Consider the following information: Rate of Return If State Occurs Probability o

Question

Consider the following information: Rate of Return If State Occurs Probability of State of Economy State of Economy Boom Stock B 19 06 Stock C 37 -.05 Stock A 65 .35 Bust 12 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return b. What is the variance of a portfolio invested 16 percent each in A and B and 68 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.) Variance

Explanation / Answer

1. To find the expected return of the portfolio, we need to find the return of the portfolio in each state of the economy. This portfolio is a special case since all three assets have the same weight. To find the expected return in an equally weighted portfolio, we can sum the returns of each asset and divide by the number of assets, so the expected return of the portfolio in each state of the economy is: Boom: E(Rp) = (.11 + .19 + .37)/3 = .2233 or 22.33%

Bust: E(Rp)= (.12 + .06 .05)/3 = .0433 or 4.33%

To find the expected return of the portfolio, we multiply the return in each state of the economy by the probability of that state occurring, and then sum. Doing this, we find:

E(Rp) = .65(.2233) + .35(.0433) = .1603 or 16.03%

2. This portfolio does not have an equal weight in each asset. We still need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get:

Boom: E(Rp) =.16(.11) +.16(.19) + .68(.37) =.2996 or 29.96%

Bust: E(Rp) =.16(.12) +.16(.06) + .68(.05) = –.0052 or –0.52%

And the expected return of the portfolio is:

E(Rp) = .65(.2996) + .35(.0052) = .1929 or 19.29%

To calculate the standard deviation, we first need to calculate the variance.

To find the variance, we find the squared deviations from the expected return.

We then multiply each possible squared deviation by its probability, than add all of these up. The result is the variance. So, the variance and standard deviation of the portfolio is:

p2= .65(.2996 – .1682)2+ .35(.0052 – .1682)2= .000696

p= (.000696)1/2= .02638 or 2.638%

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