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Can Momentum Reduce Tracking Error in Small- and Value-Tilted Portfolios?
Last week, we saw that a momentum strategy could theoretically reduce tracking error in small- and value-tilted portfolios. Today, we’ll see if this has made a difference historically.
Last week's post referenced the potential improvement that an allocation to a momentum-based stock strategy can have in terms of reducing the tracking error in small- and value-tilted portfolios. Keep in mind that momentum is the tendency for stocks that have done well in the past to continue doing well in the near term and vice versa.
One of the interesting features of momentum is that it tends to do well when small and value stocks don’t. So adding momentum to a size- and value-tilted portfolio has the potential to reduce tracking error. Using index data from AQR Capital Management, we can test this historically, with the important caveat that these are on-paper results and don’t reflect transactions costs or fees.
For the period of 1980–2011 (1980 being the first year that AQR has compiled data for its momentum indexes), I compared the tracking error of the size- and value-tilted portfolio in last week’s post* to a portfolio that allocates 80 percent of its assets to that same portfolio and 20 percent to a diversified long-only momentum strategy using AQR’s index data.**
The annual tracking error of the size and value-tilted portfolio without momentum has been about 9.6 percent per year, which indicates there’s potential for substantial underperformance and outperformance in any single year. For the portfolio that includes momentum, tracking error is reduced to 8.1 percent. This is a substantial improvement in tracking error. Note that even though this helps, you still can’t dramatically reduce tracking error without markedly reducing size and value tilts.
So what are some of the other factors to consider before adding momentum to your portfolio? First and foremost, there are no good risk-based explanations for why momentum exists. This is an important consideration, since this makes one wonder whether it will continue. Nevertheless, momentum has been extremely robust across time and asset classes and after it was discovered in the early 1990s. Second, momentum-based strategies are more trading intensive and not particularly tax efficient, so some return will undoubtedly be lost to these costs. This shouldn’t, though, have a big impact on the tracking error benefits.
Random Links and Commentary of the Week
Nothing much this week other than sharing a few songs that I’ve been enjoying:
  • Gillian Welch covering Radiohead's "Black Star"
  • Built to Spill "Else"
Jared Kizer is the director of investment strategy for BAM Advisor Services. See our disclosures page for more information.
* Portfolio composition: Dimensional Adjusted Market 2 Index: 26.5%, Dimensional US Large Cap Value Index: 8.5%, Dimensional US Small Cap Value Index: 25%, Fama/French International Value Index: 13.584%, Dimensional International Small Value Index: 12.51%, MSCI EAFE Index: 2.17%, Dimensional International Small Index: 1.736%, MSCI Emerging Markets Index: 5%, Fama/French Emerging Markets Value: 2.5%, Fama/French Emerging Markets Small: 2.5%.
** Portfolio composition: (1980–1989) AQR Large-Cap Momentum Index: 50%, AQR Small-Cap Momentum Index: 50%; (1990–2011) AQR Large-Cap Momentum Index: 30%, AQR Small-Cap Momentum Index: 30%, AQR International Momentum Index: 40%.


Momentum strategies

One thing I've noticed when combining value and momentum is that the factor loadings tend to offset each other. A deep value fund like BOSVX has a fairly substantial negative MOM loading (despite their MOM screens). DFSVX has done a better job reducing it. A fund like AMOMX has a fairly large negative value loading.

When you combine them in say a 50/50 allocation you are left with a basket of stocks with small loadings to each factor.

Assuming you have been convinced of MOM's persistance, I have a couple of questions. Since these would be two separate funds can you think of them as two separate "asset classes" and expect to receive a rebalancing bonus? Or is it right like I said above to think of it as owning a basket of stocks between two funds. Also, in the scenario you presented above did you notice you had better risk adjusted returns by adding MOM? You seem to talk about adding MOM as a way to reduce tracking error meaning if you ate ok with tracking error you don't need it. I. Your research have you been convinced adding MOM adds other benefits?
at 8/8/2012 8:00 AM


Thanks for the's a great one.

