This post is inspired by reading George Soros’s paper on reflexivity. I’ve taken the basic idea but then applied it to investing in a different way to Soros. The result is that I end up writing about a something a bit different. The implications are fairly intuitive and I think crucial to understanding why markets behave the way they do. This post is more abstract conjecture than practical advice, but hopefully I’ve managed to come up with something that manages to be thought-provoking but accessible.
Reflexivity and investing
As investors the main thing we care about is what happens to share prices in the future. The most natural starting point for thinking about this is with the fundamentals i.e. what will happen to the underlying businesses. The fair value of a business is in principle determined by how much profit it is likely make in the future and how much risk (or variance) it faces in doing so. An investor might decide to buy where they perceive the share price to be below its fair value, hoping that the share price would then converge to fair value as the future is revealed.
What actually happens to share prices in practice depends more directly on how other investors behave. Investors may have a broad range of views about the future prospects of a business and consequently its fair value. These views informs their decisions to buy or sell. The stock market aggregates these decisions at any given point in time, by moving the price until supply matches demand. Excess demand and the price goes up, excess supply and it goes down. Conventional wisdom is that this mechanism should drive prices to discover an efficient equilibrium, where they best reflect fair values based on all the information available to investors at the time. In principle this mechanism should create powerful incentives for efficient pricing to happen quickly. Investors who are able to identify opportunities when prices are higher or lower than fair value more quickly than other investors are rewarded for doing so.
Efficient pricing is not what seems to happen a lot of the time. The most obvious example of this is that aggregate valuations across the stock market as a whole oscillate slowly between extremes of boom and bust. It does not seem plausible that the often huge differences in valuation at these extremes reflect differences in what investors perceive to be the fair value of the underlying businesses at the time. There is a vague idea that ‘investor sentiment’ is important too, but how does it have such a big effect?
The idea that the stock market is not fully efficient is inherently at the core of most investing strategies. The existence of behavioural biases suggests that prices might sometimes be biased (e.g. quality is systematically undervalued) or that prices might take longer than they should to reflect new information (i.e. momentum). However, even with these biases you would still expect prices to converge towards equilibrium. They don’t really explain why the stock market as a whole oscillates between such extremes of valuation or why investor sentiment can change so much. Reflexivity may explain this better as the idea is rather more fundamental than a simple bias – it suggests that prices do not necessarily tend towards equilibrium at all.
Reflexivity in this case is basically the idea that a relationship is circular, where the behaviour of an interested observer affects the outcome that they are observing. In investing this may capture the idea that investors make decisions on the basis of their expectations about future share prices, but that these decisions then influence what future share prices turn out to be. This means that expectations about share price movements can be self-fulfilling. If investors collectively expect share prices to rise then they will buy shares causing the prices to rise, regardless of whether this correctly reflects the underlying fundamentals.
[As an aside, the way Soros applies the concept of reflexivity to investing is different. Instead of looking at the relationship between investor perceptions and share prices, he focuses on the relationship between share prices (the idea being that they embody investor perceptions in aggregate) and fundamentals i.e. he points to ways in which share prices can affect fundamentals as well as the other way round.]
The direct implication of reflexivity is that investing is not just about predicting fundamentals. Rather it is strategic. Investing is a game where the outcomes are determined by the interdependent actions of multiple players. Future share prices are driven not by how fundamentals play out, but by how other investors will behave in response to the fundamentals, and to each other’s behaviour. As John Maynard Keynes suggested, investing becomes like a beauty contest where the goal is not to be objectively correct, but rather to second guess what other investors will think is correct.
This would not necessarily make much difference if investors all viewed the game in the same way, basing their decisions on independent assessments of fair value and comparing them to the prevailing prices. Even if investors had different views about what these fair values were, over time the market mechanism would still reward those who were demonstrated to be the most correct as the fundamentals played out. The game would have a clear focal point and there would be strong incentives for share prices to tend towards efficient equilibria.
However, this is not what happens in reality. The underlying issue is that most investors do not have a mental model of how much a share is intrinsically worth. Working this out is inherently complex and arbitrary. The future profits of an investment are determined by many complex future interactions, involving both competition and macroeconomic factors. This creates a large degree of uncertainty in what these profits might turn out to be. On top of this, there is also a challenge in deciding how these future profits should be valued. What is the right discount rate to use? How should we think about quantifying risk?
Investors do not have consistent answers to these questions and so lack objective methods for valuing equities. Instead, many may use biased heuristics to make rough or relative assessments of valuation. Others may behave more strategically, attempting to anticipate and respond to the behaviour of the market. Some (including me) may decide not to rely on estimating fair value but instead invest primarily based on other characteristics they believe tend to be relatively undervalued by other investors. Others may invest based on historic share price movements. Others look at how results are going to stack up against ‘expectations’ over the next year or two. Or any combination of the above. The outcome of these divergent approaches is that share prices can become more arbitrary in the valuations they reflect.
This means that the goal of the beauty contest diverges from that of objectively estimating fair values to the broader goal of anticipating how the behaviour of other investors will drive future price movements. It becomes rational for investors to not solely base decisions on their assessments of the fundamentals, but to also take information from popular narratives, statistical analysis and price movements. If some investors rely on these information sources it makes sense for others to rely on them as well. This means that there is less of a tendency towards equilibrium. Ultimately, it means that large divergences between share prices and fundamentals can persist indefinitely.
Implications for how markets behave
The overall implication of reflexivity is that market behaviour becomes unstable and hard to predict. Investors behave strategically: they have the incentive to try to second-guess each other and adapt their behaviour in response. Share prices are the net outcome of all sorts of behaviours interacting. Some of these behaviours, like buying shares when they are below fair value, are self-correcting – the act of buying drives the price towards fair value. Self-correcting behaviours generate equilibrium. Many of the behaviours generated by a more reflexive system are self-reinforcing (e.g. trend-following) rather than self-correcting. These lead to disequilibrium – they can generate price feedback loops and self-reinforcing narratives, further compounded by confirmation bias.
