Tag Archives: Risk

Small Change Good, Big Change Bad?

Recently I posted on how many seek spiritual insight via cutting the tendency of their minds to wander, yet some like Scott Alexandar fear ems with a reduced tendency to mind wandering because they’d have less moral value. On twitter Scott clarified that he doesn’t mind modest cuts in mind wandering; what he fears is extreme cuts. And on reflection it occurs to me that this is actually THE standard debate about change: some see small changes and either like them or aren’t bothered enough to advocate what it would take to reverse them, while others imagine such trends continuing long enough to result in very large and disturbing changes, and then suggest stronger responses.

For example, on increased immigration some point to the many concrete benefits immigrants now provide. Others imagine that large cumulative immigration eventually results in big changes in culture and political equilibria. On fertility, some wonder if civilization can survive in the long run with declining population, while others point out that population should rise for many decades, and few endorse the policies needed to greatly increase fertility. On genetic modification of humans, some ask why not let doctors correct obvious defects, while others imagine parents eventually editing kid genes mainly to max kid career potential. On oil some say that we should start preparing for the fact that we will eventually run out, while others say that we keep finding new reserves to replace the ones we use.

On nature preserves, some fear eventually losing all of wild nature, but when arguing for any particular development others say we need new things and we still have plenty of nature. On military spending, some say the world is peaceful and we have many things we’d rather spend money on, while others say that societies who do not remain militarily vigilant are eventually conquered. On increasing inequality some say that high enough inequality must eventually result in inadequate human capital investments and destructive revolutions, while others say there’s little prospect of revolution now and inequality has historically only fallen much in big disasters such as famine, war, and state collapse. On value drift, some say it seems right to let each new generation choose its values, while others say a random walk in values across generations must eventually drift very far from current values.

If we consider any parameter, such as typical degree of mind wandering, we are unlikely to see the current value as exactly optimal. So if we give people the benefit of the doubt to make local changes in their interest, we may accept that this may result in a recent net total change we don’t like. We may figure this is the price we pay to get other things we value more, and we we know that it can be very expensive to limit choices severely.

But even though we don’t see the current value as optimal, we also usually see the optimal value as not terribly far from the current value. So if we can imagine current changes as part of a long term trend that eventually produces very large changes, we can become more alarmed and willing to restrict current changes. The key question is: when is that a reasonable response?

First, big concerns about big long term changes only make sense if one actually cares a lot about the long run. Given the usual high rates of return on investment, it is cheap to buy influence on the long term, compared to influence on the short term. Yet few actually devote much of their income to long term investments. This raises doubts about the sincerity of expressed long term concerns.

Second, in our simplest models of the world good local choices also produce good long term choices. So if we presume good local choices, bad long term outcomes require non-simple elements, such as coordination, commitment, or myopia problems. Of course many such problems do exist. Even so, someone who claims to see a long term problem should be expected to identify specifically which such complexities they see at play. It shouldn’t be sufficient to just point to the possibility of such problems.

Third, our ability to foresee the future rapidly declines with time. The more other things that may happen between today and some future date, the harder it is to foresee what may happen at that future date. We should be increasingly careful about the inferences we draw about longer terms.

Fourth, many more processes and factors limit big changes, compared to small changes. For example, in software small changes are often trivial, while larger changes are nearly impossible, at least without starting again from scratch. Similarly, modest changes in mind wandering can be accomplished with minor attitude and habit changes, while extreme changes may require big brain restructuring, which is much harder because brains are complex and opaque. Recent changes in market structure may reduce the number of firms in each industry, but that doesn’t make it remotely plausible that one firm will eventually take over the entire economy. Projections of small changes into large changes need to consider the possibility of many such factors limiting large changes.

Fifth, while it can be reasonably safe to identify short term changes empirically, the longer term a forecast the more one needs to rely on theory, and the more different areas of expertise one must consider when constructing a relevant model of the situation. Beware a mere empirical projection into the long run, or a theory-based projection that relies on theories in only one area.

We should very much be open to the possibility of big bad long term changes, even in areas where we are okay with short term changes, or at least reluctant to sufficiently resist them. But we should also try to hold those who argue for the existence of such problems to relatively high standards. Their analysis should be about future times that we actually care about, and can at least roughly foresee. It should be based on our best theories of relevant subjects, and it should consider the possibility of factors that limit larger changes.

And instead of suggesting big ways to counter short term changes that might lead to long term problems, it is often better to identify markers to warn of larger problems. Then instead of acting in big ways now, we can make sure to track these warning markers, and ready ourselves to act more strongly if they appear.

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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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