Monday, January 09, 2017

Robeco's Pim van Vliet has a new Low Vol book

Pim van Vliet runs one of the oldest and most successful Low Volatility funds in the world, which has now flowered into Robeco’s Conservative Equities brand of funds. It is noteworthy that it is not referred to as “low volatility,” because when he began this strategy in 2006, low volatility was not a ‘thing.’ High Returns from Low Risk is targeted at airport readers and casual investors, and is a quick read—36k words—that makes a profound point: objectively, high volatility stocks are bad investments. 

In contrast, students are taught that expected returns are an increasing linear function of risk. If investment in riskier assets generates a higher return, the only reason to focus on low or high volatility is one’s risk preference. When combined with the idea of efficient markets, this implies that investing is actually very simple: choose how much risk you can tolerate, which dictates your expected return, and diversify accordingly. 

Alas, within most asset classes, highly risky assets generate consistently lower returns than do those with average risk, and, after transactions costs are included, risky asset classes, such as options, are horrible investments for individual investors, the more so the riskier the option. Risky assets attract excessive interest from investors, and academics help them rationalize this adverse preference through their extensions of the Capital Asset Pricing Model (CAPM), all of which are very rigorous, but wrong. On the other hand, these same investors are skeptical about market efficiency, which causes them to burn money by trading too much and realizing too many short-term capital gains (which are taxed at higher rates than are long-term capital gains).

From High Returns from Low Risk

Aristotle noted that courage is a virtue situated between the extremes of cowardice—a deficiency of courage—and rashness—an excess. Courage is a good thing, and a good life requires a modest amount of it, but it is foolhardy to take too much or too little risk: so too in investing. Yet every year, new investors enter the market and are attracted to highly risky assets, and because they are taught that this should generate higher-than-average returns even if they have no alpha, they are emboldened. Yet investing in high risk assets is ill advised for two reasons: they generate higher wealth volatility and have a lower expected return.

Pim was introduced to the benefits of low volatility investing when he read Robert Haugen, who indicated in several papers that higher risk stocks do not generate higher-than-average returns. As I was researching this before it became popular, I have a strong opinion on the unimportant issue of who discovered the low vol anomaly first. Haugen did not know what he had discovered until approximately 2008, when he kept seeing his 1991 and 1995 papers referenced by the growing low volatility crowd. Haugen always emphasized that markets were inefficient, so he was an early proponent of the “factor zoo.” After all, George Douglas (1969) and Richard McEnnaly (1974) found no risk premium, yet no one mentions them.

In contrast, Bruce Lehman’s Residual Risk Revisited (1990) noted how strange it was that everyone was convinced the market index’s imperfect proxy of the “true” market was obscuring the CAPM, yet this implies residual risk should generate a sizable risk premium, which it did not. That was a big dog not barking. Then there was Ed Miller’s 1977 paper, where a greater diversity of opinions generates a lower return for high volatility assets, and that diversity of opinion correlates with volatility. In 2001, he wrote in the Journal of Portfolio Management that one should invest in low volatility equities, full stop. This is really the first academic publication to champion low volatility, and the fact that he was influenced by his earlier theory is important, because without a story that one really believes, any particular correlation becomes one of many, as with Haugen. 

That is clearly a rabbit trail quibble, however, as Pim is a gracious fellow, and is quick to give credit when he can. Another example of this is that in which he credits his colleague, David Blitz, for noting that relative rather than absolute performance affects investment manager: underperforming is a greater threat to a long-only portfolio manager than is losing money. That is, if you lose 10% in a market that is down 10%, you did average, and your assets under management will probably not be decreasing. However, if you make only 5% in a market up 15%, assets will go down. Risk is symmetrical: it can be too great or too little, because if you take too little risk, you will underperform in bull markets, which is just as bad as those who take too much risk and underperform in bear markets.

Pim noted his dismay at this finding: it would not be an easy sell to tell investors that his low-vol tilt generates better returns merely because they have lower volatility, because they would have higher relative volatility. Yet this could be precisely why the strategy presents an opportunity, in that, for a portfolio manager, low risk is actually average risk, so risk averse professionals do not invest in low, but rather in average beta stocks (aka, closet indexing).

One of my ideas that Pim highlights is that envy is more important than greed. That is, the relative risk preferences peculiar to investment professional contracting exist in individual investors themselves, as they also are not maximizing returns subject to volatility constraints, but subject to relative volatility constraints. This makes the low vol effect more fundamental and less ephemeral. If greater low vol performance were merely an institutional inefficiency, we should expect mechanisms to circumvent that, such using a Sharpe Ratio rather than total return. Yet over time, the end-of-year lists of best managers are ranked invariably according to simple raw returns within their focus, which always encourages risk-taking via the convex rewards of being at the top.

