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	14.13%	20.87%
2	14.88%	18.83%
3	16.06%	16.49%
4	17.38%	14.46%
5	17.7%	12.51%
6	19.27%	10.04%

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	16.46%	17.01%	14.4%
2	17.49%	16.39%	15.14%
3	18.25%	15.02%	16.24%
4	19.36%	14.16%	17.25%

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

Expected Return of Portfolio L-M

Year	Stock L	Stock M	Weight for Stock L	Weight for Stock M	Portfolio return (Return of L * Weight of L + Return of M * Weight of M)
1	14.13%	20.87%	0.4	0.6	18.174%
2	14.88%	18.83%	0.4	0.6	17.250%
3	16.06%	16.49%	0.4	0.6	16.318%
4	17.38%	14.46%	0.4	0.6	15.628%
5	17.70%	12.51%	0.4	0.6	14.586%
6	19.27%	10.04%	0.4	0.6	13.732%
Total portfolio returns for 6 years	95.688%
Average portfolio returns for 6 years (Total portfolio returns / 6)	15.948%

Standard Deviation of Portfolio L-M

Year	Portfolio return	Average / Mean return of portfolio	Deviation from Mean	Square of Deviations
1	18.174%	15.948%	-2.2260%	0.0496%
2	17.250%	15.948%	-1.3020%	0.0170%
3	16.318%	15.948%	-0.3700%	0.0014%
4	15.628%	15.948%	0.3200%	0.0010%
5	14.586%	15.948%	1.3620%	0.0186%
6	13.732%	15.948%	2.2160%	0.0491%
Sum of squared deviation from mean	0.1366%
Standard deviation of Portfolio L-M {(Square root of (aggregate squared deviation from mean / no. of years)}	1.5086%

Coefficient of Variation of Portfolio L-M

--- > (Standard Deviation of Portfolio / Portfolio Mean)*100

9.4595

Expected Return of Portfolio F-G

Year	Stock F	Stock G	Weight for Stock F	Weight for Stock G	Portfolio return (Return of F * Weight of F+ Return of G * Weight of G)
1	16.46%	17.01%	0.5	0.5	16.7350%
2	17.49%	16.39%	0.5	0.5	16.9400%
3	18.25%	15.02%	0.5	0.5	16.6350%
4	19.36%	14.16%	0.5	0.5	16.7600%
Total portfolio returns for 4 years	67.0700%
Average portfolio returns for 4 years (Total return / 4)	16.7675%

Standard Deviation of Portfolio F-G

Year	Portfolio return	Average / Mean return of portfolio	Deviation from Mean	Square of Deviations
1	16.7350%	16.7675%	0.0325%	0.0000%
2	16.9400%	16.7675%	-0.1725%	0.0003%
3	16.6350%	16.7675%	0.1325%	0.0002%
4	16.7600%	16.7675%	0.0075%	0.0000%
Sum of squared deviation from mean	0.0005%
Standard deviation {(Square root of (aggregate squared deviation from mean / no. of years)}	0.1100%

Expected Return of Portfolio F-H

Year	Stock F	Stock H	Weight for Stock F	Weight for Stock H	Portfolio return (Return of F * Weight of F+ Return of H * Weight of H)
1	16.46%	14.40%	0.5	0.5	15.4300%
2	17.49%	15.14%	0.5	0.5	16.3150%
3	18.25%	16.24%	0.5	0.5	17.2450%
4	19.36%	17.25%	0.5	0.5	18.3050%
Total portfolio returns for 4 years	67.2950%
Average portfolio returns for 4 years (Total return / 4)	16.8238%

Standard Deviation of Portfolio F-H

Year	Portfolio return	Average / Mean return of portfolio	Deviation from Mean	Square of Deviations
1	15.4300%	16.8238%	1.3938%	0.0194%
2	16.3150%	16.8238%	0.5087%	0.0026%
3	17.2450%	16.8238%	-0.4213%	0.0018%
4	18.3050%	16.8238%	-1.4813%	0.0219%
Sum of squared deviation from mean	0.0457%
Standard deviation {(Square root of (aggregate squared deviation from mean / no. of years)}	1.0692%

From above analysis of Portfolio F-G and F-H noted that Portfolio F-h has higher return in comparision to Portfolio F-G, Hence for a risk taking customer Portfolio F-H would be optimal one.

Since Portfolio F-H has been identified as optimal portfolio, below is the computation of for Coefficient of Variation for Portfolio F-H and absolute difference in Coefficient of Variation for portfolio L-M and F-H.

Coefficient of Variation of Portfolio F-H

--- > (Standard Deviation of Portfolio / Portfolio Mean)*100

6.3554%

Difference in Coefficient of Variation for L-M and F-H

=9.4595% - 6.3554%

3.10%