Time Diversification

As a mathematical construct time diversification is a fallacious concept.

As a conceptually appealing rule of thumb, time diversification is intuitively appealing.

From Kritzman's Financial Analyst Journal article 1994:
Time diversification is the notion that above average returns ten to offset below average returns over long horizons. Specifically, if returns are independent from one year to the next, standard deviation of annualized returns diminishes with time, ie. the distribution of annualized returns consequently converges as the investment horizon increases.

Paul Samuelson critique: although it is true that the annualized dispersion of returns converges toward the expected return with the passage of time, the dispersion of terminal wealth also diverges from the expected terminal wealth as the investment horizon expands. This result implies that, although you are less likely to lose money over a long horizon than over a short horizon, the magnitude of your potential loss increases with the duration of your investment horizon.

According to the critics of time diversification, if you elect the riskless alternative when you are faced with a three month horizon, you should also elect the riskless investment when your horizon equals ten years, or twenty years, or any duration.

This criticism applies to cross sectional diversification (ie. 1 asset vs 10 asset portfolio) as well as to temporal diversification.

Over time the growing improbability of a loss is offset by the increasing magnitude of potential losses.

The critique is based upon the following conditions holding:
(1) Your risk aversion is invariant to changes in your wealth.
(2) You believe that risky returns are random.
(3) Your future wealth depends only on investment results.

Risk aversion implies that the satisfaction you derive from increments to your wealth is not linearly related to increases in your wealth. Rather, your satisfaction increases at a decreasing rate as your wealth increases.

Financial literature commonly assumes that the typical investor has a utility function equal to the logarithm of wealth. Based on this assumption, it can be demonstrated numerically why it is that your investment horizon is irrelevant to your choice of a riskless versus a risky asset.