Question

The portfolio manager of XYZ bank recently used reports from its securities analysts to develop the following efficient portfolios;

        Expected Rate of Return    Variance
1                       8%                              25
2                      10%                             36
3                      15%                             64
4                      20%                            169
5                      25%                            324

a. If the risk free rate of interest is 3% which portfolio is best?
b. Assume that the portfolio manager would like to earn an expected rate of return of 10% with a standard deviation of 4%, is this possible?
c. If a standard deviation of 12% was acceptable to the portfolio manager, what would be the expected return and how would it best be achieved?
d. What is the expected rate of return on a combined portfolio made up of all the above 5 portfolios with an equal weighting given to each portfolio? Would the standard deviation of this combined portfolio be higher or lower than that of portfolio 3 or is it not possible to say?

Answer 1

(a) In order to determine the best portfolio of the lot, coefficient of variation needs to be computed:

Coefficient of variation = Standard deviation / Expected return

Standard deviation = Square root of variance

Expected return	Variance	Standard deviation	Coefficient of variation
8%	25	5	0.625
10%	36	6	0.6
15%	64	8	0.533
20%	169	13	0.65
25%	324	18	0.72

The lower the coefficient of variation, the better is the option.

Therefore, best among the lot is 3rd option where expected return is 15% and standard deviation is 8.

(b) Among the efficient portfolios, 10% return can be expected with a standard deviation of 6%. Therefore, 10% expected rate of return with 4% deviation is not possible.

(c) If standard deviation of 12% was acceptable to the portfolio manager, then the expected return would be calculated with coefficient of variation being 0.533 which is the best of the lot. Therefore, expected return would be = 12/0.533 = 22.5%