Answer to Question #314610 in Statistics and Probability for Entle

Question

You are deciding between two portfolios; Portfolio A which is made up of stocks and treasury bills, and Portfolio B which comprises of risky bonds and treasury bills. The table below contains information on both portfolios that you collected.

Information

Portfolio A

Portfolio B

Mean returns

0,13

0,16

Standard Deviation

0,11

0,09

Expected Returns

0,15

0,12

Threshold level

0,07

0,07

a) What is the probability that the returns of Portfolio A lie between 15 and 25 percent?

b) If the probability that the returns of Portfolio B would be greater than X is 0.2676, what is the value of X?

c) Which portfolio is the optimal portfolio considering your threshold level?

d) For the optimal portfolio found in (c), what is the probability that the portfolio will earn a return below the threshold level?

Answer 1

a.0.25-0.15=0.1

$\sigma=0.11 - 68$

$z=\frac{x_i-x}{\sigma}= \frac{0.15-0.13}{0.11}=0.1818$

$z=\frac{x_i-x}{\sigma}= \frac{0.25-0.13}{0.11}=1,09$

$1.09 \sigma$ is 74,2%

$0.1818 \sigma$ is 12.4%

74.2-12.4=61.8%

b.Z=-0.58

$X=(z \sigma)+ \mu=-0.58x0.12+0.16=0.09$

c. $SFRatio=\frac{r_e-r_m}{\sigma}$

For A:(0.15-0.07)/0.11=0.73

For B: (0.12-0.07)/0.09=0.56

For A is greater, so we should select A

d.(0.13-0.07)/0.11=0.08/0.11=0.7272

$0.7272 \sigma$ is 49.4%

P=100-49.4=50.6%