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Fitting Factors Into the Formula

Factor investing and asset allocation are two roads to the same destination, Cliff Asness and Rob Arnott say.

Paul Justice, 10/12/2012

This article originally appeared in the October/November 2012 issue of MorningstarAdvisor magazine.  To subscribe, please call 1-800-384-4000. 

Quantitative analysis in fund investing has well-established roots in the realm of attribution analysis. However, some of the observed anomalies that can lead to better practical results for investors have proved difficult to access for financial advisors. That doesn’t have to be the case.

For this issue’s Morningstar Conversation, we talk with two quant-investing legends— Cliff Asness, co-founder of AQR Capital Management, and Robert Arnott, chairman of Research Affiliates—to gain insights on where academic theory is being practically applied in the marketplace. AQR, a hedge fund shop, recently rolled out a suite of factor-exploiting products in the mutual fund arena. Gone are the days of 2-and-20 fees for access to exotic betas a la carte. Research Affiliates, through its subadvisory of PIMCO All Asset PAAIX and its Fundamental Indexing concepts, has taken active quant investing to the masses (with strong performance, to boot).

While both of these investors are renowned in both academic and practitioner circles for their cutting-edge work in quantitative analysis, they haven’t always seen eye to eye. In this conversation, we focus not on where the disagreements reside, but instead on where there is common ground. The result is some sage advice on how investors can assess and implement factor-based investing strategies today. Our discussion took place Aug. 21. It has been edited for clarity and length.

Paul Justice: Let’s start with the comparison of style and size factors. For many years, investors have used models based on asset classes. But now, we’re seeing a shift, as investors become more interested in risk factors. You guys certainly have got some skin in the game. What are your thoughts on this approach?

Cliff Asness: First, we still think a factor-based approach can make sense within an asset class. Being able to tilt a portfolio has benefits, if you’re tilting toward something good.

What you call “style,” which I would call the “value strategy” or the “value factor,” we definitely think it’s good. Within a standard long-only portfolio, a tilt toward that factor makes sense. But by its nature, that’s a very constrained position. It’s a small amount of tracking error, and more importantly, it’s very one-sided. That portfolio can own long stocks, but it’s very limited in what it can underweight.

We think a lot of these factors, not just value, are two-sided. They add value, both from what they like and what they dislike. Some people actually think that they add value more from what they dislike. We disagree with that, too. We’ve done our studies and written papers on this, and we’re very balanced on this. Most of the factors seem to be fairly symmetric. But a traditional tilted-long portfolio really only can give you one side. And a factor-based approach is generally a long/short portfolio. The value factor is not just long cheap stocks; it’s a relatively market-neutral portfolio that’s long cheap and short expensive.

We think that both a long-only and long-short factor can make your asset allocation more efficient. It’s a way of explicitly deciding where you want to take your risks, both strategically and tactically.

We’re not fans of the size factor, so I’ll skip it.

Rob Arnott: Factor-based approaches aren’t just Fama-French factors in which you’re looking at size, value, and if you throw in the Carhart model, momentum. There are those who use…

Asness: Ahem. (laughter) That was Carhart’s application of Asness’ momentum factor, but you may proceed, Rob.

Arnott: OK. (laughter) When we use the four-factor approach—value, size, momentum, along with market beta, of course—that’s only one factor-based approach. There are also those who use factor analysis to discern the differentiated and orthogonal factors that work across asset classes. So, I think we should broaden the discussion to think in terms of factor-based asset allocation, as well as factor-based investing within the stock market.

My short answer to your question is, factor based modeling, whether for asset allocation or for management within the stock market, is legitimate, sound, well-reasoned, and it is limiting. You can’t buy factors. You can only buy assets. Think about the question, Is riskfactor modeling superior to asset allocation? You can’t differentiate them. They’re two sides of the same coin. You have to implement a factor approach or an asset-based approach through the assets; that’s one nuance that is largely overlooked in this whole debate about the relevance and attractiveness of factor-based approaches.

Factor-based approaches are a wonderful tool for attribution of returns. When we view them as a limited and incomplete source of attribution, when we recognize that there are going to be gaps, that there are going to be missing elements, and when we recognize that these are not static, immutable but time-varying, then we can use factor analytic approaches or asset-based approaches almost interchangeably.

