Question

Question 1: A medium-sized finance company is considering an investment portfolio of 40% of stock A and remaining 60% in stock B over the next four years (2020-2023). Given the returns of two stocks A and B in the table below over the four-year period, calculate the following: (3.5 marks)

	Stock A	Stock B
2020	10%	9%
2021	12%	8%
2022	13%	10%
2023	15%	11%

1. Calculate the expected portfolio return, rp, for each of the four years.
2. Calculate the expected value of portfolio returns, rp, over the four-year period.
3. Calculate the standard deviation of expected portfolio returns over the four-year period.

The standard deviation of individual stocks are not required!

Answer 1

Answer A.

Weight of Stock A = 0.40
Weight of Stock B = 0.60

2020:

Portfolio Return = 0.40 * 10.00% + 0.60 * 9.00%
Portfolio Return = 9.40%

2021:

Portfolio Return = 0.40 * 12.00% + 0.60 * 8.00%
Portfolio Return = 9.60%

2022:

Portfolio Return = 0.40 * 13.00% + 0.60 * 10.00%
Portfolio Return = 11.20%

2023:

Portfolio Return = 0.40 * 15.00% + 0.60 * 11.00%
Portfolio Return = 12.60%

Answer B.

Expected Return = [0.0940 + 0.0960 + 0.1120 + 0.1260] / 4
Expected Return = 0.4280 / 4
Expected Return = 0.1070 or 10.70%

Answer C.

Variance = [(0.0940 - 0.1070)^2 + (0.0960 - 0.1070)^2 + (0.1120 - 0.1070)^2 + (0.1260 - 0.1070)^2] / 3
Variance = 0.000676 / 3
Variance = 0.000225

Standard Deviation = (0.000225)^(1/2)
Standard Deviation = 0.0150 or 1.50%