Discuss How Betas Are Obtained and Some of the Innovations

Question

Examlex · Accepted Answer

The Answer is Security returns are correlated because of a common response to market changes,and a useful measure of this correlation might be obtained by relating the return on a stock to the return on a stock market index.The Beta of a security measures how sensitive a stock's return is to the return on the market.
A Beta of 2 denotes that a stock's return is expected to increase (decrease)by 2%,when the market increases (decreases)by 1%.Similarly,a Beta of 0.5 indicates that a stock's return is expected to increase (decrease)by 1/2 of 1% when the market increases (decreases)by 1%.
The Beta of a security

( i )

divides the return of a security into market-related and unique return.When Beta is set equal to 1.5 for example,the market return is independent of the residual return,

e _ { i }

.A lower value of

e _ { i }

leaves some market return in

e _ { i }

,and the covariance of

e _ { i }

with the market will turn out to be positive.A Beta greater than 1.5 removes too much market return and results in a negative covariance between

e _ { i }

and the market.Thus,the value of Beta is unique and it is the value that exactly separates market from unique return,making the covariance between market return and residual return zero.
The use of single-index model requires estimates of Beta for each stock that is to be included in a portfolio.The Beta can be derived by subjective estimates of a Beta of a security or a portfolio.Estimates of future Beta can also be arrived at by estimating Beta from the past data.Some of the techniques used by analysts for estimating Beta are,measuring historical Betas,correcting historical Betas as the tendency of historical Betas is to be closer to the mean when estimated in a future period,and correcting historical estimates by incorporating fundamental firm data.
The Beta of a firm that can be typically estimated by using the regression analysis,is

\beta _ { i } = \frac { \sigma _ { i m } } { \sigma _ { m } ^ { 2 } }

.This formula means the covariance of the stock with the market divided by the variance of the market.

Discuss How Betas Are Obtained and Some of the Innovations

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