Asness: I agree. The distinction between factor- and asset-based approaches is somewhat artificial. You can call a market-cap weighted long-only portfolio of stocks— the ultimate asset-based approach—a factor. It’s a factor long the stock market and short cash. You can call value, momentum, size, and other ones—the carry factor, low volatility— a long/short strategy, where instead of shorting cash, you’re short other assets. To Rob’s point, they don’t have to be just individual stocks. One of the things that I think is really important in whether you believe a factor will work over time is whether it holds up for things across the asset spectrum, not just stocks, but bonds, currencies, commodities, other things.

Where I might disagree with Rob, and I admit, I’m certainly singing my own song, but there are those of us out there who are trying to make factors investable standalone. Rob is still right. They still will be done through the individual assets; the way that you invest in a momentum factor, for instance— be it long-only or a long/short—is by buying or shorting individual stocks.

But it has some teeth to say you’re investing in the factor. You’re saying, “I will follow this factor. I will stick to this.” A factor is really just a rule. A factor for the long-only stock market is a way to weight stocks; you’re essentially owning them against cash. A factor of momentum is a different way to weight stocks, where you’re long high momentum and short low momentum.

Two more quick comments. Something separate Rob is talking about is the general approach of factor analysis. That’s more of a mathematical technique, and particularly useful for things like performance attribution, and whatnot. But when I say “factors” for this discussion, I mean a particular, systematic style that we may or may not believe will generate positive returns over time and can be invested in standalone.

Finally, Rob touched on this, and I very much agree: For any factor, you can distinguish whether there’s a long-term strategic argument for it paying you, versus having a tactical opinion.

In general, I tend to focus more on strategic arguments. I think the worldwide evidence— not just in stocks for long-only factors but also for value, momentum, carry, low beta, low volatility, illiquidity—is very strong, meaning that a long-term investor in those factors will make money. That doesn’t mean there aren’t tactical arguments. Rob and I were in the same foxhole in the tech bubble, when the value factor was having a disastrous run. You can always have tactical views around that, but I’m most focused on building strategic portfolios.

There are factors where I’m unconvinced by the strategic argument. Size is one of these— that small will always be rewarded separately, for instance, from illiquidity or beta. But I can be convinced by a tactical argument.

The Greatest ‘Crazinesses’
Justice: Did you think that way about the size factor 15 years ago?

Asness: Going back 14 years when we started AQR and further back to 1992 with Goldman Sachs, we’ve never allocated passively to the size factor.

Arnott: I agree with Cliff on the size factor. Jonathan Berk, back in 1997, published a piece in the Financial Analyst Journal, titled “Does Size Really Matter?” His point was that if a company’s price goes up, its market cap goes up. If its price goes down, its market cap goes down, so size is integrally linked to price and to relative valuation.

If you extract that, and if you look at size on a fundamental basis—sales, profits, book value, or dividends—what you find is that the size effect very nearly evaporates. There is almost no size effect, except to the extent that it incorporates price and favors companies at low prices. That’s an interesting nuance that academia hasn’t paid nearly as much attention to as they should.

Justice: Do you think illiquidity has replaced size? Has it always been illiquidity in the small-cap factor that gave it its premium?

Arnott: The whole issue of risk premium, whether it’s factor-based risk premium or conventional single-factor risk premium, is really just a function of discomfort. Instead of thinking of it as a risk premium, which you can quantify in terms of volatility, beta, factor exposures, if you think of it in terms of discomfort, you’re going to get rewarded for investing in what people find frightening. It goes back to the early days of Warren Buffett, when he said the way to succeed in investing is straightforward—be greedy when others are terrified, and terrified when others are greedy. It goes against human nature. It’s frightening to do that. But the nature of the risk premium is nonstatic. It changes over time, except in regard to the fact that fear leads to lower prices and higher subsequent returns.

Let’s go back to the size factor. When small-cap companies are popular and command premium multiples, they subsequently underperform. When they’re out of favor and people are doing a flight to safety to large cap, the small cap outperforms. So, there really is a time-varying nature to market inefficiencies, except that we get rewarded for taking on discomfort.

Asness: Not surprisingly, I am probably somewhere in the middle of Rob and efficient marketers. Rob’s view is that most if not all of what’s going on here is some type of irrationality. I think that plays a big role. I am a heretic from a pure efficient-markets view, and I won’t dispute that.

