# estimated regression coefficients

What is known as the characteristic line of modern investment analysis is simply the regression line obtained from the following model:

rit = αi + βi rmt + et

Where rit = the rate of return on the ith security in time t; rmt = the rate of return on the market portfolio in time t; et = stochastic disturbance term. In this model beta i is known as the beta coefficient of the ith security, a measure of market (or systematic) risk of a security.

On the basis of 240 monthly rates of return for the period 1956- 1976, Fogler and Ganapathy obtained the following characteristic line for IBM stock in relation to the market portfolio index developed at the University of Chicago (standard errors in parenthesis):

^rit = 0.7264 + 1.0598rmt

(se) (0.3001) (0.0728)

r2 = 0.4710; F(1,238) = 211.896

Interpret the estimated regression coefficients.

Explain the meaning of the estimated r2 value.

A security whose beta coefficient is greater than one is said to be a volatile or aggressive security. Was IBM a volatile security in the time period under study? Conduct an appropriate test to answer the question.

Is the intercept coefficient significantly different from zero? If it is, what is its practical meaning? Again conduct an appropriate test to answer the question

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#### Solution Preview

Interpret the estimated regression coefficients.

The regression equation says that if the rate on return on market portfolio goes up by 1%, the return on the IBM stock goes up by 1.0598%. The alpha value simply says that when the rate of return on the market portfolio is zero, the return on the IBM stock is 0.7264

Explain the meaning of the estimated r2 value.

The value of r-square is 0.4710 which means that out of the total variance in the return on IBM stock 47.10% is explained by the regression equation build using the return on the market ...

#### Solution Summary

The estimated regression coefficients are assessed.