As European economic worries have faded, the appetite for equities has grown. A lot of good news is now firmly reflected in prices however.

European indices rose 17 per cent last year, despite minimal earnings growth.

As Goodbody's Eamonn Hughes notes, price/earnings ratios expanded from 12 to 14 last year – 15 per cent above its 10-year average, and at levels that marked market peaks over the last decade.

That doesn’t mean bullishness is misplaced.

Hughes notes that European earnings lag previous peaks, and forecasts are rising, with growth of 6 per cent and 14 per cent predicted for 2014 and 2015 respectively.

If companies deliver, P/E levels will fall and indices can move higher.

There is now less room for error however. The PIIGS – Portugal, Ireland, Italy, Greece and Spain – are all among the top 10-performing indices in the world thus far in 2014, and some trade on higher forward earnings estimates than Germany.

Sentiment indicators at peak levels and low volatility readings "provide the greatest headwind to markets in the coming months", cautions Hughes.


Justifying stretched multiples
Like in Europe, US companies need to justify stretched earnings multiples. Goldman Sachs recently cautioned that the S&P 500, having tripled since March 2009, is now "lofty by almost any measure" and faces a 67 per cent probability of a double-digit correction this year.

The index has long looked expensive if one used price/earnings ratios that averaged profits over a 10-year period, but reasonable if one looked at one-year forward estimates.

Stocks now trade on 16 times earnings, however, compared to 10.6 in August 2011. Since 1976, says Goldman Sachs, the average is just 12.6.

Valuations have been above today’s levels just 5 per cent of the time since 1976 – during the tech bubble and a brief four-month period in 2003-04.

Indices can go higher – Goldman predicts modest gains – but will require earnings growth.

A further expansion in valuation multiples is possible, Goldman admits, but adds: “It is just not probable based on history.”

Rules made to be broken
US stocks fell slightly in the first five days of the year, much to the concern of those who say the first five days can indicate stocks' year-end performance.

Former Goldman Sachs guru Jim O’Neill is a fan of the rule.

Last week, he cautioned that while it’s not especially predictive of declines, a positive start is to be hoped for. Since 1928, a five-day rally led to a 75 per cent chance of a positive year.

Since 1950, the probability rises to 82.9 per cent, he noted, adding: “Few rules in finance are as unambiguous as that.”

Well, not really. The S&P 500 rose in 75 per cent of years since 1950.

Market commentator Mark Hulbert says a positive first five days for the Dow Jones index led to a positive year on 69 per cent of occasions since 1896.

Again, the index rose most years anyway.


Reverse retirement strategy
Retirement strategies vary, but they typically involve a winding out of equities into bonds as people age, thereby protecting against any sudden market crash.

A recent study, however, suggests retirees should do the exact opposite.

The authors found those with a 30-year horizon would likely do best if they started retirement with a low equity allocation – around 20 or 30 per cent – and gradually raise it to a multiple of that level over the following decades.

The strategy particularly mitigates against the risks posed by a bear market that coincides with retirement.

By the time the market recovers, investors typically have no equities.

Overall, the study tested 10,000 possible scenarios, finding that the U-shaped equity allocation strategy tended to "reduce both the probability of failure and the magnitude of failure for client portfolios".

The study can be read at http://goo.gl/d3byf1

Why not bet on stupidity?
Google's $3.2 billion(€2.36 billion) acquisition of Nest Labs was good news for shareholders in penny stock Nestor, which briefly shot higher by 1,900 per cent after some confused investors got the two companies mixed up.

It isn’t the first such example. Prior to Twitter’s stock market flotation in November, investors piled into a bankrupt retail penny stock called Tweeter Home Entertainment, which surged 2,000 per cent before traders realised their error.

There could be the makings of a strategy here.

Betting on stupidity, it seems, can be a very profitable exercise.