But I will not dismiss that more-rational forms of risk play somewhat of a role, that there is some state of the world where cheap stocks really fall into Armageddon, that there’s some co-variance of cheap stocks with other forms of our well-being that we don’t want to bear. Some of liquidity might be irrational. If we’re not high-turnover people, we should be comfortable with illiquidity. Some of it is rational. We do see times where it’s not your own choice to hold something—where somebody else gets to decide. All else equal, I know this: If you’re presenting me with two things that were exactly the same investment but one was less liquid, even if I didn’t need it today, I would demand at least a slightly higher return on the one that was less liquid.

Perhaps I’m irrational, too. I will never deny that. But there’s at least some role for rational risk premiums. Whenever I do anything with Rob, I always think I’m going to be the heretic, and I always end up being the equivocator, because he’s a bigger heretic than me. Very disappointing to a person who sees himself as an iconoclast. (laughter)

The other thing I’ll say—and Rob and I keep emphasizing this; we just come at it from different angles—is that for each of these things there is a strategic case: Should I own it forever and always? By the way, we never really mean forever and always. If we believe value works because of irrationality, if the world ever suddenly became permanently rational, we would change our view on that, too. What we mean is, for the really long term and we really doubt it’s going away.

As an aside, every once in a while people ask me if what Rob describes as irrationality has gone away. Technology is faster, and we have CNBC, and whatnot. I point out that the two greatest conflagrations in finance, the greatest “crazinesses”—it’s not the best word I’ve ever uttered, “crazinesses,” but I’m going to stick with it (laughter)—have occurred in the past 15 years. So, I don’t spend a lot of nights worried that whatever portion of our returns comes from irrationality is going away. I might worry about the opposite, sometimes.

But we do believe that most of these factors that we’ve discussed, with size being an exception, merit a strategic asset allocation. I’m a little less aggressive than Rob. But, again, I always somehow end up less aggressive than Rob on thinking I can forecast those things. We have tactical views, certainly, in extremes, such as the peak of the tech bubble, for instance. But most of the time, we are close to our long-term strategic views.

Arnott: Let me offer a couple of quick clarifications. I agree that the strategic decision trumps the tactical. I think of risk parity as, in a sense, passive GTAA (global tactical asset allocation) and GTAA as risk parity plus tactical bets. But, historically, you find that the lion’s share of the return for GTAA comes from the strategic position in which you’re willing to embrace a particular array of asset classes.

I’d also say that, from the vantage point of market efficiency, I don’t think we’re as far apart as you’re suggesting. Case in point: We have a draft article with Harry Markowitz and Jun Liu, in which we posit a world in which true value follows a random walk and price is merely hunting for fair value. So, it follows a mean-reverting random walk, which is always trying to move in the direction of fair value. If you postulate that kind of world and just assume 90% of all price movement is legitimate and 10% is noise, that 90/10 ratio would explain 100% of the Fama/French value factor, 100% of the Fama/French size factor.

We could view these as two sides of the same coin, that Fama/French size and Fama/ French value factors are structural alpha sources, because they’re both manifestations of simple pricing error. The startling thing is that you only need 10% of individual stock volatility to be irrational noise or mispricing in order to fully explain these factor tilts.

I guess I’m saying that I’m a believer that the market is 90% efficient and 10% inefficient, and it’s the 10% inefficiency that creates marvelous opportunities to add just a little bit of value for our clients on a reasonably consistent basis for those who have a modicum of patience. Unfortunately, a lot of investors don’t even have a modicum of patience.

I love to use a concrete example to help people viscerally understand this point. Suppose I go to a client and say, “We’ve scanned your portfolio, and we found an investment that you’ve got that’s very popular and beloved. It has its finger on the pulse of the consumer like nobody else. No serious competitors. Lofty growth potential. It’s gotten to be so popular that it doesn’t have a risk premium, so we just dumped it. Apple is gone from your portfolio. We’ve searched the world high and low to find assets that are truly feared and loathed; lo and behold, we found a basket of Spanish and Greek banks. Yes, I know, some of them are going to go to zero, but the ones that don’t go to zero, they’re really cheap. So, we used the proceeds from Apple to buy a basket of Spanish and Greek banks.”

That’s not very comfortable. Do we viscerally believe that it has better than 50/50 odds of winning? I think most investors, if they sat back and thought about it, would say, “Yeah, I think it does have better than 50/50 odds of winning.” But most investors would also quickly say, “But if it doesn’t win in the first year, you’re fired.” And therein lies the challenge.

