In: Finance
You want to create a portfolio equally as risky as the market, and you have $1,400,000 to invest. Consider the following information: Asset Investment Beta Stock A $350,000 0.75 Stock B $280,000 1.10 Stock C 1.55 Risk-free asset Required: (a) What is the investment in Stock C? (Do not round your intermediate calculations.) (b) What is the investment in risk-free asset? (Do not round your intermediate calculations.)
Total Stock A & B value = Value of Stock A + Value of Stock B |
=350000+280000 |
=630000 |
Weight of Stock A = Value of Stock A/Total Stock A & B Value |
= 350000/630000 |
=0.5556 |
Weight of Stock B = Value of Stock B/Total Stock A & B Value |
= 280000/630000 |
=0.4444 |
Beta of Stock A & B = Weight of Stock A*Beta of Stock A+Weight of Stock B*Beta of Stock B |
Beta of Stock A & B = 0.75*0.5556+1.1*0.4444 |
Beta of Stock A & B = 0.9056 |
Total Portfolio value = Value of Stock A & B + Value of Stock C & risk free asset |
=630000+770000 |
=1400000 |
Weight of Stock A & B = Value of Stock A & B/Total Portfolio Value |
= 630000/1400000 |
=0.45 |
Weight of Stock C & risk free asset = Value of Stock C & risk free asset/Total Portfolio Value |
= 770000/1400000 |
=0.55 |
Beta of Portfolio = Weight of Stock A & B*Beta of Stock A & B+Weight of Stock C & risk free asset*Beta of Stock C & risk free asset |
1 = 0.9056*0.45+Beta of Stock C & risk free asset*0.55 |
Beta of Stock C & risk free asset = 1.0772 |
Beta of Stock C & risk free asset = Weight of Stock C*Beta of Stock C+Weight of Risk free asset*Beta of Risk free asset |
1.0772 = 1.55*Weight of Stock C+0*(1-weight of Stock C) |
Weight of Stock C = 0.695 |
Weight of Risk free asset =1-weight of Stock C=1-0.695=0.305 |
Inv in stock C = Weight of Stock C in C and risk free asset*(Portfolio-Stock A value-Stock B value)
=0.695*(1400000-350000-280000)=535150
Inv in risk free asset= Weight of risk free in C and risk free asset*(Portfolio-Stock A value-Stock B value)
=0.305*(1400000-350000-280000)=234850