Question

You want to create a portfolio equally as risky as the market, and you have $1,600,000 to invest.

Consider the following information:

Asset/ Investment /Beta

Stock A/ $560,000 / 0.75

Stock B/ $320,000/ 1.20

Stock C/. / 1.50

Risk-free asset Required:

(a) What is the investment in Stock C? (Do not round your intermediate calculations.)

ans: $404,445 / $530,667 / $551,894 / $504,134 / $509,440

(b) What is the investment in risk-free asset? (Do not round your intermediate calculations.)

ans: $196,906/ $181,760 / $315,555 / $179,866 / $189,333

Answer 1

Let investment in C=$x

Hence investment in risk free asset=1,600,000-(560,000+320,000+x)=$(720,000-x)

Portfolio beta=Respective beta*Respective weight

1=(560,000/1,600,000*0.75)+(320,000/1,600,000*1.2)+(x/1,600,000*1.5)+(720,000-x)/1,600,000*0[Beta of market=1;Beta of risk-free assets=0]

1=0.5025+(x/1,600,000*1.5)

x=(1-0.5025)*1,600,000/1.5

=$530667(Approx)=investment in C

Hence investment in risk free asset=(720,000-x)

=$189333