## Part – 11: CAPM (Capital Asset Pricing Model)

### What is the CAPM (Capital Asset Pricing Model)?

Every investment comes up with a certain risk. Even equity has the risk that there might be a difference between the actual and the expected return. The cost of equity is, essentially, the discount rate applied to expect equity cash flows which help an investor determine the price he or she is willing to pay for such cash flows. Investors being conservative by nature decide on taking the risk only when they can foresee the return they are expecting from an investment. Investors can calculate and get an idea of the required return on investment, based on the assessment of its risk using CAPM (Capital Asset Pricing Model).

### Calculation of CAPM (Capital Asset Pricing Model)

The cost of equity (Ke) is the rate of return expected by shareholders. It can be calculated using the formula

**Cost of equity = Risk free rate + Beta X Risk premium**

where:

**Cost of equity (Ke _{) }**

_{ = }the rate of return expected by shareholders

**Risk-free rate (rrf ) **= the rate of return for a risk-free security

**Risk premium** ( **R _{p) }**= the return that equity investors demand over a risk-free rate

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**Beta (Ba)** = A measure of the variability of a company’s stock price in relation to the stock market overall

Now let’s understand these key terminologies of the formula: –

#### Risk-free rate –

** **It is the minimum rate of return that an investor will receive if they in invest in risk-free security. Government bonds are known as risk-free securities. For a security to be risk-free security they should not have any default risk and reinvestment risk. Default risk is the risk where companies or individuals fail to repay their debt obligations. Reinvestment risk is the risk faced by an investor where the yield of the bonds is falling. As in this situation the investors have to reinvest their future income their yield or the final return of principal in securities which are lower yielding. So, not all governments securities are risk-free securities

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#### Beta –

Risk can be classified as systematic risk and unsystematic risk. Unsystematic risk is the risk that can be diversified. This risk arises due to the internal factors prevailing in an organization. For example, workers have gone for a strike, customer’s commitments are not fulfilled, the regulatory framework has a conflict with government policy, etc.

Systematic risk is the risk that cannot be diversified. It is caused due to the external factors that affect an organization. It is uncontrollable in nature. For example, interest rate raises suddenly, Fluctuations in the trading price of a security impact on the entire market, etc. This risk can be measured with a beta.

Beta measures the volatility of a security in comparison with the market as a whole.

- If the beta of a security is equal to 1 this means that if the market is moving upward by 10% the stock having beta equal to 1 will also move up by 10% and vice versa.
- If beta of a security is less than 1 it means that the security is less volatile as compared to the market. For example, a company has a beta of 0.5 this means that if the market has an upward movement of 10% the company will have an upward movement of 5% and vice versa.
- If the beta of company security is more than 1 this means that the security has high volatility. For example, if the company security has a beta of 1.5 and the stock market moves up by 10% then the security moves up by 15 % and vice versa

#### Risk premium

It is calculated using the formula Stock market return minus Risk-free rate of return. It is the return that an investor expects above the risk-free rate of return in order to compensate for the risk of volatility that a person is taking by investing in the stock market. For example, if the investor gets a return of 20% and the risk-free rate is 7% then the risk premium is 13%.

### Assumptions for the CAPM (Capital Asset Pricing Model) model

- Investors don’t like to take a risk. They would like to invest in a portfolio which has low risk. So if a portfolio has higher risk the investors expect a higher return.
- While making the investment decision investors take into consideration only a single period horizon and not multiple period horizons.
- Transaction cost in the financial market is assumed to be low cost and the investors can buy and sell the assets in any number at the risk-free rate of return.
- In CAPM (Capital Asset Pricing Model), Values needs to be assigned for the risk-free rate of return, risk premium, and beta.
**Risk-free rate**– The yield on the government bond is used as a risk-free rate of return but it changes on a daily basis according to the economic circumstances

**Beta –**The value of beta changes over time. It is not constant. So the expected return might also differ.

**Market Return –**The stock market return can be calculated as the sum of the

Average capital gain and the average dividend yield. If the Shares prices fall and outweigh the dividend yield a stock market can provide a negative rather than a positive return

### Advantages of CAPM (Capital Asset Pricing Model)

- CAPM (Capital Asset Pricing Model) takes into account the systematic risk as the unsystematic risk can be diversified.
- It creates a theoretical relationship between risk and rate of return from a portfolio.

### CAPM Application

Using the CAPM (Capital Asset Pricing Model) model, please compute the expected return of a stock where, the risk-free Rate of return is 5%, the beta of the stock is 0.50, the expected market return is 15%

So,

Cost of equity = Risk free rate + Beta X Risk premium

Risk free rate = 5%

Beta =0.50

Risk premium = (Rm-Rf)

= (15% – 5%)

=10%

Cost of equity = 5%+0.50*10%

**Cost of equity = 10%**

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