The plunge in commodity prices eases one concern for monetary policymakers worldwide — but leaves them trying to walk the narrow line between slow-growth and deflation, and may leave stocks struggling.

One of the biggest pieces of good news for policymakers worldwide this year has come in the shape of the sharp decline in commodity prices, especially in crude oil. In a world in which they may feel they are getting few breaks as they try to contain Europe’s sovereign debt crisis while trying to reignite domestic growth, the slump in commodities appears to have taken a bite out of inflation expectations and inflation rates. In turn, that eases the squeeze that consumers face in a slow-growth/no-growth economy as their income levels remain flat in absolute terms. It also means that monetary policymakers don’t need to worry as much as they otherwise would about the inflationary impact of any further monetary easing, such as a much hoped-for third round of quantitative easing by the Federal Reserve.

No silver lining comes without its cloud attached, however. It’s all too easy for ultra-low inflation to cross the narrow line that separates it from deflation — and that’s the last thing that the world’s major debtor nations — the eurozone, the United States, the United Kingdom — need. All anyone needs to do to remind themselves of what happens when deflation enters the picture is to glance at Japan and its decades-long struggle to return to economic health.

And as the chart below shows, lower inflation expectations — and the possibility of a deflationary environment taking shape — is bad news for stock market investors.

Without economic growth and the inflation that typically accompanies it, it will be hard for corporate earnings to rise. And without higher earnings and the prospect of even a slowly-growing economy with modest inflation, it’s hard to see why investors would be willing to pay higher multiples for a stagnating stream of corporate profits. The chart above shows how closely correlated expectations of what future inflation will be (as measured by inflation-protected Treasury bonds) and the value of the Standard & Poor’s 500-stock index.

No wonder stock market investors have been anxiously parsing the comments of Federal Reserve policymakers, looking for clues that they will suddenly announce not just a continuation of “Operation Twist” but a fresh round of quantitative easing. The Fed’s dilemma is clear, however: spark a rally in stocks, at the risk of creating some long-term inflationary pressures that will prove hard to contain the in the future.

There is, of course, the possibility that the relationship between inflation expectations and equities would break down if inflation rose high enough, to the point where supply constraints rather than demand proved to be the key cause for concern on the part of economists and policymakers. But that’s such a far-distant prospect for now that it may for most feel like figuring out how you’ll deal with the problems from a big lottery win before you have even bought the ticket.