**CAPM = r _{f} + β_{i} (R_{m} – R_{f})**

R_{f} = risk free rate

β_{i} = Beta of investment

R_{m} = return of market

Capital asset pricing model is well known measure to calculate return on a share on the basis of risk. CAPM formula uses risk free rate of return and adds the beta times of difference in market and risk free rate in to it.

Another explanation for CAPM is that it describes the relationship between expected return on assets and systematic risk essentially for stocks. Capital asset pricing model is widely used to calculate the __cost of capital__, pricing of securities and as stated earlier for calculation of expected returns of assets.

## Relation of risk and capital asset pricing model – Explanation

Every time a person makes an investment he wants compensation in return for taking a risk by giving his money in to the project. Moreover, time value of money is another thing which must be covered at the end of term to reach profitability.

In the formula __Beta__ helps to calculate the level of risk an investment is going to contribute to the portfolio (i.e. shares pool). The β_{i} value will be greater than 1 if the share is riskier than the market. On the other side if β_{i} results in value less than 1 then it will reduce the risk of entire portfolio.

Market risk premium (R_{m} – R_{f}) is then multiplied with *beta* to calculate the expected return on the investment. Market risk premium is basically is the estimated incremental return to take incremental risk in comparison to risk free rate of return. After that risk-free rate is added to product of market risk premium and β_{i} and result is the required return on investment or discount rate which can be used for other purposes also.

CAPM basically focuses on the question whether a stock is fairly valued and the risk and time value of money overweigh the expected return on not.

### Capital asset pricing model limitations

CAPM contains a number of assumptions behind the concept which may or may not in-line with real world scenarios. Despite of these limitations it is widely used to compare several investments due to simplicity and ease of use.

The * Beta* in the formula takes in to account the risk of share price volatility. But price volatility on upper side may not be as risky as towards the down side. Here the approach to work-back in history may not be helpful enough due to the fact that returns and risks are not generally distributed.

Moreover, another assumption underlying with CAPM is that risk-free rate of return will remain constant over the period of calculation. For example if we assume that interest rate with specific any specific bond increases over a period of time then CAPM will indicate profitability for that investment. But an increase in risk-free rate will directly influence the __cost of capital__ and can simply make stock overvalued.

Market risk premium is calculated using any market portfolio and it is only a theoretical value moreover, it is not an asset which can be an alternative to the stock for investment purpose. Typically a popular stock index is used for market risk premium calculation like S&P 500 and it may not provide a perfect comparison.

Another and most critical assumption behind CAPM is the estimation of future cash flows for discounting which may not be possible due to a number of factors. Moreover, if it is possible to estimate future cash flows precisely then essentially the need CAPM is completely diminished.

### How capital asset pricing model is useful for analysts

After taking in to account the critiques and limitations inherit with CAPM it might not be possible to say to what extent the model is useful. However, it can be valuable in several aspects which include using it as a tool to estimate the fairness of future expectation or for comparison purpose.

For instance, if an investment manager is looking in to add a stock to his portfolio have a share price of $80. The CAPM is used to see price justification with a discounting rate of 11%. Now he must compare this rate of return with the performance history of the company to reach a reasonable return expectation.

Assume that manager discovers that performance of company during last 8-years shows stock was never giving more than 9% moreover, it also underperformed with 7% returns at instances. In such a scenario the investor must not consider investing in that option without any reasonable justification about expected rate of return.

Beside to all above some other financial ratios can also be used along with capital asset pricing model to evaluate the portfolio against the market. For example assume that your portfolio is giving a return of 9% per year since last two years with risk-free return of 7%. While on the other side the market average shows a return of 10% for last 2 years with risk-free return at 7%.

This analysis between market return and your investment could be helpful to reevaluate your portfolio performance. Moreover, such comparisons also help to decide which shares should be on the portfolio and which must be dropped out to maintain the profitability and risks also.

### CAPM Conclusion

As stated earlier CAPM is typically used to evaluate if a stock is reasonably valued or not. However, a number of assumptions are inherited within this *Modern Portfolio Theory* about risk and return distribution, investor behavior, and other market realities which may not entirely exist in real world. But inspite of all these critiques it is very helpful to evaluate the reward against estimated risk to make decisions and compare available options.