# Fama and French (market premium) factor

Currently I am using the Fama and French 3 factor model to explain the performance of mutual funds using monthly returns from 2000 to 2017.

I use two market proxies: (1) RM-RF, obtained directly from Kenneth French website.

(2) Wilshire 5000-RF, obtained from Bloomberg Terminal.

RF is the 1 month U.S. t-bill.

For some reason when I run my regressions, the R-squared using (2) Wilshire 5000 as a market proxy is higher than when (1) RM was used as a market proxy.

The correlation coefficient between the two proxies is 0.93, which suggest that there differences (probably in the composition of the Fama and French market proxy).

I was just wondering if there are any technical differences between the two market proxies?

If RM is a value weighted of all investable equities in the U.S., the correlation coefficient should be much higher than .93 relative to Wilshire 5000.

Thanks.

## Update

I downloaded the return series for WFIVX (a Wilshire 5000 index fund) and I calculate a correlation coefficient of .9991 with the Fama-French market return series from Ken French's website (for 2000 to 2017)! So I think something is wrong with your .93 calculation?

Are your monthly returns over the same period (i.e. end of month $t-1$ to end of month $t$)). Do they include all distributions etc...?

## How Fama and French calculate the market return (RM)

From Ken French's webpage:

Rm-Rf, the excess return on the market, value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ that have a CRSP share code of 10 or 11 at the beginning of month t, good shares and price data at the beginning of t, and good return data for t minus the one-month Treasury bill rate (from Ibbotson Associates).

That the first digit of the CRSP share code is 1 means that the shares are ordinary common shares (and not certificates or ADRs etc...)

The CRSP coding for the 2nd digit are:

Code    Definition
0   Securities which have not been further defined.
1   Securities which need not be further defined.
2   Companies incorporated outside the US
3   Americus Trust Components (Primes and Scores).
4   Closed-end funds.
5   Closed-end fund companies incorporated outside the US
8   REIT's (Real Estate Investment Trusts).


### Does this match Fama-French market return?

Basically yes.

The below SQL code achieves a mean 0.4 basis point absolute different with the Fama-French rm factor (from their website) since 2000.

It gets a bit more dodgy in the early 1980s and I'd have to check all the details a bit better, but the big point is that you can about all the way there by:

• Only use NYSE, AMEX, and NASDAQ stocks.
• Only use regular, common shares (and no REITs)

I've included some SQL code below. (It runs on my idiosyncratic setup, and I'm including just for illustrative purposes... you won't be able to run this.):

SELECT t1.date, SUM(t1.ret * t2.prc * t2.shrout) / SUM(t2.prc * t2.shrout) as vw_ret
FROM (
SELECT t1.permno, t1.date, t1.ret
FROM q_stock.msf t1
JOIN q_stock.mse e on t1.permno = e.permno and e.event = 'NAMES' and e.date <= t1.date and t1.date <= e.nameendt -- join with events file to get share code
WHERE (exchcd = 1 or exchcd = 2 or exchcd = 3) and t1.date > 20000000 and t1.ret is not null and (shrcd = 10 or shrcd = 11)) t1

JOIN mycrsp.yyyymm_date_link l ON t1.date = l.date
JOIN q_stock.msf t2 ON t1.permno = t2.permno and l.prev_date = t2.date -- lagged by 1 month to get market cap weights
WHERE t2.prc > 0 -- good prior month price data (FF may do more than this)

GROUP BY t1.date
ORDER BY t1.date


(Note that Fama French factors have RMRF and RF so to get RM you do RM = RMRF + RF.)

• Wilshire 5000 includes REITs (about 4% of market cap I believe) so that is one possible difference. – noob2 Aug 11 '17 at 19:20
• @noob2 The no REITs changes it a little bit but honestly not that much. – Matthew Gunn Aug 11 '17 at 19:26
• Thank you sir. I thought the Fama and French market factor accounts for dividends or dividend reinvestment while Wilshire does not. However excluding REITs might explain the issue. – user28909 Aug 11 '17 at 23:21
• @user28909 I'd be surprised if the REIT thing mattered much... The CRSP return definitely does include all distributions including dividends. I'm not familiar with what the Wilshire object you've downloaded exactly is? (Note too that this all might be an non-substantive sideshow.) – Matthew Gunn Aug 12 '17 at 3:10
1. If you look closely to Frama French 1992 you will see that Fama-French exclude financials from their sample. They do not specify whether these are excluded from the market factor or not. That might be one of the differences from the Wilshire 5000 to the Fama-French market sample.

2. Another difference is that they only include stocks that have a stock returns on 24 of the preceeding 60 months. That should be another difference.

3. They only include firms with positive equity book values

If you read their data section closely I am sure you will find several other things that could make results different.

• In allocating stocks to various sub-portfolios (high BM, low BM, etc) financial firms are excluded. But I do not think they are excluded from the Market Portfolio as a whole. – noob2 Aug 11 '17 at 18:02
• See edits above – phdstudent Aug 11 '17 at 18:39
• @noob2 I agree with you; I don't believe they exclude financials from the market return calculations. – Matthew Gunn Aug 11 '17 at 19:22