Maxwell’s Demon “works like a demon” operating a small doorway between two chambers of a vessel containing gas molecules. The demon’s goal is to sort the molecules by opening and closing the doorway such that fast-moving molecules concentrate in one chamber and slow-moving molecules concentrate in the other. The temperature difference between the two chambers could drive a heat engine and therefore perform some useful operation. Maxwell’s Demon thus serves as a useful thought experiment regarding whether one can “beat” nature with a very precise and efficient demon.
We borrow the Maxwell’s Demon construct in considering a financial markets expert, seeking to “beat the market” by concentrating high-return assets in one “chamber” and low-return assets in another. A real-life investing demon (especially an academically inclined one) may use four or five or ten “chambers” or “bins” to separate assets more finely according to expected returns. For simplicity, we stick to two bins, as depicted in the following figure. (Any similarity of the investing demon to any real financial markets commentator, advisor or asset manager, living or dead, is purely coincidental.)
An investing demon can choose from many macro and asset-specific conditions and characteristics as the basis for sorting assets, such as: asset class (for example, stocks or bonds or commodities or cash); macroeconomic conditions, company accounting/financial characteristics, technical trading indicators, investor sentiment measures and even temporal (for example, calendar-related) factors. Given all these ways to sort, it is probably more useful to think of the demon as sorting expected future returns rather than assets, with the returns associated (at least temporarily) with specific assets. The difference in returns between the two bins could drive a portfolio and thereby generate wealth. The demon can never rest because the future return for a given asset changes over time, necessitating continual re-sorting.
The questions implied by this investing demon construct are:
Do any of the conditions or characteristics from which an investing demon may choose (or combinations of same) reliably predict which assets will have high and low future returns, or at least higher and lower future returns relative to each other? If so, how big could the difference in returns between the two chambers be?
How much would the demon (or the demon’s subscriber/client) have to pay the market infrastructure to assemble and maintain a portfolio that effectively exploits the demon’s work?
How much would the demon’s subscriber/client have to pay the demon to sort assets and, if delegated, form and maintain portfolios?
The material that follows explores these questions. The intent is not to demonize investing commentators, advisors and asset managers, but simply to borrow a construct found useful elsewhere.
Physicists conclude that the energy consumed by any conceptual Maxwell’s Demon would exceed the useful energy available from the corresponding temperature difference between chambers. In fact, technologists can build only imperfect approximations of Maxwell’s Demon. Might an investing demon fare better?
Is there evidence that supports belief in the inherent feasibility of the demon’s basic sorting task? The first step is to assess whether any demon could reliably discriminate between assets with high returns and assets with low returns over some actionable future interval.
There are many anecdotes of successful investing, but the story-tellers may be selectively sampling the extreme right (winner) tail of the distribution of investor experiences. A demon offering subscriber/client testimonials is unlikely to include complaints from those in the left (loser) tail.
There are also formal studies of investing outcomes for individual investors, with bottom-line conclusions such as:
…evidence indicates that individual investors on average significantly underperform the market.
…evidence from Sweden’s Premium Pension System indicates that active mutual fund traders tend to outperform passive participants, when there are no trading frictions/impediments (in other words, when passive investors help bear costs of momentum trading by active investors).
…evidence from the Taiwan Futures Exchange indicates that only 20% of individual futures day traders make money, but trading frequency by itself is not a clear profitability discriminator (suggesting that skill may be).
…the body of evidence suggests that individual stock investors tend to underdiversify and overtrade, thereby incurring relatively high volatility, trading frictions and taxes and thus realizing relatively poor performance.
…evidence suggests that individual investors who trade options in aggregate underperform their counterparts who do not because: (1) they are especially prone to overreact to past market returns; and, (2) they bear high trading costs.
