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  • Problem in Risk Free Rate Rf and Return of the Market Index Rm

    To: Dr. Attaullah Shah and to everyone that could help me out with this problem.

    I want to run the following regression

    Rp,t - Rf,t = αp, F (1 - Dt) + αp, T D+ βp, F (Rm, t - Rf, t) + βp, D (Rm, t - Rf, t )Dt + ep, t


    For this, I have Rp data, which is the returns on momentum strategy i.e. Winners-Losers portfolio both for formation and testing period with the total of 118 monthly observations in each period. Rf, t and Rm, t are the risk-free rate and the return of the market index, respectively, during the month t; Dt is a dummy variable, equal to 1 during the test period (t > 0) and 0 during the formation period (t<0), allowing us to estimate different intercepts and betas during both periods; αp, F and αp, T are the risk-adjusted abnormal returns, or Jensen’s alpha, for the formation period and test period respectively; βp, F is the systematic risk of the portfolio p during the formation period; βp, D measures the change observed in the systematic risk of portfolio p between the formation period and the test period, so that the beta for the test period is (βp, F + βp, D); and ep, t is the error term.

    Now my questions are:

    1. As the Winner-Loser portfolio (momentum strategy) returns is monthly Average Cumulative Abnormal Returns, does the Rm in the regression should also be average monthly cumulative? If so, how would I calculate it?


    2. Moreover, I have converted the weekly risk free rates to the respective months like the time period which I took is 36 months both for formation and testing. So I convert the weekly risk free rates Rf accordingly with the formula Rf(weekly)*52/12 (for example if I want 1 month Rf). Is this the right way? Or do I need to add the weekly cumulative risk free rates to get the respective monthly Risk free rates Rf? If so, how would I do it in the stata?

    3. Now, when I get the monthly Rm and Rf, I need to arrange it according to the dates of the observations in Winner-Loser portfolio (momentum strategy) file.

    4. In case of weekly data, do Rm and Rf would change accordingly?

    Sir kindly upload the files on dropbox as well. I have uploaded a dataset in case if you need it.


    Thanking you in anticipation!
    Last edited by JalalShah; 24 Nov 2014, 08:38.

  • #2
    Hi Jalal
    I assume you have weekly data and want to convert that to monthly, for that the following code might work for you. Open the weekly data where you have market returns and then use the following code, assuming that your data starts from June 2004
    Code:
    gen month=month(date)
    gen year=year(date)
    bys year month: egen rmc=total(rm)
    gen mn=(year-2004)*12+month
    gen mserial=mn-5 // to generate month serial
    bys mserial: gen tag=1 if _N==_n // to keep only one observation for each month
    keep if tag==1
    gen id=1
    tsset id  mserial
    forval i=2/10{
    asrol rmc, g(rm_C`i') s(total) w(`i') // 
    }
    "
    asrol is my new program that can be downloaded from http://www.opendoors.pk/STATA/standa...rolling-window
    Regards
    --------------------------------------------------
    Attaullah Shah, PhD.
    Professor of Finance, Institute of Management Sciences Peshawar, Pakistan
    FinTechProfessor.com
    https://asdocx.com
    Check out my asdoc program, which sends outputs to MS Word.
    For more flexibility, consider using asdocx which can send Stata outputs to MS Word, Excel, LaTeX, or HTML.

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    • #3
      Sir the link you share does not have the file and saying "page not found". The program seems very useful, however, the explanation which I saw on the website shows that it compute the means of the observation in a rolling manner. Nevertheless, as much as to my understanding, I need to calculate the geometric means of these log returns of market index Rm on the basis of each month like the way i used for portfolio construction in "asm.ado" file. Moreover, I guess it cannot be roll down in this case because geometric means will be calculated based on each month. (Correct me if I am wrong).

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