Question

Given the following probability distribution, what are the expected return and the standard

deviation of returns for Security J?

State                      Pi                              rj

    1                          0.2                           12%

    2                          0.3                           4%

    3                          0.5                           17%

Group of answer choices

12.10%; 5.93%

12.30%; 5.63%

12.40%; 5.63%

12.30%; 5.93%

12.10%; 5.63%

Suppose you hold a diversified portfolio consisting of a $6,485 invested equally

in each of 20 different common stocks.  The portfolio’s beta is 0.81.  Now

suppose you decided to sell one of your stocks that has a beta of 1.4 and to

use the proceeds to buy a replacement stock with a beta of 1.6.  What would

the portfolio’s new beta be?

Group of answer choices

1.02

0.82

0.92

1.12

0.72

A stock has an expected return of 19.1 percent.  The beta of the stock is 2.15 and the

risk-free rate is 2.9 percent.  What is the market risk premium?

Group of answer choices

7.63%

7.53%

7.23%

7.33%

7.43%

Your portfolio consists of $31,232 invested in a stock that has a beta = 1.9,

$45,024 invested in a stock that has a beta = 1, and $93,754 invested in a

stock that has a beta = 1.8.  The risk-free rate is 5%.  Last year this portfolio had

a required return of 8.3%.  This year nothing has changed except that the market

risk premium has increased by 3.8%. What is the portfolio’s current required rate

of return?

Group of answer choices

14.6%

14.3%

14.4%

14.7%

14.5%

Answer 1

Solution 1.>

Expected Return = Sum of (probabilities*return)

= (0.2*12%)+(0.3*4%)+(0.5*17%)

= 12.1%

Standard deviation:

State	Return	Mean	(return - mean)	(return - mean)^2
1	12	12.1	-0.1	0.01
2	4		-8.1	65.61
3	17		4.9	24.01

Variance = 0.01+65.61+24.01/3 = 29.877

standard deviation = variance^0.5 = 29.877^0.5 = 5.465

Hence, the correct option is (E)

Solution 2.>

New Beta : 0.81 - 1.4*(1/20) + 1.6*(1/20)

: 0.82

Hence, the correct option is (B)

Solution 3.>

Using CAPM model,

Expected Return = Risk-free rate + Beta * ( Market Risk Premium )

19.1% = 2.9% + 2.15(MRP)

MRP = 0.0753 or 7.53%

Hence, the correct option is (B)