In: Finance
Your stock portfolio consists of two American companies; Apple Inc. and Ford Motor Company. You are living in Australia and those shares are purchased in the USD. During the last 12 months, Apple’s stock went up by 40%, while Ford went down by 30%. During the same period, the USD went up by 3% against the AUD. Assume that you have invested 60% of your money into Apple and allocated 40% of your money into Ford. Furthermore, assume that the standard deviations of stock returns are 5% for Apple and 7% for Ford, and the correlation coefficient between the two stock is 0.6. (a) What is the portfolio’s return over the 12 months in the USD, (b) what is its return in the AUD, and (c) what is the standard deviation of your portfolio return? Provide all the workings (use up to 3 decimal places).
Let's first write down the information provided:
Apple | Ford | |
Weights | 60% | 40% |
Return | 40% | -30% |
Standard Deviation | 5% | 7% |
Correlation coefficient: 0.6
USD appreciation: 3%
Let the weights 60% and 40% be denoted by w1 and w2. Further, let R1 and R2 represent the returns from Apple and Ford, respectively and s1 and s2 their respective standard deviations.
a. Portfolio Return (USD)
The return on the portfolio RP can be calculated as
RP = w1R1 + w2R2 =
0.600 x 0.400 + 0.400 x (-0.300) = 0.240 - 0.120 = 0.120 or
12.000%.
This is the portfolio return in USD.
b. Portfolio Return (AUD)
For calculating the portfolio return in AUD, we can use the below formula.
Portfolio return in domestic currency = [(1 + Portfolio return in the invested currency) / (1 - Rate of appreciation of the invested currency)] - 1
Please note that if the invested currency depreciates against the domestic currency, we will use (1 + Rate of depreciation) in the above formula.
Here, the invested currency is USD and the domestic currency is AUD. During the 12-month holding period, USD appreciated by 3%. So,
portfolio return in domestic currency = [(1 + 0.120) / (1 - 0.030)] - 1 = [1.120 / 0.970] -1 = 1.155 - 1 = 0.155 or 15.464%
c. Portfolio Standard Deviation
Variance of the portfolio can be calculated using the formula
Var = w12s12 + w22s22 + 2w1w2Cov(R1R2)
where Cov(R1R2) is the covariance in the returns of Apple and Ford which, in turn, can be calculated as
Cov(R1R2) = Correlation coefficient x s1 x s2 = 0.600 x 5.000 x 7.000 = 21.
Please note that in the calculation of portfolio standard deviation, we are not converting the standard deviation into decimals and rather, we will be keeping them as whole numbers.
So, Var = (0.600)2(5.000)2 +
(0.400)2(7.000)2 +
2(0.600)(0.400)(21.000)
= (0.360)(25.000) + (0.160)(49.000) + 10.080
= 9.000 + 7.840 + 10.080
= 26.920
The portfolio variance is 26.920, so the standard deviation of the portfolio is (26.920)1/2 = 5.188%