Optimal Market-Neutral Investing

Here I describe a conceptual framework for investing that I call Optimal Market-Neutral Investing (OMNI). I don't believe that it's entirely new - certainly you see people implementing similar schemes and I believe all great value investors understand the benefits of this technique at least to some degree, whether they explain it in this manner or not. Thus, while I came up with it as primarily a prescriptive tool for myself, it's also descriptive of best practices.

Let's first clarify - what does it mean to be market-neutral? Many would describe it as having a balanced position of longs and shorts in such a way that whether the stock market as a whole goes up or not does not, on average, affect, the value of your position measured in your native currency. Yet, clearly you do care what the market does - if the market suddenly decides that the stocks you bought are worth much less and the stocks you shorted are worth much more, you lose a lot of money even if your estimate of the value of your position doesn't change.

My definition is quite different - when I say market-neutral, I literally mean you do not care what the market does. But how could you possibly not care what the market does? It's simple. Say there's some stock X priced at $10 that you think should be valued at $15. In short, you expect the stock price (adjusted for time value of money) should reach $15. So you buy some amount of X at $10, because it's clearly undervalued. But observe this - if the stock goes up to $11, you've realized gain (and would sell some part of your position, reflecting your decreased expected rate of return on the position) and if the stock goes down to $9, your edge goes up, which allows you to add to your position with an increased expectation for that additional purchase. You can solve for the position size at any given price point that leaves you market-neutral, given some set of assumptions (this includes the possibility that price action is indicative of change in value) regarding price and value.

The precise math I feel is not that important (though I may elaborate later). On no stock can we estimate all the required numerical parameters precisely enough for the explicit math to be all that helpful. The point is that for any stock that you feel is undervalued (which implies that you have some ability to compute its value independent of the market price), there's some position size greater than zero that leaves you market neutral. If the price goes up, you realize gains, if the price goes down, you're being given a larger opportunity. While we can't compute this precisely, our intuition - even emotions - can be used to arrive at this number. After all, you know when you care or not. Thus, the position size is precisely the amount at which you're neither rooting for the stock price to go up, nor down.

This is a difficult balance - part of the reason that most people are poor at investing is that people fundamentally like rooting for things to happen. We pick sides when we watch sports, even if we don't have a natural rooting interest. We root for specific people to succeed in reality shows. The specific psychological reasons for this are beyond the scope of this post, but rooting for something is entertaining for most of us. Yet, rooting for things to happen makes us biased. Almost no human has the ability to see the world in an unbiased way when he strongly prefers one outcome over another. Thus, even without any other benefit, OMNI allows one to always stay in a neutral state of mind, which allows for clearer thinking.

The other reason OMNI is preferable over other forms of value investing is if your investment basis is that some stock is undervalued, this gives you no meaningful basis for predicting its short-term price action. Note that over the short-term, the price volatility far outweighs the expected return due to valuation. Even with a fairly optimal scenario - say your stock is expected to outperform by 10% a year - that's just 4bp or 0.04% a day, which is easily overwhelmed by typical daily volatility (it's certainly not all that uncommon for stocks to go down 5-10% in one day without a significant change in valuation - that's 100+ times the expected return). In other words, any additional exposure over the amount that puts you at market-neutral does not meet any reasonable value investor's short-term risk-reward ratio. Having a strong conviction of one's valuation does not change this. The more certain you're of your valuation, the more likely that you would root for the price to go down, as opposed to up, which means the position sizing can be greater but that does not mean you need to position yourself in such a way where you must root for the price to go up. It means you're at a point where you can't take advantage of any further price declines - in other words, you're not that sure about your valuation after all and you're exposed to short-term price action, over which you have no control.

While I described this from the perspective of a long-only equity investor, everything here applies to nearly all forms of value investing, including (especially!) fixed income arbitrage, shorting based on valuation, derivatives or any other instruments. In conclusion, if you are investing primarily on the basis of value and ever find yourself hoping for the market to move in your favor in the short term, it's very likely that your risk management needs work. Certainly, almost all risk management failures by value/arbitrage-based investors (LTCM comes to mind) can probably be attributed to large deviations from OMNI.