Asness: I agree with everything Rob said there. I just have a few little things. One, he absolutely correctly gave a single example, because single examples always help. But I think Rob would agree that the whole notion of a factor is to spread these bets pretty far. These are all very small effects. When you apply Rob’s 10% of the variance, and I’ll trust him on the number, to a given stock or a given sector bet, it is very low probability. People who believe in factors—I don’t mean active management, where you go in and have some extra, superduper confident view on Greek banks beyond what we’re talking about here—would almost undoubtedly implement their belief by building a very diverse portfolio.

My version of an example is a little more disgusting than Rob’s version. It’s when you look at your carefully constructed value portfolio you throw up a little bit, because you own a lot of things the whole world is making fun of and you are underweight, don’t own, or in the case of a pure factor portfolio, you’re short a lot of the things that are beloved. You don’t feel good about it. It always makes you feel a little queasy.

Arnott: I would take that one step further. A Fundamental Index strategy has a value tilt, with a portfolio that looks a little uncomfortable. But I’ll tell you what’s really uncomfortable about Fundamental Index and value investing in general; it’s not the portfolio itself, but the trading. The trading is profoundly uncomfortable, because you’re always selling whatever is most newly beloved and buying whatever is most newly feared and loathed.

Asness: I love that point. Let me bring up another point: the momentum factor. I’m a big believer in it, and I think Rob believes in it, too. It is part of an investment truth, a part of investment behavior.

First, in a practical sense, you’re doing the exact opposite of value investing. You’re buying what’s been doing well, but it’s on a very different time horizon. It’s not a five-year winner; it’s a six- to 12-month winner.

So, you generally get a different set of stocks. You don’t get the stuff that is gigantically overvalued. You get the things that are on the move now.

Second, a reason that disciplined models, either as a final point or as a starting point, are so helpful is because it is hard to keep these two concepts—being a medium to long-term value investor, and a short- to medium-term momentum investor—at the front of your mind as important partners at the same time.

I think people are generally wired for one or the other, more probably wired to be momentum than value, as Rob is talking about. But I know not everyone is, because I personally experienced this. I know I’m not wired for momentum. I had the same running joke with one of my partners here for about 15 years. He would show me a trade, and I would sarcastically ask the same question every time: “Are we buying more of Company X simply because the price is higher than last month?” He would look at me very solemnly and say, “Yes, we are.” And I would say, “Fine, just checking.”

Momentum vs. Growth
Justice: Do we live in a world where there’s no room for growth funds?

Asness: If you define growth the way a lot of the world does as simply the opposite of value, then no, there’s not a lot of room for growth funds. There will be probably occasions where value is offering you so little, you want to look at growth, and that could happen, but it’s pretty rare, because the average value premium is fairly large, so you have to be in a pretty extreme situation where you’d want to tactically allocate toward the opposite of value, or growth.

Frankly, we believe that momentum is correlated to growth, but that it’s a better style. Growth being the opposite of value means it has a negative passive premium, a negative long-term premium. Momentum, like growth, is negatively correlated to value but has a positive premium over time.

The name of the game in this business is to find sources of return that, at the least, do not perfectly correlate with each other; it’s even better if they are uncorrelated with each other, and in a wonderful world, are negatively correlated with each other.

Momentum and value are two positive sources of return that are negatively correlated with each other.

Arnott: I’m going to push back on a couple of points you made. One, traditional value investing—traditional meaning cap-weighted value, not the Fama-French value factor— has underperformed growth since 2007 by a large enough margin that you’d have to go back to a span of at least eight years to find cumulative gains for value, relative to growth. Which means that the alpha attached to value—and whether it’s alpha or better beta is, of course, also two sides of the same coin— is sufficiently unreliable that I think you can get yourself into trouble. The genesis of the quant meltdown in August 2007 was that value had been so relentlessly successful for seven years that quant investors, looking at the performance attached to value and seeing it getting better and better, raised their confidence and raised the magnitude of their bets on value at a time when they should have been reducing it. I think there is a tactical element here that’s missing.

The second thing I’d push back on is momentum. Momentum works. Momentum on a short-term basis—by which I mean periods of time of less than a year—does prevail. What’s gone up tends to go up more. But it doesn’t work long term, and it steers us away from one of the most powerful factors at work in the capital markets that I think the Fama- French model and the four-factor variant of Fama-French miss, namely long-horizon mean reversion. They miss it, because the one piece that would capture it, the value effect, is only a crude proxy for long horizon mean reversion.