The most prominent methods used to explain the high returns on high beta assets are partial equilibrium results, ignoring the implications in a more general setting: 

1)      Frazzini and Pedersen (2010) relied on a leverage constraint, as investors reaching for the equity premium try to grab more via a higher beta with the same dollar investment.
2)      Harvey and Siddique (2000) focused on people’s preference for stocks with high co-skew, which are like lottery preferences, or risk loving preferences.
3)      Ed Miller (1977) showed how the winner’s curse implies that assets with a high diversity of potential outcomes have lower returns.
There is some element of truth in these approaches, yet they are all deficient as definitive explanations, because they imply very counterfactual things. Academics focus on rigorous solutions because general solutions do not lend themselves to the type of clean models that journals like to publish (and not coincidentally, what academics like to work on), and science is all about simplifying things to identify fundamental laws. This is a salubrious division of labor, where academics do their thing and practitioners then implement these findings in a more ad hoc way given all the realities academics assume away. Yet here these models are profoundly inconsistent with other stylized facts that suggest a deeper problem, in the same way Bruce Lehman’s noting that idiosyncratic risk having no risk premium highlighted a deep problem to the standard model.

If we take the following three empirical facts:

1.      The equity market return premium is positive (3-6% annually)
2.      High beta stocks have lower-than-average returns 
3.      Average investors choose to be long—not short—high beta stocks
You then need all of the following non-standard assumptions to generate such a result:
1.      There must be systematic factor risk for both high and low beta equities
a.       If high beta stocks did not have a systematic risk exposure independent of the market,  arbitrage would ensure any beta premium is a linear function of beta
2.      Some investors must be maximizing relative risk
a.       If all investors were maximizing absolute risk, no rational investor would be long in the high beta equities, because they have strictly dominated Sharpe ratios.
b.      If all investors were maximizing relative risk equities would not have a return premium.
3.      Some investors should exogenously prefer high beta assets
a.       Without such investors, the high beta assets would have higher-than-average returns, even with relative preferences, because of the effects of the absolute risk preference investors.
Now, this is a messy result, but such is reality (I show this in a paper here). Frazzini and Pedersen’s model implies beta arbitrage (there's only one 'factor'), but a zero-beta portfolio long low beta stocks and short high beta stocks will generate considerable volatility. If that is anticipated, their pricing formula would then include this factor, and the high beta assets would have a greater-than-average return because of the high residual, yet non-diversifiable, volatility in high beta assets. In Harvey and Siddique’s world, for skewness to have a strong effect (e.g., 3% expected return reduction for high vol assets), either investors are risk loving globally, or the equity risk premium should be 15% (Pim published a paper on this here). In Miller’s world, there is a massive arbitrage available to those sufficiently hyper-rational to see this behavioral bias, in that they will adjust their ex ante estimation in light of their knowledge of the subjective valuation prior distribution, which implies massive inefficiency. As it is very difficult to make money in asset markets, assuming that the market is patently irrational is not very compelling.

It is important to note that the current situation is really less of a low volatility than a high volatility puzzle. It is easier to explain why the low volatility stocks have higher returns than expected by the CAPM, yet remain lower than the mid-volatility stocks, than it is to explain why the high volatility stocks have lower-than-average returns, yet people clearly are generally long them (e.g., popular broad indices include these positions). Most importantly, because high volatility stocks have such low returns, low vol targeting actually outperforms the market as a whole.

The flatness of the risk premium, when combined with the incentives to go long in the volatile stocks above, creates higher-than-average low volatility returns. With respect to the reasons why risky equities draw individuals or fund managers outside of a mean-variance or mean-relative variance approach, the list of potential reasons is quite long:

·         Information cheap. Risky stocks such as Tesla are in the news a great deal, and their large price fluctuations are indicative of new information (i.e., news). That makes it easier to generate an opinion, long or short, and because of difficulties in shorting stocks, most long investors are looking at those stocks they want to buy.
·         Lottery preference. This could be called the skewness preference (Harvey and Siddique). They are simply lottery ticket preferences, in that, just as the most extreme lotteries with 100 million payouts generate the highest revenues because they offer the greatest upside, stocks that generate large upsides offer the most interest to investors. Robert Sapolsky has noted that monkeys generate spikes in dopamine when they perceive random rewards, highlighting the addictive quality of gambling, and the convex nature of the human brain’s preference for “more” in stochastic contexts.
·         Long bias compliment. As most long equity investors tend to think equities will rise—otherwise they would be out of the equity market—it then follows that the higher beta stocks will do better in those environments. Indeed, if you invest only in high volatility assets during up months for the market as a whole, your Sharpe dominates a low volatility tilt.
·         Alpha overconfidence. If you have alpha, it makes sense to focus on stocks that can go up 40% rather than 20%; the bias towards high volatility stocks is rational contingent upon this assumption.
·         Alpha signaling. Recognizing that those who know they have alpha are investing in highly volatile stocks, investing in them—and getting lucky—is a way to sell yourself to potential investors. Investors see one’s focus on high volatility stocks as a consistent signal that the asset manager knows he has alpha.
·         Alpha discovery. If you wonder whether you have alpha, it is best to buy some volatile stocks, as it will be obvious after a year whether or not you do.
·         Winner’s curse. People will tend to buy stocks for which they have the highest relative expectation. Stocks with the greatest disagreement will tend to have the greatest volatility, and their owners will be those who are most biased (Ed Miller’s paper).
·         Agency problems. Portfolio managers often receive a quasi-call option on their strategy. To take an extreme example: portfolio managers are fired if they lose money, but if they make money, they receive 10% of the profits. Such a payoff is maximized when the underlying strategy has the highest volatility. A fund complex also faces this payoff, in that fund inflows are convex, so have many risky funds within every style category, some of which will be category winners.
·         Representativeness bias. To get rich, you have to take risk. Some faulty, but plausible, logic then implies that taking a lot of risk will make you rich. 
·         Leverage constraints. If you are constrained by regulations or conventions (e.g., 60-40 equity-bond allocation), and think the market is going up, then you can increase your return by allocating your equity in the higher beta stocks (Frazzini and Pedersen’s “betting against beta” model).
·         Ignoring geometric return adjustment. People should look at the expected total return, which is reduced by the variance. People should anticipate this by making this adjustment, but often do not, which favors the higher volatility stocks.
In summary, there are many reasons other than the standard model that draw people to high volatility stocks, which then hurts their returns on average. Pim discusses his introduction to stock investing and highlights how the biases above directed his interest into a particular volatile stock, one that he could readily form an opinion upon and that could potentially generate out-sized returns.

