Time diversification refers to the notion that time diversifies risk, implying that the volatility of risky assets falls over long periods of time. This characteristic is based on the independence of returns. Obviously, the simplified independence assumption does not hold, and in no way are we suggesting this is a novel insight. The impact of time diversification on portfolio risk has been a running debate for decades,3 with several prominent financial economists arguing on both sides, most recently Kritzman (2015). A key element in this discussion is an investor’s view on the behavior of financial markets, namely, the existence and strength of short-term continuation and of long-term reversion.4
The existence of rising holding-period volatility when moving from monthly to annual holding periods is well accepted, given the presence of positive, albeit weak, correlation between monthly returns. In the finance realm, we know this as momentum. A comprehensive set of research has been undertaken on this persistent phenomenon, including work by Moskowitz, Ooi, and Pedersen (2012), who find “time series momentum in virtually every instrument we examine.” We (Aked, Mazzoleni, and Shakernia ) recently contributed to the discussion, relating the equity return momentum to the persistence of macroeconomic cycles; our work is based on the research of Adam, Marcet, and Nicolini (2016).
More academically controversial is the acceptance of mean reversion, or negative correlation, in returns over longer periods of time. The challenge lies in quantitatively proving that it does, because longer holding periods necessarily result in much smaller independent datasets, which leads to statistical problems. As such, the question of whether mean reversion exists becomes a philosophical issue with many believing in,5 and others categorically denying, its existence.
Despite the inherent challenges of generating statistical proof, we posit that long-term mean reversion exists in returns, driven at least, but not exclusively, by the reinvestment of distributions. Recall that a decline in measured annualized return volatility over longer holding periods implies and requires longer-term mean reversion to exist.
We submit that academia’s preoccupation with statistical significance should not keep us from investigating long-term holding-period volatility assumptions. Consider the story of the man who looks under a lamppost for keys he lost on the other side of the street—because under the lamppost is where the light is!6 Further analyzing the already-illuminated area of short-term risk is easy, but doing so precludes our learning about the time periods that matter most for investors.
To shed more light on the issue, we create a theoretical equity index investment with a fixed and known dividend. Over short-term horizons, both its dividend cash flows and its capital price changes drive its returns. Unsurprisingly, the volatilities of its total returns and of its price returns are very similar, because the volatility of its dividend cash flows is low relative to the volatility of its capital price changes.
Moving through time, over a period from a decade to a quarter-century, the path of capital prices will lead to larger or smaller capital allocations from reinvested dividends. These two forces, the capital price and the capital accumulation from reinvested dividends, offset each other and lower investment risk; in other words, share prices and capital accumulation due to reinvested cash flows are inherently negatively correlated.7 Eventually, the impact of the initial investment on its future return becomes much less important, and the predominant influence on the investment’s expected return comes from the path of future unknown reinvestment prices.
After undertaking the math, we plot the expected shape of the investment volatility for this theoretical asset. As expected, we observe that investment volatility declines from the annual holding period until it reaches its lowest point, which interestingly occurs when the holding period is approximately one-and-a-half times the ratio of price to cash flow. For example, if a cash-flow yield is 5% (equivalently, a price-to-cash-flow ratio of 20 times), the holding period of lowest volatility is around 30 years.8