John Lim

**I RECENTLY WROTE** about the fallacy of time diversification. Time diversification is the widely held belief that market risk declines as our holding period lengthens. It’s one of the cornerstones of many investors’ approach to asset allocation and risk management.

Financial theory, however, refutes time diversification because market risk—as measured by standard deviation—actually increases with longer holding periods. The math tells us that the dispersion of potential results widens with longer time horizons. This counterintuitive insight rests on the assumption that total returns have a normal, bell-shaped distribution and that year-to-year returns are uncorrelated.

As an example, if stocks have an average historical return of 5% with a standard deviation of 30% and you hold for 30 years, the worst 1% of possible outcomes is a cumulative 90% loss. History teaches us that losses of this magnitude are within the realm of possibility. During the Great Depression, the Dow plunged 89% from its 1929 peak. It didn’t reach new highs, at least in nominal terms, until 1954—or 25 years later. Similarly, in 2002, the Nasdaq Composite index closed 78% lower than the peak it reached in 2000. It would take 15 years for the Nasdaq to return to its prior 2000 high.

But there’s a major weakness in the argument against time diversification. Recall that it assumes that annual returns are *uncorrelated*. In other words, stock returns are assumed to take a random walk around their mean. While this assumption may be reasonable most of the time, it falls apart over longer time horizons and at market extremes.

Consider what happens after the stock market experiences a major decline. First, dividend yields climb. It’s estimated, for example, that the dividend yield of the overall stock market was close to 14% in July 1932, when the Dow reached its Great Depression low.

As share prices decline, the expected return from stocks rises. The Gordon equation states that the return we can expect from stocks are a function of dividends and the growth in dividends. By raising the dividend yield, tumbling stock prices sow the seeds for higher future returns.

Result? A lost decade for stocks would set the stage for higher expected returns in the decade that followed. In other words, returns over long time periods aren’t random, but rather negatively correlated. What I’m describing, of course, is reversion to the mean. It’s the countervailing force that lowers the probability of long market streaks—both positive and negative. This doesn’t mean that a 30-year bear market could never happen. It’s just far less likely than standard statistical theory would predict.

The other major argument in favor of time diversification: Most people save and invest over many decades. Such dollar-cost averaging substantially lowers the risk of stock investing during our working years, because we’re buying over time, rather than at a single price that could prove to be a market peak.

DI love Langston’s comment about investing bringing him closer to his father. The same happened with my husband and it brought them closer than they had ever been. It’s not all about the money.

Along with the previous time vs. risk article, these make up two of the most important entries on HD and I believe I’ve read them all.

The primary avenue I used to get my Dad’s full attention growing up was to ask him financial and investment questions. The year after college I figured out this was what really turned me on and I went to business school, learned how to do linear regression, the supporting statistics, etc., with a simple calculator and fell in love with math. In so doing I started to realize that my Dad was right about almost everything. : ) I went home and explained this to him and the next 10 years were some of the best of my life as we worked together, me the geek, he the oracle telling me how the math actually applied to the real world.

Not long into this my Dad showed me an article in a serious financial rag that touted a “new” multivariate linear regression technique to beat the market. His gut knew better, but he didn’t show it until I started laughing and told him you could get any answer you wanted by selecting bogus independent variables. To quote my econometrics prof: “Statistics is a method of drawing straight lines between unwarranted assumptions and foregone conclusions”.

Thank you for that beautiful story, Langston.