TABLE 13-7 An Investment Specialist Claims That If One Holds a Portfolio

question 5

Multiple Choice

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.

Note: 2.94942E-07 = 2.94942*10⁻⁷
-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) H₀: ρ ≥ 0 vs. H₁: ρ < 0.
• B) H₀: ρ ≤ 0 vs. H₁: ρ > 0.
• C) H₀: r ≥ 0 vs. H₁: r < 0.
• D) H₀: r ≤ 0 vs. H₁: r > 0.