Question

which of the following statements is correct?

A. the beta of a portfolio of stocks is always smaller than the betas of any of the individual stocks

B. If you found a stock with a zero historical beta and held it as the only stock in your portfolio, you would, by definition, have a riskless portfolio

C. The beta coefficient of a stock is normally found by regressing past returns on a stock against past market returns. One could also construct a scatter diagram of returns on the stock vs. those on the market, estimate the slope of the line of best fit and use it as beta. However, this historical beta may differ from the beta that exists in the future.

D. The beta of a portfolio of stocks is always larger than the betas of any of the individual stocks.

E. It is theoretically possible for a stock to have a beta of 1.0. If stock did have a beta of 1.0 then, at least in theory, its required rate of return would be equal to the risk-free (default-free) rate of return.

Answer 1

Answer is Statement C

Let us eliminate the incorrect statements:

Statement A and D are incorrect. Beta of portfolio is weighted average of the beta of stocks in portfolio. Since it is an (weighted) average, it is usually larger than the smallest Beta of all stock constiuents and smaller than the largest Beta of all stock constituents. So option A and D are incorrect.

Statement B is also incorrect. Remember Beta represents only the systematic risk or the market risk. But a stock has both systematic and unsystematic risk. This implies, a zero beta stock may still have some unsystematic risk and hence cannot be equivalent to a risk free portfolio.

Statement E is incorrect, because if Beta is 1, required rate of return will be equal to that of expected market return. By CAPM equation, required rate of return on stock = Risk free rate + Beta * (Expected market return - Risk free rate). With Beta = 1, Required rate of return on stock = Expected market return.

Statement C is factually correct. Moreover, the beta that we calculate using the historical data may differ from what we experience in future, since Beta is dynamic.