Reflexivity means that the stock market as a whole is susceptible to self-fulfilling shifts in sentiment, generally prompted by macro concerns or perceptions of aggregate valuation. Price feedback can reinforce sentiment and cause share prices to trend for extended periods. This can lead to bubbles and crashes. Eventually, when share prices become sufficiently detached from fundamentals, sentiment can reach an inflection point and shift the other way. This leads to the stock market oscillating between extremes over time.
Bubbles and panics are very clear examples of reflexivity in action. It’s easy to see from these extreme cases that prices sometimes become detached from fundamentals and driven by self-fulfilling expectations. The broader insight is that this is basically what is happening the whole time. Perceptions of fundamentals are still relevant though they can be rather arbitrary. Without objective benchmarks, investors tend to judge the valuations of different stocks relative to one another. At an aggregate level prices are driven to a large extent by the short term macroeconomic narrative, with the result that they vary far more across the cycle than they should.
To the extent that investors do consider aggregate valuations, they focus on how they compare to historic averages. There is little regard to whether the valuations are objectively cheap. The inherent circularity and arbitrariness in thinking about valuations this way is troubling. If we have little idea whether current valuations are objectively justified, what reason is there to think that historic average valuations are in some way ‘correct’? Self-referencing historic valuations would simply perpetuate the mistakes of previous generations of investors. Indeed, objective analysis has tended to suggest that equity valuations have always been far too low relative to other assets, given their historic returns and risk (the equity premium puzzle).
How to take advantage
Hopefully the idea of reflexivity should be fairly intuitive. I think it really gets at the heart of why investing can be so difficult. I’ve fully embraced the idea that the stock market is really not very efficient at all, and that share prices only loosely relate to fair value.
The main insight that I take away is that it’s important to think strategically. You don’t get rewarded for being objectively correct. You get rewarded for predicting what the market will do next. This means that in addition to having an objective view of fundamentals and future prospects, you should ideally understand the market’s subjective view and why it is incorrect.
An analogy that shows why it is important to understand the market’s subjective view comes from ‘levels of thinking’ in poker. A naive poker player might employ first-level thinking and make decisions solely based on how strong their own hand is. A player using second-level thinking would think about what their opponent’s hand might be and play in response to it, giving them scope to bluff when they think their opponent is weak. Third-level thinking means thinking about what your opponent may think your hand is e.g. ‘they’re bluffing because they think I am weak’. At the fourth level you think about what your opponent thinks you think their hand is e.g. ‘they think I’m bluffing because they think I think they’re weak’. And so on and so forth. The insight from this is that in a strategic game the key is to understand what level your opponent is thinking at and react accordingly by also thinking at the next level up.
In the stock market, the levels of thinking are more complex to define – it depends on how other investors are playing the game. They can sometimes (but not always) relate to how far into the future you anticipate. For example, a naive investor might buy a share because they believe the results for the next year will be ahead of analyst expectations. At the next level an investor might infer from market behaviour that other investors have already anticipated this correctly and instead invest based on what they believe the outlook will be for the year after that. And so on…
So why not just cut to the chase and make your time period forever? After all, this is the objectively correct answer. Well you should definitely think about this, but you should also be aware that if other investors aren’t looking so far ahead, then you could be wrong for a very long time. The ideal strategy is more complex and accounts for how far ahead other investors are looking as well.
There is another classic psychological experiment I’ve seen reported in a few places which illustrates this point. In it, subjects are asked to write down a whole number between one and one hundred and told that whoever picks the number closest to two-thirds of the average guesses of all the participants wins a prize. You can think about this problem with similar levels of thinking to the poker analogy. At the first level, a participant might anticipate that others would pick at random, in which case the best guess would be two thirds of 50 i.e. 33. At the second level you should pick two-thirds of this, i.e. 22, and so on. Taking this deduction to its logical conclusion the ‘correct’ answer is zero. However, it only wins the prize if all the other participants also solve the problem correctly (and even then you would share the prize with everyone else). The number that actually wins can vary depending on the sophistication of the audience.
In investing, ‘levels’ of thinking may be particularly relevant to understanding how macroeconomic narratives affect share prices. I find that much of the speculation on future market movements you read in the media tends to be based on naive, first level type thinking. For example, it might be based on whether companies are likely to hit their earnings projections this quarter, the next GDP growth stats or what the Fed’s next interest rate decision might be. The stock market as a whole tends to be a bit more sophisticated than that, though it is hard to say by how much. At a guess I’d say it more closely reflects aggregate expectations of what will happen over the next two years or so. If you wanted to get involved in the macro speculation game, this would suggest you should be trying to think at least two years ahead.
For individual shares, the more useful and practical insights about market behaviour generalise across shares rather than solely apply to specific situations. Behaving strategically implies understanding the systematic mistakes the market tends to make, how they correct themselves over time and from this how to exploit them. I’ve discussed this idea at more length in this previous post, where I contrasted the ‘valuation’ and ‘behavioural’ perspectives on investing. The significance of reflexivity to your strategy can be very different depending on which of these approaches you take. If you follow an approach of directly assessing valuation yourself and invest where prices are below fair value, reflexivity implies that you need patience. Share prices should tend towards fair value as the future is revealed but this may often take a long time. If you follow a behavioural approach you need humility. It’s not possible to predict shorter term market behaviour very precisely, so it’s important that your strategy allows you to respond to mistakes quickly.