## Don’t ignore the risk-free rate of return

Don’t ignore the risk-free rate of return

It may be more accurate to say, use the correct risk-free rate of return in your performance calculations. But the key take away from this note is that the risk free rate of return matters in creating accurate performance statistics for your marketing materials and performance reports. The risk-free rate of return is the theoretical rate of return that will be earned by an investment with zero risk. The risk-free rate serves as the basis for deriving asset valuations in models like the Capital Asset Pricing Model and the Black Scholes option pricing model. The risk-free rate is also fundamental to the calculation of risk adjusted performance measures like the Sharpe ratio and the alpha from CAPM that fund managers chase and tout in their materials.

Typically, the US 90-day treasury bill rate is used as a proxy for the risk-free rate. Since the Global Financial Crisis investors have become accustomed to exceptionally low interest rates. From December 2008 to February 2022 the average yield on a 90-day t-bill rate was 0.47%. However, thanks to the Federal Reserve’s current campaign to reduce inflation, the current yield on a 90-day treasury bill is around 5.50%. Unfortunately, most fact sheets we see are still using a risk-free rate of between 0.25% and 0.50%. The result is fund managers are sending out inaccurate and upward biased performance measures. The easiest way to see this is to look at the impact of changing the risk-free rate on two of the most commonly used measures of risk adjusted performance: alpha and the Sharpe ratio.

## 1. Alpha

Alpha for a fund is calculated from the CAPM Formula

The usual approach to calculating the alpha and the fund beta is to use linear regression. There are two key takeaways regarding the risk-free rate and calculating alpha.

- You should be using excess returns in your calculations. If you don’t, then your alpha will be biased upwards by the risk-free rate.
- If you are calculating your alpha using the wrong risk-free rate you will bias your alpha upwards if the risk-free rate is too low and bias your alpha downward if your chosen risk free rate is too low as you can see in the table below.

The table below shows the impact of the risk-free rate on the alpha you report.

## 2. Sharpe Ratio

The Sharpe Ratio is defined as the excess return for a portfolio (or fund) divided by the risk of the portfolio.

The calculation assumes that the Portfolio Return and the Risk-free rate are calculated over the same period, this means that the risk-free rate you use for your calculations should change over time and should be measured over the same period as the period you use to calculate the annualized portfolio return. We can see in the table below the impact of the risk-free rate on Sharpe Ratios.

In short, if the portfolio return and risk are constant, increasing the risk-free rate decreases the Sharpe ratio because the returns in excess of the risk-free rate decrease. This means that firms using inappropriately low risk-free rates in their performance calculations are reporting inflated Sharpe ratios.

While this may seem like a Nerd’s eye view of performance calculations, fund managers and fund marketers need to remember that allocators care about the details. When you catch their attention, they will recalculate these statistics. Finding that the statistics you provided them with are biased or just plain wrong is an easy reason for them to move on to the next fund. Even if they continue to speak with you, you will find that you must work that much harder to build you credibility and earn an allocation.