Consider the following information: Your portfolio is invested 28 percent each i

Question

Consider the following information:

Your portfolio is invested 28 percent each in A and C and 44 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected return             %

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

Variance            

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

Standard deviation             %

State of Probability of Rate of Return If State Occurs Economy State of Economy Stock A Stock B Stock C Boom .22 .369 .469 .349 Good .38 .139 .119 .189 Poor .28 .029 .039 .094 Bust .12 .129 .269 .109

Explanation / Answer

PART A CALCULATION OF EXPECTED RETURN

State of economy

probability

Combined return

Expected return

boom

.22

.369×.28+.469×.44+.349×.28

.4074

.4074×.22=.089628

good

.38

.139×.28+.119×.44+.189×.28

.1442

.1442×.38=.054796

poor

.28

.029×.28+.039×.44+(-.094×.28

-.00104

-.00104×.28=-.0002912

bust

.12

-.129×.28+(-.269×.44)+(-.109×.28)

-.185

-.185×.12=-.0222

Total expected return=.08962+.054796-.0002912-.0222

                      =.1219248

CALCULATION OF VARIANCE AND SD

State of

Economy

A

B

C

Boom

.22

.369

.469

.349

Good

.38

.139

.119

.189

Poor

.28

.029

.039

-.094

Bust

.12

-.129

-.269

-.109

.12664

.14804

.1092

A²=.22(.369-.12664) ²+.38(.139--.12664) ²+..28(.029--.12664) ²+..12(-.129-12664)

=.023458

B²=.22(..469-.14804) ²+.38(.119--.14804) ²+..28(.039--.14804) ²+..12(-..269-.14804)

=.02764

C²=.22(..349-.1092) ²+.38(.189--.1092) ²+..28(.094--.1092) ²+..12(-..109-.1092)

=.03227

P²= C²W²+ C²W²+ C²W²+2 W WCOVARIANCE

A=0.1531

B=.16

c=.179

D=.568

State of economy

probability

Combined return

Expected return

boom

.22

.369×.28+.469×.44+.349×.28

.4074

.4074×.22=.089628

good

.38

.139×.28+.119×.44+.189×.28

.1442

.1442×.38=.054796

poor

.28

.029×.28+.039×.44+(-.094×.28

-.00104

-.00104×.28=-.0002912

bust

.12

-.129×.28+(-.269×.44)+(-.109×.28)

-.185

-.185×.12=-.0222

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