Preliminary Thoughts on Cognition

In my previous post, I talked about an economy as a self-organizing computational system that consists of economic agents. But automated systems aside, economics agents are largely human. Thus one can't understand an economy without understanding the idiosyncratic nature of human cognition - here's my take. Note that I'm not that well-read in cognitive sciences or psychology and my use of terminologies may be contrary to how they are used by experts in various fields.

A human mind, much like an economy, itself is a distributed computational system. The manner in which this distributed computation works requires close examination. First, different areas of the brain are responsible for different functions. Neurofunctional analysis reveals that some areas have specific functionalities across all humans, while other kinds of specialization based on brain locality show variation with some statistical patterns. Neverthelesss, the picture we have is that of a self-organizing, physical, computational network.

But that's not the whole picture. In fact, it's not even the most useful one. Imagine using a modern computer to build a multimedia web site. You'd be using various software packages to record sounds, videos and take photos, perhaps edit them using other software packages and test them out using yet another software package and upload them to some remote server. While it's clear that a lot of different hardware components were working together to help you achieve this goal, the interaction at the hardware level, by itself, would be entirely incomprehensible, and without understanding the interaction at the software level - betweenvarious software packages and the operating system (which themselves are composed of interacting processes) coordinated by the user and the system to achieve the desired outcome. It's not that your mouse, keyboard, CPU, RAM, hard disk, monitor, video card, motherboard, USB ports, etc, didn't work together - but that the specific activity cannot be meaningfully comprehended (or even distinguished from any other activity) by examining interaction at that level.

Likewise, while simple forms of cognition can be understood as interaction among different areas of the brain, more complex cognitive tasks not only engage different areas of the brain, but also different global processes, each of which is utilizing multiple areas of the brain. This is the second picture we have of the mind - the mind as a self-organizing computational network of mental processes. This is a virtual network built on top of the physical network. Keep in mind that as with computers, exactly what constitutes a single "process" depends on the point of view - often what is recognizable as a single process can also be seen as a group of processes and so on. This sort of issue exists with genes, species, culture, race, etc, but the inability to precisely delineate does not stop us from using the concepts usefully in communicating knowledge. To conclude, if the key to understanding economics is understanding the nature of interaction between economic agents as well as the nature of economic agents, the key to understanding the human mind is understanding the nature of interaction between mental processes as well as the nature of mental processes.

The Computationalist Theory of Economics - Introduction

Economic activity is computation.

Let me first note that this view is not new. While googling "Computationalist Theory of Economics" results in zero hits as I'm writing this, computationalism is a fairly common view among researchers in cognitive psychology and computer science. Furthermore, computational models are becoming entrenched, from physics, chemistry and biology to sociology, economics and finance. Thus both the idea that physical and social phenomena can be seen as essentially computational and the more pragmatic notion that they can be modeled by computation are gaining mind share, owing in part to the ubiquity of digital electronic computers.

But noting that research in this area is not particularly well-known in the general public, even those who are economically literate, and in the interest of sharing my thinking without being encumbered by existing literature that I haven't read, I will present things as I see, without much in the way of formal acknowledgement except where I see fit. This isn't to say other works haven't influenced me, but much of this thinking is a result of internal synthesis and a product of the zeitgeist. Many others likely stumbled upon this way of thinking after being exposed to pieces of it in unrelated context. It's not a coincidence that the area is named in different ways with a slightly different focus - complexity economics, agent-based computational economics, cognitive economics, just to name a few. Some economists claim that they have accounted for it all along, whereas others disagree with its usefulness. The taxonomy of knowledge is fuzzier than the rigid structure of attribution gives it credit for. I'll use this fuzziness as an excuse to avoid the mind-numbing tediousness that is proper scholarly attribution.

Before we restrict ourselves to economics, let's review why computation is a useful model for real-world phenomena:

Completeness

Insofar as real world phenomena deal with finite data, finite computation can fully describe all real world phenomena. While there's not as much evidence that reality is finite, reality as we perceive it, to the extent that cognition depends on computational mechanisms, likely is finite. Furthermore, even if cognition isn't finite computation, all concrete communication of cognition is essentially finite. In fact we lack the ability to explicitly reason about that which cannot be finitely described. Thus, we lose nothing of essence by considering all reality as computation.

Reducibility

All computation is reducible to simple models of computation, which allows for both theoretical mathematical analysis as well as practical computational exploration of phenomena.

