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

question 152

Multiple Choice

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)\(H _ { 0 } : \rho \geq 0 \text { vs. } H _ { 1 } : \rho < 0\)
• B)\(H _ { 0 } : \rho \leq 0 \text { vs. } H _ { 1 } : \rho > 0\)
• C)\(H _ { 0 } : r \geq 0 \text { vs. } H _ { 1 } : r < 0\)
• D)\(H _ { 0 } : r \leq 0 \text { vs. } H _ { 1 } : r > 0\)

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Definitions:

Secondary Circular Reaction

is a developmental phase in early childhood identified by Piaget, in which infants repeat actions that affect the environment, indicating the beginning of intentional behavior.

Primary Circular Reaction

The stage in early infancy when a child begins to repeat actions on their own body that originally occurred by chance, indicating early cognitive development.

Babinski Reflex

The Babinski reflex is a neurological sign observed in infants when the sole of the foot is stroked, the big toe moves upward or toward the top surface of the foot, and the other toes fan out.

Tertiary Circular Reaction

A stage in Piaget's theory of cognitive development where infants try out new behaviours to see what results they have, displaying early elements of experimentation.