Question

Consider the following case:

Rajiv is an amateur investor who holds a small portfolio consisting of only four stocks. The stock holdings in his portfolio are shown in the following table:

Stock	Percentage of Portfolio	Expected Return	Standard Deviation
Artemis Inc.	20%	6.00%	23.00%
Babish & Co.	30%	14.00%	27.00%
Cornell Industries	35%	12.00%	30.00%
Danforth Motors	15%	5.00%	32.00%

The expected return on Rajiv’s stock portfolio is a) 10.35% b) 7.7625% c) 15.52% d) 13.9725%

Suppose each stock in the preceding portfolio has a correlation coefficient of 0.4 (ρ = 0.4) with each of the other stocks. If the weighted average of the risk (standard deviation) of the individual securities in the partially diversified portfolio of four stocks is 28%, the portfolio’s standard deviation (σp) most likely is   28% a) less than b) equal to c) more than

Answer 1

a)

Expected Return of Portfolio (E(rp) can be computed with following equation:

Ε(rp) =Συ; * r,

where,

w = Weight of stock in Portfolio

r = Return of stock.

Thus, Expected return on Rajiv's Portfolio would be:

Erp) = 0.2 * 0.06 + 0.3 * 0.14 +0.35*0.12 +0.15 * 0.05

Erp) = 0.1035

E(rp) = 10.35%

Correct answer: a) 10.35%

b)

Correct answer: a) less than 28%

Standard deviation of a partially diversified portfolio is always less than its weighted average of standard deviation due diversification effect.

Hope it will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.