“Diversification is the only free lunch in investing.”

-Harry Markowitz

(Well, sort of…)

Diversification is one of those investment ideas that everyone agrees with and almost nobody does well enough. Most investors diversify across stocks. More sophisticated investors diversify across asset classes. Even more sophisticated investors diversify across factors such as value, momentum and quality. Then, having constructed these apparently diversified portfolios, they often make a surprisingly concentrated bet on exactly how each factor should be defined.

A recent paper by Anthony Renshaw, Yurong Gu, Matt Candar and Andrew Ang, “Diversification All the Way Down: Multifactor Investing Within Factors, Across Factors and Across Time”, argues that this is a mistake. Diversification shouldn’t be something you do once at the top of the portfolio. It should be applied repeatedly, at every level of the investment process.

The first level is the most interesting: diversify within the factor itself.

Consider value. We often talk about “the value factor” as though value were an observable characteristic like height or weight. It isn’t. Value is an idea that has to be measured, and there are many possible measurements. Book-to-price is value. Dividend yield is value. Free cash flow can measure value. So can profit or a valuation measure adjusted for intangible capital.

The usual approach is to select one of these and call it the factor. But this creates an unnecessary source of model risk. If the underlying phenomenon is real but our measurement is noisy, relying on one signal makes our portfolio dependent on the peculiarities of that particular measurement.

Renshaw and his co-authors instead combine signals. Their value exposure is actually divided into two different types. “Cyclical value” uses traditional measures such as book-to-price and earnings yield, while “enhanced value” incorporates profit, intangible capital and free cash flow. The distinction matters because the two versions of value behave very differently. Their active-return correlation in the study is only 0.13.

That is a remarkable number considering that both portfolios supposedly represent the same factor.

There is a useful lesson here that extends far beyond factor investing. A phenomenon and our measurement of the phenomenon are not the same thing. If several imperfect signals contain information about the same underlying effect, averaging them can reduce measurement error in much the same way that owning several stocks reduces company-specific risk.

The paper then moves one level higher and diversifies across factors. Its portfolio contains four sleeves: cyclical value, enhanced value, momentum and quality. Because their active returns are only weakly correlated, combining them produces a higher information ratio than any individual sleeve. Over the roughly 21-year backtest, the multifactor portfolio produces an information ratio around 1.0.

This is the part of diversification investors understand best. Value can struggle while momentum works. Momentum can crash while quality holds up. You don’t necessarily need to know which factor will work next if you have several positive-expectation strategies whose bad periods don’t coincide.

But the authors then add a third layer: diversification across time.

Rather than holding fixed factor weights, they allow modest tactical changes using three different timing models. One looks for market environments resembling previous environments. Another uses recent factor momentum. A third examines movements in underlying factor exposures.

And the result here is almost more interesting because it isn’t spectacular.

Over the most recent three years, timing raises the information ratio from 1.83 to 1.92. Over the full 21-year period, however, the difference is essentially zero: about 1.00 versus 0.99.

This shouldn’t be dismissed as a failure. It may actually reinforce the paper’s broader message. The big gains don’t come from making better forecasts about what will happen next. They come from making the portfolio less dependent on any single forecast, signal or factor.

That is a much less exciting proposition than predicting the next factor rotation, but probably a more useful one.

There are obvious reasons not to take the reported numbers too literally. This is an internally designed backtest associated with a commercial index product, and the reported results are gross rather than a long live out-of-sample record. The timing models in particular offer plenty of room for specification choices. The 21-year result showing essentially no benefit from timing should probably carry more weight than the much better recent result.

But the central insight doesn’t depend on believing the exact backtest.

Investors naturally think about diversification horizontally. They look to add another stock, another factor, another strategy. The paper suggests thinking vertically as well. Diversify the measurements used to identify an edge. Diversify the implementations used to capture it. Diversify across genuinely different edges. And if you want to time those edges, perhaps diversify the timing models too.

The deeper principle is that uncertainty exists at every layer of a system. We are uncertain about securities, uncertain about factors, uncertain about our measurements and very uncertain about which regime comes next.

Diversification shouldn’t merely protect us from being wrong about which stock to own.

It should protect us from being wrong about how we think the whole thing works.

Disclaimer

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Except where otherwise indicated, the information contained in this article is based on matters as they exist as of the date of preparation of such material and not as of the date of distribution of any future date. Recipients should not rely on this material in making any future investment decision.