Hack the market

A friend recently asked me what I considered to be the “axioms” of alpha-seeking trading strategies. I think there are a few, but probably the one that seems to me most important is that the atomic element of a trading strategy should always be a portfolio as opposed to a single instrument.

In a scenario of perfect knowledge, this wouldn’t be true. If you somehow *know* with certainty that crude will go up or that Citigroup will go down, then concentrating all of your resources into a position based on that belief might be reasonable. But knowledge seldom comes in such a neat package (and will frequently be illegal to act upon when it does!).

Instead, knowledge will typically come in more conditional and less certain forms: “commodities tend to rise during periods of FUD [Fear-Uncertainty-Doubt]” or “companies who announce stadium naming rights deals tend to under-perform.” In some cases, perhaps the knowledge on which you’ll base your strategy can be quantified probabilistically.

Depending on the nature and quality of the knowledge or hypothesis that forms the basis for a given strategy, one can adapt one’s portfolio construction/optimization based on customized relationships amongst the potential portfolio constituents. But one doesn’t need to be so fancy to see the concrete benefits of our first axiom. Below I detail a simple strategy I’ve put together to explore the forces involved.

The strategy I’ve built constructs a completely random, equally weighted long-short portfolio every day and liquidates the portfolio at the end of the day. Specifically, everyday the strategy:

1. Looks at all equities in the database that are available to trade. There were a bit more than ~4K equities available on any given day for this test.
2. Constructs a portfolio composed of N equities selected at random from the available equities. The portfolio has a fixed number of dollars available to it ($500K) and thus each position within the portfolio will be of size $500K/N or less. Orders are always scaled down so that we’re trading round lots (ie, qty%100=0) and if we can’t buy 100 shares of a particular name (eg, Berkshire Hathaway) then that money goes unused until the following day.
3. Half of the components in the portfolio are bought and half are sold so that we have a dollar-neutral portfolio.
4. Positions are entered at the open and exited at the close. (For these kinds of position sizes, this turns out to be a reasonable assumption, as we’ve illustrated here.)Â No stops are employed.

That’s it. The strategy only exposes ONE parameter for tweaking: N – how many names to hold in the portfolio. I varied this parameter across the set { 2, 4, 6,…, 12 } and ran each value 100 times across one year of data.

By selecting the portfolio’s components randomly, I’m trying to ensure that the strategies are truly non-predictive and thus should have an expected return of $0 without applying friction. By creating a dollar-neutral portfolio, I’m trying to ensure that we’re not accidentally capturing beta. What I’m looking to illustrate is the relationship between the number of elements comprising the portfolio and the risk-adjusted performance of the strategy.

As the following distributions illustrate, the strategy does indeed seem appropriately non-predictive. The distributions are normal and shifted to the left due to the application of realistic fees & commissions. As I’d warned in my very first series of posts, the random set of strategies did produce some nice-looking outliers, but we’re past being fooled by this pyrite of data-mining bias.

Also in terms of showing volatility’s relation to (even trivial) diversification, the experiment did not disappoint. While there’s essentially no relation between the profitability of a strategy and the portfolio size, there is a strong negative relationship between the volatility of the strategy and the diversification employed. Furthermore, the benefits of diversification happen quickly and soon taper off as we can see when we look at the table and chart comparing the number of elements in our portfolio with the average vol across the hundred relevant strategies.

There’s nothing new about this result. Harry Markowitz had explained these phenomena with infinitely greater rigor over half a century ago! But judging from what is published in popular “trading strategies” books and periodicals and even the baseline capabilities of algorithmic trading platforms, it appears that people persist in trying to beat the market without using what is perhaps their most potent weapon.

There’s an almost good reason for this that’s like the parable of the fellow who loses his key on the street but decides to limit his search to the area illuminated by a nearby lamppost. When asked where he’d lost the key, he indicates that he’d lost it somewhere on the street but was searching under the lamppost because the light was so much better there. Writing a single instrument strategy can be difficult enough on its own and adding instruments can make it substantially more difficult. But that’s also not a good reason to persist in limiting the scope of one’s efforts!

While there’s no claim to originality in this example, I hope that it’s nonetheless illuminating to see that even an intentionally non-predictive strategy can be mechanically improved. And we haven’t even applied all of the lessons of portfolio construction that we might have. Thus, while writing a worthwhile strategy remains difficult, one can see that there are some very well understood baseline tools that can be mechanically applied to any strategy that will yield material improvements.

performance analysis, portfolio management, strategy development