Question

Note: Part a, b and c are not related to each other. a. Portfolio Man wants to create a portfolio as risky as the market and he has $1,000,000 to invest. Given this information, fill in the three missing values of the following table: Asset Investment Beta $170,000 1.6 $140,000 1.5 $130,000 $200,000 Risk-free asset b. An asset's reward-to-risk ratio is defined as its risk premium divided by its standard deviation It is a useful statistic to summarize the asset's risk-return trade-off. Consider the following information: Stock A has a reward-to-risk ratio of 0.4 and stock B has a reward-to-risk ratio of 0.33. Stock A's risk premium is 8%, stock B's risk premium is 10% and the market risk premium is 7%. The correlation between stocks A and B is 0.6. Assume the CAPM holds. A portfolio consisting of stocks A and B has 20% more systematic risk than the market. Calculate the total risk of this portfolio. c. Julia invests 20% of her wealth in the risk free asset and the rest in FB shares and BHC shares. The risk premium on FB shares is 10%, the risk premium on BHC is 7% and the market risk premium is 8%. Julia's total portfolio of the three assets is 10% less risky than the market portfolio. Calculate the weight of FB in her portfolio. Assume that the Capital Asset Pricing Model holds.

Answer 1

a.

Total Amount to be invested = 1,000,000

Total Amount invested in Assets A,B,C & D = 640,000

Hence, amount invested in Risk-free assets = 360,000

Let us calculate the respective weights in the portfolio :-

А в с Asset Weight Amount 170,000.00 140,000.00 130,000.00 200,000.00 360,000.00 1,000,000.00 0.17 0.14 0.13 0.20 0.36 1.00 10

Asset Amount Weight 170000 =D4/$D$9 B 140000 =D5/$D$9 130000 =D6/$D$9 200000 =D7/$D$9 360000 =D8/$D$9 =SUM(D4:D8) =SUM(E4:E8)

We know that beta of risk-free asset = 0

Our target is to create a portfolio which is as risky as the market.

Hence, beta of targeted portfolio = 1

We will use the goal seek function to find out the Beta of Asset D, such that weighted average beta of the overall portfolio = 1

D E F G H I J к M 1.6 1.5 Asset Amount А 170,000.00 B 140,000.00 130,000.00 200,000.00 360,000.00 1,000,000.00 Weight Beta 0.17 0.14 0.13 0.20 0.36 1.00 0.27 0.21 0.14 0.38 1.1 1.8753 0 11.00 Goal Seek ? X Set cell: To value: By changing cell: $F$71 OK Cancel

Hence, Beta of Asset D = 1.875