Although you wouldn't know it over the last five years or so -- with the NZ sharemarket up 16 per cent per annum and world sharemarket up 12.4 per cent pa -- share investing involves risk, as there is always the chance that stockmarkets go down for an extended period before they go up again.

Much of the continued rise in stockmarkets has been because they have been becoming progressively more expensive. Consequently, perhaps more than ever before, investors are wondering whether US shares are overvalued and, if they are, whether a big downward move is likely.

These are big questions because where the US markets go generally the world follows. However, most local discussion of investment matters focuses on what happened on the NZ stockmarket yesterday and why. Whilst talking about what happened yesterday might be fun, unfortunately it is pretty much redundant because it happened yesterday.

Markets are reasonably efficient which means information is more or less immediately factored into prices so by the time you read that a company has problems its share price has already reacted. Therefore knowing why its shares fell by 10 per cent yesterday doesn't really improve your investment decisions going forward unless you get the info before everybody else does, and that can be problematic if the FMA finds out.

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In fact reacting to the news after the event could actually be harmful because you may be making an investment decision on the assumption that the share price has not priced in the new information.

Where the future is considered, many fund managers ignore the theory and the facts, and simply assume that stockmarkets will increase in value at high rates. That makes their fees look less unreasonable and the terminal sum in their KiwiSaver models appear attractive.

On the rare occasion that fund managers acknowledge that sharemarkets are expensive they, in keeping with the golden rule that "all news is good news", frequently describe the market as being "a stock pickers market".

This of course alludes to the unrealistic notion that when the market falls their clients' portfolios will not. Good luck with that.

Anyway back to the "is there a crash looming?" scenario.

There is considerable personal risk for a journalist speculating on where the markets are overvalued and the risks of a crash, not least because no one knows the answer and because fate being what it is generally if you conclude that stock markets are poised for a fall they will in all probability move sharply upward and if you conclude that they are fairly valued a crash within a few days is virtually certain.

Despite those risks we will look at some recent research from Rob Arnott's Research Affiliates Group (RA) and a paper by some PhD's from Harvard University which focuses on those big questions -- is there a theoretical basis for the increased valuation of the US sharemarket and can you identify a stockmarket bubble?

First off we need some numbers on the valuation of the US stockmarket. In a recent report UK group, Longview Economics, made the point that a widely used valuation measure for the US sharemarket, the Shiller PE, is now at 29.8x versus a long term average of around 20x.

Previous peaks have been in September 1929 and 2000. Both of these occurrences were followed by major stockmarket falls. It's not necessary to know how the Shiller PE is calculated, just that it's a measure of expensiveness, and more importantly it is not a great indicator of sharemarket performance in the short term.

The RA analysis asks whether there is some factor explaining why stockmarkets should be getting more expensive. The good news is that there is but the bad news is that RA still reckons that markets are overvalued. Specifically the March 2017 paper, The Fair Value of the Equity Markets, finds that investors are willing to pay a higher price for shares when economic volatility is low.

The research finds that since about 1881 the volatility of the economy in terms of real output growth and inflation has reduced by about 80 per cent driven by technological innovation and improvements in monetary policy.

The analysis suggests therefore that there is good reason why stockmarkets have become progressively more expensive. The quid pro quo is however that higher valuations and lower risk means lower returns from the stockmarket in the future.

The Harvard study entitled Bubbles for Fama was published in February and its purpose was to evaluate Professor Eugene Fama's controversial assertion that stockmarkets do not exhibit price bubbles that can be identified by investors at the time. Specifically the study looked at whether a sharp price increase in some sector of the stockmarket would necessarily be followed by a crash.

The study found that whilst sharp price increases don't necessarily predict low returns going forward they do indicate a much higher probability of a crash in the future.

Specific attributes of the price increase period prior to a crash include high volatility, high stockmarket turnover and lots of new shares being issued.

On this basis it doesn't look like a crash is imminent today as volatility on the US stockmarket certainly isn't high and there are more shares being bought back by companies than are being issued.

So what do these studies tell us?

Firstly that whilst stockmarkets are a lot more expensive than in the past there is an economic rationale for this -- they are less risky and thus merit a higher valuation.

Secondly, based on the Harvard study, a crash doesn't look imminent.

However, the attributes of a pre-crash market identified by Harvard may have helped to avoid a recent local investment disaster. The big tech crash that was inflicted on investors by the rash of 2013/2014 vintage technology IPO's was preceded by rapid price appreciation and a huge issuance of new stocks.

The Harvard study thus supports the golden rule that IPO's generally are not good for your financial health.