Challenge to the Fama French Three Factor Model

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richard
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Re: Challenge to the Fama French Three Factor Model

Post by richard » Tue Oct 09, 2012 7:11 pm

Jerry_lee wrote:1. You are right that SD is an incomplete measure of risk in a multifactor world. But investors still care about SD, and some care almost exclusively about it (for them, tilted portfolios are ideal). Further, there are plenty of discussions about additional small/value risks (timing of losses matter as much as magnitude), and most of us have lived through those in '07-'08. Multi-factor models simply give us a richer appreciation of all the ways markets reward risk, allowing us to pick and choose amongst them as our circumstances dictate. Larry might be focused on minimizing one-in-a-generation downturns with low beta/high tilt allocations, I might prefer a balance of large/small/growth/value and shorter term debt without the low beta emphasis, while you might which to hold mostly economically healthy companies (TSM) and take additional interest rate and credit risk. Each of these decisions has pros/cons, and we should seek to understand them and choose the avenue that is best for us.

I certainly agree that, to the extent an investor has a particular interest in SD (or is otherwise different from the "representative investor"), then they can profitably tilt away from the market portfolio.

One problem I often see is a statement essentially to the effect: SD is a terrible yardstick, 3F is much better, this can be shown by a tilted portfolio lowering SD risk. Having said SD is inadequate, it does not seem proper to then use it

The second problem is the notion that tilting is good for everyone. Not everyone can have a particular issue with SD.

Jerry_lee wrote:2. When I think of diversification, I look to its multiple meanings. Security diversification is once consideration, asset class diversification is another (and you may restrict your definition of "asset classes" as distinct portfolios such as stocks/bonds/TIPS/cash with maybe regional considerations), and diversification by sources of risk/return is yet another. You are right, nothing in the FF research tells us HOW to invest according to the 3F or 5F model. No such paper such as Portfolio Selection exists in the multi-factor world. So it is up to investors to read the research, and apply it according to their circumstances and interpretations.

I would be very careful to take interview or video snipits out of context or depend on them exclusively. In the case of French, I believe he was comparing a TSM portfolio (almost no small/micro cap exposure) to S&P/Micro Cap portfolio (almost no mid cap exposure) held in the same factor adjusted allocations (TSM = 85% S&P/15% Micro). In this case, focusing on security diversification, TSM is more diversified (3,000 vs 2,500 names), and you might think excluding mid-caps is more problematic than small/micro given the relatively larger % of the former on a cap weighted market basis.

This is DFA's summary of the French statement I referenced: "Can investors build a better portfolio by combining asset classes that have low correlations? It is possible, explains Ken French, but not in the way that most investors attempt it. Some think they can enhance diversification by eliminating mid caps and concentrating on only large and small cap stocks because these asset classes are less correlated. Ken explains that portfolio variance is determined not only by correlation, but also by variance of the individual asset classes and, critically, by their weighting in the portfolio. He emphasizes that throwing out mid caps is equivalent to doubling up on the risk of large and small caps, which is the opposite of diversification." French's statement is a video at http://www.dimensional.com/famafrench/2 ... ssion.html

Jerry_lee wrote:But, it is no great stretch to understand that there are multiple risks that drive returns, and these risks are not perfectly correlated. Actually, over intermediate/long periods, pure long/short return factors have negative correlation's and positive expected returns, so holding asset classes that target those risk/return dimensions fully does provide a multi-factor diversification benefit. We cannot deny that size risk or value risk has historically provided a return diversification during periods when the equity risk premium is negative, nor that when the ERP is above average, we have also seen zero or negative value and size returns. We don't need academic studies to understand that there is a portfolio benefit to holding multiple distinct risks (with positive expected returns) vs isolating one or two.

The FF 3F model says, in essence, that the returns of a portfolio can be entirely explained by exposure to the three factors. To the extent the model is accurate, it does not leave a place for any additional benefits from lack of correlation between large and small or value and growth.

It is of course only a model, not a complete description of reality. However, if low correlations added to the explanatory power, one would expect additional terms that capture the additional correlation factor. I've never seen a formal model with such a factor. Do you know of one?

