Question

Question 4 (This question is from the Week 9 Tutorial) Alice has an investment portfolio that paid the rate of return of 23%, 12%, - 34%, 18% and 10% over the last five (5) years. Required:

a. Calculate the arithmetic average return and the geometric average return of this portfolio ?

b. If the following information is available for Alice’s portfolio in the forecast for next year, calculate the expected return and identify the risk of return by computing the variance and the standard deviation. State of economy Probability of the economic state Rate of Return Boom 0.55 25% Normal 0.30 17% Recession 0.15 -8%

c. If the beta of this portfolio is 1.2, the risk-free rate of return is 7%, how much is the risk premium applied in calculating the systematic risk of this portfolio using the Capital Asset Pricing Model (CAPM)? (1 mark)

Answer 1

SOLUTION:

a) Arithmetic Average Return

Arithmetic Average Return = sum of all the return / no of the return

i.e., arithmetic average return = R1+R2+R3+…+R n / n

                                             = 23 %+12 %+(-34 %)+18 %+10 % / 5

                                            = 29/5

                                            =5.8 %

Geometric Average Return

Geometric average return = [(1+r1)*(1+r2)*………(1+rn)]^ 1/n -1

                                         = [(1+r1)*(1+r2)*(1+r3)*(1+r4)*(1+r5)] ^1/5 – 1

                                         = [(1+0.23)*(1+0.12)*(1+ (-0.34))*(1+0.18)*(1+0.1)]^ 1/5 -1

                                         = [(1.23)*(1.12)*(0.66)*(1.18)*(1.1)]^ 1/5 -1

                                         = [1.180162368]^1/5 -1

                                         =1.033685329-1

                                         = 0.033685329

=0.3368*100

=3.3685

=3.37%