Use the following information on states of the economy and stock returns to calc

Question

Use the following information on states of the economy and stock returns to calculate the standard deviation of returns. Assuming that all three states are equally likely. (

3.calculate the expected return on a portfolio of 60 percent Roll and 40 percent Ross by filling in the following table:

Use the following information on states of the economy and stock returns to calculate the standard deviation of returns. Assuming that all three states are equally likely. (

3.calculate the expected return on a portfolio of 60 percent Roll and 40 percent Ross by filling in the following table:

Explanation / Answer

a.This portfolio does not have an equal weight in each asset. We first 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:

And the expected return of the portfolio is:

E(Rp) = .30(.3225) + .20(.1625) + .10(–.0725) + .40(–.1775) = 0.051

b-1 and b-2

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, and then sum.The result is the variance. So, the variance and standard deviation of the portfolio is:

Variance = .30(.3225 – .051)2 + .20(.1625 – .051)2 + .10(–.0725 – .051)2 + .40(–.1775 – .051)2 = 0.04701

Standard deviation =  (.04701)^.5 = 0.216818

2. To calculate standard deviation first of all we have to calculate expected retrun follwed by variance .As  all three states are equally likely.

Expected return = -9+16+25 /3 = 10.67%

Variance = .34(-.09 – .1067)2 + .33(.16 –.1067)2 + .33(–.25 –.1067)2 = 0.02087

Standard deviation = (0.02087)^.5 = 0.14446

3. Expected return on a portfolio

Expected return on portfolio = 13.24%

Boom: E(Rp) = .25(.19) + .50(.43) + .25(.24) = 0.3225 Good:    E(Rp) = .25(.17) + .50(.17) + .25(.14) = 0.1625 Poor: E(Rp) = .25(-.04) + .50(-.14) + .25(.03) = -0.0725 Bust: E(Rp) = .25(-.16) + .50(-.22) + .25(-.11) = -0.1775

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