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...

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