Friday, September 29, 2006

The Principle of No Arbitrage and The Beauty of Relative Comparison

Fixed income pricing is super cool. I've not seen this side of financial valuation since I've gotten to college and now that I've been exposed to it, I feel drawn into it. I've always thought of finance as more of an art than it is science... and even if it is usually on instruments that don't have a definite stream of cash-flow, and most results are based on expectations rather a focus on the present relative to other things in the present. Bond pricing is the latter, of course, and one thing: everything... EVERYTHING... is based on the principle of no arbitrage.

I think that's pretty cool, as I've never really dived into the quantitative side of things... but the way mathematics really help in making money here lies in the fact that certain functions MUST equal to other functions (after taking into account certain transaction costs, which diminishes with scale), or else one can always buy the cheap instrument and sell the expensive until the spread narrows with exploitation. And the beauty of that is, even if one were to be wrong in predicting the future, one only has to be less wrong than the other side of the hedge and there is money to be made. Returns are made by locking in inefficiencies rather than soothsaying the future.

But, most attractive opportunities out there are exploited, and spreads which exist out in the real world are often miniscule in that one has to commit billions of dollars in capital and leverage for the trade to make sense. Or else, there are also more and more exotic options available to the clever and the brave, playing with eurodollar futures and interest rate swaps to pocket the difference between locked in linear term structures and positive convexity LIBOR rates (I don't have any idea what I'm talking about anymore). And this takes huge amounts of capital, and is very much an economies of scale thing.

Today it hit me... that's exactly why fixed income returns are on average lower than that of equity returns over the historical average. You have all these math geniuses seeking the midas touch, and there are really only so many trades that can be done, and the fact that so many bright and talented people are out there everyday taking advantage of snippets make it very difficult to make abnormal gains. The factors that go into fixed income pricing, although complicated as hell, is still a system one can exploit effectively, by valuing one instrument relative to another, and making small and yet almost risk free returns. Equities, on the other hand, are different in that there's always more "expectation" or "unquantifiable" factors involved, and the risks an equity investor takes on are almost always more of a "business" calculation rather than mathematics. Of course, it's where most excess return come from over risk free, but it's also where the most volatility lies. And there really is no system in equity, only philosophy, contrast to fixed income, where everything falls into place beautifully in advanced quantitative valuation--and though expectations regarding the short-term volatility of interest rates, general movements of the term structure, and such and such--the expectations are still not USED to make money, but used to take an advantage of an inefficiency in pricing between two functions.

I'm confusing myself, better stop writing and start learning more...

Monday, September 18, 2006

Good stocks is like good underground music

Finding undervalued stocks is a lot like finding new underground punk rock bands. You try out everything that nobody has ever heard of before, and then you start liking a few of them. You get more and more excited about them, and then you get to "own" them, and it feels good when nobody else knows about it.

When the stock/band sellout, you sell them out of your portfolio. And viola, and the process starts again.

Friday, September 08, 2006

Shortfalls in the Use of Modern Finance Theory in Equity Investments

I've always wondered why exactly so many practitioners of investment valuation have fallen for the concepts delineated in modern financial theory in applying them to the determinant of the "correct" price of a business. It's not as if the concepts of risk and error are infallible, but research analysts and investors alike set target prices and returns based on a certain way numbers are crunched. Assumptions are made about a certain company in its ability to produce cash-flows, or in comparing it to other businesses that are similar (preferably exactly alike) in the industry, and then a recommendation or investment decision appears magically based on the results. I'm not arguing the merits of modern financial theory in giving the investment community a valuable tool to ground a thesis, or to descibe a certain investment in the language of statistics and arithmetic. I'm arguing that the way people choose to perceive our theories in modern finance as anything but incorrect and infallible is wrong. The assumptions that most individuals choose to attribute to a model, or an investment thesis is quite often based on their opinion of what is correct. However, many fail to capture "correctness", and instead capture an ersatz of such which is a motley composition of past results, blanket assumptions of expected risk and return, greed, or fear.

Case in point, some might view DCF models and relative multiple models to be the holy grail of investment valuation, and that armed with these tools, one can have the midas touch in stock picking. Of course, many realize--too many bad investments later--that things are not always what they seem, and just because they have bought or sold a stock based on their perceptions and assumptions, does not mean the market will be kind enough to support that assumption and narrow the gap between perceived value and actual market price. Now, modern finance theory, although genius, must be analyzed from the perspective of one that is detached from its use. Those that stick fast to the explanations offered by serendipitous combinations of certain costs of capital, market risk, volatility, growth rates, expected returns, etc. will often find it difficult to question these.

Cost of capital, for one, especially that one used in the CAPM model, is really a function that determines a correct "discount" rate based on experiences of the past. How that measures up to performance of a certain company in the future is anybody's guess, as there has never been (at least not to my knowledge) any studies that have shown that CAPM is flawless in its ability to predict future risk with data from the past. I know of no greater hoax than the assumption of a WACC or Cost of Equity. Beta, for example is one of the most absurd variables. The concept that risk of equity can successfully be measured with a regression of how the stock price of the business in question correlates with the performance of the market over a range of the past seems almost silly or even stupid. Although price performance may indeed have certain correlations, the value of a business certainly should not, and to look towards beta as if its a knob to where risk and return, and thus the value of a business, can be adjusted accordingly is fundamentally wrong. The risk that beta measures does not differentiate between upside and downside risk, and it has no way of predicting whether or not the future upside or downside of a business will still be the same. Cost of debt may have its merits if a business is predictable or stable enough to constantly borrow at the same rates as it has been in the past, but even cost of debt fails to consider future issuance, retirement, or refinancing of debt and at what rates companies might be able to borrow at that point in time. And when one consideres the inaccuracies in predicting a "market risk" in the equation, the picture gets more blurry.

Thus, a classic case of "garbage in, garbage out" exists, where if certain variables in a model simply don't make sense, the results of that model will not make sense either. Of course, the Godly redeeming feature is the epsilon attached at the end of the equation which accounts for "errors and unsystematic risk", which vindicates all the absurdities. However, one must realize that most of the time, it is certainly due to "errors and unsystematic risk" in market perception that investors can successfully take advantage of them and intelligibly make an investment decision and make returns. I would argue that most excess return can only be garnered with security analysis in finding and analyzing specific and unsystematic characteristics of a business that can be predicted with reasonable certainty. Risk is a perception and a personal preference, and should be discounted according to an investor's own definition of how much risk to take.

Valuation is never meant to be a "precise" science, and since more often than not, human nature tends to err towards optimism and hope, variables are often assumed to be more on the bright side of things. Of course, it is only with that that investment bubbles and euphoria is born, where a "new economy" is coming that warrants infinite growth and opportunities. And even if assumptions do not go out of hand to such an extent, most of the times, those that analyze an investment develop a certain love for the investment and an urge to attribute positive characteristics where none exists factually. Of course, when expectations are not met, or when markets disappoint, assumptiosn prove to be wrong, and the price regresses to the "true" value of a business absent of any emotion or optimism attached.

Investing is more of an art than science, and though mathematics is a must in calculating NPV, liquidation value, or market comparables, it should be done in such a way that error is made in the name of conservatism, and the preservation of capital and risk-aversion should be the first and foremost philosophy in making good returns. Mathematics and philosophy may have found thier common grounds in logic, but perhaps not so much yet in the world of investment valuation.