Passive Investing Is An Over-Fitted Strategy

The conflict about over-fitted market timing strategies versus passive investing has more to do with marketing and sales than with sound quantitative analysis. It appears that the main objective of this conflict is to calm passive investors and discourage market timers. But both face known or hidden risks.

I will briefly discuss in this article passive investing and market timing strategies.

I will start with market-timing strategies and the usual arguments against them from academics and market professionals. The frequent claims are that market-timing strategies are in most cases over-fitted to historical data or the outcome of multiple comparisons and data-mining bias.

Academics propose to cure over-fitting using some ambiguous methods that adjust metrics for data-mining bias and most professionals propose passive investing as the alternative solution for avoiding the perils of market timing.

My position is that any arguments about over-fitted strategies in support of passive investing are attempts to create an artificial image to attack, also known as a straw man in logic. The reason for this is that backtested strategies over a sufficiently long data sample to minimize over-fitting have the same probability of failure as passive investing strategies. I further claim that passive investing is equivalent to an over-fit using a set of hidden features, or predictors.

The golden cross market timing strategy 

Let us look below at the performance of the long-only golden cross timing strategy in adjusted SPY ETF data since inception:

Buy if MA(f) > MA(s)
Sell is MA(s) < MA(f)

where f and s are the periods of the fast and slow moving averages, respectively.

Below is the SPY chart with buy and hold and timing-strategy performance for f = 50 and s = 200, which is a popular choice for the moving average periods:

The timing strategy outperforms buy and hold on a both absolute and risk adjusted basis. Annualized return for the strategy net of commission of $0.01/share is 9.42% versus 9.36% for buy and hold while maximum drawdown is -19.45% versus -55.19%, a significance improvement. This results in a MAR (CAGR/Max. DD) of 0.48 for the timing strategy versus 0.17 for passive buy and hold.

The usual argument made by proponents of the Efficient Market Hypothesis (tenured professors and candidates for tenure) that this is an over-fitted timing strategy determined in hindsight. I agree but my point is that this is a straw man argument in support of passive investing. A passive investing strategy also rests on hindsight.

To start with, if we vary the fast moving average f from 5 to 50 and the slow moving average s from 100 to 500, both in increments of 5, and consider all the strategies resulting from the various combinations we find out that an overwhelming percentage of them, nearly 98%, outperform buy and hold on a MAR basis.  Actually, the f = 50, s=200 choice results in median MAR performance.

The usual response from the passive investing proponents is that this strategy will fail in the future. I again agree but a passive investing strategy can also fail for similar reasons, i.e., changing market conditions. This is the form of a passive strategy:

Buy and hold
Exit according to some performance or investments horizon criterion

As it may be seen, passive buy and hold is still a strategy no different in principle from a timing strategy. But what is more important is that many, including academics and practitioners, do not realize that the features, or predictors, of this strategy are hidden.

The hidden features of passive investing

In machine learning terminology, the timing strategy uses one feature: d = MA(f) – MA(s). Actually, this is an engineered feature from the two basic features based on the moving average values. The strategy is long when d > 0 and exits when d < 0. The strategy will cease to perform well when d will not be able to generate sufficient returns. For example, this can happen during long periods of whipsaw where the signal to noise ratio decreases significantly, limiting the accuracy of the strategy.

In passive investing there are hidden features that are used in support of this strategy.

  • Markets tend to rise over the longer-term
  • Drawdown never reaches 100%
  • Recoveries from maximum drawdown are sufficiently quick

In fact, whereas a golden-cross strategy might have been the outcome of brute force optimization or some crude machine learning or other quantitative method, passive investing appears to be the outcome of mental learning, or a hybrid approach, known as quantamental in modern terminology. However, passive investors usually do not understand, or underestimate, the impact of the hidden features. For example, if in the future recovery from a drawdown in the order of 50%, similar to the one generated by the financial crisis, takes many years, let us say 10 or even longer, then many passive investors will be forced to sell at a large loss to cover their living expenses.

Therefore, although timing strategies can fail when the features used are unable to distinguish the signal from the noise, passive investing strategies can fail because some of the hidden features they were based on cease to be valid.

As I argue in my SSRN paper Limitations of Quantitative Claims About Trading Strategy Evaluation, knowing when market conditions are about to change is much more important than any quantitative claims about over-fitting. The same holds about passive investing because as I have argued above it is an over-fitted strategy.

Note that any references in this article to over-fitted strategies exclude those that result from naive data-mining. There is a large class of such strategies that are worse than random and most fail almost immediately in forward testing because during design they exploit features that have no economic value but align temporarily with some other features that do. But this is a different subject for another article.  The conclusion here is that passive investors face similar risks as market timers that employ well-designed strategies do. In the former case, the features that may compromise performance are hidden, not known, or not discussed. It is quite possible that the future hides many surprises for passive investors, “do nothing” fund managers and “pedestrian type” market timers.

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Charting and backtesting program: Amibroker

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2 Responses to Passive Investing Is An Over-Fitted Strategy

  1. Drew Wells says:

    Is the post-1989 Nikkei experience a concrete example of the sort of hidden risk facing passive strategies to which you refer?

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