# Risk-Free Return Calculations and Examples

## What Is Risk-Free Return?

Risk-free return is the theoretical return attributed to an investment that provides a guaranteed return with zero risks. The risk-free rate of return represents the interest on an investor's money that would be expected from an absolutely risk-free investment over a specified period of time.

### Key Takeaways

• Risk-free return is a theoretical number representing the expected return on an investment that carries no risks.
• A risk-free return doesn't really exist, and is therefore theoretical, as all investments carry some risk.
• U.S. Treasuries are seen as a good example of a risk-free investment since the government cannot default on its debt.
• As such, the interest rate on a three-month U.S. Treasury bill is often used as a stand-in for the short-term risk-free rate, since it has almost no risk of default.

## Risk-Free Return Explained

The yield on U.S. Treasury securities is considered a good example of a risk-free return. U.S. Treasuries are considered to have minimal risk since the government cannot default on its debt. If cash flow is low, the government can simply print more money to cover its interest payment and principal repayment obligations. Thus, investors commonly use the interest rate on a three-month U.S. Treasury bill (T-bill) as a proxy for the short-term risk-free rate because short-term government-issued securities have virtually zero risks of default, as they are backed by the full faith and credit of the U.S. government.

The risk-free return is the rate against which other returns are measured. Investors that purchase a security with some measure of risk higher than a U.S. Treasury will demand a higher level of return than the risk-free return. The difference between the return earned and the risk-free return represents the risk premium on the security. In other words, the return on a risk-free asset is added to a risk premium to measure the total expected return on investment.

## How to Calculate

The Capital Asset Pricing Model (CAPM), one of the foundational models in finance, is used to calculate the expected return on an investable asset by equating the return on a security to the sum of the risk-free return and a risk premium, which is based on the beta of a security. The CAPM formula is shown as:

Ra = Rf + [Ba x (Rm -Rf)]

where Ra = return on a security

Ba = beta of a security

Rf = risk-free rate

The risk premium itself is derived by subtracting the risk-free return from the market return, as seen in the CAPM formula as Rm - Rf. The market risk premium is the excess return expected to compensate an investor for the additional volatility of returns they will experience over and above the risk-free rate.

## Special Considerations

The notion of a risk-free return is also a fundamental component of the Black-Scholes option pricing model and Modern Portfolio Theory (MPT) because it essentially sets the benchmark above which assets that have risk should perform.

In theory, the risk-free rate is the minimum return an investor should expect for any investment, as any amount of risk would not be tolerated unless the expected rate of return was greater than the risk-free rate. In practice, however, the risk-free rate does not technically exist; even the safest investments carry a very small amount of risk.

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