Analysts David Blanchett, Michael Finke and Wade Pfau discuss optimal portfolio for the long run. There is surprisingly little agreement among academics about the existence of time diversification, which we define as the anomaly where equities become less risky over longer investment periods. This study provides the most thorough analysis of time diversification conducted, using 113 years of historical data from 20 countries (over 2,000 years of total return data). We construct optimal portfolios for 20 different countries based on varying levels of investor risk aversion and time horizons using both overlapping and distinct historical time periods.


We find strong historical evidence to support the notion that a higher allocation to equities is optimal for investors with longer time horizons, and that the time diversification effect is relatively consistent across countries and that it persists for different levels of risk aversion. We also note that the time diversification effect increased throughout the 20th century despite evidence of a declining risk premium. Although time diversification has been criticized as inconsistent with market efficiency, our empirical results suggest that the superior performance of equities over longer time horizons exists across global equity markets and time periods.

Optimal Portfolios for the Long Run

The primary critique of time diversification is theoretical and the primary defense empirical. Samuelson (1963) and Bodie (1995) point out that if stocks are less risky in the long run there is a free lunch for long-run equity investors. Bodie (1995) emphasizes the fact that time diversification violates the Black-Scholes option pricing model. If time diversification exists, then options hedging long-run equity risk should reflect a decreasing likelihood of loss over longer time periods (they don’t).

Historically, stocks in the United States haven’t been very risky over long-run holding periods. Campbell and Viceira (2003) argue that empirical evidence shows that stock returns are not independent and identically distributed over time (they tend to mean revert), which implies that long-run stock returns may be predictable and that long-run investors should overweight equities2. The authors find that the annualized standard deviation of stocks is actually lower than annually reinvested T-bills after just under 30 years. This leads to the counterintuitive conclusion that risk-averse investors should demand stocks as a hedging strategy against a long-run drop in real consumption.

Via: ssrn