There’s an old stock-market saying: As January goes, so goes the year.

Let’s hope so, as the year started strong.

In the last 55 years, the “January Barometer” has significantly misgauged the Standard & Poor’s full-year results only five times, according to a study by Yale Hirsch, author of the annual Stock Trader’s Almanac.

The first five trading days are especially significant: Since 1950, there have been 35 occasions when those days have registered a gain for the S&P 500 index, and those were followed by full-year gains 30 times.

There are all kinds of theories for the January effect. Perhaps it’s a self-fulfilling prophecy – with investors buying after a strong start, thereby bidding stock prices up further.

Or maybe January is a time of fresh market analysis after the distractions of the holidays.

We just don’t know.

But it’s not hard to understand Tuesday’s big gain. Investors were thrilled that minutes from the Federal Reserve’s December meeting suggest the long cycle of interest-rate hikes is near an end.

Why are low interest rates so good for stocks?

First, because low rates allow consumers and companies to borrow more, giving them more to spend. That boosts corporate profits, driving stock prices up.

The second reason has to do with the endless tug of war between competing types of investments such as stocks and bonds.

Many interest-bearing investments such as bonds and bank accounts are very safe. Stocks often provide higher returns – but at much greater risk.

Stocks, therefore, have a harder time competing for investors’ dollars when safer bonds and savings accounts offer fat yields.

One of the ways of gauging stock risks is to look at the ratio of a stock’s price to the company’s earnings per share for the last 12 months. The higher this price-to-earnings ratio, the riskier the stock.

Paying $30 a share for a stock with $1 in earnings means a P/E ratio of 30. Obviously, it would be preferable to pay $10 a share, for a P/E of 10.

The same figures can produce a stock’s earnings yield – 12 months’ earnings divided by current price. The $30 share has a 3.33 percent earnings yield ($1 divided by $30), and the $10 share a 10 percent earnings yield ($1 divided by $10).

Obviously, the 10 percent yield is better than the 3.3 percent yield.

Earnings represent an increase in the company’s value that is likely to drive the stock’s price upward.

An investor with a wad of cash should consider all this when choosing between stocks and interest-paying alternatives.

Today, for example, one can earn 4.3 percent to 4.8 percent in safe two-year bonds and certificates of deposit. And the earnings yield on the S&P 500 is about 5.5 percent (a P/E of 18).

That’s not a big difference, and investors who think interest rates will continue rising would probably prefer safe bonds.

But the Fed minutes suggest there’s now less risk of higher rates harming earnings. So many investors are jumping to stocks, and the greater demand is driving share prices up.

It’s safe to say any news that’s good for corporate earnings is good for stock prices. When the good news comes at the start of the year, it puts investors in a cheerful mood – making it more likely the January effect will be a self-fulfilling prophecy.

Jeff Brown is a business columnist for The Philadelphia Inquirer.