Show all work to the question below ? State of Economy Rate of Return If State Occurs

Show all work to the question below ?

Transcribed Image Text:

State of Economy Rate of Return If State Occurs Probability of State of Economy Stock A Stock B Stock C Boom .10 .35 .40 .27 Good .60 .16 .17 .08 Poor .25 -.01 -.03 -.04 Bust .05 -.12 -.18 -.09 a. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio? b. What is the variance of this portfolio? The standard deviation? Solution: 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: b. Boom: Rp.30(.35) + .40(.40) + .30(.27) = .3460, or 34.60% Good: Rp.30(.16) + .40(.17) + .30(.08) = .1400, or 14.00% Poor: Rp.30(-.01)+ .40(-.03) + .30(-.04) = -.0270, or -2.70% Rp.30(-12)+ .40(-.18) + .30(-.09) = -.1350, or -13.50% Bust: And the expected return of the portfolio is: E(Rp)=.10(.3460) + .60(.1400) +.25(-.0270) + .05(-.1350) E(Rp) .1051, or 10.51% 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, then add all of these up. The result is the variance. So, the variance and standard deviation of the portfolio are: p=.10(.3460-.1051)+.60(.1400 -.1051)+.25(-.0270-.1051)+.05(-.1350 -.1051) Op=.01378 Op = .013781/2 Op.1174, or 11.74% (Please also see Homework 6 Excel Examples for computation on Excel) Q6: Returns and Standard Deviations: Consider the following information: Rate of Return If State Occurs State of Economy Probability of State of Economy Stock A Stock B Stock C Boom .10 .35 .40 .27 Good .50 .16 .15 .08 Poor .25 -.02 -.03 -.04 Bust .15 -.12 -.18 -.10 C. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio? d. What is the variance of this portfolio? The standard deviation? (Please follow above example to solve this question) State of Economy Rate of Return If State Occurs Probability of State of Economy Stock A Stock B Stock C Boom .10 .35 .40 .27 Good .60 .16 .17 .08 Poor .25 -.01 -.03 -.04 Bust .05 -.12 -.18 -.09 a. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio? b. What is the variance of this portfolio? The standard deviation? Solution: 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: b. Boom: Rp.30(.35) + .40(.40) + .30(.27) = .3460, or 34.60% Good: Rp.30(.16) + .40(.17) + .30(.08) = .1400, or 14.00% Poor: Rp.30(-.01)+ .40(-.03) + .30(-.04) = -.0270, or -2.70% Rp.30(-12)+ .40(-.18) + .30(-.09) = -.1350, or -13.50% Bust: And the expected return of the portfolio is: E(Rp)=.10(.3460) + .60(.1400) +.25(-.0270) + .05(-.1350) E(Rp) .1051, or 10.51% 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, then add all of these up. The result is the variance. So, the variance and standard deviation of the portfolio are: p=.10(.3460-.1051)+.60(.1400 -.1051)+.25(-.0270-.1051)+.05(-.1350 -.1051) Op=.01378 Op = .013781/2 Op.1174, or 11.74% (Please also see Homework 6 Excel Examples for computation on Excel) Q6: Returns and Standard Deviations: Consider the following information: Rate of Return If State Occurs State of Economy Probability of State of Economy Stock A Stock B Stock C Boom .10 .35 .40 .27 Good .50 .16 .15 .08 Poor .25 -.02 -.03 -.04 Bust .15 -.12 -.18 -.10 C. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio? d. What is the variance of this portfolio? The standard deviation? (Please follow above example to solve this question)