If markets are efficient, the market portfolio is always on the efficient frontier. As I'm fond of quoting, Fama has repeatedly said TSM is efficient. It holds multiple distinct risks in appropriate proportions. Tilting might be a good idea if you want to take additional risk in the hope of higher returns. Tilting might be a free lunch ex ante, but only if markets are not efficient.

richard
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Re: Challenge to the Fama French Three Factor Model

Post by richard » Tue Oct 09, 2012 7:16 pm

Jerry_lee wrote:In all cases, we are discussing an investor with a long time horizon with a desired return necessary to reach real future return objectives while minimizing the risks that are most acute to them. That a TSM/TBM portfolio can be right for every investor (even if it is the average of all investors) simply cannot be true.

No portfolio is right for every investor.

I'm with Cochrane (although he should say "representative" rather than "average"):

"Do not forget, the average investor holds the market. If you’'re pretty much average, all this thought will lead you right back to holding the market index. To rationalize anything but the market portfolio, you have to be different from the average investor in some identifiable way"
http://faculty.chicagobooth.edu/john.co ... 3Q99_4.pdf If you haven't read it, I'd highly recommend reading the paper.

BTW, if you're not arguing from an efficient market perspective or don't believe the three factor model (perhaps modified by momentum) is the leading model for equity portfolio analysis, then we might well be talking past each other. If you're relying mostly on historical returns, I'd point out that we don't have nearly enough data.

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Re: Challenge to the Fama French Three Factor Model

Post by ClosetIndexer » Tue Oct 09, 2012 7:30 pm

Richard, this is not about "a particular interest in SD". The point is, some risks are more important to some investors; other risks are more important to other investors. It depends on one's personal situation. J_l does a good job of explaining the tradeoffs.

TSM gives one particular mix of risks and a given level of return. Who is to say that it is the "appropriate" mix for any given individual? The only thing we know is that in an efficient market it is the appropriate mix for the (weighted) average of ALL investors. It also has some advantages as far as cost efficiency, particularly for taxable investors. But there is no reason to assume that those advantages outweigh the potential advantages of small, large, growth, or value tilts for every individual investor's situation.

Your comments about correlations not adding explanatory power don't make sense to me. It is simply a linear model. The benefits in terms of standard deviation-adjusted returns seen from low correlations between the factors aren't some magical thing separate from the model; they are included in its modeled returns.

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Re: Challenge to the Fama French Three Factor Model

Post by Naikansha » Tue Oct 09, 2012 11:12 pm

[quote="bschultheis"][quote="LadyGeek"]
(To the new investors: This is an advanced investing topic and can be safely ignored.)[/quote]

Thanks for including this statement LadyGeek.

I would only add that, in my opinion it can be ingored not only by new investors, but by investors who are successful investors, have been around the block a few times and consider themselves "sophisticated" investors.


I only point this out because when someone reads this thread, there is a tendency to think that somehow this is important.

It isn't. As Lady Geek says, it can be safely ignored.

Bill[/quote]

I don't agree. While I will not use this information to make future decisions about my investments, it is important for me to understand WHY I will not do so, rather than simply regard the thread as relevant only to afficianados. Thanks to those who were discussing the models, I've learned quite alot and appreciate the update on the academic thinking.

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Re: Challenge to the Fama French Three Factor Model

Post by Jerry_lee » Wed Oct 10, 2012 10:01 am

richard wrote: Numbered to clarify responses
1. I certainly agree that, to the extent an investor has a particular interest in SD (or is otherwise different from the "representative investor"), then they can profitably tilt away from the market portfolio.

One problem I often see is a statement essentially to the effect: SD is a terrible yardstick, 3F is much better, this can be shown by a tilted portfolio lowering SD risk. Having said SD is inadequate, it does not seem proper to then use it

The second problem is the notion that tilting is good for everyone. Not everyone can have a particular issue with SD.


2. This is DFA's summary of the French statement I referenced: "Can investors build a better portfolio by combining asset classes that have low correlations? It is possible, explains Ken French, but not in the way that most investors attempt it. Some think they can enhance diversification by eliminating mid caps and concentrating on only large and small cap stocks because these asset classes are less correlated. Ken explains that portfolio variance is determined not only by correlation, but also by variance of the individual asset classes and, critically, by their weighting in the portfolio. He emphasizes that throwing out mid caps is equivalent to doubling up on the risk of large and small caps, which is the opposite of diversification." French's statement is a video at http://www.dimensional.com/famafrench/2 ... ssion.html


3. The FF 3F model says, in essence, that the returns of a portfolio can be entirely explained by exposure to the three factors. To the extent the model is accurate, it does not leave a place for any additional benefits from lack of correlation between large and small or value and growth.

