Many of you will be familiar with the fact that past returns from notable stock indices, such as those in the US, are a biased indicator of the likely future returns to investing in equities. The problem is that due to war, government interference, and financial collapse, some stock markets disappeared altogether, wiping out investors. In some countries this has even happened multiple times. Historical stock indices that went to zero tend not to be remembered, and so are under-sampled. The result is ‘survivorship bias‘, a problem that shows up in many other research questions as well. When these defunct investments are put back in the sample, average returns are quite a bit lower than when you look at just, for example, the NY stock exchange.

A lesser known result is that a broader and representative sample of stock histories shows that investing over long time horizons doesn’t reduce the variability of your return. Contrary to convention wisdom, even young savers need to diversity across different assets types and countries in order to get that effect and be confident of retiring in comfort:

“One of the most enduring question in finance is the persistence of investment risk across time horizon. This issue of time diversification is crucial to long-term asset allocation decisions.

There is a widespread view that the longer the horizon, the more investors benefit from investing in equities. Young investors, for instance, are typically advised to allocate more to equities than those whose retirement is imminent, on the grounds that equities are less risky over long horizons. A common rule of thumb is that the percentage of stock allocation should equal 100 minus an investor’s age.

Some researchers claim to have found empirical evidence that equities are less risky over long horizons because of mean reversion. Mean reversion implies that the variance of stock retums does not grow linearly with time, contrary to a random walk. As a result, several authors have claimed that greater equity allocations are justified on the grormds that shortfall risk lessens as the horizon is extended.

This conclusion seems hardly justified. Previous findings of mean reversion have considered seventy years or so of U.S. data. For long-horizon retums, say ten years, this implies only seven truly independent observations, which seems insufficient to support robust conclusions about the risk of ten-year equity investments. The problem is that, with a fixed sample size, the number of efiective observations diminishes as the investment horizon lengthens. Another problem is that markets with long histories may not represent investment risk for reasons of survivorship bias.

One solution is to expand the sample by adding cross-sectional data. We describe the distribution of long-term returns for a sample of thirty countries for which we have long series of equity prices. The empirical evidence expands on the work of Jorion and Goetzmann (1999) and substantially extends results described by Dimson, Marsh, and Staunton (2002), who analyze a century of stock market returns in fifieen countries.

The results are not reassuring. We find no evidence of long-term mean reversion in the expanded data sample. Downside risk declines very little as the horizon lengthens. In addition, U.S. equities appear systematically less risky than equities of other markets.

Mean reversion is analyzed first in terms of variance ratio tests. There is no evidence of mean reversion from variance ratio tests across this sample, taking into account statistical properties of these tests. Furthermore, markets that sufiered interruption displayed mean aversion, or the opposite of mean reversion. Therefore, statistical properties such as high average retums and mean reversion may be an artifact of survival. Probabilities of losses on equities are reduced very slowly, if at all, with the horizon. In fact, shortfall measures such as value at risk (VAR) sharply increase with the horizon.

There is, however, some positive news. Diversification across assets pays. Over this century, a global stock market index would have displayed less downside risk than any single market. The conclusion is that across-country diversification is more effective than time diversification.” (HT Ben Hoskin)