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 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 i ndex and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 inde x, 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  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 i  ndex and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 inde  x, 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 for the coefficient of X in the regression equation is -7.019. Since this value is smaller than the critical value at a 5% level of significance (which is -2.064), we can reject the null hypothesis and conclude that the prison stocks portfolio is negatively related to the S&P 500 index. The measured value of the test statistic for the coefficient of X is -7.019, which is the t-statistic with a p-value of less than 0.05 (the level of significance), indicating significant evidence that the prison stocks portfolio is negatively related to the S&P 500 index.

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