multiverse
There are many conceptions of our world and its underlying nature, each seemingly more creative than the last. One of my favorites – adopted by all serious fans of Star Trek as well as some physicists who’ve run rather far afoul of friar Occam’s good rule - posits the existence of a multiverse. There are various such stories, but the basic idea is that at every quanta in time the universe partitions itself off into an infinitude of parallel instances of itself, each representing a different branch of realized possibilities. In this one, I decided to become a surfer while in that one I went into finance and in that one I led the US to its first-ever world cup victory. While we only experience the particular universe we happen to be situated in, the multiverse represents the simultaneous execution of all possible universes. Under this view, we really do live in the best of all possible worlds.
This idea has surprising utility. While its cosmological implications might represent the extreme psychedelic fringe of the continuum, at the other ends lies actuarial science, the foundations of risk management and, yes, a variety of option pricing techniques.
In the universe of the simplified algorithmic trader we’ve been discussing, there are at least three ways in which this unfolding of possibilities can be considered. In the first case, we can vary the decision-making of the strategy itself; in the second, we can vary the market conditions upon which the strategy will base its decision-making and in the third case we can vary both. They are all forms of scenario analysis.
When we talk about varying the decision-making of the strategy itself, there’s a range of possible adjustments we might make. We could be speaking of actually swapping out the entire strategy itself – eg, going from a trend-following to a mean-reverting strategy. Or we could talk about changing characteristics of a given strategy. For example, to reuse our first simple sample strategy – the morning range breakout – we had a few natural “levers” or parameters which we could modify about the strategy without fundamentally changing its underlying behavior. That strategy exposed two such parameters: what to trade and how long to wait before putting its trades onto the market (that is, the length of the morning range).
If we take this idea of permuting a strategy by way of its parameters and combine it with the idea we discussed last time and back test each of these permutations, we arrive very close to the idea of parameter optimization of a strategy. The only missing piece is the idea of ranking the results of each of these strategies. This turns out to be somewhat more complicated than it might appear and we’ll consider it in a later post.
Assuming a simple case where we disregard risk management practices and simply rank the strategies by return on investment (ROI), we can see that parameter optimization is a bit of a misnomer as we’re not so much optimizing the strategy as we are searching for the best strategy within a set of strategies defined by the ranges of each of the parameters we’re considering. This is at best a weak form of optimization and is perhaps better characterized as a search problem.
Before considering the utility and limitations of this kind of parameter optimization we’ll next take a look at the second form of scenario analysis in which instead of permuting the strategy by way of its parameters, we change the market conditions in which the strategy operates. This will be the topic of our next post.
