One of the most famous proofs in financial theory is that dividends do not matter, tax excepted. Whether a company pays profits to investors or reinvests them makes no difference to its theoretical value and it was enough to win a Nobel memorial prize in economics for Franco Modigliani and Merton Miller.

So much for theory. In the real world, investors are entranced by dividends – so much so that they are starting to look dangerously overvalued, especially in the US.

High-yielding American stocks have traded at higher valuations than low-dividend or non-dividend payers intermittently over the past two years, as investors search for alternatives to bonds with negligible interest rates.

Now the highest-yielding quartile of the S&P 500 is trading at a multiple of 16 times forward earnings, higher than any time in data going back to 1994, according to Dan Morris, a strategist at JPMorgan Asset Management (the wider market is on 14 times).

There is more going on than just the hunt for yield. Investors want quality too, with reliable dividend payers trading even higher – Coca-Cola is trading at 19 times while Switzerland’s Nestlé is above 18 times.

Investors face three dangers. First, it is easy to keep treating high dividends as the indicator of value they have always been. A high divi is no longer an indicator of a cheap stock.

Second, for valuations to stay this elevated, interest rates have to stay rock-bottom. If signs of economic recovery push up bond yields, dividend-paying bond proxies will be less in demand; investors will also be more willing to buy longer-duration, growth-oriented low-dividend stocks.

Finally, the obsession with yield is hurting the economy. Howard Silverblatt at Standard & Poor’s says 406 of the S&P 500 companies now pay a dividend, the most since November 1999. The more investors push for payouts, the less companies have to invest. With few other sources of growth, dividends matter a lot.

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