Question
In: Finance
You want to create a portfolio equally as risky as the market, and you have $1,400,000...
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.)
Solutions
Expert Solution
| 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
jeff jeffy answered 1 year agoRelated Solutions
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