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You have $100,000 to invest in either Stock D, Stock F, or a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 11.4 percent. Assume D has an expected return of 14.9 percent, F has an expected return of 10.8 percent, and the risk-free rate is 5.95 percent. If you invest $50,000 in Stock D, how much will you invest in Stock F? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Sagot :

tutorAnne

Answer:$20,000 will be invested in StocK F

Explanation:

The expected return of portfolio is calculated as  

Portfolio Expected Return =  (wD x rD) + (wF x rF) + (wR x rR) ............................

Where;

 Portfolio expected return = 11.4%

wD = Weight of the amount invested in Stock D  which is calculated as

Amount invested in Stock D / Total amount invested

= $50,000 / $100,000 = 0.50

rD = Expected Return from Stock D = 14.9%

wF = Weight of the amount invested in Stock F= ?

rF = Expected Return from StocK F = 10.8%

wR = Weight of the amount invested in risk free = one minus the weight of the other two assets= 1 - wD - wF = 1 - 0.50 - wF = 0.50 - wF

rR = Expected Return from Risk free = 5.95%

Putting  all the values into the  equation, we

that

0.114= (0.50 x 0.149) + (wF x 0.108) + ((0.50 - wF)  x 0.0595

0.114= 0.0745 + (wF x 0.108) +0.02975 -0.0595wF

0.114- 0.0745  =wF 0.108 +0.02975 -0.0595wF

0.114- 0.0745--0.02975=wF 0.108-0.0595wF

0.00975=wF (0.108-0.0595)

0.00975=wF 0.0485

wF ==    0.00975/0.0485

wF==0.2010  rounded to 0.20

Recall that wF = Amount invested in Stock F / Total amount invested

0.20= Amount invested in Stock F / $100,000

Amount invested in Stock F = 0.20x $100,000 = $20,000

Therefore, $20,000 will be invested in StocK F

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