There are also a very large number (thousands) of formal and informal studies of historical data on doing the demon’s basic task by sorting assets and/or asset classes based on variables such as:
- Measures of performance of the overall economy (economic indicators)
- Financial performance or other accounting variables of the companies tied to the assets (market capitalization, book-to-market value or other fundamental variables)
- Historical price trend and/or other measures of trading behavior of the assets (momentum effect, volatility effects and other technical indicators)
- Surveyed or inferred sentiment/expectations of investors/management (buyback/issuance activity, futures activity, options activity, short selling activity and other sentiment indicators)
- Time of the year, month, week or day (calendar effects)
- Political conditions (political indicators)
There is considerable diversity in the methods used in these studies, making it difficult to infer the robustness of the results for any one study and to compare results across studies. Investing demons should therefore adopt a stance of considerable skepticism about stock-picking studies.
Moreover, many of the these studies are hypothetical to the extent that they do not realistically address all the market frictions (such as transaction fees and bid-ask spreads) inherent in portfolio management. More fundamentally, evidence of successful asset sorting in these studies may derive from sampling practices that measure luck within random fluctuations rather than persistent abnormal returns. In other words, available studies may be pervasively infected with biases, such as:
Survivorship or data availability bias: “The disaster ate my evidence (of a disaster).” An investing demon may, through ignorance, exclude some extremely bad returns from a sample.
Confirmation bias: From Paul Simon: “A man hears what he wants to hear, and disregards the rest.” For example, the demon may intentionally dismiss some disastrous returns as “incredible” outliers. Or the demon may ignore studies that cast doubt upon an embraced sorting strategy.
Look-ahead bias: “If I had traded based on this indicator over the past ten years, my portfolio would be up 1000%.” However, a demon using the indicator in real time would not have the data from the entire sample period to determine the buy-sell trading thresholds for the indicator. Well-known stock market anomalies may be much less reliable in rational practice than they appear in hindsight.
Data snooping bias: “I checked a thousand different indicators on my dataset, and found one that really works!” But, if there is randomness in the outcomes from a set of indicators/parameter settings, some will outperform by luck (with no assurance of continuing to do so). For example, just because one of a thousand coin-flippers “achieved” a high percentage of heads during one period does not mean the same coin-flipper will experience a high percentage of heads in a future period. For the investing demon, the past outperformance of an indicator as measured by an analysis substantially contaminated by data snooping bias is unlikely to persist at the historical level.
“Second-hand smoke” data snooping bias: “A famous guru [who tried a thousand indicators] says that this indicator is golden. I checked, and it is.” An investing demon copying another demon’s homework does not know how much data snooping bias comes with it.
Publishing bias (similar to second-hand data snooping bias): Uncounted instances of null (uninteresting) strategy test results on common datasets may be unsubmitted for publication or rejected for publication, thereby suppressing the detectable intensity of actual snooping.
Some research that seeks to correct the performance of characteristics/indicators/parameters for data snooping bias finds that:
…evidence from an array of tests on simulated and real stock market price series indicate that trading rules based on simple moving averages sometimes beat a buy-and-hold approach and sometimes do not, depending mostly on series drift and return autocorrelation and somewhat on return volatility. Such rules do not intrinsically enhance risk-adjusted performance.
…evidence from the past few decades indicates that professional technical traders using high-frequency data may well earn abnormal returns in the S&P 500 Index futures market. However, other traders may fail because they use lower-frequency data, bear higher trading friction and are less resilient to losses.
…evidence from tests of an extensive set of technical trading rules as applied to emerging foreign exchange markets indicates that profitability of technical analysis, after correcting for data snooping bias, may be illusory.
…even though S&P 500 index timing rules based on fundamental indicators and investor sentiment indicators might significantly beat a buy-and-hold benchmark when evaluated in isolation, this outperformance generally evaporates after correcting for data snooping bias. In other words, luck is the dominant differentiator of rule performance.
Based on return histories across the entire sample period, only 0.6% of [mutual] funds exhibit truly positive long-term four-factor (market, size, book-to-market and momentum) alphas after expenses and trading costs, while 26.6% exhibit truly negative alphas. The balance of 72.8% of funds display skill just sufficient to cover expenses and trading costs.
None of the 6,402 rules tested on the S&P 500 index, after adjusting for data mining bias, generate statistically significant outperformance. More complex/nuanced rules, or other financial data sets, might indicate abnormal returns.
