| Consider the following information: |
| Rate of Return If State Occurs | ||||||
| State of | Probability of | |||||
| Economy | State of Economy | Stock A | Stock B | Stock C | ||
| Boom | .15 | .350 | .450 | .330 | ||
| Good | .45 | .120 | .100 | .170 | ||
| Poor | .35 | .010 | .020 | −.050 | ||
| Bust | .05 | −.110 | −.250 | −.090 | ||
| Requirement 1: |
| Your portfolio is invested 30 percent each in A and C and 40 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) |
| Expected return of the portfolio | % |
| Requirement 2: |
| (a) | What is the variance of this portfolio? (Do not round intermediate calculations. Round your answer to 5 decimal places (e.g., 32.16161).) |
| Variance of the portfolio |
| (b) | What is the standard deviation of this portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) |
| Standard deviation | % |
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:
Boom: E(Rp) = .30(.35) + .40(.45) + .30(.33) = .3840 or 38.400%
Good: E(Rp) = .30(.12) + .40(.10) + .30(.17) = .1270 or 12.70%
Poor: E(Rp) = .30(.01) + .40(–.20) + .30(–.05) = –.0920 or –9.20%
Bust: E(Rp) = .30(–.110) + .40(–.250) + .30(–.90) = –.16 or –16%
And the expected return of the portfolio is:
E(Rp) = .15(.3840) + .45(.1270) + .35(–.0920) + .05(–.16) = .0746 or 7.46%
- What is the variance of this portfolio? The standard deviation?
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:
sp2 = .15(.3840 – .0746)2 + .45(.1270 – .0746)2 + .35(–.0920 – .0746)2 + .05(–.16 – .0746)2 = .02 8061
sp = (.02546).5 = .1675 or 16.75%
