Question

The following information indicates percentage returns for stocks L and M over a 6-year period:

Year	Stock L Returns	Stock M Returns
1	14.02%	20.19%
2	14.59%	18.23%
3	16.99%	16.41%
4	17.29%	14.41%
5	17.5%	12.43%
6	19.27%	10.41%

In combining [L−M] in a single portfolio, stock M would receive 60% of capital funds.

Furthermore, the information below reflects percentage returns for assets F, G, and H over a 4-year period, with asset F being the base instrument:

Year	Asset F Returns	Asset G Returns	Asset H Returns
1	16.17%	17.06%	14.39%
2	17.24%	16.44%	15.3%
3	18.44%	15.34%	16.48%
4	19.23%	14.13%	17.42%

Using these assets, you have a choice of either combining [F−G] or [F−H] in a single portfolio, on an equally-weighted basis.

Required: Calculate the absolute percentage difference in the coefficient of variation (CV) between the stock portfolio [L−M] and the portfolio which outlines the optimal combination of assets.

Answer 1

Step 1: Find Coefficient of variation of stock portfolio L-M

Workings:

Step 2: Find Coefficient of variation of asset portfolio F-G & F-H

Workings:

Step 3: Compare the co-efficient of variations

Expected Return of asset F-G is 16.76% and of F-H is 16.83%. Thus, the optimal combination of assets is F-H having the higher expected return. Coefficient of variation of assets F-H is 7.931%

Coefficient of variation of Stock portfolio L-M = 9.185%

The absolute percentage difference in the coefficient of variation (CV) between the stock portfolio [L−M] and the portfolio which outlines the optimal combination of assets [F-H] = 9.185% - 7.931% = 1.254% or 1.25%