Question

Your stock portfolio consists of two European companies; Volkswagen (VW) and Arcelor Mittal (AM). You are living in Australia and those shares are purchased in the Euro. During the last 12 months, VW’s stock went up by 5%, while AM went up by 2%. During the same period, the Euro went down by 3% against the AUD. Assume that you have invested 50% of your money into VW and allocated 50% of your money into AM. Furthermore, assume that the standard deviations of stock returns are 4% for VW and 6% for AM and the correlation coefficient between the two stock is 0.3.

Calculate (a) the portfolio’s return during the 12 months in the EUR, (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)

Answer 1

For a two stocks portfolio,

Portfolio return =

Rp = w1 x R1 + w2 x R2 and

Part (a) the portfolio’s return during the 12 months in the EUR,

R_p = 50% x 5% + 50% x 2% = 3.500%

Part (b)

its return in the AUD = [(1 + Portfolio return in EUR) / (1 + Rate of depreciation of EUR)] - 1 = (1 + 3.5%) / (1 + 3%) - 1 = 0.485%

and (c) the standard deviation of the portfolio return =

σp = [(50% x 4%)2 + (50% x 6%)2 + 2 x 50% x 50% x 0.3 x 4% x 6%]1/2 = 4.074%