Page 106 - DMGT207_MANAGEMENT_OF_FINANCES

Unit 5: Cost of Capital

Other things being equal, the higher the beta, the higher the required return and lower the beta, Notes
the lower the required return.
Illustration 14: B Co. Ltd., wishes to determine the required rate of return on an asset Z, which
has a beta of 1.5. The risk free rate of return is 7%, the return on market portfolio of assets is 11%.
Thus we get:

Kz = 7% + 1.5 (11% – 7%) = 7% + 6% = 13%
The market risk premium 4% (11% – 7%) when adjusted for the assets index of risk (beta) of 1.5,
results in a risk premium of 6% (1.5 × 4%). That risk premium when added to 7% risk-free return,
results in 13% required return.

Assumptions of CAPM

1. Market efficiency: The capital markets are efficient. The capital market efficiency implies
that share prices reflect all available information.

2. Risk aversion: Investors are risk-averse. They evaluate a security's return and risk in
terms of the expected return and variance or standard deviation respectively. They prefer
the highest expected return for a given level of risk.
3. Homogenous expectations: All the investors have the same explanation about the expected
return and risk of securities.

4. Single time period: All investors can lend or borrow at risk-free rate of interest.
5. Risk-free rate: All investors can lend or borrow at a risk-free rate of interest.
Interpreting Beta: The beta of a portfolio can be easily estimated by using the betas of the
individual assets it includes. Suppose w , represent the proportion of the portfolio's total rupee
1
value represented by asset j, and let , denotes beta of the asset, the portfolio beta

p = (w ×  ) + (w ×  ) + ………….. ( × n) =  w × 
1 1 2 2 1 1

of course  = I which means that 100 per cent of the portfolio's assets must be

included in the computation.
Portfolio betas are interpreted in the same way as the betas of individual assets. They indicate
the degree of responsiveness of the portfolio's return to changes in the market return. For
example, when the market return increases by 10 per cent, a portfolio with a beta of 0.75 will
experience a 7.5 per cent increase in its return (0.75 × 10%).
Again since beta measures the relative volatility of a security's return, in relation to the market
return, it should be measured in terms of security's and markets' covariance and markets variance.
Thus b1 can be measured by:
Cov   Cor  Cor
 = (K i , K )  1 m jm  1 jm
m
1 2 2
  m  m
Where, k = The expected return on non-diversifiable security
i
K = The expected return on market portfolio
m
 = Standard deviation of the security
1
 = Standard deviation of the market portfolio
m

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