Use the following information for problems 123 Anna will inv

Use the following information for problems 1,2,3

Anna will invest $10,000 this year into one of two stock portfolios, Portfolio A or Portfolio B. The average percentage return on her investment in Portfolio A will vary according to the overall performance of the U.S. economy, as shown below:

            Performance of U.S. Economy                    Percentage return on Portfolio A

                        Poor                                                                -5

                        Typical                                                           5

                        Very good                                                      12

Notice that an investment in Portfolio A will actually lose money this year if the economy performs poorly.

Based on leading economic indicators, there is a 50% chance that the economy will perform poorly this year and a 20% chance that economic performance is very good. Based on this economic forecast, the mean and standard deviation of the return on portfolio B are known to be m_B = 2.0, and s_B = 7.24.

1. Find the mean percentage return for Portfolio A based on the economic forecast.

a)1.4

b)4.4

c)6.4

d)–4.4

e)None of the above

2.       Find the standard deviation for Portfolio A based on the economic forecast.

a)46.79

b)52.42

c)7.24

d)6.84

e)None of the above.

3.       If Anna would like to minimize the uncertainty (variability) in her investment, should she invest in Portfolio A or Portfolio B?

a)Invest in portfolio A since it has smaller standard deviation than Portfolio B.

b)Invest in portfolio A since it has Larger standard deviation than Portfolio B.

c)Invest in portfolio B since it has smaller standard deviation than Portfolio A.

d)Invest in portfolio B since it has larger standard deviation than Portfolio A.

e)The answer cannot be determined because the standard deviation for Portfolio A cannot be calculated based on the given information.

Solution

P[poorly economy]=0.50

P[very good economy]=0.20

hence P[typical economy]=1-0.50-0.20=0.30

so distribution of A is

A :                      -5             5             12

Probability:         0.50          0.30         0.20

1. so mean of A=E{A]=-5*0.50+5*0.30+12*0.20=1.4 (option a)

2. var(A)=E[A²]-E[A]²=25*0.5+25*0.3+144*0.2-1.4²=46.84 (option e)

3. answer is c)