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 measured value of the test statistic is
A)-7.019
B)-0.503
C)0.072
D)0.357

Question

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 measured value of the test statistic is
A)-7.019 
B)-0.503 
C)0.072 
D)0.357

Quizplus · Accepted Answer

The measured value of the test statistic is -7.019, which is obtained from the coefficient of X in the regression analysis. As it is greater than the critical value of -2.064, we can reject the null hypothesis and conclude that the prison stocks portfolio is negatively related to the S&P 500 index at a 5% level of significance. Thus, the investment specialist's claim that holding a portfolio that moves in the opposite direction to the market index can reduce the variability of the portfolio's return seems to hold true in this case.

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