# The Gordon Equation: how to calculate expected returns for equities

The Gordon Equation1 is a popular rule of thumb for gauging expected equity returns.

It’s been used by investing luminaries such as the late great John Bogle, Bill Bernstein and others to get a sense of what the future could hold for our investments in the long term.

All good investment plans rely on having some idea of your investments’ growth prospects. Using average historical return data is one way of estimating your chances, but it’s not necessarily the best.

The Gordon Equation is arguably a better signal because it bundles current valuations and long-term trend data into one simple formula – one which anyone can calculate.

I’ll take you through it now, and explain how it works.

I’ll also deliver the customary caveats and misuse warnings. (Now that you could have predicted!)

### The Gordon Equation formula

The Gordon formula can be applied to any broad equity market index, such as the MSCI World or FTSE All-Share.

It looks like this:

Expected real return from equities = Current dividend yield + Real earnings growth

Let’s try plugging in some numbers:

Expected return FTSE All-Share = 4 + 1.4 = 5.4% (annualised2)

Expected return MSCI World = 1.7 + 1.4 = 3.1% (annualised)

That’s it. The Gordon Equation tells us that prospects for the UK over the next couple of decades are pretty cheery overall, while it douses our flame for global developed markets.

So where did I get those plug-in numbers from?

### Current dividend yield

The dividend yield is the percentage return paid by your holdings as dividend income.

For a tracker fund, the dividend yield is the total dividend payments (over the last 12-months, typically) divided by the Net Asset Value (NAV).3

Grab the dividend yield from an index tracker that follows the market you care about, and you’ve got the first half of the Gordon Equation.

I got the 1.7% above from the current yield of the iShares MSCI World ETF.

The 4% came courtesy of the Vanguard FTSE All-Share Index Trust.

Expect the numbers quoted to vary a little, depending on your source. For example, Vanguard’s FTSE 100 ETF has a slightly different yield to its index fund (which varies again by Inc or Acc version.)

Don’t stress it – expected returns have all the accuracy of nerf gun darts. They are not laser-guided munitions and can only get us into the splash zone.

### Real earnings growth

For the second number, we’re talking about the expected annualised growth rate of earnings per share. Yes, we are!

By earnings I mean corporate profits and by real I mean after inflation is stripped out.

Some versions of the Gordon Equation refer to real dividend growth instead. In the long-term it’s all the same hamburger, as rising profits and dividends usually go together like early marriage and divorce.

We’re looking for a long-term trend rate and we’re looking for a credible source to give it to us.

Here’s a few taken down from the Credible Source Shelf:

• Investing sage Bill Bernstein recommended a 1.32% real dividend growth rate for the US in his excellent book, The Investor’s Manifesto.
• That’s similar to the 1.4% real earnings growth forecast by fund provider Research Affiliates for global developed markets.
• Then there’s the 1.5% real earnings growth for developed markets calculated by AQR, another fund provider with a great track record in research. AQR also proposes a 2% figure for emerging markets.

In my examples I plumped for the middle ground of 1.4%. Different practioners use different assumptions, so pick your poison and don’t drop into the bookies on the way home.

Incidentally, these three sources all adjust their aim to take into account the increasing use of share buybacks.

### Handle me with care

As I’ve hinted, the Gordon Equation isn’t a trip to the future in a Delorean, but neither is it a crackpot prophecy.

The equation has a decent track record of guiding expectations into the right ballpark, over the long-term.

If you consult Gordon everyday like a Magic 8 ball then you’ll constantly get a different answer, because the dividend yield varies in tune to the rise and fall of market P/E ratios.

I suggest you use it annually to keep your plan on track. Combine it with our piece on estimating your overall portfolio expected return to keep a grip on the bigger picture.

The Accumulator

1. Finance professor Myron Gordon of the University of Toronto created the Gordon Equation. []
2. i.e. The expected average annual return. Note annual returns will not be smooth in practice! []
3. Technically the yield you’ll receive as an investor is the total dividend divided by the market price, but for trackers price and NAV are usually the same. []

• 1 FIRE v London March 5, 2019, 2:20 pm

I’ve been meaning to write a post like this for ages but hadn’t, and wouldn’t have written one as good as this anyway.

I use this rule of thumb a lot and find it to be useful. Less so for market indices, where it is hard to get a feel for earnings growth, but more for individual companies. I find stockopedia useful to see earnings growth and analyst projections for growth.

Nearly all of my portfolio has a total divi yield plus recent/projected annualised (nominal, not real) profits growth of at least 9pc.

• 2 pca March 5, 2019, 5:28 pm

In my pension-forecasting spreadsheet I use current dividend yield as a guesstimate for future real growth. I’m hoping actual growth turns out higher than this, in which case I’ll either have more money when I retire, or retire earlier. If I used the Gordon formula, I’d be saving a little less into my pensions/ISA just now, and might end up slightly worse off as a result. You could go the whole hog and assume zero real growth when it comes to planning savings amounts.

• 3 oldie March 6, 2019, 4:44 pm

Thanks for clear explanation but also the sources of the data.

I have also seen a third factor sometimes used…
“sentiment” expressed as any change in P/E ratio over the period in question. Not sure where you would get it from?

• 4 e17jack March 6, 2019, 5:17 pm

Wow… 9%!

May i ask how you have achieved this forecast – what makes up your portfolio given that the broad indexes above have forecasts in the 4-5% range?

• 5 The Investor March 7, 2019, 8:21 am

“Siri, show me how someone ends up trying to beat the market by active investing.”

Wow… 9%!

May i ask how you have achieved this forecast – what makes up your portfolio given that the broad indexes above have forecasts in the 4-5% range?

😉

• 6 MrOptimistic March 8, 2019, 6:58 pm

Does it matter if you re-read invest the dividends?

• 7 MrOptimistic March 8, 2019, 9:45 pm

Sigh. Sorry meant re-invest.