Question

The following table presents forecasted returns for three companies under various potential states of the economy:

State	Probability	Stock X	Stock Y	Stock Z
Above Average	10%	38.4%	28.0%	43.8%
Average	45%	15.1%	9.0%	12.0%
Below Average	30%	-2.0%	-4.0%	-7.0%
Recession	15%	-12.1%	-6.0%	-15.7%
Weight		55%	30%	15%

What is the expected return on a portfolio of these three companies constructed according to the weights given in the table? (Report answer in percentage terms and round to 2 decimal places. Do not round intermediate calculations).

Answer 1

SOLUTION:-

The expected return on each is stock is calculated in the following chart;-

  

State	Probability	Stock X	Stock Y	Stock Z	Expeted return ( stock x)	Expeted return ( stock Y)	Expeted return ( stock Z)
Above Average	10%	38.4%	28.0%	43.8%	3.84%	2.8%	4.38%
Average	45%	15.1%	9.0%	12.0%	6.795%	4.05%	5.4%
Below Average	30%	-2.0%	-4.0%	-7.0%	-.6%	-1.2%	-2.1%
Recession	15%	-12.1%	-6.0%	-15.7%	-1.815%	-.9%	-2.355%
Total	100%				8.22%	4.75%	5.325%

EQUATIONS USED IN ABOVE CHART WERE AS FOLLOWS;-

Expected return = probability * given return

      Expected return (stock X)= (probability * given return of (stock X) in each state)

Expected return (stock Y) = (probability * given return of (stock Y) in each state)

    Expected return (stock Z) = (probability * given return of (stock Z) in each state)

The expected return on a portfolio of these three stocks are calculated in the following chart;-

Stocks	Expected return of each stock (ER)	weights (W)	ER* W
stock X	8.22%	55%	4.521%
stock Y	4.75%	30%	1.425%
stock Z	5.325%	15%	.799%
Total			6.74

EQUATIONS USED IN ABOVE CHART WERE AS FOLLOWS;-

The expected return on a portfolio = (Expected return on each stock (ER) * weight of each stock (W))

The expected return on a portfolio = 6.74%