As markets on both sides of the Atlantic have gone into overdrive, the more cautious pundits are beginning to sound warning notes.
In the UK, leading investment manager Tony Dye, of Phillips & Drew Fund Management (PDFM), has been thrust into the spotlight, with his decision to sell shares to raise his cash levels to 15 per cent - historically a high level for any investment manager where the norm is usually closer to 5 per cent.
So far, Mr Dye's strategy has yet to pay off, and a number of his big pension fund clients are concerned that he has missed out on some of the extraordinary stock market gains of the past few months.
From almost exactly 3,000 points two years ago, the FT-SE 100 index (the "Footsie") of leading blue-chip stocks has risen to a tad under the magical 4,000 barrier - or a rise of nearly 33 per cent. This only continues the broad upward sweep of the London stock market since the early 1980s.
In the US, the picture looks even more "overheated" (as the stock market jargon puts it).
The Dow Jones Industrial Average of leading American companies is up 55 per cent over the past two years, with the strongest gains coming in the past 10 months.
The chief fear overhanging this edifice, on Wall Street and in the City, is that the US Federal Reserve (equivalent to our Bank of England) will raise interest rates. As soon as that happens, most people agree the markets will suffer a sizeable correction, even if it does not qualify for the epithet "crash".
Even so, many private investors must be sharing some of Tony Dye's concerns. The markets do seem high, "frothy" even, in the jargon. It has been said that the valuation measures the City uses in deciding whether shares look cheap or expensive will soon lose touch with any sort of reality.
To many people, Mr Dye's 15 per cent of cash - while keeping most of the rest in the stock market - might still seem unnecessarily risky. However, Mr Dye is unusual among his colleagues in that he is prepared to stick his neck out to even this extent. If he is wrong, his clients will have lost out; his strategy only works if his timing is right.
Others, however, believe the stock market, at least in the UK, can continue its upward flight of the plast few months. Paul Killik, of London-based stockbroker Killik & Co, says: "I don't believe London is too expensive, especially while bond markets look so cheap, relative to inflation." The financial results of companies continue to be buoyant, while the economy also continues to produce good news.
But regardless of whether the market will continue up or is poised to tumble, the experts have one overriding message to private investors: sit tight.
Brian Tora, chairman of the investment strategy committee at stockbroker Greig Middleton, says: "If you are selling when the market looks high, you also have to know when to go back into the market, and many people fail on that count."
Mr Killik is equally persuaded of the merits of a buy-and-hold approach: "It's almost as dangerous being out of the market as it is being in it. Generally, it's best not to try to predict how the market will go". This is on the basis that in the long term it should inexorably go up.
There are some exceptions to this rule of sitting tight. If you have a substantial expenditure coming up in the near future, it may make sense to sell some holdings now and put the cash on deposit in the meantime. That way, if the market does fall, the money you need is safe - although you will have to grin and bear it if the market continues to rise.
Likewise, if you are suffering sleepless nights at the thought of a downturn, for your own peace of mind do feel free to liquidate some of your holdings.
One other exception would be if you had only recently come into a substantial sum of cash and were considering whether to invest it. Elspeth May, head of personal financial services at accountant KPMG, says: "My advice to clients would be that if you have a lump sum now then you could justify holding it on deposit until it is clearer where the market is headed."
Her proviso is that even with a decent interest rate of 6 per cent, income after tax and post-inflation may amount to a real investment return of just 1.5 per cent - hardly lucrative whatever the stock market outlook.