Across the entire sample, technical trading is generally not profitable. On average, the trading rules yield significant profits for only 3% of stocks. This result is consistent for different intervals and for both NYSE and NASDAQ stocks.
…technical analysis can be significantly profitable when applied to relatively immature stock indices (NASDAQ Composite and Russell 2000) but not when applied to mature stock indices (DJIA and S&P 500).
This research on data snooping bias is a foundational threat to the belief of both investing demons and their subscribers/clients in the ability of demons to sort future asset returns accurately and reliably.
An inverse form of data snooping involves focusing on a single indicator but intensively searching for subperiods or subsamples (ranges of indicator values) that generate good results without understanding why the indicator works sometimes or in some ranges but not others. This mode of snooping incorporates luck not by iterating an indicator or parameter setting but by iterating subsets of data in search of one for which a given indicator works.
A second foundational threat to the value proposition of investing demons is evidence that financial asset returns have “wild” power law distributions rather than “tame” (such as normal) distributions. Yet many formal studies of financial markets determine statistical significance and therefore devise portfolios based on an assumption that the asset return distributions are tame. But the statistical anchors of mean, standard deviation and significance variables do not touch bottom in the indicated power law environments. The following sources address this wildness.
…most investors, thinking linearly, tend to undervalue (overvalue) antifragile (fragile) assets. The antifragile portfolio uses a small fraction of available funds to stay long (short) exceptionally antifragile (fragile) assets, pending unpredictable volatility spikes that drive their values dramatically up (down). Portfolio positions are asymmetrically leveraged (as with options) to limit downsides but not upsides. Position values tend to bleed slowly until unpredictably exploding upward. The balance of funds is idly as safe as possible.
…analysis suggests that widespread loose treatment of non-linearities in financial markets models (forecasting tools) tends to (1) bias forecasts in one direction and (2) amplify the importance of small-probability events, thereby enabling a contrarian approach of exploiting anti-fragility (strategies with infrequent, large, unpredictable positive payoffs).
…evidence from surveys of relevant research indicates that academia has made little progress in finding practical ways for investors to protect even diversified portfolios from extreme events (crashes).
…evidence suggests that fear of disasters accounts for large fractions, perhaps most on average, of both the equity risk premium and the volatility risk premium. …conclusions may be important for understanding the MPT-resistant risks inherent in exploitation of the asset risk premiums.
…investors may want to ponder whether the fat tails of financial asset return distributions (and those for the outputs of many other complex systems) present risks that “normal” statistical methods cannot mitigate.
…”normal” statistical metrics and associated risk management methods do not work in the realm of Black Swans (including financial markets). Redundancy, not optimization, helps manage risk in this realm.
…unpredictable “Black Swans” drive history, and the human mind is blind to them. …overuse of Gaussian statistics reflects a fundamental flaw in the way people look at the world. …the highly uncertain framework of power laws best describes socioeconomic behaviors.
For our demon, the wildness of financial asset return distributions means that just one or a few essentially unpredictable “outlier” asset returns will, based on average returns, make a hot bin cold or a cold bin hot. Said differently, temperature (average) may be a usefully informative measure for well-behaved gas molecules, but it is not for assets returns with wild distributions. This wildness seems like God’s game of keep-away from investing demons (and their subscribers/clients).
A third foundational threat to the value proposition of investing demons is evidence that financial markets adapt such that anomalies are transitory. Asset sorting strategies therefore do not work the same way twice. More abstractly, the act of exploiting characteristics of an inferred distribution of investing returns changes the characteristics. The following sources address market adaptation:
…evidence indicates that, after a two-year post-publication window of opportunity, investors should expect to capture only about two-thirds of the gross magnitude of published stock market anomalies.
…evidence indicates that declining trading friction and improving trading technology have stimulated higher turnover, faster incorporation of private information and greater market efficiency over the past 15 years.
…evidence from the past few decades indicates that professional technical traders using high-frequency data may well earn abnormal returns in the S&P 500 Index futures market. However, other traders may fail because they use lower-frequency data, bear higher trading friction and are less resilient to losses.
