A friend tips you off on a hot stock: Sure Thing Mines Ltd. You only have $10,000 to invest but you want to invest more. Assume that you can borrow an additional $5,000 by short-selling the risk free asset (issuing T-Bills). You purchase $15,000 worth of shares in Sure Thing Mines Ltd. The expected returns and standard deviations of the two assets are outlined in the table below:
$$\begin{array} { | c | c | c | }
\hline \text { Asset } & \begin{array} { c }
\text { Expected } \
\text { Return }
\end{array} & \text { Beta } \
\hline \text { T-Bills } & 5.5 \% & 0 \
\hline \begin{array} { c }
\text { Sure Thing } \
\text { Mines }
\end{array} & 15 \% & 1.70 \
\hline
\end{array}$$ What is the beta of the portfolio?
A)1.50
B)1.70
C)2.50
D)2.55
E)2.70

Question

A friend tips you off on a hot stock: Sure Thing Mines Ltd. You only have $10,000 to invest but you want to invest more. Assume that you can borrow an additional $5,000 by short-selling the risk free asset (issuing T-Bills). You purchase $15,000 worth of shares in Sure Thing Mines Ltd. The expected returns and standard deviations of the two assets are outlined in the table below:
$$\begin{array} { | c | c | c | } 
\hline \text { Asset } & \begin{array} { c } 
\text { Expected } \
\text { Return }
\end{array} & \text { Beta } \
\hline \text { T-Bills } & 5.5 \% & 0 \
\hline \begin{array} { c } 
\text { Sure Thing } \
\text { Mines }
\end{array} & 15 \% & 1.70 \
\hline
\end{array}$$ What is the beta of the portfolio?
A)1.50
B)1.70
C)2.50
D)2.55
E)2.70

Quizplus · Accepted Answer

The beta of the portfolio is calculated as a weighted average of the betas of the individual assets. Since you are investing $15,000 in Sure Thing Mines with a beta of 1.70 and short-selling $5,000 in T-Bills with a beta of 0, the portfolio beta is: (15,000/10,000) * 1.70 + (−5,000/10,000) * 0 = 2.55.

A Friend Tips You Off on a Hot Stock: Sure