We must highlight that our model provides a guide to the characteristic of holding-period volatility for perpetual assets. In reality, our assumptions that cash flows have zero volatility and that prices do not have any continuation or reversion characteristics are not defendable. That said, the characteristic of initially falling, then rising, annualized volatility in the very long term is instructive and should influence how investors manage their portfolios. We simply posit that—even for those who do not believe in the long-term reversion of asset prices—an asset having larger price volatility than cash-flow volatility demonstrates significant total-return reversion.
Beyond the threshold of minimum volatility and the uncertainty of the value of reinvested dividends, the historical price volatility of an asset increases substantially. Revisiting the time diversification discussion, we can credit points to supporters of both sides of the argument: time diversification is helpful—at least up to the point in time when long-term uncertainty about the value of reinvested cash flows from dividends begins to lead to rising volatility. Simply, the longer the investment horizon, more is subject to unknown forces. Who could possibly know what market environment investors will face far out in the future? At very long horizons, uncertainty dominates and volatility rises, and we, as investors, become pawns in the game of the market.
So Why Does All This Matter?
Having made the case that volatility does change with the time period used to measure it, we would like to explain why this matters, or should matter, to investors.
First, it behooves us as investors to understand which volatility measure will be the most accurate predictor of risk in our portfolios. The frequently reported volatility measure based on monthly or daily returns is useful if we care about understanding how our monthly or daily returns may vary. If, instead, we want to understand the volatility of a portfolio that could service our retirement spending needs, then we ought to consider risk measures with the characteristics of long holding periods. We encourage investors to search beyond the light of the lamppost where the data are less easily found.
On a similar note, although our article focuses solely on one definition of absolute risk, the standard deviation of returns, we encourage investors to adopt a balanced view of risk by considering various risk metrics. Importantly, let’s not forget the role of maverick risk in investment decisions and investment errors (Arnott, 2003).
Second, the relationship between risk and holding period can help inform other critical decisions, such as determining at what frequency investors should rebalance their portfolios. Research suggests that a portfolio of diversified assets gains additional return from diversification itself.9 Interestingly, the level of extra return gained from the “diversification benefit” depends on asset-class volatility, which implies that a portfolio will achieve the greatest extra-return benefit by rebalancing over the holding period of highest volatility. Because the highest volatility seems to consistently occur when the holding period approaches one year, which also happens to be the time period separating continuation and reversion of asset returns, our analysis provides additional support to the ongoing debate related to the frequency of rebalancing.
Additionally, we find that for most asset classes, the volatility of the total return declines when holding periods are measured in decades, making it easier to predict returns when measured volatility is at its lowest. This suggests that for most asset classes, it is optimal to predict returns over a long time frame—up to an extent!
Estimating the wealth of an investment portfolio over an extremely long horizon is futile, because over the very long run, the compounded value of reinvested dividends or required distributions will depend on a myriad of possible paths of capital prices, which creates an uncomfortably massive range of possible wealth outcomes.
Whereas our fast-paced, performance-obsessed world taunts us to assess our portfolios over very short horizons, most investors actually have a sufficiently long horizon to enjoy the benefits of time diversification.10 While we may logically understand and appreciate this, do we exhibit the patience and courage to hold the course when experiencing the inevitable bouts of short-term pain and disappointment?
To better tolerate the discomfort of uncertainty, perhaps it’s best to heed the timeless advice offered by the likes of Shakespeare and Leonardo da Vinci. As the latter aptly said 500 years ago:
Patience serves as a protection against wrongs, as clothes do against cold. For if you put on more clothes as the cold increases, it will have no power to hurt you. So in like manner you must grow in patience when you meet with great wrongs, and they will be powerless to vex your mind.
In the simplest approach, we assume that a fixed annual cash flow per share, y, is used to buy additional shares, h. In this case, we can calculate the annualized holding period return of this investment as
Simply, in the short term, a falling price allows us to buy more shares with our cash flow. Alternatively, a rising price leads to a smaller increment in share ownership. This negative relationship between price, S, and shares, h, means that the return naturally becomes negatively correlated across longer time periods. The ratio of the return variance for holding period n, to the capital price variance, can be approximated as the following relationship: