Question

1. Suppose you own a 4-security portfolio composed of Apple, AT&T, Microsoft and Verizon. You expect a return of 19%, 12%, 18% and 22%, respectively, having invested $4,500, $2,500,$3,000, and $4,000, respectively. What is the expected return on the portfolio?

   		13.9%
   		15.7%
   		17.1%
   		18.4%

2.

1. Consider a stock which earns 5%, 7% 18% when the economy is bad, normal, or good, respectively. Further, suppose that the probability that the economy is bad, normal, or good is 0.15, 0.60, or 0.25, respectively. What is the expected return on the stock?

   		9.45%
   		11.85%
   		13.25%
   		15.75%

3.

1. Consider a stock which earns 5%, 7% 18% when the economy is bad, normal, or good, respectively. Further, suppose that the probability that the economy is bad, normal, or good is 0.15, 0.60, or 0.25, respectively. What is the standard deviation of the stockâ s return? Assume that the expected return is 12%.

   		2.93%
   		3.47%
   		4.17%
   		5.60%

Answer 1

1.

Stock	Amount invested	Weights	Return
Apple	4500	32.1%	19%
AT&T	2,500	17.9%	12%
Microsoft	3,000	21.4%	18%
Verizon	4,000	28.6%	22%

Total amount invested in the portfolio = $4500 + $2500 + $3000 + $4000 = 14000

Weight of Apple in the portfolio = w1 = 4500/14000 = 32.1%

Weight of AT&T in the portfolio = w2 = 2500/14000 = 17.9%

Weight of Microsoft in the portfolio = w3 = 3000/14000 = 21.4%

Weight of Verizon in the portfolio = w4 = 4000/14000 = 28.6%

Return on Apple = R1 = 19%

Return on AT&T = R2 = 12%

Return on Microsoft = R3 = 18%

Return on Verizon = R4 = 22%

Expected return on the portfolio is calculated using the formula:

Expected return of the portfolio = E[RP] = w1*R1 + w2*R2 + w3*R3 + w4*R4 = 32.1%*19% + 17.9%*12% + 21.4%*18% + 28.6%*22% = 18.391% ~ 18.4% (Rounded to one decimal place)

Answer -> 18.4%

2.

State of Economy	Probability	Return
Bad	0.15	5%
Normal	0.60	7%
Good	0.25	18%

We have the following data:

p1 = 0.15, p2 = 0.6, p3 = 0.25

R1 = 5%, R2 = 7%, R3 = 18%

Expected return is calculated using the formula:

Expected return = E[R] = p1*R1 + p2*R2 + p3*R3 = 0.15*5% + 0.6*7% + 0.25*18% = 9.45%

Answer 2 -> 9.45%

3.

State of Economy	Probability	Return
Bad	0.15	5.0%
Normal	0.60	7.0%
Good	0.25	18.0%

It is given that the expected return is 12%, i.e., E[R] = 12%

We have the following data:

p1 = 0.15, p2 = 0.6, p3 = 0.25

R1 = 5%, R2 = 7%, R3 = 18%

Variance is calculated using the formula:

Variance = σ2 = p1*(R1-E[R])2 + p2*(R2-E[R])2 + p3*(R3-E[R])2

Variance = σ2 = 0.15*(5%-12%)2 + 0.60*(7%-12%)2 + 0.25*(18%-12%)2 = 0.000735+0.0015+0.0009 = 0.003135

Standard deviation is squareroot of variance

Standard deviation = σ = (0.003135)1/2 = 5.59910707166777% ~ 5.60% (Rounded to two decimals)

Answer 3 -> 5.60%