Page 69 - DMGT207_MANAGEMENT_OF_FINANCES

Management of Finances

Notes Cor = Correlation coefficient between the returns of individual security and the market
im
portfolio
 = Standard deviation of returns of individual security
i
 = Standard deviation of returns of market portfolio
m
A beta coefficient is a relative measure of the sensitivity of an assets’ return to changes in the
return on the market portfolio. Mathematically, the beta coefficient of a security is the security’s
covariance with the market portfolio divided by the variance of the market portfolio. The beta
factor is the measure of volatility of systematic risk of a security or investment in the portfolio.
The beta factor of the market as a whole is 1.0. A beta of 1.0 indicates average level of risk while
more or less than that the security’s return fluctuates more or less than that of market portfolio.
A zero beta means no risk. The degree of volatility is expressed as follows:
1. If the beta is one, then it has the same risk profile as the market as a whole, the average risk
profile.
2. If the beta is less than one, it is not as sensitive to systematic or market risk as the average
investment.
3. If beta is more than one, it is more sensitive to the market or systematic risk than the
average investment.
Beta Factor of a Market Portfolio

If the return from the market portfolio rises or falls, we should expect a corresponding rise or
fall in the return from an individual share. The amount of this corresponding rise or fall depends
on the beta factor of the share. The beta factor of an investor’s portfolio is the total of the
weighted average beta factors of each security in the portfolio. As the market portfolio represents
all shares on the stock market, it follows that the beta coefficient of the market portfolio must be
1, and all other betas are viewed relative to this value. Thus, if the return from the market
portfolio rise by says 2%, the coefficient would be:

Increase in return on investment 2%
  1
Increase in return on market portfolio 2%
CAPM indicates the expected return of a particular security in view of its systematic or market
risk. The value of a share price is determined in relation to investment in shares of individual
companies, rather than as a portfolio.
In practice, for estimation of beta factor the following regression equation is used:
R =  +  R + e
i i i m i
Where,
R = Rate of return of individual security
i
 = The intercept that equals the risk free rate (R )
i f
 = Beta factor of he individual security
i
R = Market of return
m
e = Random error, which reflects the diversifiable risk of individual security
i
Illustration 1: Wipro provides you the following informations. Calculate the expected rate of
return of a portfolio:
Expected market return 15%
Risk-free rate of return 9%

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