It is a lesson for those who, like Tony Dye, the head of the fund management firm PDFM, attempt to predict when the big shifts in the stock market are about to happen.
Mr Bernstein says that if during one 14-year period he analysed you switched out of US equities into cash for just the five best trading days in the market - out of a total of 3,500 days - you would have doubled your money, and perhaps have felt reasonably good about it.
But if you had just gone to sleep and held on to the shares all the time without trying to be clever, you would have trebled your money, leaving the investor who got the timing wrong languishing far behind, at the bottom of the performance table.
The clever investor may still have been right about the general direction in which the market was heading but, as Mr Bernstein says: "Market timing is a risky strategy."
The painfulness of getting it wrong is being rubbed in by the renewed bull market in the US. It is an old saying, but a reliable one, that the final upward burst is usually associated with a stampede of private investors to buy.
This is now happening in a big way in the US. It seems to have been behind the move onwards and upwards to levels where, in a rational world, vertigo ought really to be taking hold.
If the US trend goes into reverse, the UK will certainly be dragged down in its wake, even though we have not witnessed the same mad scramble by private investors.
The inflow to mutual funds - the US equivalent of our unit trusts - is set to reach a record $200 billion by the end of the year, and the money ploughed into the funds has doubled in two years to $2.2 trillion. The Dow Jones index is up more than 1,000 points to more than 6,500 since July, with nearly half of the rise taking place since the presidential election.
It is almost certainly the case that most of the investors piling into US shares are sensible enough to realise that the risks of a sharp correction are rising as rapidly as the breathtaking performance of the market.
Indeed another old proverb, the one that says you can pile into a rising market because there is usually a bigger fool waiting to pick up the stock when you spot the turn and decide to sell, is probably just as true today as it was in 1987, and in every other market bubble in memory. The psychology driving investors has not changed much since the Dutch tulip mania more than three centuries ago.
Moreover, this determination to follow the herd has a certain amount of statistical common sense to back it, as Mr Dye of PDFM - the fund management arm of Union Bank of Switzerland - has found to his cost. By being contrary, and switching some of his shares into cash too early, he has pushed his funds to the bottom of the performance league tables. He was right, but too early.
The downside risk of following the herd wherever it leads is often not as large as it looks. The 1987 crash in the UK simply took share values back to the level at the beginning of that year.
There was money to be made by switching into cash, as Sir James Goldsmith famously did. But success in that strategy comes back to whether you are brilliant or plain lucky about the exact timing.
If there is a 500-point fall in the US stock market now, comparable with Black Monday in 1987, the only people who would lose money among mutual fund investors would be those who invested more recently than a month ago. There would have to be a truly spectacular crash for any but the latecomers to feel real pain.
This euphoria in the markets, deeply suspect as it is, has spread from equities to bonds (though in the case of bonds the UK has missed the latest rally, probably because it seems unlikely to join the EMU club, and it also faces a serious risk that interest rates will rise again soon).
Russia's first Eurobond issue since the 1917 Revolution was enormously oversubscribed 10 days ago, while the prices of high- quality bonds are rising rapidly in the US and continental Europe.
For such a flood of money to be going into bonds, investors must be assuming that inflation and interest rates are under control. Furthermore, the markets seem to regard this as compatible with steady growth, rather than the stop-go of the past. How else can shares remain so strong?
While the consensus is that the trend of inflation has moved permanently down, there is rather less agreement about whether low inflation is now a permanent feature of developed economies or whether a renewed cycle of inflation, though with lower peaks, is about to return.
The most interesting and basic question raised by this downward shift in inflation expect- ations is whether it will be accompanied by an equally dramatic shift in the behaviour of shares and bonds. This refers not to a repeat of the cycle of boom- and-bust in the markets but to a different relationship between the two forms of investment.
You have to be more than a certain age to remember it, but in the late 1950s something quite extraordinary happened. Until then, pounds 1,000 invested in shares paid a higher income than pounds 1,000 invested in bonds, because shares were riskier. This was a fundamental rule of investment.
Since 1957, the reverse has been true, with the return from bonds sticking well above that from shares, which were henceforth perceived as a better bet.
With hindsight, the explanation proved simple: until the late 1950s, low inflation maintained the capital value of bonds and made their guaranteed returns a good investment compared with shares, whose dividends are not guaranteed and whose capital has no repayment date.
Then along came inflation and turned the relationship upside down. Because inflation ate away at the fixed capital values of bonds, they became far riskier to hold than shares.
Since the late 1950s, it has been a complete illusion - what one fund manager describes as "reckless conservatism" - to regard bonds and bank deposits as safe investments. They have been the quickest way to penury for long-term investors.
Mr Bernstein's book includes a timely reminder of how unthinkable that shift in the relationship between bonds and shares appeared in the 1950s.
We pour data from the past into the investment models used to make decisions. But they cannot predict a fundamental change in behaviour. The long-term outlook for inflation is changing now, just as it did in the 1950s. Something equally surprising may be happening deep in the undergrowth.
One possibility is that if the low inflation conditions of the first half of the century are reviving, bonds will become a much better long- term buy than they have been in recent decades.
But even if that is true, we cannot be sure of when it will happen - now or in 10 years' time. The truth is that betting on the timing of any change of trend in the markets is the riskiest investment of all.