SCENARIO 12-7
an Investment Specialist Claims That If One Holds

Short Answer

SCENARIO 12-7
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. $$\begin{array} { l r r r r } \hline & \text { Coefficients } & { \text { StandardError } } & { \text { T Stat } } & { P \text {-value } } \\\hline \text { Intercept } & 4.8660 & 0.3574 & 13.6136 & 0.0000 \\\text { S\&P } & - 0.5025 & 0.0716 & - 7.0186 & 0.0000 \\\hline\end{array}$$
-Referring to Scenario 12-7, 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) $H _ { 0 } : \rho \geq 0$ vs. $H _ { 1 } : \rho < 0$
b) $H _ { 0 } : \rho \leq 0$ vs. $H _ { 1 } : \rho > 0$
c) $H _ { 0 } : r \geq 0$ vs. $H _ { 1 } : r < 0$
d) $H _ { 0 } : r \leq 0$ vs. $H _ { 1 } : r > 0$