You have $100,000 to invest in either Stock D, Stock F, or a risk-free asset. You...

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. If D has an expected return of 13.6 percent, F has an expected return of 9.7 percent, the risk-free rate is 3.8 percent, and you invest $50,000 in Stock D, how much will you invest in Stock F?

Expert Solution

Expected return=(Proportion of investment in stock D)*(Expected return on stock D) + (Proportion of investment in stock F)*(Expected return on stock F) + (Proportion of investment in risk free asset)*(Expected return on risk free asset)

11.4%=(50000/100000)*(13.6%) + (Proportion of investment in stock F)*(9.7%) + (Proportion of investment in risk free asset)*(3.8%)

Let the amount of investment in stock F be x
Amount of investment in risk free asset=y

11.4%=(50000/100000)*(13.6%) + (x/100000)*(9.7%) + (y/100000)*(3.8%)
11.4%*100000=50000*13.6% + x*9.7% + y*3.8%
11.4%*100000-50000*13.6% = x*9.7% + y*3.8%
4600 = x*9.7% + y*3.8%

Again, 50000/100000+x/100000+y/100000=1
50000+x+y=100000
x+y=50000
y=50000-x
Substituting this value, we get
4600 = x*9.7% + (50000-x)*3.8%
4600 = x*9.7% + 50000*3.8%-x*3.8%
4600 = x*(9.7%-3.8%) + 1900
4600 -1900= x*0.059
2700= x*0.059
=>x=2700/0.059=45762.71186

Answer: The amount of investment in stock F should be =$45762.71186

jeff jeffy answered 3 hours ago

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