New Evidence That Time Diversification Exists, Violates Black-Scholes

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Time diversification, the idea that risk drops the longer you hold a stock, is controversial. Finance theory says that it doesn’t exist, but there is some empirical evidence that it does. Proponents of time diversification have mostly focused on U.S. markets over  the last century to prove their case, but a new study has taken a much broader view, 20 countries over 113 years, and has found statistically significant evidence that time diversification is a real effect that analysts should take into account when making recommendations.

Time diversification contradicts accepted theory

The research team, composed of Morningstar director of retirement research David Blanchett, Texas Tech University Professor Michael Finke, and American College Professor Wade Pfau, is well aware that time diversification contradicts accepted theory. “The primary critique of time diversification is theoretical and the primary defense empirical,” they write. “Time diversification violates the Black-Scholes option pricing model.”

To test theory they looked at how different portfolios would have performed over time spans ranging from one to twenty years, both for individual countries and in the aggregate. They also included varying levels of risk aversion to account for variations in performance. The result was that even the most risk averse investors should allocate a very high percentage of their portfolio to equities: more than 70 percent.

risk aversion and time diversification

Level of diversification

But the level of time diversification, while statistically present in all 20 countries the team reviewed, varied dramatically. Taking the two extremes, in Australia it was almost always correct to put 80 percent or more of your portfolio in equities, while investors in Switzerland with moderate risk aversion should have less than 30 percent of their holdings as equities.

time diversification diff countries

“The considerable differences in the optimal allocation… could potentially be a result of the different level of historical returns experienced by each country,” they write. “It may be that those countries that experience higher historical equity risk premiums (ERPs) are more likely to have positive estimated slope values [stronger time diversification].”

Even though this speculation may not be correct, it highlights the problem that time diversification poses. It isn’t supposed to exist, so even if investors are convinced that they should be taking it into account, they can’t because the necessary analytical tools don’t really exist. Time diversification means including auto-correlation (past stock performance impacts current behavior), something that is ruled out by current models.

Practical implications

Blanchett, Finke, and Pfau put forward one possibility, what they call the AR(5) model, but it’s clear that more work has to be done if analysts want to account for time diversification. “These findings have important practical implications for individual and institutional investors with long investment periods, such as investors in target-date mutual funds and pension funds,” they write.

time diversification with monte carlo

An analyst using the AR(5) model would make dramatically different suggestions for asset allocation, so this isn’t a purely academic question. If time diversification is real and being ignored, then a lot of value is being lost by long-term investors.

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