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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 10.7 percent. Assume D has an expected return of 14.2 percent, F has an expected return of 10.1 percent, and the risk-free rate is 5.6 percent. If you invest $50,000 in Stock D, how much will you invest in Stock F

Respuesta :

Answer:

You will invest $18,000 in Stock F.

Explanation:

This can be calculated using the portfolio return formula as follows:

PR = (wD * rD) + (wF * rF) + (wR * rR) ............................ (1)

Where;

PR = Portfolio expected return = 10.7%, or 0.107

wD = Weight of the amount invested in Stock D = Amount invested in Stock D / Total amount invested = $50,000 / $100,000 = 0.50

rD = Expected Return from Stock D = 14.2%, or 0.142

wF = Weight of the amount invested in Stock F = Amount invested in Stock F / Total amount invested = ?

rF = Expected Return from StocK F = 10.1%, or 0.101

wR = Weight of the amount invested in risk free = 1 - wD - wF = 1 - 0.50 - wF = 0.50 - wF

rR = Expected Return from Risk free = 5.6%, or 0.056

Substitute all the values into equation (1), we have:

0.107 = (0.50 * 0.142) + (wF * 0.101) + ((0.50 - wF) * 0.056)

0.107 = 0.071 + (wF * 0.101) + ((0.50 * 0.056) - (wF * 0.056))

0.107 - 0.071 = (wF * 0.101) + 0.028 - (wF * 0.056)

0.036 - 0.028 = (wF * 0.101) - (wF * 0.056)

0.008 = wF(0.101 - 0.056)

0.008 = wF0.045

wF = 0.008 / 0.045

wF = 0.18

Since,

wF = Amount invested in Stock F / Total amount invested

We then substitute and solve for Amount invested in Stock F as follows:

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

Amount invested in Stock F = 0.18 * $100,000 = $18,000

Therefore, you will invest $18,000 in Stock F.

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