Equivalence

There are multiple equivalent computational models, to name a few: turing machines, lambda calculus, recurrent neural networks, cellular automata and unrestricted grammars. Each model of computation is universal and is capable of emulating every other model of computation.


What is economy?

Now that we've established the mental framework in which to discuss economics, we can ask: what sort of computational system is an economy? What does it compute and how? In what ways can we map the concepts derived from traditional economics to this new framework?

The basic unit of this computational system is an economic agent, which is also a computational system. Each economic agent then computes bids (which are simply offers made to others to exchange one type of goods and/or services for another in some concrete amounts) based on his ability to produce, his preferences in regards to consumption, bids made by others and other information that can affect any of those. A market, then is a collection of related bids, or an environment in which bids meeting certain criteria are made. Whenever bids are matched transactions occur and the matched bids disappear. A collection of markets, combined with production systems (which can be seen as a special form of market - after all all production is transformation of one for or another and the ability to transform that production mechanisms give you, is a natural bid, based on which artificial bids are made) forms an economy. Note that neither the notion of a market, nor the notion of an economy, is precise. These are concepts.

I think it's fairly intuitive to see that an economy then is a computational system that consists of economic agents who are themselves computational systems, one that is largely self-organizing by way of computation of bids. How this self-organization comes about and the variety of different forms it takes, not to mention how and why specific organizations work are open questions that we'll explore.

The Solution

So I was in bed one night and as I was falling asleep, suddenly this idea for solving the credit crisis came to mind. After a few days of deliberation, here's what I ended up submitting to change.gov:

To whom it may concern,

I'd like to propose a new policy tool that bridges the gap between monetary and fiscal authorities, one that should not only help us deal with the ongoing credit crisis as it stands now, but should work as a calibration tool, much like the fed funds rate, under normal conditions.

We're in the midst of a credit crisis and facing the threat of deflation. Between Keynes, Friedman, Schwartz and even present Fed chairman Bernanke, whether you're a Monetarist or a Keynesian, the academic case for expanding the money supply and making sure that it gets to the economy (for those who care about wonky concepts such as money velocity) is well-established. In fact, I'm sure you're working right now on a fiscal stimulus package and ensuring that it has the desired effect on price stability and employment.

However, as both the popular backlash against and continued calls for various types of bailouts demonstrate, investing a large amount of money on short notice is a huge political challenge. How it gets invested has a large impact on many individuals' lives - there will be winners and losers, no matter the decision and the process invites uncertainty, speculation and rent-seeking behavior. While I have more faith in the team President-Elect Obama has assembled than I had in any administration in the past, the sheer difficulty of the task must not be underestimated. The political difficulty of engineering and implementing a fair solution, not to mention engineering the perception of fairness ensures that the incoming administration will walk a tight rope, despite the general mandate it enjoys. Most importantly, any specific fiscal stimulus is unlikely to become an enduring template for future administrations. The Obama administration may figure out a way to spend the money in a way that enhances America's long-term well-being and competitiveness, but there's no guarantee that future administrations will be as successful. Furthermore, it invites the question: if there's a way to spend money wisely, shouldn't we have already been doing it prior to the crisis? In short, while we all understand that printing money and spending it wisely will end the crisis, the uncertainty inherent in an ad hoc process is essentially what allowed the crisis to persist as long as it has.

That's probably enough introduction now - here's my humble proposal: let every taxpayer borrow from the Federal Reserve member banks (probably indirectly through other institutions; what's important is that the loan end up on the Fed's balance sheet) the amount necessary for them to pay federal taxes, at an interest rate set by the Federal Reserve. I will refer to this program as TLP for Tax Lending Program from here on.

Let's set aside the implementation details (what should the maximum allowable balance be; how should be we determine the initial interest rate; whether the Federal Reserve should issue bonds to fund this; how should it be administered, etc) for time being. To understand why TLP will work, it's necessary to understand why and how traditional tools of monetary policy work. Without getting into great detail, in essence, low target rates are maintained by expanding monetary base, which lowers banks' cost of funds and thus lowers the cost of borrowing for all users of credit. Thus credit and money velocity expand with a corresponding inflationary effect. However, when bank balance sheets are impaired, credit spreads are high and capital market liquidity for loans is low, lowering the risk-free rate does not have a corresponding effect on credit, as illiquid assets on banks' balance sheets have a higher rate of return (relative to their resale value) than new loans they can make at rates borrowers are willing to accept. Furthermore, faced with the possibility of deflation, credit spreads expand for all risky loans because each dollar is worth more in scenarios they default than in scenarios where they don't (this lack of comparability of the value of dollar is partially why credit spreads seem extreme relative to any reasonable probability of default). Thus, we're seeing a drop in credit availability, especially outside of the government subsidized residential mortgage market.