It is of course only a model, not a complete description of reality. However, if low correlations added to the explanatory power, one would expect additional terms that capture the additional correlation factor. I've never seen a formal model with such a factor. Do you know of one?

If markets are efficient, the market portfolio is always on the efficient frontier. As I'm fond of quoting, Fama has repeatedly said TSM is efficient. It holds multiple distinct risks in appropriate proportions. Tilting might be a good idea if you want to take additional risk in the hope of higher returns. Tilting might be a free lunch ex ante, but only if markets are not efficient.


1. It isn't correct to say that "not everyone can have a problem with SD". Yes they can. What you should say is that "not everyone will want to efficiently lower SD at the expense of taking on other risks". That is what tilting can do. There is not one-size-fits-all for any approach, and I would argue the "3 fund portfolio" is the one that is bandied about here as that portfolio (that everyone should own)...we do get the half-hearted "there are more than one road to (name your city)", but we see the underlying message.

2. This is the problem I have with discussing/debating these interviews/articles. Half the time, they are misrepresented, the other half, they are taken out of context. I'll go into some detail here because this hanging on every word from an article/interview drives me nuts.

Here is what Ken actually says:

Brad: Is it possible to build a better portfolio by combing assets with low correlations?

KEN: It's certainly possible, but not in the way people often do it. (after discussing risk adjusted return vs lower variance, Ken decides to JUST discuss lowering portfolio variance)
Lets start with the US equity market portfolio....People say they can reduce the variance by throwing out mid caps and instead holding just the S&P 500 and Micro Caps. That almost certainly will not reduce the variance. Why not? It certainly reduces the correlations across their assets. Micro? Not all that highly correlated with the S&p 500. Certainly less correlated than madcaps that they throw out and replace with Microcaps and S&P 500. So by throwing out madcaps, they've reduced correlations. The trouble is when I think about the variance of the portfolio, its determined not just by the correlations between asset classes, but also by variance of asset classes and critically the weight of the asset classes.


Ken then goes on to create an example where you start with 55% S&P 500, 40% mid cap, and 5% micro. Hopefully that isn't the market portfolio he is referring to, because as of 9/30, the Russell 3000 is a whopping 72% large cap, 20% mid cap, and 8% small cap (and when you compare this to the S&P 500, which is 86% large, 14% mid cap, you see that for all intents and purposes, they have almost the same breakdown). So already we have an example that doesn't fit reality. But let's say he wasn't referring to the market portfolio, and just a 3 fund allocation: 55% S&P 500, 40% mid cap, and 5% micro. He then goes on to say that you cannot reduce variance by pulling 45% (let's assume he meant 40%, but that is mistake #2 that makes this example irrelevant) out of mid cap and splitting it between S&P 500 and micro. But then he gives us an alternative portfolio that is 90% S&p 500 and 10% micro. That most certainly does have lower variance than the 55/40/5 allocation he suggested above. From 1926-2011, the 55/40/5 had an SD of 22.4 vs 21.4. Why? A lower load on size in portfolio #2 compared to portfolio #1 (0.00 vs 0.12). To match size factors, we'd instead have to use 82% S&P 500, 18% micro cap. And here, we do see the SD between the two portfolios. Even so, this example doesn't fit with his premise above, so I am not sure what to do with it?

But after going through all this to show you that these comments don't fit what you are saying AND the examples don't fit the comments, I submit: who cares? People shouldn't be adding small and value tilts to the market to reduce variance. They should do so to earn higher returns, and returns from different sources of risk that will smooth their return stream over long periods. Want lower variance? Add bonds instead. By applying the 3 (or 5) factor model, it simply increases the choices they have in how to construct a portfolio to meet an objective based on their preferences. You yourself derided standard deviation as a measure of risk above, why use this example on variance to prove your point?