So, I would agree that momentum works and makes sense, but if you follow it too vigorously, you’re going to miss some really, really interesting opportunities.

Asness: All right, well, now we’re starting to have fun. (laughter) First, I will not sit here and beat the drums and say that long-only, cap-weighted value is the only way to go. A pure factor bet over those eight years has done better than a long-only value tilt, and I think Rob and I would agree on that.

But just to get realistic, a lot of these factors individually have Sharpe ratios somewhere in the vicinity of 0.3 to 0.5, which would be a wonderful Sharpe ratio. Take the low end of that; say long-only constraints get you to 0.3. A nine-year underperformance is less than a one-standard-deviation event. These things are all very long term. I wrote a paper on momentum investing having a 30-year failure in Japan and why I thought it still made sense.

So, Rob has a very appropriately long time horizon on many things. I would say it should be long on other things, too. It doesn’t mean we shouldn’t invest in better forms of value. I can argue for factor-based value investing, long and short. Rob can argue for fundamental indexing. It doesn’t mean we should give up on making them better. But eight years is not so crazy.

Another point: We measure very carefully how cheap cheap stocks are versus their norm. That might sound like a tongue-twister, but that’s how you define them; they’re the cheaper stocks. Sometimes, they’re a little cheaper, sometimes they’re much cheaper. At the peak of the tech bubble, they were the cheapest we’d ever seen against growth stocks. Going into the quant meltdown in August 2007, they were right around median. I remember this, because I have some of those days tattooed on my liver. We were monitoring it. Even though quant had grown a lot, we did not see evidence that basic cheap-versus expensive was no longer worth pursuing.

We did see that when a whole bunch of people tried to get out the same door; it was a disaster. It sent the value spread—as we called the cheap versus expensive—up to the mid-90s in percentile, meaning that cheap was not as cheap as it was at the peak of the tech bubble, but it was very cheap.

But the very fact that it wasn’t so insane at the beginning is part of why it recovered so quickly. One thing I find ironic is that August 2007 was a month that aged many a quantitative investor. But if you look at the monthly data, you won’t find much, because two thirds of it reversed in the next 10 days. That month was really about survival. Many of us survived, some didn’t. If you ran your portfolio at reasonable amounts of tracking error, or if you used reasonable amounts of leverage, it was quite survivable and quite short term, and thankfully, it reversed itself.

The last point I’ll mention is momentum. Rob is right. If you include some momentum, you do have less of a pure value tilt. They’re negatively correlated. But they’re not perfectly negatively correlated. Rob made the point that momentum doesn’t work over the long term for holding the same positions. I fully agree with that, but I think it’s kind of obvious, too. Momentum is about the short to medium term. We do use value and momentum simultaneously. But one way of thinking about it is value as an investing position and momentum as a trading position. Long term, you own your investing positions and you trade around them with your trading positions.

Momentum is not meant to say that you will never own a stock that’s cheap. It says, you will wait until it starts to come off the bottom, that it’s not always easy to pick that bottom, and by waiting to see some of it, you are a better and more consistent investor. Once it starts to come off the bottom and these two effects agree, they can agree for a very long time. So, momentum is, of course, more about the short term and more about timing, but combining that with a mostly value strategy, you end up still as a value investor; you just try to be a little more cowardly about getting in and then aggressive about ramping it up when it starts to work.

When I want to criticize someone for buying what’s expensive on real long horizons, I often call them “a momentum investor operating a value time horizon.” That’s a geeky way to say that they’re buying what’s done better, but they’re buying what’s done better over five and 10 years, which tends to be when you want to do the opposite. So, I don’t think there’s any inconsistency or any problem adding momentum to a value strategy. I think it makes it better. But you wouldn’t want to use that as your long-term single strategy.

Arnott: I like your mention of the time horizon. Using momentum on a three- or five-year basis to make investment decisions, we agree, would be a disaster. Unfortunately, that’s the way most people act.

You know what the answer would be if I go to a client and say, “We found this strategy that has performed horribly over the past three to five years, and we found this manager who’s the quintessential manager of this strategy and does it in a more intense and focused way than most. His numbers are unbelievably bad. Let’s invest with him.”

Yet, it’s often the right thing to do. An intense, focused, deep-value emerging-markets manager in 2002—just imagine trying to hire that manager!

