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Choose your villains wisely. In a world where Donald Trump is president of the United States, and Vladimir Putin is boss of Russia, it's amazing that some people insist on losing sleep over Janet Yellen.

The indictment against her rests on the undeniable fact that the chair of the U.S. Federal Reserve has demonstrated a shocking tendency to behave like a central banker and actually, you know, raise interest rates. After years in which stock market investors wallowed in the pure bliss of near-zero borrowing costs, this tendency strikes some observers as practically criminal.

What's the menace to society from higher rates? As yields improve on bonds, people may choose to stampede out of stocks in search of safer alternatives. If that occurs, Yellen will have murdered this bull market.

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Or so the story goes. Don't believe it.

Despite all the gnashing of teeth about Fed policy, there's no reliable link between interest rates and the stock market outlook. The supposed relationship exemplifies what the venerable British commentator Andrew Smithers calls stockbroker economics: things your financial professional tells you that just aren't true.

The rate fable sounds so sensible because it's usually pitched as a simple matter of comparing relative value. Every investor, we are told, faces a fundamental choice: bonds or stocks. To decide between these assets, investors are advised to look at how much the stock market is spitting out in terms of earnings. If the earnings yield happens to be better than the yield from a high-quality bond, investors understandably choose stocks. Otherwise, they turn to bonds.

Sounds convincing, doesn't it? But history shows there's no necessary tie between earnings yields and bond yields.

Yes, there are times, like 1981 to 1997, when the two tango together, cheek to cheek. But there are also eras, such as 1950 to 1968, when they waltz far apart from each other.

To put this more plainly, stocks sometimes thrive when interest rates go up, and sometimes they don't. "The historical relationship between the stance of Fed policy and the value of the U.S. stock market has been weak," says John Higgins of Capital Economics.

Smithers concurs—vehemently.  He says the supposed link "is not only nonsense but the most egregious piece of data mining that I have encountered in the 60-plus years I have been studying financial markets."

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The unstable link between stocks and bonds reflects how very differently the two assets react to changing economic conditions. Inflation guts the purchasing power of most bonds because those assets pay fixed amounts that aren't adjusted for rising prices. In contrast, a burst of inflation is nowhere near as bad for stocks, because rising prices boost corporate earnings—and, therefore, share prices.

As a result, smart investors don't just compare current yields on bonds and stocks and pick the one that is higher. They also consider how inflation and growth will develop over the next few years before deciding which of the two is more attractive.

Right now, there's no particular reason to think rising rates will sink the stock market. In fact, any Fed tightening could be a positive sign for stocks if it indicates the central bank believes the economy is more robust.

Let me stress that this doesn't mean investors should double down on this geriatric bull market. While rising rates are unlikely to end the rally in stocks, other things could.

For instance, there's the unsustainable trend of companies paying out more than they earn to shareholders, in the form of dividends and share buybacks. There's also the chance that wages will start to climb in today's stronger economy and cut into corporate earnings.

Worry about these concerns, if you must. But leave Janet alone.

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