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

question 61

Short Answer

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. $$\begin{array}{l}\text { Coefficients } \bullet \text { Standard Error } \bullet \text { T Stat } \bullet \text { P- }\\\begin{array} { l r r r r } \hline & \text { Coefficients } & \text { Standard Error } & \text { T Stat } & \text { P-value } \\\hline \text { Intercept } & 4.8660 & 0.3574 & 13.6136 & 0.0000 \\\text { S\&P } & - 0.5025 & 0.0716 & - 7.0186 & 0.0000 \\\hline\end{array}\end{array}$$
-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) $H _ { 0 } : \rho \geq 0$ 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. $H _ { 1 } : r > 0$

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Definitions:

Data Collection

Data collection involves systematically gathering, measuring, and analyzing information from a variety of sources to gain insights, inform decisions, or support research objectives.

False Claims

Unfounded assertions or statements, often deceptive or fraudulent, made by individuals or organizations, usually for personal or financial gain.

United States

A country located in North America, consisting of 50 states and a federal district, known for its significant influence on global politics, economy, and culture.

Ethical Situation

A scenario involving moral principles or practices where decisions about right and wrong are addressed.