Consider the following information: Rate of Return If State Occurs State of Prob

Question

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

.33

.43

.23

  Good

.55

.18

.14

.12

  Poor

.25

.05

.08

.06

  Bust

.05

.13

.18

.10

  

b-1

What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)

b-2

What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Consider the following information:

Explanation / Answer

We first need to find the return of the portfolio in each state of the economy.  

Solution; Note : As weight of securities are not given so assuming equal weight I.e. 1/3 or 0.33 each

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) = .33(.33) + .33(.43) + .33(.23) = .3307 or 33.07% Good : E(Rp) = .33(.18) + .33(.14) + .33(.12) = .1452 or 14.52% poor : E(Rp) = .33(-0.05) + .33(-0.08) + .33(-0.06) = -0.0627 or -6.27% Bust : E(Rp) = .33(-0.13) + .33(-0.18) + .33(-0.10) = -0.1353 or -13.53%                         And the expected return of the portfolio is:                         E(Rp) = .15(.3307) + .55(.1452) + .25(–.0627) + .05(–.1353) = .1070 or 10.70% What is the variance of this portfolio? sp2 = .15(.3307 – .1070)^2 + .55(.1452 – .1070)^2 + .25(–.0627 – .1070)^2 + .05(–.0.1353 – .1070)^2 = 0.0183644 What is the standard deviation? sp = Square root of (.018364) = .1355 or 13.55%

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