Even so, shares and consequently funds still look cheap say international commentators such as Dr Shane Oliver, head of investment strategy and chief economist at AMP Capital Investors in Australia.
Not everyone says it's a bull market yet. AMP Capital here in New Zealand says that what we're seeing is a "genuine bounce", not a bull run.
No one who can ever time the bottom of a market perfectly is the message. Sometimes short upswings called "dead cat bounces" are followed by another downturn.
That's exactly what happened earlier this year. Wall Street commentators were predicting in January that market bottom was close and it may be time to invest again. But US markets in particular had another sharp decline before hitting new lows in March.
It's also unlikely after such momentous events in world stock markets over the past 18 months that we'll proceed without some further hiccups and it's up to each investor to decide when the time is right to start investing. AMP Capital's head of investment strategy in New Zealand Jason Wong says that closer to the end of this year it will be harder to be optimistic about equity values as we are now.
Here in New Zealand the NZX market has been rising rapidly and fairly consistently since March and is now back at levels not seen since late 2008 . That's rises of more than 25%. However with the reporting season here, which is currently underway is expected to test the bull's perseverance.
Over the ditch Dr Oliver has some interesting data available about the effect of cyclical upturns on Australian shares, which are popular with New Zealand investors. A typical bull market, he says has seen shares rise by 132% on average since 1950.
As a general rule the earlier investors get in on a genuine rebound the better the gains. On the other hand, even if we have started another bull run, the markets won't peak again overnight and you've not lost all if you haven't invested yet.
Whatever you decide to do, don't jump in without a plan. Read Wall Street Journal correspondent Brett Arends' 12 "rules" for investing in the Next Bull Market before investing. The rules contain sensible advice that is all too often forgotten, such as ignoring what everyone else is doing, being truly diversified, treating forecasts with a grain of salt etc.