The bottom line from these considerations is that investing demons appear to face stiff odds in accomplishing their basic task of dependably sorting financial assets based on future returns. The case against reliably substantial financial markets predictability may not be airtight, but any potential leaks seem small and hard to find. …[A]ny edges available are probably small, not highly reliable, linked to common sense (but not obviously) and eventually (soon?) lost to market adaptation.
As noted above, many studies of financial asset returns do not address all the market frictions (such as trading fees and bid-ask spreads) inherent in implementing real portfolios. These frictions can be decisive for investing demon subscribers/clients seeking to extract wealth from the demon’s basic output of assets sorted according to future returns.
An individual acting as his own investing demon incurs costs for the computing power, analysis software and variable/indicator data needed to support asset sorting. The more complex the analysis and the more exclusive and therefore potentially informative the data, the higher these “search” costs. An individual delegating this basic sorting task to some other investing demon bears these costs as part of the demon’s due (next section).
An individual acting as his own portfolio manager incurs:
- Broker fees when buying “hot” assets and selling “cold” ones according to an investing demon’s sorts. In general, the smaller the portfolio (in dollars), the greater the percentage impact of these transaction fees.
- Asset liquidity costs (bid-ask spreads). The difference between bid and ask represents the opposing desires of buyers wanting a bargain and sellers wanting a premium, resulting in different distributions of prices available to buyers (from sellers) and to sellers (from buyers).
If the investing demon re-sorts hot and cold assets frequently, transaction fees and liquidity costs accumulate rapidly. A diligent demon takes these trading frictions into account explicitly by sorting on net rather than gross future asset returns based on clear trading assumptions. An individual delegating portfolio management to an investing demon bears these frictions indirectly as portfolio balance debits. Research often (but not universally) indicates that:
…evidence indicates that investors learn to trade less as they gain experience, perhaps due to the immediate feedback associated with transaction costs, but they do not learn to diversify or avoid the disposition effect.
…evidence of variations in liquidity across asset classes, within asset classes and over time indicates that investors should incorporate liquidity as a decision factor in asset class allocation, security selection and trade timing. Instances of illiquidity may be bargains for long-term investors. Anticipation of liquidity changes may enable superior returns for traders.
…evidence indicates that many (but not all) well-known stock return anomalies derive their profitability from short positions in firms with low credit ratings during deteriorating credit conditions, with shorting constraints and illiquidity limiting exploitation.
…investors may want to ensure that they base trading strategies on real-time expectations net of search costs and comprehensive trading frictions, with a substantial margin to accommodate data snooping bias.
Accurately incorporating realistic trading frictions into backtests, especially over the long term, is very difficult, because these frictions vary considerably over time.
Other trading frictions may also come into play depending on broker rules (for example, account balance requirements) and sorting strategy implementation approach (for example, stock borrowing costs for short sellers). Impact of trading, wherein the process of position accumulation or liquidation itself moves the asset price, may come into play for big players and especially illiquid assets.
An individual delegating portfolio management to an investing demon bears additional non-trading operational costs such as investment company reporting, compliance and marketing as portfolio balance debits.
A more subtle drag on portfolio performance relative to investing demon sorting returns derives from reconciling capital availability with opportunity availability. A chosen asset sorting strategy may at some times locate many “hot” assets (more than can reasonably be addressed with a limited amount of capital) and at other times no “hot” assets (forcing capital to go idle).
Above and beyond reimbursement for trading frictions and other operational costs (if they manage client funds), investing demons require payment for the insight they offer in sorting financial assets based on future returns.
Media that proffer investing advice want subscription fees or eyeballs on advertisements. Research indicates that:
Academics studying financial markets want employment (and tenure) and funding of their studies. Research indicates that:
Expert equity analysts want employment by brokers and asset managers. Research indicates that:
…the stream of research on (mostly sell-side) equity analysts generally supports beliefs that: earnings forecasts tilt toward optimism; analyst forecasts are a little better than quantitative models; some analysts are consistently better than others; and, conflicts of interest materially affect forecasts.
…aggregate distribution of analyst recommendations is a coincident or lagging stock market indicator. Those firms that appear to be most realistic (honest) with their distribution of recommendations provide the best advice.
