1. a) If the expected rate of return on the market portfolio is 14% and the risk-free rate is 6% find the beta for a portfolio that has an expected rate of return of 10%. What assumptions concerning the portfolio and/or market conditions do you need to make to calculate the portfolio's beta.
Elaborate assumptions in terms of CAPM, Rational Investors and security market line.
b) What percentage of the portfolio must an individual put into the market portfolio in order to achieve an expected rate of 10%.
Illustrate in a graph with Expected Return as the Y axis and Beta as the X axis the Risk-free Portfolio (A), the market-Portfolio (B) and the portfolio with 10% return above.
2. Ms. Bessie, manager of Everchanging Mutual Fund, know he fund currently is well diversified and that it has a CAPM beta of 1.0. The risk-free rate is 8% and the CAPM risk premium [E(Rm - Rf] is 6.2%. She has recently become aware of APT measures of risk and knows that there are (at least) two factors: Industrial Production κ1 and inflation κ2. The equation for APT is
E(Ri) - Rf = [k1-Rf] bi1 + [k2-Rf] bi2
E(Ri) = 0.08 + [0.05]bi1+ [.11]bi2
a) If the portfolio's current sensitivity to the Industrial production factor is bp1 is -.5 what is the sensitivity to the inflation factor.
b) If she rebalances her portfolio to keep the same expected return but reduce exposure to inflation to 0 (i.e bp2 = 0) what will the sensitivity to the industrial production factor.