**Capital asset pricing model** (**CAPM**) is a method of estimating the risks of investing in a particular stock. It is mainly used by financial analysts and investors to decide what price they should pay for a particular stock. It was first used and developed by Harry Markowitz in 1952. Harry described the relationship between an investor’s risk and the expected return in **CAPM**. According to Markowitz, (2008), “the expected return of a particular security or a portfolio is equal to the rate on a risk-free security plus a risk premium. If the security or portfolio does not meet or exceed the required return, then the investment should not be entered into” (pg. 91). It means that, if Stock A is riskier than Stock B, the price of Stock A should be lower to compensate investors for taking on the increased risk.

The investors use this assessment to check if the required rate of return has an increase in value and if there is a presence of any inherent risk level of the asset. Academic researchers may use this method of risk assessment while studying momentum presence in stock prices. In addition, using **CAPM** as a part of momentum helps to identify whether the momentum investing is profitable or losing. **CAPM** also helps to identify if the risks are systematic or non-systematic. In systematic, the risk is related to the overall stock market like the BSE 100 index, whereas, non-systematic indicates the risk of a particular portfolio or company or industry (Novak, 2015).

## Describing the **CAPM** formula

The **CAPM **formula is;

Required (or expected) Return = RF Rate + (Market Return – RF Rate)*Beta

or

ER_{i}= R_{f}+ β_{i}(ER_{m}- R_{f})

Where, ER_{i}= Expected return of investment, R_{f}= Risk-free rate, β_{i}= Beta of the investment, ER_{m}= Expected return of market, and (ER_{m}- R_{f}) = Market risk premium.

Investors may first analyze the beta value in the **CAPM** model and then follow on to calculate the variance-covariance formula to calculate beta. The same process should be used for finding the risks of investing in particular stocks. **CAPM** always follows the momentum of stock analysis (Novak, 2015).

## Methods and steps for **CAPM** assessment

The **CAPM** analysis needs a series of steps to assess the risks of investing in a stock. The steps are;

- Gather the stock exchange and index data.
- Calculate the Beta coefficient.
- Find the risk free rate.
- Calculate the market returns.
- Input the values into the
**CAPM**formula. - Calculate the
**CAPM.** - Hypothesize that the assets returns are linearly related to the betas of the assets and find the nonlinearity of the model.

## Steps to calculate the Beta coefficient

Beta coefficient is the ratio between covariance and variance values. Covariance is the measure that indicates the movement of two stocks. On the other hand, variance indicates the movement of stock from its mean value. The formula for the beta coefficient is;

**Step 1:** Calculate the covariance and the variance values of the stock prices. Covariance and variance have a complex formula as presented below. However, using excel one do not have to use this complex formula.

**Step 2:** Collect the stock and index-based data of either the complete market or a set of companies.

**Step 3:** Choose the date and the closing date and set them on ascending order of date. Calculate the fractional daily returns using the method shown below.

The formula is (2638.1/2894.2-1) or the current value/previous day value -1. Now, find the values for both the index and the chosen company. The evaluated values will give % change in the stock prices.

**Step 4:** Calculate the covariance/variance using the formula in excel sheet. It will give the beta value.

=COVARIANCE.P(latest BSE index % change:last BSE % change value, latest company stock % change:last company % change value)/VAR.P(latest BSE index % change:last BSE % change value)

## Alternate step for calculation of beta value

Since, beta is calculated by conducting regression between the percentage change in stock prices and the percentage change in the overall stock market, one may also conduct the regression method for beta assessment.

- Firstly follow steps 1 to 3 from the previous section.
- Then choose the Data Analysis option from data toolbar in MS Excel.
- Next, choose the regression analysis. Y range must be the stock prices range for the particular company or the industry and X range should cover the complete market index values.

**Step 4:** The value under the tag X variable 1 and Co-efficient value is the beta coefficient value.

## Finding the risk free rate

The Risk-Free rate is a hypothetical rate of return of an investment that may have zero risks and the investors expect this amount to receive from an investment with zero risks (Pravin and Dhananjay, 2019). In other words, **CAPM** relates expected returns from an asset and portfolio to its systematics risk or Market risk.

- Compute the excess return for various stock and market proxy. Excess return is the earning above the risk-free return by the investor. It is also determined by calculating the difference between the actual return and the expected return.
- For risk-free return, n number of days. Treasury bill rates needs to be considered for risk-free return proxy. One may also consider risk free rate value as the rate of interest on the 364 days Treasury bill.
- Calculate by deducting the risk-free return from the actual return.

## Measure the market returns

The daily returns should be calculated for both the individual stocks as well as the market index using the following equation. Use only daily values for daily returns, and never use annualized values or averaged values.

Returns = Stock current price – Stock price n-days ago/Stock price n-day ago x 100

After finding all the values for **CAPM**, impute the values and conduct the assessment. **CAPM** is not testable because true market portfolio cannot be measured as it may include all assets such as financial, real as well as human and not just equity stocks.

#### References

- Chavan, P. and Dhananjay, P., 2019. An Empirical Test of Capital Asset Pricing Model with reference to S&P BSE Sensex Index.
*International Journal of Multidisciplinary*,*4*(2), pp.52-58. - Markowitz, H.M., 2008. CAPM investors do not get paid for bearing risk: a linear relation does not imply payment for risk.
*Journal of Portfolio Management*,*34*(2), p.91. - Novak, J., 2015. Systematic risk changes, negative realized excess returns and time-varying CAPM beta.
*Finance a Uver*,*65*(2), p.167.

### Avishek Majumder

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