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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 5 months ago

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