Question

Suppose you have predicted the following returns for stocks ABC and XYZ in three possible states of the economy:

            State                Probability       XYZ                ABC

            Boom              0.50                 -5%                  25%

            Normal            0.30                 10%                 10%

            Recession        0.20                 12%                 -5%

1. Calculate the expected return on ABC.

2. Calculate the expected return on XYZ.

3. Suppose you construct a portfolio with ABC and XYZ exclusively. You allocate 40% of your investment to ABC, and 60% to XYZ. What is the expected return on the portfolio?

4. Without calculation, what kind of correlation between ABC and XYZ do you see? Is this correlation good or bad for the portfolio? Please explain.

Answer 1

1) & 2).
Expected Return On ABC & XYZ respectively.

State	Probability (A)	XYZ (B)	A*B	ABC (C)	A*C
Boom	0.50	-5%	-2.50	25%	12.50
Normal	0.30	10%	3.00	10%	3.00
Recession	0.20	12%	2.40	-5%	-1.00
Exp Return			2.90		14.50

Expected Return into ABC Is 14.50 & XYZ is 2.90 respectively.

3). For a Construct a portfolio with ABC and XYZ exclusively.
Allocate 40% of investment to ABC, and 60% to XYZ.
expected return on the portfolio is..
= (40% of ER of ABC) + (60% Of ER of XYZ)
=(40%*14.50)+(60%*2.90)
=5.80+1.74
=7.54

4). Without Calculation, we can say that both portfolio are same under normal state where return of stock are nutral into game, but in case of recession state its quite good under Stock of XYZ Where return is postive, but negative into ABC Stock, however Into Boom state of affairs its negative into XYZ as compare to ABC is positive looks quite good.
   this kind of correlation is not good for the purpose of making vast portfolio scenario comparing to others factors into considering.