Essays on the Time Diversification Puzzle

Abstract

What is the relationship between risk and investment horizon? Since Samuelson’s (1969) theoretical proof that risk and time are unrelated, a half century of debate and controversy has ensued, leaving time diversification as one of the most enduring puzzles of modern finance. Over this time, the literature has developed along four identifiable streams of scholarship, with no stream demonstrating an ability to unravel the puzzle. Today, we have the same fragmented and contested debate that inspired Kritzman’s (2000) lament that the time diversification had become a referendum on risk. Faced with the protagonists’ entrenched positions, we offer an innovative approach to investigating the puzzle. Motivated by a critique of the literature, and an examination of the institutional setting, we provide positive insights into the relationship between risk and investment horizon by examining ten different measures on common terms. We find that the protagonists in the debate are each correct in their assessment of the puzzle on their own terms, and that resolution to the debate may hinge on more than simply the basis upon which risk is measured. Using a nested methodological approach, we advance the debate by considering whether alternative accumulation models and competing asset allocation approaches influence the relationship between risk and investment horizon. From the perspective of a long-horizon investor (e.g. a defined contribution plan member) faced with the puzzle, we find that alternative accumulation model specifications introduce the risk of the investor encountering wildly different terminal wealth outcomes. Moreover, for the investor with finite horizons, we find that asset allocation informed by a target can produce superior return and risk characteristics. We conclude that the relationship between risk and investment horizon is highly contextual, and that the time diversification puzzle is properly viewed from the perspective of a trinity of interrelated factors: risk, the accumulation model, and asset allocation strategy.