Homework Assignment #3 ECO 3223, Fall Semester 2017 Due: Friday, December 8th at

Question

Homework Assignment #3 ECO 3223, Fall Semester 2017 Due: Friday, December 8th at the beginning of class Table 1: Stand-Alone Risk and Expected Return for Selected Assets Asset A Asset B Expected Rate of Return 5% 15% Std Deviation of Rate of Return 10% 30% 1. Use the information provided in Table 1 to calculate (1) the expected value of the rate of return, and (2) the standard deviation of the rate of return for a portfolio of 1/2 Asset A and 1/2 Asset B in each of the following cases: a. pA,B 1.00 bpaB = 0.50 c. PAB=0.00

Explanation / Answer

1.

Expected return of the portfolio = (50%*Return of asset A + 50% * return of asset B)

Expected return of the portfolio =50%*5% + 50%*15%

Expected return of the portfolio = 10%

2.

Standard deviation (portfolio) = (Wa^2 * SDa^2 + Wb^2 * SDb^2 + 2*Wa*Wb*SDa*SDb*ab)^.5

Here,

Wa = weight of asset A

Wb = weight of asset B

SDa = Standard deviation of Asset A

SDb = Standard deviation of Asset B

ab = Correlation coefficient between Asset A & B

A.

If ab = 1

Then

Standard deviation (portfolio) = (.5^2 * 10^2 + .5^2 * 30^2 + 2*.5*.5*10*30*1)^.5

Standard deviation (portfolio) = 20%

B.

If ab = .5

Then

Standard deviation (portfolio) = (.5^2 * 10^2 + .5^2 * 30^2 + 2*.5*.5*10*30*.5)^.5

Standard deviation (portfolio) = 18.03%

C.

If ab = 0

Then

Standard deviation (portfolio) = (.5^2 * 10^2 + .5^2 * 30^2 + 2*.5*.5*10*30*0)^.5

Standard deviation (portfolio) = 15.81%

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