Question

The market portfolio has expected return of 12% and risk of 19%, and the risk free rate is 5%. According to the capital market line (the line that connects the risk free rate to efficient frontier), what is the portfolio weight for the risky market portfolio if an investor wants to achieve 8.5% return? What about 16.2%? And 19% return?

Answer 1

In Capital market line, if the weight of risky portfolio is p, then the weight of risk free asset is 1-p

Total return of the combination =

1) 8.5% return

plugging in the numbers we get

8.5%= (p X12%) + (1-p) X 5%

8.5=12p+ 5 - 5p

8.5=7p+5

7p=8.5-5=3.5 => p=3.5 /7 =0.5

Hence, the weight of risky market portfolio is 50%

2) 16.2% return

plugging in the numbers we get

16.2%= (p X12%) + (1-p) X 5%

16.2=12p+ 5 - 5p

16.2=7p+5

7p=16.2-5=11.2 => p=11.2 /7 =1.6

Hence, the weight of risky market portfolio is 160% and weight of risk free asset is -40%. Minus sign indicated that instead of investing, we must borrow at risk free rate and invest in the risky asset

3) 19% return

plugging in the numbers we get

19%= (p X12%) + (1-p) X 5%

19=12p+ 5 - 5p

19=7p+5

7p=19-5=14 => p=14 /7 =2

Hence, the weight of risky market portfolio is 200% and weight of risk free asset is -100%. Minus sign indicated that instead of investing, we must borrow at risk free rate and invest in the risky asset

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