Question

You can form a portfolio of two assets, A and B, whose returns have the following characteristics:

                   Expected Return         Standard Deviation           Correlation

A                  8%                           30%

                                                                                                     .7

B                  18                                44

a. If you demand an expected return of 15%, what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 3 decimal places.)

Stock           Portfolio Weight

A

B

b. What is the portfolio’s standard deviation? (Use decimals, not percents, in your calculations. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Standard deviation %

Answer 1

a. If you demand an expected return of 15%, what are the portfolio weights?

The return of a portfolio is the weighted average return of the securities which constitute the porfolio

Let weight of Stock A be x

Stock	Weight	Expected Return (%)	Weight*Expected Return
A	x	8.00	8x
B	1-x	18.00	18-18x

Portfolio Return = Weight*Expected Return

15 = 8x + 18 -18x

18x-8x = 18-15

10x = 3

x = 3/10

= .3

weight of Stock A = .300 = 30.000%

weight of Stock B = .700 = 70.000%

b. What is the portfolio’s standard deviation?

Portfolio Standard Deviation = [(WA*SDA)^2 + (WB*SDB)^2 + (2*WA*WB*SDA*SDB*CorAB)]

where

WA - Weight of stock A =.3

WB - Weight of stock B =.7

SDA - Standard Deviation of stock A = .3

SDB - Standard Deviation of stock B = .44

CorAB - Correlation coefficient = .7

Portfolio Standard Deviation = [(.3*.3)^2 + (.7*.44)^2 + (2*.3*.7*.3*.44*.7)]

= (0.0081+0.094864+0.038808)

= 0.141772

= 37.65%