Time Diversification Frontiers and Efficiency Frontiers: Implications for Long-Term Portfolio Management (Digest Summary)

The authors examine the validity of the widely followed wealth management policy of time diversification to reduce risk from buying equities—namely, that increasing the investment horizon lessens the probability of both absolute and relative losses on a stock holding. Applying option-pricing theory to address financial loss in terms of both its likelihood and size, they create a representation of risk in a time diversification frontier. They analytically combine this frontier with Markowitz’s longstanding efficiency frontier to identify ideal investment points for both frontiers. They conclude by examining the consequences of some key behavioral research findings on the use of time diversification.

At first glance, it may seem that the authors are merely providing confirmation for a financial adviser’s customary rule of thumb that stocks are best suited as long-term investments, but closer consideration reveals that their findings offer subtlety of insight. The authors’ use of option-pricing theory furnishes productive conceptual leverage when combined with a focus on a particular definition of risk. Viewing risk as the applicable cost of hedging in terms of put option prices, the authors identify the conditions under which time diversification is the most robust. Those conditions would be when investment growth is high and annualized volatility is low. Their derived time diversification frontier schematically represents those growth/volatility combinations at which time diversification can transition between effectiveness and uselessness, which are investment “tipping points” worth knowing.

Extending their construct’s analytical reach into the known territory of the efficiency frontier, the authors lay out a sound theoretical foundation for the merits of using index funds over active management in portfolio choices. Index funds, or alternatively, balanced portfolios that include bonds, have a natural niche in the middle range of the efficiency frontier. That positioning coincides exactly with their optimal position along the time diversification frontier at which point the rewards of an extended investment horizon can be obtained.

Finally, the authors identify the sources of investor biases that can be detrimental (i.e., underestimation of future investment growth and overestimation of volatility) or beneficial (i.e., aversion to extremes) within this framework. The identification of these sources helps direct advisers toward techniques that would be the most productive responses to combat such perceptual flaws.

The authors build their conceptual foundation using academic findings, but their main goal is to supply practical guidance by applying theory. They carefully illustrate the dimensions of the relationships between the variables under scrutiny (asset values, risk, returns/growth, and risk/volatility) and how those relationships evolve over time. Given the centrality of option-pricing theory to the discussion, additional detail is conveyed visually in several short appendices, which include three-dimensional representations of the behavior over time among put option prices, expected growth or annualized volatility, and the investment horizon, as well as a final summary of the derived time diversification frontiers.

The authors acknowledge a potential weakness in their time diversification model. First identified in the academic literature by Pastor and Stambaugh (Journal of Finance 2012), the weakness is the effect of forecasting uncertainty as captured by the term “predictive variance.” Because uncertainties related to expected returns and the values of model parameters exist, as well as incomplete specifications attributable to the potential exclusion of relevant variables, ex ante time diversification can be reduced. This weakness forces the authors to make a relative, as opposed to absolute, case on the merits of their argument, noting that time diversification is favored under conditions of higher over lower expected returns, lower over higher expected volatility, and non-extreme portfolios. But the broad sense of their approach is nonetheless preserved.

The emphasis on the short term is often salient in finance, business, and life in general. This research, which focuses on providing measured and principled advocacy for the accessible benefits of the long term, could thus be seen by some as contrarian. But discounting the researchers’ findings would be a disservice to the investing community, particularly to individual investors whose chief advantage relative to professionals may be their ability to wait out market perturbations with fundamentally sound investment choices. Providing empirical support for the advice of such an investment luminary as John Bogle is definitely more than an exercise in restating the obvious.