Question

(a) In CAPM framework, there are risks that are diversifiable. What are the non-diversifiable risks? (2 marks) (b) See table 1 below. With respect to the CAPM, which of the following asset would have the greatest impact on the expected return if there is a rise in the expected market return? (2 marks) Table 1 Asset Standard Deviation Beta Asset 1 22% 0.5 Asset 2 15% 1.2 Asset 3 20% 0.9 (c) Suppose the following information about a stock is known. It trades on the Hong Kong Exchange (HKEx). The current HK risk-free rate is 2.5% and the average historical annual return for HK stocks is 10%. The beta of the stock is 1.25. What is the expected return of the stock using the CAPM formula? (2 marks) (d) Consider a portfolio comprises two stocks, A and B (refer to table 2 below), with equal amount of money invested in each. Table 2 State Probability A B Boom 30% 15% 20% Bust 70% 5% 1% i. Compute the portfolio return in each state. ii. Compute the expected return for the portfolio. iii. Compute the standard deviation for the portfolio. (2 marks) (2 marks) (4 marks)

Answer 1

a) The risk that are non-diversifiable is the risk which is common across all the securities and the market, also known as the systematic risk. This is measured in terms of beta. Some of the examples of systematic risk are interest rate change, natural disaster, Civil war within the country impacting the daily activities.

b) The asset that would have the greatest impact with the change in the market return is the one which has the highest beta because in CAPM model beta is the measure of risk hence asset 2will have the highest impact.

c) The expected return according to CAPM model is

Risk free rate + beta *(market return – risk free rate)

= 2.5 + 1.25*(10 – 2.5)

=11.875%

d) -i) The portfolio return in each state Boom (0.5 * 15 +0.5 * 20) 17.50% Bust (0.5 * 5+0.5 * 1) 3% (ii) А State Boom Bust Probability 0.3 0.15 0.05 Probability * A 0.045 0.035 Probability *A^2 0.00675 0.00175 B 0.20 0.01 Probability *B probability * B^2 Covariance calculation 0.060 0.012 0.3*(0.15-0.08)*(0.2-0.067) 0.007 0.00007 0.7*(0.05-0.08)*(0.01-0.067) 0.002793 0.001197 0.7 0.0800 0.00850 0.0670 0.01207 0.00399 expected return for the portfolio (0.08 * 0.5 +0.067 * 0.5) 7.35% Standard deviation A (0.0085 - 0.082)^(1/2) 4.58% Standard deviation B (0.01207 - 0.0672)(1/2) 8.71% The standard deviation for the portfolio would be (0.5^2 * 0.0458^2 +0.5^2 * 0.0871^2+2*0.5*0.5*0.00399)^(1/2) 6.65%