…analyst stock price targets are not good predictors of actual stock price potentials. Analysts exhibit this poor performance because they want to express optimism about the stocks they cover and have no compensation incentives or public accountability related to stock price targets.
…portfolios built using aggregate analyst recommendations may produce gross outperformance, but transaction costs absorb excess returns. Moreover, privileged investors get the jump on analyst-driven trades.
Newsletter sellers want subscription fees. Research indicates that:
…the aggregate market timing ability, positive performance persistence and stock picking ability of investment newsletters are unimpressive. Finding good gurus, able analysts, is no easier than identifying solid stocks.
Financial advisors want advisory fees, either as a percentage of account balance or a fixed fee. Research indicates that:
…evidence indicates that advisors improve retail investor portfolio performance after minimizing conflicts of interest and accounting for self-selection bias.
…financial advisors tend to influence individual investors toward more diversified portfolios, thereby on average lowering both return and variability. Evidence does not support beliefs that advisors substantially help or hurt risk-adjusted returns for mixed portfolios or equity-only portfolios.
…in the absence of equity investment manager performance data that demonstrates strong and persistent net outperformance of the broad market, individual investors are likely better off buying and holding low-cost index funds directly.
Mutual fund managers and hedge fund managers want management fees, normally as a percentage of account balance. Research indicates that:
…evidence casts doubt on the existence of U.S. mutual fund manager skill and indicates that fund performance is more likely to reverse than persist.
…evidence from benchmarking against real investment alternatives rather than factor models does not support belief that investors are better off buying low-cost index funds instead of actively managed mutual funds with strong past performance.
…evidence suggests that SumZero participant long (short) investment propositions have intermediate-term (short-term) value.
…evidence from a fairly large sample of ValueInvestorsClub.com recommendations indicates that belonging to such a group can be profitable, with profitability concentrated within a few weeks after posting and among the recommended securities with the small market footprints.
…actual hedge fund investor return/risk experience, due to the timing of entries and exits, is much worse than that indicated by the continuously measured returns and volatilities of the funds themselves.
What’s an investing demon, who must earn a living, to do?
Many investing demons appeal to rationality using historical data and statistics, but these demons often incorporate sampling/analysis biases and an assumption of tamely distributed returns (see THE DEMON’S DRUDGERY above). Some demons appeal to greed by fostering belief that the rewards from investing, with their proprietary advice, are very large and reliable. Other demons appeal to fear by arguing that, without their proprietary advice, investors stand to lose capital in the face of looming disasters. Do any or all of these approaches work to attract and retain subscribers/clients?
Research, such as the following, suggests that investing demons can effectively exploit individual investor naivete and lack of self-confidence:
There is, further, research that indicates investing demons can survive and thrive via naive appeals to fear/greed and emphasis on entertainment/controversy (interesting stories) rather than scientific rigor, as follows:
…evidence from simple tests on a limited sample indicates no relationship between the forecasting accuracy of and the attention paid to U.S. stock market gurus. It seems that other factors drive investor attention, which tends to concentrate on a very few gurus.
…forecasters trying to beat other forecasters tend to take extreme public positions that reflect the motivational bias of competition. An investor considering the public forecasts of gurus should probably shift asserted probabilities away from 0% and 100% toward 50%.
Andrew Lo observed that: “…if one tortures a dataset long enough, it will confess to anything!” Investing demons may well be able to survive by torturing confessions from historical data and offering the confessions to potential clients as proof of buried treasure (marked on their proprietary maps).
In association with assertions of high returns and low risk, investing demons may engage in active defense with respect to any public missteps, such as the following (as encountered in the course of testing a large sample of public forecasts for the U.S. stock market):
10. You took my statement out of context, leaving out all the obfuscating elaboration, conditional clauses, counterpoints, big-picture equivocations and past statements. Your judgment is unfair.
9. I was close enough. You should give me credit.
8. I will be right eventually; I just don’t know when. (Or: I was right all along, but my timing was off.)
7. I may be wrong on some little things, but I’m dead right on all the big ones. The big ones far outweigh the little ones.
6. I provide risk assessments based on historical tendencies, not forecasts. You should not call it wrong. The low probability scenario happened; it was just bad luck.
