derivatives), risk management (e.g., IRRBB), and cash flow discounting.

Nowadays, the (Risk Free Rate) RFR swap rates (SOFR for USD, €STR for EUR for example) are used, but you usually have a choice for other swap curves (legacy reasons) like different OIS swaps (e.g. the Fed funds swaps).

Scholarly work

There are several papers on why treasuries are not a good proxy for the risk free rate (usually based on convenience yield arguments). See for example Decomposing Swap Spreads by Feldhütter et al..

Practitioners

Bloomberg for example does not even offer government bond curves as a choice for the risk free interest rate in all of their derivatives pricers (OVME, OVML, SWPM, DLIB etc.)

Clearing houses and exchanges

It's also standard for clearing houses and exchanges like LCH and CME to use these RFR rates for discounting (done with risk free rate) and Price Alignment Interest (PAI) calculations, which is the interest rate paid on the collateral that is held.

For example, transition to €STR happened in July 2020 on LCH Group and the CME; Link for CME announcement

Regulators

Regulators also don't see government curves as the appropriate risk free rates. See for example:

EBA final report

> ..., since there is no universal risk-free spot rate curve per currency, it is left to institutions to select it, in line with paragraph 115(n) of the 2018 EBA GL.

Now 115(n) is not very specific and states that

> An appropriate general ‘risk-free’ yield curve per currency should be applied (e.g. swap rate curves). That curve should not include instrument-specific or entity-specific credit spreads or liquidity spreads.

However, the BIS is a bit more specific and writes

> discount factors must be representative of a risk free zero-coupon rate. An example of an acceptable yield curve is a secured interest rate swap curve

Although ESTR is unsecured, (explanation for this choice can be found on the ECB Website) it is the used as the official risk free rate for price alignment interest and discounting at major CCPs and it would be difficult to argue why one would not use €STR based on my teams opinion for IRRBB computation.

Books

Hull; Options,Futures and Other Derivatives, 8th edition P.77 also explains why treasury rates are not recommended as risk free rates because:

> .. dealers argue that the rate implied by treasury rates is artificially low, because they must be purchased by institutions for regulatory purposes (emphasis LCR, NSFR,...) and some more reasons

## Answer by phdstudent (score 4)

https://quant.stackexchange.com/a/82137

It's super easy ... the standard is to just use the risk-free rate from Fama-French 1993. (my apologies I cited and linked the wrong paper before).

The paper simply states: "RF is the 1-month bill rate". Page 10.

The data is available for free here: Fama-French 3-factors.

The last column is the risk-free rate. As written on the data file:

> The 1-month TBill rate data until 202405 are from Ibbotson Associates. Starting from 202406, the 1-month TBill rate is from ICE BofA US 1-Month Treasury Bill Index.

Now you may ask what is the Ibbotson Associates? You can find that risk-free rate on the SBBI yearbooks that got discontinued in 2024, and that is why the source for the data change.

## Answer by Richard Hardy (score 3)

https://quant.stackexchange.com/a/82138

The monthly return on a 5-year treasury bond is not known in advance, so it is not risk free. The monthly return on a 1-month T-bill is known in advance (assuming the U.S. government never goes bankrupt and always repays their creditors), so this an actual risk-free rate.

However, see AKdemy's answer on why government bond yields are not the preferred choice of risk free rate in the industry. RFR swap rates are recommended instead.