SCENARIO 13-7
an Investment Specialist Claims That If One Holds $\rho$

SCENARIO 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.

-Referring to Scenario 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) H₀ : $\rho$ $\ge$ 0 vs.H₁ : $\rho$ $\lt$ 0
B) H₀ : $\rho$ $\le$ 0 vs.H₁ : $\rho$ $\gt$ 0
C) H₀ : r $\ge$ 0 vs.H₁ : r $\lt$ 0
D) H₀ : r $\le$ 0 vs.H₁ : r $\gt$ 0