Financial theory tends to focus on a notion of risk limited to what we might be termed ‘‘trivial perils’’, those having to do with price fluctuations liable to appear in a relatively stable overall environment. Doesn’t history frequently show that radical alterations in the environment provoke price variations comparable to mood swings? Maybe we just do not know how to analyze major risks. Maybe we do not know how to prevent them.
Examples have demonstrated that rather than base their expectations on past mathematical averages, investors tend to detect correlations between past events. At the beginning of his chapter on ‘‘the state of long-term expectation’’, Keynes wrote:
It would be foolish, in forming our expectations, to attach great weight to matters which are very uncertain. It is reasonable, therefore, to be guided to a considerable degree by the facts about which we feel somewhat confident, even though they may be less decisively relevant to the issue than other facts about which our knowledge is vague and scanty. For this reason the facts of the existing situation enter, in a sense disproportionately, into the formation of our long-term expectations; our usual practice being to take the existing situation and project it into the future, modified only to the extent that we have more or less definite reason for expecting a change.
How is such a judgment to be formulated? Investors tend to make a fetish out of economic ‘‘factoids’’, such as for how many months, at some time in the past, did the market anticipate and predict economic recovery. And yet they interpret such anecdotal data by connecting the ‘‘dots’’ that get their attention in accordance with the ‘‘paths’’ they map out. As with the Impressionists (and most especially with Georges Seurat), investors spend a great deal of their time connecting details. The brain is organized in order to detect correlations. Numerous studies have shown that investors revise their predictions by overemphasizing new information in relation to pre-existing and long-term data.
Curiously enough, the mechanism of risk analysis is altogether different. Rather than behave as they do when forming expectations, investors often use historical (mathematical) volatility to assess the risk of a possible investment. Experience shows that volatility constitutes an excellent basis for risk evaluation; what skyrockets may plummet just as precipitately.
That said, the relationship between risk and return is not as fluid as theory would have it (we shall return to this point). The connection between risk and return is not a detail. It is not because a portfolio presents high risk that one may reasonably expect to win the ‘‘sweepstakes’’. Moreover, unforeseen correlations do crop up; they merely were not noted in the past. Last but not least, volatility evolves along with time. One may think that the dispersion of returns (additional volatility) would increase in times of economic and political uncertainty. The sensitivity of a financial asset to market variations may be estimated historically, but this should only be the basis of ongoing anticipation. Volatility also must be anticipated.

Untimely surprises are especially dangerous when one is counting on the income drawn from one’s portfolio. Capitalization is based on the principle that all such revenues are reinvested and that values may consequently be compared at several points in time. In reality, investors will want to redeem earnings or liquidate a portion of their investments before the date of termination. One may be (or at least feel) compelled to sell off one’s investments at a time when prices are low, which is a disagreeable surprise. If investors regularly liquidate a portion of their investments in order to remain afloat, they will be especially aware of the risk of doing so at a time when prices are heading downwards. Stock market crises compress the per-share value of a portfolio to such an extent that more shares have got to be sold in order to draw the same revenues. Once prices rise again, it will be that much more difficult to compensate through capitalization for the transfers conceded when prices were low.
Let’s take as an example an investor who retired at the end of 1998 at the age of 60 with e300,000 invested in a stock-indexed fund (a fund that follows a market index; see Chapter 9). Suppose that this recent retiree had the intention of eking out an existence thanks to the e18,000 annually withdrawn from his portfolio. If the latter had provided a regular annual return of 8 percent, it would have produced e24,000 each year in dividends and capital gains, and he would have been able to cope with the withdrawal of e18,000 per year. But from 1999 through 2001, the stock exchange went down by about 40 percent! By the end of 2001 the portfolio would have been worth only e180,000. It would have taken annual returns of 10 percent over the following period to allow for the withdrawals. Quite obviously, everything would have been different had the crisis taken place 20 years later. During that period the portfolio would have been enriched by e24,000 – 18,000 = 6,000 per annum, that is 2 percent per year. It would have increased by 50 percent and a 40 percent loss in 2020 would still have left e270,000 in the portfolio. Average 8 percent returns would have permitted scheduled payments of the required annuities. The one way to survive a stock market crisis that comes too early is to diversify one’s portfolio and employ financial instruments that do not all go down at the same time. Such diversification limits portfolio volatility.
Does historical volatility measure the risk of investment for the future? Fluctuations in the vicinity of the average may give a precise idea of the risk, but this is the case if – and only if – the law of probability remains unchanged. If observations of the past are to prove useful when forecasting the future, it is necessary for the law of probability to be stable in time. Is this the case? Just like the laws of mortality, the law of probability is not a known quantity; it can only be estimated on the basis of past series. Compare the probability of stormy weather. Tomorrow’s skies may be predicted as a function of meteorological parameters, provided that the climate is not fundamentally altered. Consider global warming; weather forecasting is of little avail in the event of a phenomenon rendering history obsolete! And in a stock market crisis, investors may have the impression that everything is crashing. From 1989 through 1999 at the Paris Bourse, 95 percent of reported monthly returns ranged from +12.75 percent to – 11.25 percent, which means that 5 percent of the time, returns were greater than +12.75 percent or lower than – 11.25 percent; hence there had been a monthly loss greater than 11 percent for 2.5 percent of the time (or once every three years). In some cases losses become downright catastrophic – in October 1987 shares plummeted by 22 percent in a month; in September 2001 it took just a week for them to lose 18 percent of their previous value. That is twice as much as the lower limit of the range of confidence over the 10 previous years! Yet up to now, the market has always recovered. Even if stock market performances are approximately akin to a random walk and even if their distribution resembles a normal law, this is not what happens at the extremes. Pronounced monthly highs and lows, bubbles and crashes occur, not as often as the normal law indicates, but more often than the normal law can possibly foresee. As Bernstein states:
At the extremes, the market is not a random walk. At the extremes, the market is more likely to destroy fortunes than to create them. The stock market is a risky place.