Also here, we see how cautious Fama and French are in these interviews & how trying to pin a position on their comments is nonsense. Ken goes on record as saying: (from the example above) if we pull the 40% out of mid caps and put it in the risk-free rate, we will PROBABLY reduce the variance of our portfolio. REALLY? Do we have to qualify that a portfolio with 40% in t-bills will have less variance than 100% stocks? And here we see, in almost every answer FF give in these interviews, comments are qualified beyond belief. Adding 40% t-bills MAY reduce variance? (Fama) Holding the market or large growth stocks is fine as an efficient portfolio (NOT THE EFFICIENT PORTFOLIO) as long as they do it in a diversified manner -- in effect all portfolios that are diversified are OK? That isn't an answer...that is a hedge.

So, as you can see, even if you wanted to invest absolutely according to what a particular person says, it is next to impossible to extract their exact beliefs from these short interviews. I mean, DFAs summary of Ken's comments don't even correspond with his comments! All he is talking about is lowering portfolio variance from adding higher risk asset classes. You don't need an interview to know you cannot do that.

3. This is not a valid point. As I have said before, the FF study was an ASSET PRICING model study. Not a PORTFOLIO CONSTRUCTION or MANAGEMENT piece. It did not say a word about how to combine assets in a portfolio to achieve some degree of efficiency. It said nothing about the invalidation of Modern Portfolio Theory or the view that combining less than perfectly correlated assets in a portfolio reduces risk and increases return (below and above a weighted average return of all holdings) when periodically rebalanced. FF ONLY said that the CAPM was no longer valid, as we needed additional factors to explain returns.

All we can say is there are distinct risk/return patterns, so combining them in a portfolio (much like securities with distinct risks/returns) produces a diversification benefit beyond looking at each in isolation. This really cannot be disputed except to take the view that the risks are all a version of the stock/bond premium (and therefore perfectly correlated). Is this the position you are taking?

And further, lets clarify this "market is on the efficient frontier" business. No one knows what is/is not on the EF except with hindsight. The market is a broadly diversified (by security) portfolio of mostly large and more growth oriented stocks. It is no more or less "efficient" than a large growth index or a small value index. It does NOT, however, have much exposure to distinct risks and returns. It by definition has 0.0 exposure to size and value. 100% of its return comes from the equity premium, or beta (which of course is circular because it's used to calculate beta). And it is not accurate at all to say it holds anything in "appropriate" percentages. It holds what it holds. Maybe OK for some, but not for all.

Finally, Investors who tilt aren't just wanting to take more/higher risks in hopes of higher returns. We want to diversify our returns (not 100% from beta, as the market since 2000 has shown: ERP = +0.2%/year, Size = +4.3%/year, Value = +5.4%/year), or wish to control their risk via their stock/bond allocation more precisely than by holding the safest stocks, or want to hold shorter-term bonds in their balanced portfolio without decreasing overall expected returns vs a market/long-term bond portfolio.

There are may appropriate allocations for many different investors spread across size, value, stock/bond, term, and credit dimensions. The probably that a TSM/TBM and "age in bonds" (the two prevailing one-size-fits-all solutions here) allocation is right for anyone is extremely remote.
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Jerry_lee
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Re: Challenge to the Fama French Three Factor Model

Post by Jerry_lee » Wed Oct 10, 2012 10:13 am

richard wrote:
Jerry_lee wrote:In all cases, we are discussing an investor with a long time horizon with a desired return necessary to reach real future return objectives while minimizing the risks that are most acute to them. That a TSM/TBM portfolio can be right for every investor (even if it is the average of all investors) simply cannot be true.

No portfolio is right for every investor.

I'm with Cochrane (although he should say "representative" rather than "average"):

"Do not forget, the average investor holds the market. If you’'re pretty much average, all this thought will lead you right back to holding the market index. To rationalize anything but the market portfolio, you have to be different from the average investor in some identifiable way"
http://faculty.chicagobooth.edu/john.co ... 3Q99_4.pdf If you haven't read it, I'd highly recommend reading the paper.

BTW, if you're not arguing from an efficient market perspective or don't believe the three factor model (perhaps modified by momentum) is the leading model for equity portfolio analysis, then we might well be talking past each other. If you're relying mostly on historical returns, I'd point out that we don't have nearly enough data.


