Question

you would like to combine a risky stock with a beta of 1.68 with U.S. Treasury bills in such a way that the risk level of the portfolio is equivalent to the risk level of the overall market. What percentage of the portfolio should be invested in Treasury bills?
a) .32 b).40 c).50 d).60 e) .68

Answer 1

\(\underline{\text { SOLUTION }}\)

Calculation of Percentage of Portfolio

Assume that the weight as \(\mathrm{x}\)

\(\mathrm{x} \times(\) Beta of \(\mathrm{Stock})+(1-\mathrm{x}) \times(\) Beta of \(\mathrm{T}-\) Bills \()=1\)

\(\mathrm{x} \times(1.68)+(1-\mathrm{x}) \times(0)=1\)

\(1.68 \mathrm{x}+(1-\mathrm{x}) \times 0=1\)

\(1.68 x+0=1\)

\(\mathrm{x}=\left[\frac{1}{1.68}\right]\)

\(\mathrm{x}=0.5952\)

Percentage of Portfolio invested in Treasury Bills \(=0.5952\) or \(60 \%\)