TABLE 13-7
an Investment Specialist Claims That If One Holds

TABLE 13-7
An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the market index like the S&P 500, then it is possible to reduce the variability of the portfolio's return. In other words, one can create a portfolio with positive returns but less exposure to risk. A sample of 26 years of S&P 500 index and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 index, is collected. A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y) on the returns of S&P 500 index (X) to prove that the prison stocks portfolio is negatively related to the S&P 500 index at a 5% level of significance. The results are given in the following EXCEL output.
$$\begin{array} { l c c c c } \hline & \text { Coefficients } & \text { Standard Error } & \text { T Stat } & { p \text {-value } } \\\hline \text { Intercept } & 4.866004258 & 0.35743609 & 13.61363441 & 8.7932 \mathrm { E } - 13 \\\text { S\& P } & - 0.502513506 & 0.071597152 &- 7.01862425 & 294942 \mathrm { E } - 07 \\\hline\end{array}$$
-Referring to Table 13-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 index, the appropriate null and alternative hypotheses are, respectively,

A) $H_{0}: r \leq 0$ versus $H_{1}: r>0$ .
B) $H_{0}: r \geq 0$ versus $H_{1}: r<0$ .
C) $H_{0}: \rho \geq 0$ versus $H_{1}: \rho<0$ .
D) $H_{0}: \rho \leq 0$ versus $H_{1}: \rho>0$ .