5. My public statements may be sometimes wrong, but I am 100% right in my private newsletter. You have to pay for truly valuable advice.
4. Since I am rich and famous, I must be smart. Since I am smart, I must be right. Quid est demonstrandum. No need to check up on me any more.
3. If brokers weren’t so manipulative and investors so gullible, what I said would happen would have happened. You should give me credit for my elegant and compelling argument.
2. The Plunge Protection Team (or the President, or the Vice President and his cabal, or the Treasury Secretary, or the Federal Reserve, or the devious prime brokers, or the Japanese, or the Chinese, or the EU) intervened to prop up the market. You shouldn’t count that against me.
1. I was not wrong. You are an ass. [Many variations...some investing demons can be quite crude.]
0.5. You are just trying to make everyone else look bad so people will subscribe to your service.
0. What forecast? Let me tell you about a great new investment opportunity!
How can an investor sort the good demons from the bad ones? Lawyerly research suggests that:
Read the demon’s general disclaimer (often linked at the bottom of site pages). Does it say something like: “It should not be assumed that the trading recommendations or advice will be profitable or that they will not result in losses.” Do you believe the marketers or the lawyers?
Find the assumptions made about returns claimed by the demon:
Are claimed returns cherry-picked or do they comprise steady outperformance over a reasonably long period of time? (There is often not enough information to tell.)
Does past performance commence with a strong return burst (perhaps based on backtesting) and then moderate (perhaps in real trading)? Such a scenario may indicate picking a start date at the beginning of a non-repeating lucky streak. At the end of the streak, the luck is gone.
If the demon manages multiple services, are they all outperforming, or just the one being promoted? The latter case suggests the possibility of luck rather than skill in the promoted fund.
Are returns claimed by the demon from real trading or from a hypothetical backtest? Look for disclaiming statements such as: “Hypothetical performance results have many inherent limitations… One of the limitations is that they are generally prepared with the benefit of hindsight.” Exhaustive backtesting (data snooping) may well discover non-repeating lucky streaks rather than reliable patterns. Moreover, hypothetical trade timing may assume favorable entry and exit points that a real-life trader is very unlikely to achieve systematically.
Are returns based on trades signaled by a hypothetical, in-sample indicator threshold? In other words, does the demon present the history of an indicator and show that trading when the indicator crossed above or below certain thresholds would have generated fabulous returns? This approach incorporates look-ahead bias, because a trader using the indicator in real time would not have the data from the entire sample period to determine trading thresholds.
What are the assumptions about trading frictions? Look for disclaiming statements such as: “Performance reflects gross profit or loss and is exclusive of commissions, trading fees and subscription costs.” Assumptions about trading frictions (including about buy and sell prices with respect to the bid-ask spread) can have very large impacts on profitability for strategies that involve frequent trading and/or options. Also, in general, the less money one has to invest, the more trading frictions depress returns.
Are the returns claimed by the demon clearly tied to an amount of capital required to implement them, or are capital requirements hazy? If the frequency of a demon’s recommended trades is sometimes so slow that assumed position sizes leave a portfolio in cash, or so fast that the portfolio does not have the cash to exploit them all, then portfolio returns may be substantially lower than the demon’s per-trade statistics.
What are assumptions about the cost of the demon’s service as a drag on portfolio profitability?
Are the returns claimed by the demon for closed positions only, suggesting the possibility of a bow wave of underwater positions kept open and excluded from analysis?
How do the demon’s claims square with fundamental beliefs about the level of financial markets efficiency and wildness, and about human nature? Specifically:
Is there rigorous research that supports the existence of reliable returns of the magnitude claimed for the type of strategy employed by the demon (see THE DEMON’S DRUDGERY above)? More generally, is there credible research that supports the existence of reliable returns of the magnitude claimed for any investing strategy? In other words, does it seem too good to be true?
Why have market makers, hedge fund managers or other sophisticated investors not discovered and extinguished the asserted market opportunity?
If the demon can reliably generate very large returns, why is the demon bothering to sell and administer an advisory service rather than easily getting rich by investing?