Yes, I've been a vocal critic of this view as well, as it makes absolutely no sense. While we can say that the market is the aggregate of the "average" investor, what we really should say/mean is that the market is dominated by a handful of very large institutional investors that set prices. Something north of 80% of trading is done by a handful of mega-wealth investors. Why would Joe Blow, with $1M and very unique circumstances completely different from Yale's endowment want to simply buy the weighted average holding determined by a few really big investors?

There are reasons to hold TSM portfolios (esp. in conjunction with other holdings), but doing so because everyone else is doing it is not only wrong, it isn't true. We owe it to ourselves to be more critical than this.
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grok87
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Re: Challenge to the Fama French Three Factor Model

Post by grok87 » Fri Oct 12, 2012 5:29 am

Jerry_lee wrote: In short-term panics and sell-offs, all risks tend to show up, and your losses maybe exacerbated by the amount of size, value, term, or credit risk you take relative to a traditional "Tobin" market/t-bill allocation.


Can you please flesh this out a bit with some examples? It doesn't seem to be true IMHO. I think in a great depression scenario market risk and size/value showed up but that was not a short term panic. In the most recent short term panic (if that is what we are calling 08) small value outperformed.
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Re: Challenge to the Fama French Three Factor Model

Post by Jerry_lee » Fri Oct 12, 2012 9:26 am

grok87 wrote:
Jerry_lee wrote: In short-term panics and sell-offs, all risks tend to show up, and your losses maybe exacerbated by the amount of size, value, term, or credit risk you take relative to a traditional "Tobin" market/t-bill allocation.


Can you please flesh this out a bit with some examples? It doesn't seem to be true IMHO. I think in a great depression scenario market risk and size/value showed up but that was not a short term panic. In the most recent short term panic (if that is what we are calling 08) small value outperformed.
cheers,


Well, when I think short-term, I think a few months to a few years. From the perspective of a 30 year retirement or a 20 year period of saving for retirement, a few years is certainly short-term. Maybe not short in the sense of the crash of '87, but that is what I mean. I contrast this with longer periods when, say, the cap-weighted market has failed to produce a real return (the 15 years ending in 1943, the 17 years ending in 1981, the 13 years through last month, etc.). A decade or more, we are obviously moving from short-term to long-term.

As far as small/value tilted portfolios' tendency to lose more in the short-term declines, we don't have enough of them to draw statistical conclusions, but we can certain make that case on an economic basis. To check this, lets observe 3 "total market" portfolios with increasing tilts to small and value. The first (#1) is CRSP 1-10, with no tilt. The second (#2) has a mild 0.2/0.2 tilt to small and value. The third (#3) has a moderate 0.4/0.4 tilt to small and value. Instead of just showing TSM and SV portfolios, these are actually reasonable allocations investors would hold, so it is more realistic as to what someone would have experienced:

Code: Select all

                   #1            #2         #3
1929-1932        -68.5%       -73.9%     -77.9%
1937             -34.7%       -38.2%     -42.6%
1969-1974        -27.7%       -38.3%     -44.4%
2000-2002        -37.9%       -17.4%      -0.1%
2007-2008        -33.0%       -37.2%     -40.4%


So, outside the 00-02 market, which had more to do with the unraveling of the tech bubble than a total market collapse, the smaller and more value oriented you were, the more you lost. And we know investors are risk averse, and they rationally demand a higher return for holding assets that perform even worse during general market declines (hence the higher expected returns of tilts to small and value).

On the bond front, things are a bit less clear. "Default" was negative in 4 of these 5 periods, so that clearly looks like a risk premium, "Term" (20yr minus 1mo) was actually positive in 3 of these 5 periods, so that is a bit more fuzzy. Based on past performance, it appears as though TERM risk doesn't fully manifest itself in the sense of losses during market declines, but instead unexpected inflation. Obviously a period of rising prices and interest rates present real problems for LT bonds. From 1926-1981, 20yr bonds had no additional return above t-bills, for example. From 1965-1981, LT bonds had a real return of -50% -- an even worse long-term loss than we can find for US equities. Probably should expect a return premium for taking that kind of risk. If you should take a lot of TERM risk (beyond 5 years), that is another question.
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