Question

You want to create a portfolio equally as risky as the market, and you have $1,000,000 to invest. Given this information, fill in the rest of the following table: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Asset Investment Beta

Stock A $165,000 0.80

Stock B $350,000 1.09

Stock C ? 1.27

Risk-Free Asset ? ?

Answer 1

Weight of Stock A (WA) = $165,000/1,000,000 = 0.165

Weight of Stock B (WB) = $350,000/1,000,000 = 0.35

If, portfoli is as risk as market, the beta of the portfolio must be equal to 1.

By using porfoli beta formula we can find weight of Stock C

βp =1 = WA x (0.80) + WA x (1.09) + WC x (1.27) + Wrf (0)

1 = 0.165x (0.80) + 0.35 x (1.09) + WC x (1.27) + Wrf (0)

1 = 0.1320 + 0.3815 + WC x (1.27) + 0

Wc x1.27 = 1-0.1320-0.3815

Wc = 0.4865/1.27

Wc =0.38307087

So, Dollor investment in Stock C

= 1,000,000 X 0.3831 = $383,070.87

Investment in Risk free asset

= 1,000,000-165,000-350,000-383,070.87

= $ 101,929.13

Beta of risk free asset is zero.