Quantitative Portfolio Management

Chapter 2Forecasting

It is very difficult to predict, especially the future.

Possibly Niels Bohr

For a non-gambler, investing money into moving things makes sense only when he or she is able to predict, more or less, where those things are moving. Predictability is actually not that bad in physics describing dynamics of matter by various ordinary or partial differential equations. The horizon of physical predictability is still limited by the Lyapunov exponentiation of nearby orbits. This exponential accumulation of uncertainty in a formally deterministic system is a signature of dynamical chaos, which almost invariably appears in dimensions greater than two.¹ For financial assets, it is also easier to predict returns over shorter horizons, mainly due to higher costs of faster trading (Chapter 5). The rules of the game and clear players' stimuli such as greed and fear provide a degree of dynamical description to the markets (Sec. 2.5), but those dynamics are very noisy due to many dimensions/participants often making noisy decisions. In addition, actions of the more powerful and moneyed participants—informed traders—reduce the degree, and shorten the horizon, of price predictability. After all easy signals are arbed out, which they surely are, we are left with a pretty low predictability of future returns—on the order of bps² per day—vs stock volatility.

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