What is Capital Asset Pricing Model? How to calculate it?

As we discuss in previous post about Dividend Discount Method to calculate Cost of Equity. Now we discuss another method that is CAPM (Capital Asset Pricing Model).

 Capital Asset Pricing Model (CAPM): It measure rate of return based on risk on investment. There are two type of risk - diversified risk which can be minimise due to diversify the investment and another is non- diversified risk which can affect all firms like change in government policy, inflation, purchasing power etc. This model is based on some assumptions related to investors preferences ( investors are risk averse) and market efficiency (no tax, no investor can affect market price, no transaction cost, no restriction on investment, all investors have same market knowledge etc.).

Beta is the measure of systematic risk and it is always between in 0.5 to 1.75. It can be positive or negative.If it is below 1 it means the asset is less volatile than market or you can say the price of the asset does not change with change in market condition. And vice versa.

Advantages of CAPM:

·         It is easy to calculate.

·         It consider systematic risk which affects all diversified portfolio.

Disadvantages of CAPM:

·         It does not consider unsystematic risk which affects only particular stock.

·         The value of beta is never remain same.

·         The risk free rate changes daily because it is yield on government securities.

Formula:

K_e = R_f + b (K_m – R_f)

Β_i = Co-variance _{i, m} / Variance_m

= Co relation coefficient between market and stock * ( standard deviation of stock return / standard deviation of market return)

W here,        

K_e = Cost of Equity

R_f = Required rate of return on risk free security

B = beta coefficient

K_m = required rate of return on market portfolio of investment

Co-variance _{i, m} = co variance of stock return with market return

Variance_m = variance of market return

Example: Suppose Company X expected return on the market is 10% and beta is 0.7. The risk free rate is 5%.Find out the cost of equity.

Solution:

K_e = R_f + b (K_m – R_f)

= 5% + 0.7 (10% - 5%)

= 8.5%

If K_e is lower than investors required rate of return it means stock is overvalued and it’s time to sold it and if higher than required rate of return then it is undervalued and investors must buy it.

Example: Companies Investment information is given below:

Company	Initial Investment Rs.	Dividend	Market Price
X	30	10	50
Y	20	5	25
Z	45	12	100

Risk free return = 7%

Find out the required rate of return on market.

Solution:

Company	Dividend	Capital Appreciation	Total	Initial Investment Rs.
X	10	20	30	30
Y	5	5	10	20
Z	12	55	67	45
			107	95

K_m = Total Return / Initial Investment

= 107/ 95

=112.63%

Example: Find out the beta coefficient if the standard deviation of Company A is 11% and market is 15%. The co-relation coefficient is 1.25.

Solution:

Co-relation coefficient between market and stock * ( standard deviation of stock return / standard deviation of market return)

= 1.25 * (15 / 11)

= 1.70

It shows that Company A’s share price changes more with change in market condition.