In the long run, we’re all still exposed to risk

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)

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  • IMASBA

    “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.”
    Is that so weird? I mean inflation will make long term investments seem better, but from a purely statistical viewpoint it really shouldn’t matter whether I invest $100 in a one year investment every year for 10 years or I invest $100 once in a 10 year investment. Long term investments in technology and infrastructure may be better for society overall, but a) most private investment is in speculative hot air and land/noble metals, not technology and infrastructure, and b) the original investor probably won’t receive the additional gains to society in monetary form and hence they won’t be included in his accounts. So isn’t this “enduring question in finance” just the result of a misinterpretation of statistics?

    • Jess Riedel

      >  from a purely statistical viewpoint it really shouldn’t matter whether I invest $100 in a one year investment every year for 10 years or I invest $100 once in a 10 year investment.

      >So isn’t this “enduring question in finance” just the result of a misinterpretation of statistics?I don’t think so.  The two options you describe both stretch over 10 years.  The correct comparison will be between a young person (who invests over, say, 4 decades) and an old person (who invests over one decade).

      • Jess Riedel

        (Bad formatting because of DISQUS’s bad interface.  My comment starts at “I don’t think…”)

      • IMASBA

        “The correct comparison will be between a young person (who invests over, say, 4 decades) and an old person (who invests over one decade).”
        Is it? the article clearly talks about choosing a type of an investment, if you have only 10 years to live you cannot choose to invest over 40 years so there would be no question at all. It seems to be about the correct choice for people who have many years of life left.

        And then there is this:

        “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: [...]“

      • Jess Riedel

        > the article clearly talks about choosing a type of an investment, if you have only 10 years to live you cannot choose to invest over 40 years so there would be no question at all

        The full problem is “what balance should be made between bonds and equities, given one’s level of risk aversion”.  The conventional wisdom is that young people, who can diversify better across time, are better off with more equities as a fraction of their investment than an older person *with the same risk aversion*

  • http://www.facebook.com/profile.php?id=723726480 Christopher Chang

    Young people have streams of future regular earnings that are much larger than that of old people.  So they start from a more diversified position, and are in a better position to absorb risk if the expected returns justify it.

    The multi-trillion dollar question, of course, is whether today’s stock market has sufficiently high expected returns…

  • http://twitter.com/danielharan Daniel Haran

    So, we’re measuring risk by variance in stock prices, while recognizing that the real risk is in things like “war[s], government interference, and financial collapse, some stock markets disappear[ing] altogether”

    Before making further conclusions about portfolio management, wouldn’t it make sense to take a second look at our definition risk?

    Related: has anyone done for finance what psychologists did for economics? That issue of risk sounds as dicey as homo economicus.

  • Alessandro Carraro

    I think this study misses the point.
    The diversification you get from investing mostly in equities when young is due to the fact that you tend to have less money when young.
    Assuming that returns across time are roughly uncorrelated, you want to have the same amount of risk in each year of your life (as this time diversification will lower risk without much affecting return). So when young you probably want to leverage as your available assets are small compared to your lifetime earnings and when old you want to de-leverage as your assets are now relatively large when compared with your life-time earnings. Ideally you’d need to calculate your lifetime earnings and risk the same percentage each year.
    The length of the investment is a minor concern. Not increasing the amount of risk you run compared to your life earnings isn’t…

    • Jess Riedel

      > The diversification you get from investing mostly in equities when young is due to the fact that you tend to have less money when young.

      I don’t think this is correct.  If you have Y dollars when you’re young and X dollars when you’re old, then you could always invest the Y dollars as if you were old (i.e. bond-heavy) and X-Y of the X dollars as if you were young (i.e. equity-heavy).

      • Alessandro Carraro

        All I am saying is that you should trying to keep the amount of risk you run invariant through your life. If you manage your risk only in relation of your saving, you will inevitably over-expose yourself to the periods of time went your saving are at a maximum.
        You really have 2 forms of wealth: your explicit wealth and your ability to earn income in the future. If you invest based only on the first you’ll run too much risk when you are in your fifties most likely…
        Imagine you live 100 years: work from 20 to 60 and retire from 60 to 100. You always earn the same wage and save the same percentage. At 60 your saving will likely reach their maximum. Even at 20% equity, you’d be running more risk than on year 1 on 100% equity (since you’d have 40 x 20% = 8 time more equity investment).

  • Tom P

    Price/dividend ratios don’t wander off to infinity, so either prices or dividends must mean-revert to keep the ratio balanced.  Consequently, even if the statistical evidence for mean-reversion in prices is weak, dividends do not seem to exhibit any mean-reversion at all, so the reversion must be coming through prices.

    Additionally, I’m not sure why survivorship bias would be a problem in studying stock return predictability — are markets where returns are forecastable more likely to survive for a long sample?

  • Douglas Knight

    “the likely future returns to investing in equities” is meaningless without something for comparison. Events that wipe out equities almost always wipe out bonds, too, so such a comparison is not biased and so the equity premium is quite mysterious. Cash is often wiped out by such events, too, and even sometimes human capital. 

    Comparing investing in one country to investing in many countries is a real comparison, though I don’t know why he leaves out eastern bloc markets.