First, if you look at four-factor regressions of daily return data of BOSVX and DFSVX since BOSVX's inception and through 6/2012 the MOM loadings have been -0.08 for BOSVX and DFSVX has been at 0.02. So DFA has been slightly positive on MOM over that period and BOSVX slightly negative but definitely not deeply negative.

One caveat to the above is that the momentum loadings on both of these strategies go negative if you back out the negative momentum embedded in the HML factor and then re-run the regression. If you want to see an example of this let me's pretty interesting.

Second, don't agree with your observation re: AMOMX whether you are looking at live or index data. Using live data the HML loading has been +0.03 so basically zero and using their index data the HML loading has been -0.07 (all these analyses are through 6/2012 and use monthly data).

So by combining the two you don't get an offsetting result.

I'll have to get back to you on risk-adjusted returns. I don't have that info right in front of me. I suspect the answer is yes but let me confirm.
at 8/8/2012 10:25 PM

Re: Can Momentum Reduce Tracking Error in Small- and Value-Tilted Portfolios?

Thanks for the reply.

For AMOMX I used the monthly data off their website and factors off Ken French's web site. I used excel for the regression. For BOSVX I used yahoo so that could be suspect data. I'm glad you got different results because from what I saw combining HML and WML sort of cancelled each other out.

Don't have the data in front of me but I thought AMOMX the HML was like -.2 and WML was +.3. I'll have to check again.

Another question I have is if I'm right (which doesn't sound like its true) is a .3 loading about all we can expect from a MOM fund.

I would like to see what it looks like when you back out the negative momentum in HML. I've never heard that before.

BTW Built to Spill is One of my favorite bands of all time. How they never blew up is beyond me. The Perfect From Now On album will change your life (thick hippe accent)
at 8/9/2012 2:25 PM

Reply 2

I just re-ran my AMOMX Index and live fund return numbers from scratch just to make sure they were right.

For the index series over the period of 1/1980-6/2012 and using Ken French's research factors plus momentum I come up with:

MKT  1.10
SMB -0.03
HML -0.07
MOM  0.37

For the live fund over the period of 8/2009-6/2012 I come up with:

MKT  1.05
SMB  0.04
HML  0.03
MOM 0.34

All the AQR data is taken from their website. So this shows that there's not the degree of growth bias that you might think, indicating that momentum is a distinctly different strategy from a growth strategy.

I do think you are right on where loadings for AQR's long-only strategies shake out. I doubt you'll see them go much above a 0.30 to 0.40 from what I've seen but that's still significant exposure.

As another side note so far they've tracked the index pretty closely at about 1.5 percent annualized tracking error and actually outperformed the index by about 7 bps/month net of management fees.

I got to see Built to Spill about a year or so ago here in STL at the Pageant...absolutely great show.

at 8/9/2012 4:58 PM


So back to the other thing I'd mentioned on the relationship b/w HML and MOM.

If you run the following regression using Ken's data - HML regressed on UMD - you find that HML has about a -0.30 loading on UMD. This means that HML itself is really a combination of "true" value + negative momentum. It's even worse if you do the same analysis using the benchmark factors, meaning the momentum loading is even more negative. This is one of the reasons why the returns of the HML research factor have been higher than the returns of the HML benchmark factor.
at 8/9/2012 5:08 PM

Re: Can Momentum Reduce Tracking Error in Small- and Value-Tilted Portfolios?

Interesting...It really shows the value of the momentum screens that those funds use.

I guess I can do it myself but does it work the other way where MOM has a negative value loading?

All we need now is one fund that has a high loading on all four factors. Maybe even a cheap passive arbitrage fund and a carry trade fund. We could all be our own little hedge funds. Of course the difference is we would make ourselves money.
at 8/10/2012 7:49 PM

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