A lot depends on the answer. If Wall Street topples, European and Asian stockmarkets will follow like dominoes. European shares have been underperforming anyway, but South-east Asian markets have, in the past six months, staged a strong recovery to their pre-crisis levels or beyond and even Tokyo has started to recover.
The longer US equities continue at levels that have made pessimistic pundits uncomfortable for more than two years, the more certain some of them become that a dreadful crash is in the offing. But is this inevitable? Or to turn the question around, what would haveto be true to justify current stockmarket valuations?
There are several approaches to valuing shares. Sushil Wadwhani, the newest recruit to the Bank of England's Monetary Policy Committee used one, the workhorse of equity analysts, to conclude in a recent article that the Standard & Poor 500 index was 20-30 per cent overvalued. Since the article was written, the index has gained another 20 per cent.
The basic formulation says the dividend yield plus the expected real growth in dividends over the long run should equal the real interest rate plus an equity risk premium. In other words, investors equalise the expected real returns from rival assets in the long run - although real-life adjustments are needed, including an adjustment for share buybacks.
Plugging in cautious estimates for the other elements in the formula delivers a stockmarket level considerably lower than it is now. One possible justification for higher valuations is higher prospective dividend growth than the historical average of 1.9 per cent or a higher yield, something that many proponents of the "new economic paradigm" certainly believe.
But as equity analysts are over-optimistic about earnings four-fifths of the time, this seems a slender reed on which to hang massive optimism.
There is scant evidence that a new era of higher productivity is dawning.
Besides, as Mr Wadwhani points out, the new paradigmers explain their optimism on the grounds of increased competition, which would tend to reduce corporate profits. So there is an internal inconsistency in this explanation for high US share prices.
Besides, there is extraordinarily strong evidence that over hundreds of years and in all sorts of stockmarkets, real returns on equity trend towards around 7 per cent. This has been documented for the US by Jeremy Siegel, a professor at the University of Pennsylvania's Wharton Business School. While the real return can vary over shorter periods, over most 50 or 70 year periods it lies in that narrow range. The same is true in the UK back into the 19th century, according to CSFB's Gilt-Equity study, and the bank has also confirmed it for Japan and Germany this century, although with dislocations like the hyperinflation of the Twenties in the latter case.
Although there is no obvious theoretical reason why the number should be 7 per cent, the striking evidence suggests that any period of outperformance will be followed by a period of underperformance.
With the compound rate of real returns on US shares over 13 per cent since 1982, this seems to indicate pessimism about Wall Street is well- founded. Shares are not the most overvalued they have ever been by comparison with this long-run trend, but they are getting close.
Jonathan Wilmot from CSFB notes in a recent report, however, that stockmarket disasters have always resulted from some external shock such as war, the Opec price shock, or the extended policy failures of the Thirties.
Without another shock, real returns on equities will slow towards trend but may be able to sustain that trend for another 20 years or more. The parallel is the 40-year bull run of the mid-19th century, he suggests.
Optimists have another argument, namely that the equity risk premium required by investors has declined. Jeremy Siegel's research also established that, since 1802, equities have outperformed bonds more than two-thirds of the time over five-year holding periods and 99.4 per cent of the time over 30-year holding periods.
Over one year, returns on equity are three times more volatile than returns on bonds but over 20 years slightly less volatile. This suggests that there is no real rationale for an equity risk premium at all. And since the late Fifties, when equity yields famously started to yield more than bonds instead of less, the case has strengthened. The risk of world war looks remote, communism has collapsed, policymakers have learnt how to react to financial crises, inflation is low and growth may be more stable than in the past.
Demographic change could be helping too: if ageing western populations are saving more for their retirement there is higher demand for equities from investors.
The trouble is that all these arguments must be true in order to explain why the apparent risk premium on US equities - although not shares elsewhere in the world - has dropped to zero.
On cautious assumptions it is actually slightly negative.
Michael Hughes, the head of strategy for ING Asset Management, says: "There will not necessarily be a crash but if you are a long term investor you will be better off elsewhere because you are not being paid anything at all to take equity risk."
Mr Wadwhani was equally cautious in his paper. The equity risk premium is about as low as it has ever been and is unlikely to fall further. It might rise, and anyway returns are likely to revert to their long-run trend, he concludes.
Bigger pessimists take a different approach. For example, research by Phillips & Drew emphasises the fact that the growth of the US economy depends on share prices continuing to rise because the expansion is built on declining private saving.
Capital gains make households feel rich enough to spend more than they earn, but without the gains they will stop. Without the economic growth, corporate profits will collapse, which could in turn trigger the Wall Street crash.
The final verdict ought to go to one of the gurus of finance theory, however.
Burton Malkiel, the Princeton professor who wrote the classic A Random Walk Down Wall Street, concluded last year: "I don't think it's possible for even the Almighty to know whether a market is over- or under-valued."