A market risk premium formula is calculated by deducting a risk-free rate of return from the expected risk of return or from the market rate return. It is used by investors to determine the level of risk against risk-free investment.

## Explanation:

The investors want to balance the risk with the expected return on their investments. The market risk premium is a strategy to evaluate the risk of investing in stocks compared to using guaranteed risk-free assets. More precisely, the market risk premium is the variance between the risk-free rate and the expected return on the market portfolio.

It equals the slope of the security market line (SML), which graphically represents the capital asset pricing model (CAPM), describing risky securities. The market risk premium reflects the required, historical, and expected return rates.

The historical aspect is the same for all the investors as it is based on what really happened in the market. However, the required and expected market premiums tend to vary depending on risk tolerance and investment styles of different investors.

Mathematically, the formula to calculate market risk premium has two representations:

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

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

The explanations of the first method of a market risk premium formula calculation include three steps. The first step implies determining the expected rate of return, focusing on the preferences of investors.

The compensation for the additional risk directly depends on their risk enthusiasm. The second step is determining the risk-free rate of return that is the return expected in case investors would take no risk. According to the third step, the market risk premium formula is to be calculated by deducting the risk-free rate from the expected rate of return.

The second method of computing the market premium risk can be easily applied in practice. First, it is necessary to identify the market rate of return based on a benchmark index. The majority of analysts refer to the S&P 500 for collecting and interpreting past performance. Other benchmark indexes are Nasdaq, the Dow Jones Industrial Average, and DJIA.

Second, the risk-free rate of return for a particular investor is to be established. Third, the deduction of the risk-free rate of return from the market return will derive the market premium risk formula. The country risk premium (CRP) is another important term that means extra premium or return for investors to compensate for the higher risk in investing in foreign countries compared to the domestic market. The CRP is necessary for estimating additional returns for investors working with other countries.

These calculations help the investors in determining the level of risk against risk-free investment. However, it should be stressed that they do not guarantee a rate of return or any income. While no investment can be totally risk-free, governmental bills and bonds are recognized as fail-proof, and it is unlikely that they would default on financial obligations.

As for the returns on individual stocks, they depend on volatility that is relative to the market and can change significantly. The application of market risk premia aims to increase the potential profit from assets’ risk premium via a range of financial instruments. The investors generally use risk assessments, including the market risk premium, as part of a complete investment strategy.