## 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 premiumMarket Risk PremiumMarket risk premium refers to the extra return expected by an investor for holding a risky market portfolio instead of risk-free assets. Market risk premium = expected rate of return – risk free rate of returnread more represents the slope of the security market lineSecurity Market LineThe security market line (SML) is the Capital Asset Pricing Model (CAPM). It gives the market's expected to return at different levels of systematic or market risk. It is also called the 'characteristic line' where the x-axis represents the asset's beta or risk, and the y-axis represents the expected return.read more (SML). The formula for market risk premium is derived by deducting the risk-free rate of returnRisk-free Rate Of ReturnA risk-free rate is the minimum rate of return expected on investment with zero risks by the investor. It is the government bonds of well-developed countries, either US treasury bonds or German government bonds. Although, it does not exist because every investment has a certain amount of risk.read more 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**

##### Table of contents

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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:

**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.****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.****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:

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

**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 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%

### 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

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 marketAn Equity MarketAn equity market is a platform that enables the companies to issue their securities to the investors; it also facilitates the further exchange of these stocks between the buyers and sellers. It comprises various stock exchanges like New York Stock Exchange (NYSE).read more 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 appetiteRisk AppetiteRisk appetite refers to the amount, rate, or percentage of risk that an individual or organization (as determined by the Board of Directors or management) is willing to accept in exchange for its plan, objectives, and innovation.read more 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 riskMarket RiskMarket risk is the risk that an investor faces due to the decrease in the market value of a financial product that affects the whole market and is not limited to a particular economic commodity. It is often called systematic risk.read more premium and beta plus the risk-free rate of return.

### Recommended Articles

This article has been a guide to the Market Risk Premium Formula. Here we discuss how to calculate market risk premium for the investors using its formula and examples and a downloadable excel template. You can learn more about financial analysis from the following articles –

- Calculate Equity Risk PremiumCalculate Equity Risk PremiumEquity Risk Premium is the expectation of an investor other than the risk-free rate of return. This additional return is over and above the risk free return.read more
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- Formula FormulaImplied volatility is one of the important parameters and a vital component of the Black-Scholes model, an option pricing model that shall give the option’s market price or market value. The implied volatility formula shall depict where the underlying volatility in question should be in the future and how the marketplace sees them.read more of Implied Volatility Of Implied VolatilityImplied volatility is one of the important parameters and a vital component of the Black-Scholes model, an option pricing model that shall give the option’s market price or market value. The implied volatility formula shall depict where the underlying volatility in question should be in the future and how the marketplace sees them.read more
- Book to Market RatioBook To Market RatioThe book to Market ratio compares the book value of equity with the market capitalization, where the book value is the accounting value of shareholders’ equity. In contrast, market capitalization is determined based on the price at which the stock is traded. It is computed by dividing the current book value of equity by the market value.read more

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