Asness: You are entirely right. Of course, we both live in the paradoxical world that we want to convince our clients of this, but we do not want to convince the whole world.

Arnott: I’m not worried about that.

Asness: No, I’m not either. But I tend to complain about people with shorter time horizons, but I need them in the world. Value strategies work partially because people are irrational. If they stop being irrational, whatever amount of value comes from irrationality would go away. Again, I don’t think either of us would argue that the world is getting more rational. But it is a little weird. Sometimes, we complain about the hand that feeds us.

Quant Traps
Justice: What are the traps that some quants have fallen into that prevents them from being as successful as you guys have been?

Arnott: As quants, we’re drawn to data. The more data the better. We’ll tend to wander wherever the data leads us, which means data-mining. We all do it. The more ready we are to acknowledge that we’re data-mining, the more ready we are to acknowledge the pitfalls of data-mining and avoid some of those pitfalls.

An interesting example is another amazing event in recent years, the growing role of high-frequency trading and its role in the flash crash or more recent events with Knight Capital. Today, two thirds of all trading in the stock market is a high-frequency-trading algorithm trading with a high-frequency-trading algorithm, computer with computer. Only one third of trading is people actually buying and selling, because they want more or less of a particular asset.

One of the implications of this is that the market is probably getting less efficient, not more; it is getting more short-term oriented, not less. High-frequency or algorithmic trading, in turn, winds up being data-mining raised to a level that can be very dangerous. For Knight, it turned out to be existential risk.

A quant needs to have some anchoring in terms of core beliefs. Successful quants would typically hew to a view that what an asset is worth to the long-term investor does matter. To the extent that the markets have constantly shifting expectations, speculations, fads, bubbles, and crashes, we’re more likely as a patient long-term investor to profit by contra-trading against these fast trading programs.

Asness: Data-mining is a problem for quants. I actually have argued for years that it’s a big problem for active managers also. Their form of data-mining is the ones that have gotten lucky over time, thinking that they’re actually good at it.

Arnott: That’s a very important insight.

Asness: Quants maybe have more powerful tools to data-mine. But on the other hand, to Rob’s point, we have some hope of knowing that we’re data mining and dealing with it. And echoing what Rob said, there are really two ways to protect yourself from data mining. One is having an economic story for why what you see works actually works. Now, of course, it could be a harebrained story just to fit the data, so you should always look for other things that fit that story, other examples.

What we’ve talked about at my firm for the last couple of years is why low-volatility investing works. We think we have a pretty integrated story, which is that it works because of another thing that scares investors, maybe with good reason: leverage. If investors eschew leverage, and they’re scared, all else equal, of a leveraged strategy, that will actually lead to low-beta and low-volatility investing working. That’s a story we’ve found very consistent around the world.

A second way to guard against data-mining, and this is vital and perfectly dovetails with what Rob was saying, is to add an out-of-sample test. As quantitative investors, we don’t dream about what other people dream about—you know, cars, significant others, houses, jewelry. We dream about out-of-sample tests. I know that makes us a little odd, but it is what we want to get out of life.

An out-of-sample test is this. You’re sitting there in 1990 and you’ve written a dissertation on momentum investing and how it works well with value investing. Having it work over the next 22 years at a similar level really, really makes you feel better about the fact that maybe this isn’t data-mining, maybe it’s real. That has actually been my personal experience. It’s hard not to be a believer when you’ve seen these things work out of sample.

Though there’s another place you could do out-of-sample testing: other places you haven’t looked at yet. For example, if you go back to 1990, when I was starting my career, saying to Goldman Sachs, where I was about to start working, “Hey, let’s wait 22 years and see if it works, and if it does, let’s pounce.” That would have been a bad career move.

So, one thing that we did early was to look at other places. Does the same thing work for other countries? Does it work to choose where in the world to invest? And then, does it work to choose bond markets or currency markets? You might have to think to yourself, what does value mean in this place? What does momentum mean in this place? If you can define the concepts, simply and straightforward, and it holds up, you can get some confidence without waiting 22 more years.

Profit Opportunities
Justice: Jack Bogle criticizes factor investing for its lack of conformity in how many factors exist. Let’s see if we can come to an agreement here. We’ve already ruled out size as a factor that matters. We’ve said that value is real, as is low liquidity, and it sounds like you’re now agreeing on low volatility and possibly dividend-paying stocks?