Theoretically, however, monetary stimulus has worked, in the sense that there's now one borrower who has more incentives than ever to borrow: The Unites States Federal Government. In fact, if the US Government was as sensitive to interest rates as private sector entities were, monetary policy would work by making fiscal stimulus seem economical. Unfortunately for Monetarists, the US Government is almost entirely insensitive to interest rates in the short term and is only moderately sensitive in the medium term, for political reasons I've mentioned earlier, as well as bureaucratic overhead. Federal budget cannot easily be changed according to the needs of monetary policy.

TLP largely avoids the shortcomings of existing mechanisms. First, it bypasses the banking intermediaries and supplies credit directly to individuals. Second, it works from the more flexible revenue side and can be fine-tuned without political negotiations. Third, it's less likely than existing mechanisms to lead to asset price distortion. Banks are largely homogenous in terms of the incentives they face and are much more likely to direct the funds towards a single asset class to produce a bubble. Furthermore, with TLP be in place, monetary stimulus will require a smaller adjustment in rates to produce the same effect, reducing any tendency of monetary stimulus to cause malinvestments. Fourth, it leaves no permanent imprint on the budget. Part of everyone's fear regarding fiscal stimulus is the worsening budget picture and the long term threat of inflation it implies. TLP, by temporally moving revenue to a future date, much like other monetary tools, can be used to mitigate deflation in the present without affecting the longer term picture. Furthermore, at a reasonable rate, it should be a small source of revenue.

One objection that could be raised is the idea that the US households are overleveraged and cannot take on additional debt. This concern, aside from being an alarmist half-truth, does not favor direct government spending over TLP. Ultimately, TLP transforms the meaning of money or government liabilities in general. Presently, money is implicitly backed by future tax revenue. Under TLP, money will be backed by past tax receivables as well as future tax revenue. Neither system can function without an underlying economy that supports the level of government spending and the idea that the US government can borrow against future tax revenue, but not against past tax receivables is illogical. If anything, households, being more sensitive to both total debt amounts as well as ongoing debt servicing, are more likely to be able to make sensible adjustments.

While I propose TLP as an enduring policy tool, not merely something that can sustain us through this credit crunch, there's one benefit that is specific to the current situation. Should TLP go into effect, much of the money borrowed should go towards paying off higher-interest rate existing loans, whether mortgage loans or credit card debt. Without considering the direct effect it has on the bottom line of banks, it gives secondary markets a huge amount of information regarding the future performance of those loans. Clearly, one won't take out a loan from the government that will be hard to discharge in a bankruptcy to pay off a more easily discharged loan, if he's considering bankruptcy. Conversely, large loans with high rates that are not being paid off essentially imply that the borrower either has other high interest-rate loans he needs to pay off first, has little income and did not pay much in the way of income tax, or is considering defaulting on the loan, all of which are negative signs. Thus, the introduction of TLP can add one-time clarity in the secondary market for assets backed by consumer loans.

My hope is that TLP will free the US government from being encumbered by concern for short-term monetary policy and allow them to focus on long-term economic issues, whether energy independence, sustainability, global competitiveness, income disparity or budget deficit. All fiscal actions ultimately have monetary implications, but some fiscal actions, without TLP, cannot have its monetary effect temporarily reversed or transferred to a future date by the Federal Reserve. This limitation restricts the government's ability to set its own long term economic agenda and act upon on them. If TLP had already been in place, for instance, I'm fairly certain that we could cut the budget deficit and repeal Bush tax cuts while not having those measures have a large deflationary effect. In fact, TLP offers an intriguing possibility of running a balanced budget or even budget surplus in the long run without facing the possibility of deflation.

It is ultimately with hope that TLP can be administered and used correctly, by the incoming administration, by the Federal Reserve and by the American people that I humbly make this proposal. Should you have any questions, please do not hesitate to contact me. Otherwise, good luck.

Sincerely,

Pricing Uncertainty

What do you all think?