**Formula of Market Risk Premium (Table of Contents)**

## What is Market Risk Premium Formula?

The term “market risk premium” refers to the extra return that is expected by an investor 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 rate of return 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**

### Explanation of the Market Risk Premium Formula

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

**Step 1:** Firstly, determine the expected rate of return for the investors based on their risk appetite. Higher the risk appetite, higher would be the expected rate of return to compensate for the additional risk.

**Step 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 good proxies for the risk-free rate of return.

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

**Step 1:** Firstly, determine the market rate of return which is the annual return of a suitable benchmark index. The return on the S&P 500 index is a good proxy for the market rate of return.

**Step 2:** Next, determine the risk-free rate of return for the investor.

**Step 3:** 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 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. 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%

**Market risk premium will be-**

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 one year, during which the government bonds have given an average 5% return. Based on the given information, determine the market risk premium.

For the calculation of 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%

### Market Risk Premium Calculator

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

It is important for an analyst or an intended investor 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 is borne by the investor. Basically, the risk premium covers expected returns and historical returns. The expected market premium usually differs from one investor to another based on their 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 of the asset plus the risk-free rate of return.

### Recommended Articles

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