Question

# Given the following probability distribution, what are the expected return and the standard deviation of returns...

 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%

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?

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?

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?

14.6%

14.3%

14.4%

14.7%

14.5%

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)