Many people suggest that the recovery in equity prices since 2009-2010, seen around round the world but particularly in the American Nasdaq, S&P500 and DJIA, does not represent a general economic improvement. Instead, they believe that these numbers are simply being buoyed by new money pumped into the system. I don't think this argument holds, and I will attempt to explain why. First let's consider why we think people hold equities. Essentially, people hold equities because they expect a given real return for a given risk profile. In our simplest model, people hold portfolios of assets based on their risk tolerance, their subjective judgements over probabilities, and their preferences. Adding in banks, insurers, pension funds and so on makes the overall picture more realistic, but doesn't change our theory much. People pick financial intermediaries that hold the assets according to our preferences—the intermediaries add value through scale, or through providing a payments system and settling accounts.
Why might electronic money printing (which we call "quantitative easing" or QE) affect equity prices?
Well, firstly, we might not expect an effect from quantitative easing under one circumstance. QE increases the amount of narrow money we have—that is the number of notes, coins and bank reserves in the system. Generally we think broad money—which includes bank accounts people can debit or write checks on, and is much, much larger—is what interacts directly with the real economy. The ratio of broad money to narrow money is called the money multiplier, and usually a rise in narrow money leads to an even bigger rise in broad money—but this multiplier is not stable. It's at least possible (although not historically typical) that a rise in narrow money could be completely counteracted by a fall in the money multiplier.
But assuming this doesn't happen, there are three reasons why QE might boost equity prices. First would be because it increases inflation and the future price level. If prices rise, cash is worth less, so relative to a given nominal amount of cash, all things being equal a given equity is worth more. In other terms, the firms' nominal expected returns would rise.
The second reason is that in a depressed economy monetary easing like QE may boost real growth, which we would expect to raise any given company's expected real returns. It might also reduce the risk of very bad economic outcomes. Since equities are riskier than bonds, gilts and cash they pay a risk premium to those who hold them—a higher return (lower price) to compensate for this. If risky outcomes in general become less likely, these risk premia might narrow, making equities more desirable and expensive.
The third reason QE might raise stock prices is because it increases overall social wealth, and thus may lead to greater risk-tolerance overall, if people are willing to bear more risk as they get wealthier, and thus shift towards riskier assets like equities.
In each of these three, the jump in equity prices comes from fundamental factors. One could certainly drive up stocks by creating lots of inflation, but we can easily check if that's what's happening by looking at inflation. Any real/relative growth in equities would refute that explanation. In contrast, real growth, reduced risk and shifted preferences due to extra wealth are all legitimate reasons for higher equity prices.
Accounts of why QE buoys stocks without improving fundamentals (and hence part of the argument that stock indices are not good proxies for economic health) tend to rely on a narrative that QE "flows into equities". But as explained, people try to hold their wealth in the portfolio that fits closest to their preferences. If QE money did "flow into equities" then people would now be holding more of their wealth in stocks than they wanted to—they would rapidly rebalance their portfolio. Typically people needn't even do this themselves, because their pension fund will do so for them. QE has to improve the fundamental factors in order to boost equities.