Back to Pim’s book: he presents a “law of three”—omne  trium perfectum—all good things come in threes. In this context, the law of three is low vol, momentum, and value. His value metric is a form of price-to-income ratio, such as dividend yield or P/E. I am skeptical of a law stating 3 is the cardinality of attributes for Platonic forms, but agree that, in this case, it is a handful and not a factor zoo of dozens.

His basic formula for generating a good long equity portfolio is first, to look only at those stocks with lower-than-average risk. He uses volatility, but one could use beta as well (they give similar results), and the benefit of using beta is that, because it is normalized cross-sectionally, one merely has to remember to target stocks with betas less than 1.0, rather than knowing the current median stock volatility (in the US, 30%).  A simple filter of excluding stocks with betas higher than 1 is great advice: it lowers risk and increases returns, and helps you avoid getting sucked into the biases listed above. If you constrain your stock picking to low risk stocks, you are swimming with the tide.

His portfolio formulation is refreshingly clear. First, normalize momentum and value using percentiles, sum them, apply to the “low vol” half of stocks, and viola, you have a darned good portfolio. He shows you can even do this using Google’s stock screener. Alas, or fortunately for Pim, this is difficult, and so if you really want to do this, it would be better simply to pay Robeco a fraction of a percent to do so, as they will be more diligent in monitoring the portfolio and adjusting for many issues not mentioned merely because they distract from his presentation. 

Pim notes that this “low vol” anomaly is not restricted to developed country equities. He has found it in emerging markets, and within equity industry sectors. He notes it has been found in corporate bondsequity options, movies and private equities, but he could have added penny stocks, IPOs, real estate, currencies, futures, and sports books.

Investors would be wise to follow simple rules for investing. Those with the humility that comes from wisdom will be relieved to know that they can optimize their investments by merely focusing on lower-than-average risk stocks that make money, generate dividends, and have performed well. Those who need the advice most—average equity investors—are least likely to take it, so I am not worried that a regime shift is in play.

Personally, I am not a big fan of momentum, as while it works over time, it fails massively on occasion, as in 2009, when we had an adverse 4-standard deviation event in the US. Nonetheless, I can see how one can look outside this case and find, in the words of AQR’s Cliff Asness, that value and momentum are “everywhere.” I do, however, prefer his method of putting metrics into percentile space rather than a Gaussian variable, in that expected returns are more linear in a percentile z-score. I also appreciate the fact that he does not create a hierarchy of factors, as do many, in which a “value factor” is a combination of 6 metrics (e.g., the Bloomberg Equity Model), which is then added to 5 other such composite factors.

If there is no risk premium in general so many seminal economic models are extinguished that it simply will not happen ('no science ever defends its first principles' Aristotle). Further, the fact that people are not so much greedy as envious highlights the fact that economics has a profoundly limited relevance, because while in practice people merely want to out-do their neighbors, this is not something anyone admits they should be optimizing, and certainly is infeasible for a society. Economists can explain behavior using profit maximization or cost minimization, because each is consistent with both greedy and envious utility functions, so it is useful for many parochial applications. 

Yet this constitutes a partial equilibrium analysis. To the extent that economists want to prove certain macro policies are socially optimal, they return to a utilitarian world in which people do not care about relative wealth. This is simply untrue, and is relevant to why high marginal tax rates are popular regardless of whether they would bring in more revenue: bringing the top down is sufficient motive for most people (why most people loathe the Laffer curve, as it highlights their base interest in a higher marginal tax rate). With this flawed assumption, macro-economists are no more profound than are historians when analyzing a 'macroeconomy', as their fundamental motivator—individual wealth, however broadly defined—is defective and so does not generalize.

I used to think it would be good to convince others that the standard utility model is wrong, but now I am happy to let the consensus exist in perpetuity because of both the Serenity Prayer (“focus on what you can do”), and professionally, I am all-in on low volatility. Pim van Vliet is not keeping this powerful economic insight secret, but I am confident that most people will ignore his advice to their detriment.