Question 2 Suppose that the date when Lehman Brothers filed for bankruptcy is taken as the...

Transcribed Image Text:

Question 2 Suppose that the date when Lehman Brothers filed for bankruptcy is taken as the approximate start of the late 2000s financial crisis. Suppose also that you have two share prices for each of N=600 sampled banks measured, respectively, 100 days before the date when Lehman Brothers (LB) filed for bankruptcy, and 100 days after. Some of those N banks had large investments in subprime mortgages before the financial crisis started. You want to study the impact of the financial crisis on the share prices of banks that had large investments in subprime mortgages versus those that did not. You employ the regression equation log(price)i = Po + BSUBPRIME + CRISIS + SUBPRIME * CRISIS; + i, for banks i=1,2,...,N, and obtain the following OLS regression estimation results Dependent Variable: log(share price) Method: Least Squares Included observations: 600 Variable SUBPRIME CRISIS SUBPRIME*CRISIS R-squared Coefficient Std. Error 0.892 0.127 0.103 0.081 -0.159 0.061 -0.053 0.021 0.127 Sum of Squared Residuals 57.233 Adjusted R-squared Akaike Information Criterion Schwarz Bayesian Criterion where SUBPRIME is a dummy variable equal to 1 if the bank had large sums invested in subprime mortgages before the crisis, 0 otherwise; CRISIS is a dummy variable equal to 1 if the share price measure is taken 100 days before the collapse of LB, and 0 if it was taken 100 days after. (a) What does Po measure? What does B + B measure? What does P + B measure? Design an appropriate test to assess the conjecture that banks that invested heavily in subprime experienced a significantly larger decrease in the share price after the crisis than those that did not invest in subprime. Indicate clearly the null and alternative hypotheses, the name of test statistic and the probability distribution that it follows under the null hypothesis. [6 marks] (b) What value does the Adjusted R-squared of the regression take? [6 marks] (c) What values do the Akaike Information Criterion (AIC) and the Schwarz Bayesian Criterion (SBC) take for this regression? Explain the similarities and differences between the AIC, SBC and Adjusted R-squared. [9 marks] (d) Test the null hypothesis that R-squared is zero. What is the alternative hypothesis? Indicate the name of the test statistic and the probability distribution that the test statistic follows under the null. [9 marks] Question 2 Suppose that the date when Lehman Brothers filed for bankruptcy is taken as the approximate start of the late 2000s financial crisis. Suppose also that you have two share prices for each of N=600 sampled banks measured, respectively, 100 days before the date when Lehman Brothers (LB) filed for bankruptcy, and 100 days after. Some of those N banks had large investments in subprime mortgages before the financial crisis started. You want to study the impact of the financial crisis on the share prices of banks that had large investments in subprime mortgages versus those that did not. You employ the regression equation log(price)i = Po + BSUBPRIME + CRISIS + SUBPRIME * CRISIS; + i, for banks i=1,2,...,N, and obtain the following OLS regression estimation results Dependent Variable: log(share price) Method: Least Squares Included observations: 600 Variable SUBPRIME CRISIS SUBPRIME*CRISIS R-squared Coefficient Std. Error 0.892 0.127 0.103 0.081 -0.159 0.061 -0.053 0.021 0.127 Sum of Squared Residuals 57.233 Adjusted R-squared Akaike Information Criterion Schwarz Bayesian Criterion where SUBPRIME is a dummy variable equal to 1 if the bank had large sums invested in subprime mortgages before the crisis, 0 otherwise; CRISIS is a dummy variable equal to 1 if the share price measure is taken 100 days before the collapse of LB, and 0 if it was taken 100 days after. (a) What does Po measure? What does B + B measure? What does P + B measure? Design an appropriate test to assess the conjecture that banks that invested heavily in subprime experienced a significantly larger decrease in the share price after the crisis than those that did not invest in subprime. Indicate clearly the null and alternative hypotheses, the name of test statistic and the probability distribution that it follows under the null hypothesis. [6 marks] (b) What value does the Adjusted R-squared of the regression take? [6 marks] (c) What values do the Akaike Information Criterion (AIC) and the Schwarz Bayesian Criterion (SBC) take for this regression? Explain the similarities and differences between the AIC, SBC and Adjusted R-squared. [9 marks] (d) Test the null hypothesis that R-squared is zero. What is the alternative hypothesis? Indicate the name of the test statistic and the probability distribution that the test statistic follows under the null. [9 marks]