3 Time Diversification

Kritzman

Although an investor may be less likely to lose money over a long horizon than over a short horizon, the magnitude of a potential loss increases with the length of the investment horizon.

The notion that above-average returns tend to offset below-average returns over long horizons is called time diversification.

Specifically, if returns are independent from one year to the next, the standard devia- tion of annualized returns dimin- ishes with time. The distribution of annualized returns consequently converges as the investment horizon increases.

Kritzman (2015) What Practitioners Need to Know About Time Diversification

Kurtti

Academics have long debated the concept of time diversification, which questions whether time reduces the risk for stock investors or not. Prominent academics, led by Paul Samuelson, have shown (usually mathematically, employing utility functions) that time doesn’t reduce risk. However, investors and financial advisors generally believe that risk decreases with time.

Defining loss risk as the expected loss considers both the probability of loss and its average depth, making this metric effective for fat-tailed returns.

For investment horizons of less than 4-7 years, empirical loss probability has been lower than what is predicted by a theory based on normally distributed, independent and identically distributed (i.i.d.) daily returns. Conversely, when losses occur, they have been deeper than what the theory predicts. This appears to be due to the fat-tailed nature of the returns, which is maintained by the correlation in the return time series.

Long-term loss risk, as measured by the expected loss, decreases over time (with reasonable stock allocation levels). Time diversification works when the investment horizon is long and the investment level is sensible.

At 100% stock allocation, in the short term (less than a few years) loss risk initially increases and then levels off. Time diversification only begins to work after more than five years.

Time diversification requires a shorter time to start working as the investment level (Kelly fraction) decreases.

Loss risk decreases over the long term as a function of time, but for most investors, the psychologically significant drawdown risk may be the limiting factor.

Mean reversion is not needed to explain why the empirical long-term standard deviation and loss probability for stocks are lower than theory predicts. A too-small sample size (a too-short return history) can largely explain the phenomenon.

Stock return history is very short and underestimates the real long-term investment risk. A short return history typically does not include the rarest events (returns) that will occur over a long enough time frame.

[Kurtti (2023) Time diversification works (eventually)](Time diversification works (eventually)