Answer:
You will invest <u>$18,000</u> 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 <u>$18,000</u> in Stock F.
