1. Describe the assumptions behind the classical linear regression model and the three diagnostic tests we discussed in class, the commands you would use in Stata to test each of them, how you would determine if they are violated, and what you can do to correct it if the assumption has been violated or the diagnostic indicates something may be unusually affecting the results of the regression.

Use the fund.dta data file to answer questions 2&3.  Use the data as-is; do not transform any variables, winsorize, or remove outliers.  The file contains the monthly returns of a two different fundsthe Long Fund and the Hedged Fund from the period January 1, 2001 to December 31, 2010 with the following variables

2. Perform an analysis of the Long Fund'sperformance using the CAPM, Fama & French 3-factor, and Carhart 4-factor models.  Calculate the annualized risk adjusted performance using the CAPM, Fama & French 3-Factor, and Carhart 4-Factor models.  Determine if standard errors should be adjusted for the presence of heteroskedasticity using White's test (estathettest command in Stata) and indicate if the p-values are calculated using robust standard errors by placing/removingthe asterisk after the p-value column heading.  Round coefficient estimates to four decimal places (i.e. 0.12345 as 0.1236) and the p-value to three decimal places (i.e. 0.00005 as 0.000).

(a) Complete the following table:

* indicates p-values are calculated using robust standard errors.

(b) Determine which factor(s) are significant in describing the Long Fund's performance and interpret their meaning.  How confident are you the fund under/over performed after accounting for the risk implied by the models?

(c) Which model would you choose as the best model to evaluate performance? Why?

3. The Hedged Fund uses a dynamic hedging strategy by shorting the S&P 500 index in months in which the manager believes the market will drop.  The returns of the Long Fund and the Hedged Fund are identical in months when the dynamic hedging strategy is NOT used.You have been hired to determine how this dynamic hedging strategy affects the performance of Hedged Fund and how it compares to the performance of the Long Fund.

(a) Calculate summary statistics for the returns of the Long Fund, the Hedged Fund and the risk-free rate over the entire period and separately for the months when the dynamic hedge is in place (hedged=1) and not (hedged=0). Compare the results.

(b) Analyze the performance of Hedged Fund using the CAPM and compare it with the results of the CAPM regression of the Long Fund in question 1 above.  What is the Hedged Fund's risk-adjusted performance (Jensen's alpha)and is it better or worse than the Long Fund?  What Is the Beta of the Hedged Fund and how does it compare to the Long Fund?

(c) Rerun the CAPM regression for the Hedged Fund and include the hedged dummy variable (hedged) and an interaction term between the hedged dummy variable (hedged) and the market factor (mktrf).   What is the annualized risk-adjusted performance of the Hedged Fund in the months when the fund is NOT hedged using the dynamic hedging strategy?

(d) What is the annualized risk-adjusted performance of the Hedged Fund in the months when the fund IS hedged using the dynamic hedging strategy?

(e) What is the Beta of the Hedged Fund in the months when the fund is NOT hedged?

(f) What is the Beta of the Hedged Fund when the fund IS hedged?

(g) Perform a test to determine if the Beta of the Hedged Fund in the months when the fund is NOT hedged is different from the market's Beta (provide proof with the F-statistic and p-value of the test).

(h) Perform a joint test to determine if the Beta of the Hedged Fund in the months when the fund IS hedged is different form the risk free Beta (provide proof with the F-statistic and p-value of the test).

Bonus: Compare the results of the Hedged Fund's performance to the Long Fund's performance. Which would you choose? Why?

4. You are interested in studying whether or not replacing the CEO in poorly performing firms lead to improved performance. You have collected 150 announcements where the CEO has been replaced due to poor past performance and have carefully selected a control group of 150 poorly performing firms that were in the same industry, with the same size, and financial characteristics that did not replace their CEO to compare with.  You want to use the CAPM as the model of expected returns andhave downloaded the needed return and factor data for the 60 months before and 60 months after CEO replacement.  You havegeneratedan indicator or dummy variable named "replace" indicating whether the CEO was replaced (replace=1) or not (replace=0).For all observations you regress the monthlyexcess return of the of the firms' stock (exret) on the excess return of the market (mktrf), the dummy variable (replace)plus interactions to get the following output.

. regexretc.mktrf##i.replace, robust

Linear regression        Number of obs =   28339

  F(  4,   179) =  150.42

Prob> F      =  0.0000

  R-squared     =  0.7770

  Root MSE      =  .06579

                 (Std. Err. adjusted for 300 clusters in permno)

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|               Robust

exret|      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]

----------------+----------------------------------------------------------------

mktrf|  1.526597   .0969259    15.75   0.000     1.027402    1.539931

      1.replace |   .0152862   .0025584     5.97   0.000    -.0103347    .0237707

|

replace#c.mktrf |

             1  |-.2084841   .1177799     1.77   0.018    -.2439317    .0408999

|

|

 _cons |  -.0100909   .0019186     5.26   0.000    -.0133049   -.0187680

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Answer the following questions on the next page.

(a) What is the annualized excess performance (Jensen's Alpha) of the firms that DID NOTreplace their CEO?

(b) What is the annualized excess performance (Jensen's Alpha) of the firms that replaced their CEO?

(c) What is the Beta of firms that DID NOTreplace their CEO?

(d) What is the Beta of firms that firms that replaced their CEO?

(e) Interpret your findings from A-D above?

(f) Is there any additional indicator or dummy variable(s) that you could create that would help you determine if actual improvement occurred?  If so what?

Attachment:- linear regression model.rar