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Updated on May 8, 2024
Article byWallstreetmojo Team
Edited by
Reviewed byDheeraj Vaidya, CFA, FRM

## What is the Market Risk Premium Formula?

The term “market risk premium” refers to the extra return that an investor expects for holding a risky market portfolio instead of risk-free assets. In the capital asset pricing model (CAPM), the market risk premium represents the slope of the security market line (SML). The formula for market risk premium is derived by deducting the risk-free rate of return from the expected or market rate of return.

Mathematically, it is represented as,

Market risk premium = Expected rate of return – Risk-free rate of return

or

Market risk premium = Market rate of return – Risk-free rate of return

For eg:
Source: Market Risk Premium Formula (wallstreetmojo.com)

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### Explanation of the Market Risk Premium Formula

The formula in the first method can be derived by using the following simple four steps:

1. Firstly, determine the expected rate of return for the investors based on their risk appetite. The higher the risk appetite, the higher the expected rate of return to compensate for the additional risk.

2. Next, determine the risk-free rate of return, which is the return expected if the investor does not take any risk. The return on government bonds or treasury bills is a good proxy for the risk-free rate of return.

3. Finally, the formula for market risk premium is derived by deducting the risk-free rate of return from the expected rate of return, as shown above.

The formula for the calculation of market risk premium for the second method can be derived by using the following simple four steps:

4. Firstly, determine the market rate of return, which is the annual return of a suitable benchmark index. The return on the SP 500 index is a good proxy for the market rate of return.

5. Next, determine the risk-free rate of return for the investor.

6. Finally, the formula for market risk premium is derived by deducting the risk-free rate of return from the market rate of return, as shown above.

### Examples of Market Risk Premium Formula (with Excel Template)

Let’s see some simple to advanced examples of the Market Risk Premium Formula

#### Example #1

Let us take an example of an investor who has invested in a portfolio and expects a rate of return of 12% from it. However, in the last year, government bonds have given a return of 4%. Based on the given information, determine the market risk premium for the investor.

Therefore, the calculation of market risk premium can be done as follows,

• Market risk premium = 12% – 4%

Based on the given information, the market risk premium for the investor is 8%.

#### Example #2

Let us take another example where an analyst wants to calculate the market risk premium offered by the benchmark index X&Y 200. The index grew from 780 points to 860 points during the last year, during which the government bonds have given an average 5% return. Based on the given information, determine the market risk premium.

To calculate Market Risk Premium, we will first calculate the Market Rate of Return based on the above-given information.

• Market rate of return = (860/780 – 1) * 100%
• = 10.26%

Therefore, the calculation of market risk premium can be done as follows,

• Market risk premium = 10.26% – 5%
• Market risk premium = 5.26%

You can use the following Market Risk Premium Calculator.

 Expected Rate of Return Risk Free Rate of Return Market Risk Premium Formula

 Market Risk Premium Formula = Expected Rate of Return – Risk Free Rate of Return 0 – 0 = 0

### Relevance and Use

An analyst or an intended investor needs to understand the concept of market risk premium because it revolves around the relationship between risk and reward. It represents how the returns of an equity market portfolio differ from that of the lower risk treasury bond yields owing to the additional risk that the investor bears. The risk premium covers expected returns and historical returns. The expected market premium usually differs from one investor to another based on risk appetite and investment styles.

On the other hand, the historical market risk premium (based on the market rate of return) is the same for all the investors as the value is based on past results. Further, it forms an integral cog of the CAPM, which has already been mentioned above. In the CAPM, the required rate of return of an asset is calculated as the product of market risk premium and beta plus the risk-free rate of return.