You have a portfolio worth $86,000 that has an expected return of 11.2 percent. The portfolio...

You have a portfolio worth $86,000 that has an expected return of 11.2 percent. The portfolio has $17,800 invested in Stock O, $25,600 invested in Stock P, with the remainder in Stock Q. The expected return on Stock O is 15.5 percent and the expected return on Stock P is 12 percent. What is the expected return on Stock Q?

Multiple Choice

8.92%
9.60%
10.27%
11.20%
12.97%

Solutions

Expert Solution

Total Amount invested in the portfolio = $86000

Stock O

Amount invested in stock P = $17800

Weight of stock O in the portfolio = WO = Amount invested in stock O/Amount invested in the portfolio = 17800/86000 = 0.206976744186047

Expected return on stock O = E[RO] = 15.5%

Stock P

Amount invested in stock P = $25600

Weight of stock P in the portfolio = WP = Amount invested in stock P/Amount invested in the portfolio = 25600/86000 = 0.297674418604651

Expected return on stock P = E[RP] = 12%

Stock Q

Amount invested in stock Q = $8600 - $17800 - $25600 = 42600

Weight of stock Q in the portfolio = WQ = Amount invested in stock Q/Amount invested in the portfolio = 25600/86000 = 0.495348837209302

Expected return on stock Q = E[RP]

Portfolio

Expected return of the portfolio = E[RP] = 11.2%

Expected return of the portfolio is calculate using the formula:

Expected return of Portfolio = E[RP] = WO*E[RO] + WP*E[RP] + WQ*E[RQ]

11.2% = 0.206976744186047*15.5% + 0.297674418604651*12% + 0.495348837209302*E[RQ]

11.2% = 0.0320813953488372 + 0.0357209302325581 + 0.495348837209302*E[RQ]

11.2% = 0.0678023255813954 + 0.495348837209302*E[RQ]

0.495348837209302*E[RQ] = 0.0441976744186046

E[RQ] = 0.0441976744186046/0.495348837209302 = 8.9225352112676% ~ 8.92% (Rounded to two decimals)

Expected return on stock Q = E[RQ] = 8.92%

Answer -> 8.92%

jeff jeffy answered 1 year ago

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