## HW2

### All assignments must be completed using a software or programming language that allows the manipulation of matrices and vectors. No canned statistical packages are allowed.

To complete this assignment, you will need two datafiles: portfolio_returns_48.txt and fac- tors_ﬀ.txt. The two  files are zipped into  one file, called homework2_files.zip and can be found on  my website. Once unzipped, they will be in text format, separated by tabs. The first file contains returns of 48 industry portfolios, whose exact definition can be found in Siccodes48.txt also in the zipped file. The second file contains 3 portfolio returns which will be used as risk factors. The factors are labeled in the file itself. This homework reproduces some of the results in Fama and French (1993), published in the Journal of Financial Economics. The ultimate goal is to test the CAPM and a multi-factor asset-pricing model.

### 1.Let the  return  of  the  market  portfolio  at  time  t be  denoted  as RMt. The  returns  of  all  other portfolios are denoted as Ri and the  risk-free  rate  is rft    金融计量经济学代写

(a)For each asset, run the followingregression:

(b)From the  previous  steps,  you  must  have 48 is and 48   Plot  the  with  ±2SE?

Are the  pricing errors () big?  What do you conclude?

(c)Plotthe against E () ; the latter computed as the unconditional mean of the excess return of industry i: The CAPM dictates that there must be a close relationship between  the  and  the  expected  excess  return. Do  you  observe  such  a  relationship? What do you conclude?

(d)Reconcilethe evidence in part b and c?

### 2.Let the returns on the SMB and HML portfolios be denoted by RSMBt andRHMLt,respectively.  金融计量经济学代写

Those factors have been proposed by Fama and French (1993) as additional risk factors. You will use the SMB and HML factors to see if they improve over the performance of the CAPM. Note that RSMBt and HMLt are already in excess of the risk free rate.

(a)For each asset, run the followingregression:

(b)From the  previous  steps,  you  must  have  .  Plot  the with ±2SE? Are  the  pricing errors  () big?  How  do the results  compare  to what you found in question 1.a.? What do you conclude?

(c)Producethree  graphs,  plotting  each  of  the  against  E () ; the ticular,  your  first  graph  should  plot  the  48 against  E () and should be directly comparable to what you obtained in question 1.b. Do you observe a relationship between excess returns and the various risk prices? Do you think that SMB and HML are priced factors?  Why?  Is a three-factor Fama-French  model more suitable  at capturing the fluctuation in equity returns? In answering the questions, refer to your empirical results.  金融计量经济学代写

(d)For an exact definition of the SMB and HML portfolios, go to the Fama and French (1993) article, or to http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-html. Do you think that the SML and HMB  returns  are  real  risk  factors? Why? Can you provide economic intuition to justify your answer? (HINT: Don’t  spend too much time on this question.)