## What is the risk-free rate?

Analysts use the risk-free rate to calculate various valuations. In this article, we discuss what the risk-free rate is and why it used.

#### Definition

This risk-free rate is rate of return on asset assuming there is no risk on the investment. This is a theoretical measurement as all investments carry a degree of risk. The yield of the 10 year government bond is typically used as the risk-free rate. This is the minimum return an investor should expect from a risk-free investment.

#### When is the risk-free rate used?

The risk-free rate is used in calculating expected return on a security by taking into account the risk of the asset by using the capital asset pricing model (CAPM).

#### Capital asset pricing model formula:

Expected return of investment = Risk Free Rate + Beta of the security (Market Risk Premium)

The beta of a stock measure how risky the stock is in comparison to the broader market. If a stock as a beta of 1 it means the risk of the stock is in line with the market, a beta of more than 1, it means it is more volatile than the market. A beta of less than 1 means it is less volatile than the market.

The market risk premium is calculated as = Expected return of the market – Risk Free Rate

Investors want to be rewarded with higher returns if they are to invest in riskier assets. This formula can give investors an expected rate of return on the asset for undertaking higher risk.

#### Example of CAPM:

An investor wants to find out what an expected return was for a security called XYZ.

The risk-free rate is 1.25%, the expected return for the market 9%, the beta on the stock is 1.5

Using the formula above the expected return of investment = 1.25 + 1.5 (9-1.25)

=10.5%

This figure of 10.5% can give the investor an indication of what the expected return is for the level of risk this security holds. The investor can then evaluate whether it is a good investment for them in terms of what they expected return is. These figures are not definite returns as they are based on historical data.

Lauren Hua is a private client adviser at Fairmont Equities.

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