Question

Use the following information to answer the next seven questions.

Suppose there are three potential states of the economy for next year: good, normal, and bad. Each state has equal probability to occur, that is, the probability is 1/3 for all of them. Returns of asset A and B in each state are given in the following table.

	good	normal	bad
A	0.20	0.08	-0.01
B	0.15	0.10	-0.04

1. Find out the expected return of a portfolio with equal weight invested in A and B.

2. Find out the standard deviation of a portfolio with equal weight invested in A and B.

3. You plan to invest in assets A and B, and hope your portfolio to have an expected return of 8.6%. How should you allocate your money on A and B?

4. What is the standard deviation of the portfolio you formed in the previous question?

Answer 1

1) Expected Return of Asset A = 1/3(.2) + 1/3(.08) + 1/3(-.01)

= .067+ .027 - .003

= .091

Expected Return of Asset B = 1/3(.15) + 1/3(.1) + 1/3(-.04)

= .05 + .03 - .013

= .067

Now to find return on Portfolio with equally distributed Weights

= .5(.091) + .5(.067)

= .0455 + .0335

= .079 OR 7.9%