Friday, February 12, 2010

Optimal Position Sizing

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.

ty phone booth. tip of the hat to you.


Also, I know I haven't been posting hands in the last few posts...that's because I haven't been spewing too often or been playing poorly. The purpose of creating this was to hold myself accountable to poker deficiencies, of which none are present at the moment so don't be hatin.

Tuesday, February 9, 2010

Book Reviews: Intermarket Analysis by Murphy and Market Wizards by Jack S.

In my opinion, these are the two books trading novices should read first. Market Wizards is written for the average layman-the technical terms are sparse, but enough to familiarize yourself with the very basics if you have Wikipedia by your side, and is more of a character study of traders themselves. Perhaps it is just me, but one of the most intriguing aspects of anything I've enjoyed is the profiles of individuals partaking in that activity. Eccentric personalities abound in this classic tome, and you really get a feel for the type of people who are attracted to trading. When reading this, you should continually be asking yourself how well you can identify with the people being interviewed. You will never succeed as a trader if you don't have the right mindset or personality for it: Can you cope with continual losses lasting up to several months? Are you willing go with your gut when you find a profitable position? Do you have the discipline to follow your system when every technical indicator and chart is telling you to go the opposite direction? This book is a must for anyone beginning to consider trading for a living.

Intermarket Analysis appeals to a broader demographic: it hardly focuses at all on trading or strategies, but is more like an indepth look at macroeconomic tendencies. For traders, many people recommended me to read Pring or Murphy on technical analysis to begin with. I strongly disagree with this advice and feel that narrows your market analysis and could have you barking up the wrong tree for several years. Intermarket analysis focuses on the fundamentals of market movements and is increasingly important in this day and age given the rising economic prosperities of other countries, something a lot of people can relate to if they follow global news at all. What happens to the aggregate price of commodities as the dollar weakens? How do other countries benefit (or suffer in some cases) when America raises interest rates? How can we use bond and yield curve charts to forecast economic conditions? Really, this book focuses heavily on how currencies, commodities, bonds, and stocks are all inter-related, a key concept I know many overlook.