Arnott: Low volatility has tremendous merit, because the largest anomaly in the finance world is that the capital asset market line empirically is flat to inverted instead of upward-sloping. As so often is the case, the biggest profits in our business are found in areas where finance theory and the real world part company. Finance theory says, returns should be linearly linked to beta, and that line should start at the risk-free rate and move linearly upward to reward more beta with more return. The empirical reality is totally different from that, creating a wonderful investment opportunity.

The size effect is simply capturing the value effect through the back door. The value effect itself is—and here I’m going to be controversial—a proxy for price error, also through the back door. There are companies that deserve premium or discounted valuation multiples. Those companies will typically have discounted or premium valuation multiples on average, over time. But you can’t say the reciprocal. Companies that have the higher or the lower valuation multiples don’t always deserve it, and they do tend to self-select, so that there’s more premiumvalued stocks than there should be, creating the value effect.

I think the dominant effects at work are pricing error, which is proxied by value. Momentum and—I would give a nod to Cliff—liquidity also enter the picture. What the four-factor model misses is both liquidity and the fact that value is merely proxying for mispricing instead of capturing it in a more direct way.

Let me give a concrete example. We have a draft paper, in which we look at a whole array of some of these new popular quasi-indexes— call them strategy indexes—like Fundamental Index, risk-efficient, and so forth. We take these indexes and turn them upside down. We run them completely backwards, turning the algorithm on its head. Instead of getting a negative alpha matching the magnitude of the alpha of the original strategies, we get a positive alpha. It’s often even bigger than the original strategies, which tells us that when people think that their thesis—their basis for developing a strategy or a strategy index—is well founded, all they’re really capturing is factor tilts. When we turn these strategies on their heads, if they still wind up capturing the same factor tilts, they still add value. And if they capture the factor tilts even more intensely because they’re such bizarre strategies, they capture them even bigger. It’s a very fun way to turn the whole notion of strategy indexes upside down, including our own.

Asness: I’m looking for a model like that, because that way, if one day I wake up and accidentally buy what I was supposed to short, I’m completely safe. (laughter) Seriously, Rob and I completely agree on the core set of factors. I might think value is working more for irrational reasons than Rob does, but we absolutely agree that it’s one of, if not the, core factor. I share Rob’s view on size. Momentum, we agree on.

Low beta, Rob is right.The empirical capital asset pricing model is a failure over very long periods. I do think Rob tends to dismiss all theory too quickly (laughter). Rob cites his papers, I cite mine, and it’s like a Western duel with tumbleweeds blowing around. So, I’ll cite another one. It’s not mine, but a few people at AQR have written a paper extending the capital asset pricing model to include leverage aversion. People are unwilling to do one of the assumptions of the capital asset pricing model: lever up the market portfolio. It doesn’t prove that it’s the cause of low-beta investing, but it leads directly to a much flatter line and to the low beta effect.

Some famous person said that it takes a theory to beat a theory. I’m not dismissive of all theories, but I share Rob’s dismissiveness of the single-factor capital asset pricing model. We can pretty much put that to bed, given a century or so of evidence.

I think anything illiquid should, in theory, pay an illiquidity premium. It’s harder to do empirical tests here, but I think what evidence exists suggests that it does. I wonder, however, considering the places you typically buy illiquidity— private equity, venture capital, things like that—whether the end customer gets a good enough deal net of the gigantic fees to capture the illiquidity premium. That is a separate question from whether illiquidity is a real factor. I’m somewhat cynical about whether investors can capture it net of costs, but I’m not cynical about whether it exists.

When you leave the world of individual stocks and start looking at yield curves and currencies, you get a very distinct strategy called the carry strategy that does get rewarded over time. As many investors will know, occasionally it gets whacked pretty hard. In geek-speak, it’s a negatively skewed strategy. Including those periods, it’s had a very attractive long-term return. You do have to size it at a level that those periods don’t kill you. But we think carry is a pretty pervasive factor around the world.

Arnott: Just one closing observation. I’m not as dismissive of theory as Cliff thinks.

Asness: Maybe just my theories.

Arnott: (laughter) I have tremendous admiration for the advances made in the academic community in deepening our understanding of how markets function and how markets should function.

I’m very dismissive of those that think that theory is reality. Theory is an approximation of the real world, and there are some marvelous profit opportunities in the gap between theory, between the way the world ought to work, and empiricism, the way the world does work.

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