Question

Assume that the risk-free rate increases while the degree of risk aversion in the economy is unchanged. Illustrate how this affects the Security Market Line on a separate diagram. Explain what happens to the CAPM return on (i) a zero beta asset and (b) an asset with a beta of 1 following the increase in the risk-free rate. Provide the economic intuition for both.

Answer 1

The CAPM security market line is graphical representation of the CAPM expected return equation which states that expected return (ER) = risk free rate (r_f) + * (return on market portfolio (r_m) - r_f)

The risk (measured by beta) is plotted on the x axis and the ER is on the y axis with the r_f as the intercept. Since we are given that the risk aversion remains unchanged but only the risk free rate has increased, this should only make the SML line intercept point on y axis move up with the slope remaining the same as before.

As we can see in the diagram also, that in case of the r_f moving up, the SML line will simply move up the y axis and since the risk aversion is same, the slope will remain the same.

(i) An asset with zero beta will have return equal to r_f, hence its return will simply increase to new r_f as can be seen in the diagram

(ii) For an asset with beta equal to 1, which is like market portfolio, the return will increase and again by the same amount as the increase in the r_f. We understand the CAPM states that beta is the measure of the risk and we should be paid for only taking that risk and in case of zero risk, (beta = zero) we should earn risk free rate. Hence when only r_f changes with no change in risk aversion, it only means that the minimum return for the economy has increased to new r_f , hence SML line just moves up parallel to previous line on y axis.