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3 Simple Equations All Investors Should Know

By:
Susie Poppick
4 min read
- Getty Images
Getty Images

Whether you love to buy and sell stocks or barely understand what's going on in your retirement account, there's a good chance you could benefit from learning more about the math behind the stock market.

Here are three fundamental equations that the savviest investors know. Relatively easy to understand, they will help you choose the right stocks and funds and, most important, keep your expectations about future returns grounded in reality.

Equation 1

S&P 500 dividend yield + about 4.5% = the expected long-term return on stocks

This formula, known as the Gordon equation, assumes stocks get their ultimate value from being able to one day return earnings to investors. (That's true whether or not a company currently pays a dividend or reinvests in the business.) Anything above or below that is a result of investor sentiment.

You can look up the current S&P 500 dividend yield, which is about 2% now, at multpl.com; the 4.5% is how much you can expect dividends to grow based on the past. So today the expected long-run return is 6.5%. Adviser and author William Bernstein says thinking about this number brings you down to earth in boom years, and can reassure you when the market is down.

Equation 2

A 1.5% expense ratio = more than 40% of your money after 40 years

Mutual fund and adviser expenses seem so tiny— just 1% or so. But math professor Jordan Ellenberg, author of How Not to Be Wrong, says that over many years "expenses add up—or, more mathematically precisely, they multiply up."

Put $100,000 into a fund with a 1.5% expense ratio, assume a 6% underlying return, and you'll get about $560,000 after 40 years. With the same pre-expense return in a very low-cost index fund charging 0.1%, you'd have $990,000. To see for yourself the true long-term costs of a fund you are considering, use the mutual fund fees calculator at Bankrate.com.

Equation 3

Net income / shareholder equity = return on equity

Return on equity is a classic measure of a company's ability to put shareholders' money to good use. (Equity is roughly the cash investors put into the business, plus retained earnings.) Calculate a stock's ROE using the balance sheet and income statement.

Looking for consistent ROE of 15% or more "helps steer you toward profitable companies and away from speculation," says Robert Zagunis of the Jensen Funds, which screen for stocks with 10 years of high return on equity, like 3M.

Read more investing fundamentals from Money 101:
How do I know if I should buy a stock?
Should I invest in stocks or in a stock mutual fund?
How often should I check on my retirement investments?

Correction: This story has been updated to reflect the current S&P 500 dividend yield.

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