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	14.65%	20.28%
2	14.27%	18.83%
3	16.87%	16.47%
4	17.61%	14.61%
5	18%	12.37%
6	19.84%	10.64%

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	16.47%	17.03%	14.16%
2	17.2%	16.27%	15.01%
3	18.17%	15.32%	16.35%
4	19.12%	14.44%	17.43%

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% Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places (for example: 28.31%).

Answer 1

Solution:

A) Expected Return of Portfolio L-M:

Year	Stock L	Stock M	Portfolio return(L*0.4+M*0.6)
1	14.65%	20.28%	18.03%
2	14.27%	18.83%	17.01%
3	16.87%	16.47%	16.63%
4	17.61%	14.61%	15.81%
5	18.00%	12.37%	14.62%
6	19.84%	10.64%	14.32%
Expected Return of Portfolio L-M			16.07%

Standard Deviation of Portfolio L-M:

Year	Portfolio return	Mean of Pf Return	Deviation from Mean	Square of Deviations
1	18.03%	16.07%	1.96%	0.04%
2	17.01%	16.07%	0.94%	0.01%
3	16.63%	16.07%	0.56%	0.00%
4	15.81%	16.07%	-0.26%	0.00%
5	14.62%	16.07%	-1.45%	0.02%
6	14.32%	16.07%	-1.75%	0.03%
Total				0.10%
Standard Deviation = Square root of 0.10%/6	1.31%

Coefficient of Variation of Portfolio L-M = (SD of Portfolio / Portfolio Mean)*100 = 1.31/16.07 * 100 = 8.15%

B)

Expected Return of Portfolio F-G:

Year	Stock F	Stock G	Portfolio return(F*0.5+G*0.5)
1	16.47%	17.03%	16.75%
2	17.20%	16.27%	16.74%
3	18.17%	15.32%	16.75%
4	19.12%	14.44%	16.78%
Expected Return of Portfolio F-G			16.75%

Standard Deviation of Portfolio F-G:

Year	Portfolio return	Mean of Pf Return	Deviation from Mean	Square of Deviations
1	16.75%	16.75%	0.00%	0.00%
2	16.74%	16.75%	-0.02%	0.00%
3	16.75%	16.75%	-0.01%	0.00%
4	16.78%	16.75%	0.03%	0.00%
Total				0.00%
Standard Deviation = Square root of 0.10%/6	0.01%

Expected Return of Portfolio F-H:

Year	Stock F	Stock H	Portfolio return(F*0.5+H*0.5)
1	16.47%	14.16%	15.32%
2	17.20%	15.01%	16.11%
3	18.17%	16.35%	17.26%
4	19.12%	17.43%	18.28%
Expected Return of Portfolio F-H			16.74%

Standard Deviation of Portfolio F-H:

Year	Portfolio return	Mean of Pf Return	Deviation from Mean	Square of Deviations
1	15.32%	16.74%	-1.42%	0.02%
2	16.11%	16.74%	-0.63%	0.00%
3	17.26%	16.74%	0.52%	0.00%
4	18.28%	16.74%	1.54%	0.02%
Total				0.05%
Standard Deviation = Square root of 0.10%/6	0.92%

As we can observe, among Portfolios FG and FH, both offer approximately same returns but if we were to choose one between them, we choose Portfolio FG as it has little to none standard deviation i.e., the portfolio is less volatile compared to Portfolio FH. Therefore, the optimal portfolio among the two is FG.

Coefficient of Variation for Portfolio F-G = 0.01/16.75 * 100 = 0.06%

Hence,

Difference in Coefficient of Variation for L-M and F-G = 8.15 - 0.06 = 8.09%