Question

Consider the following information about three stocks. Assume you create your own portfolio and the weightage of the portfolio for the following stock is as follows: 50% of stock A, 30% of stock B and 20% of stock C.

Nigeria Economy	Probability of Happening	stock A	stock B	stock C
Expansion	0.4	26%	40%	50%
Normal	0.3	20%	30%	35%
Recession	0.3	15%	25%	10%

Required:

1) Find the portfolio expected return. (Hint: Only one answer.)

2) Find the standard deviation?

Answer 1

Solution :-

(i)

Expected Return of Stock A = ( 0.40 * 26% ) + ( 0.30 * 20% ) + ( 0.30 * 15% ) = 20.9%

Expected Return of Stock B = ( 0.40 * 40% ) + ( 0.30 * 30% ) + ( 0.30 * 25% ) = 32.5%

Expected Return of Stock C = ( 0.40 * 50% ) + ( 0.30 * 35% ) + ( 0.30 * 10% ) = 33.5%

Now Portfolio Expected Return = ( 0.50 * 20.9% ) + ( 0.30 * 32.5%) + ( 0.20 * 33.5% ) = 26.90%

(ii)

Now Variance = 0.50 * ( 20.9% - 26.90% )² + 0.30 * ( 32.5% - 26.90% )² + 0.20 * ( 33.5% - 26.90% )

= 36.12%

Standard Deviation = ( 36.12% )^1/2 = 6.01%

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