Question

Based on the information given below, calculate (a) the portfolio’s return in the last 12 months in the USD, (b) its return in the AUD, and (c) the standard deviation of the portfolio return. Provide all the workings (use up to 3 decimal places).

Your stock portfolio consists of two American companies; Alphabet and GM. You are living in Australia and those shares are purchased in the USD. During the last 12 months, Alphabet’s stock went up by 20%, while GM went up by 3%. During the same period, the USD went down by 2% against the AUD. Assume that you have invested 40% of your money to Alphabet and allocated 60% of your money to GM. Furthermore, assume that the standard deviations of stock returns are 7% for Alphabet and 4% for GM, and the correlation coefficient between the two stock is 0.2

Answer 1

a). 12 months return in USD = (investment in Alphabet*return on Alphabet) + (investment in Google*return on Google) = (40%*20%)+(60%*3%) = 9.80%

b). Since, USD goes down by 2% against AUD, AUD has weakened so, return in AUD will be USD return*(1+2%) = 9.80%*(1+2%) = 10.00%

c). Covariance between Alphabet and Google = correlation*Standard deviation of Alphabet*Standard deviation of Google = 0.2*7%*4% = 0.00056

Portfolio variance = (weight of Alphabet*SD of Alphabet)^2 + (weight of Google*SD of Google)^2 + (2*weight of Alphabet*weight of Google*covariance)

= (40%*7%)^2 + (60%*4%)^2 + (2*40%*60%*0.00056) = 0.0016288

Portfolio standard deviation = variance^0.5 = 0.0016288^0.5 = 4.04%