In theory, stocks should provide a greater return than safer investments like Treasury bonds. The difference in return is called the equity risk premium, and it is what you can expect from the overall stock market above a risk-free return in bonds.

There is a vigorous debate among experts about the methods used to calculate the equity premium and, of course, the resulting answers. In this article, we'll take a look at these methods—particularly the popular supply-side model—and the debates.

## Why Does It Matter?

The equity risk premium helps to set portfolio return expectations and determine asset allocation. A higher premium implies that you would invest a greater share of your portfolio into stocks.

The capital asset pricing also relates a stock's expected return to the equity premium. A stock that is riskier than the broader market—as measured by its beta—should offer returns even higher than the equity premium.

### Key Takeaways

- The equity risk premium is the extra return investors should get from stocks versus bonds in exchange for taking on the greater risk inherent in stocks.
- There are four ways to calculate the equity risk premium but experts disagree about which is the best.

## Greater Expectations** **

Compared to bonds, we expect better returns from stocks due to the following risks:

- Dividends can fluctuate, unlike predictable bond coupon payments.
- When it comes to corporate earnings, bondholders have a prior claim while holders of common stock have a residual claim.
- Stock returns tend to be more volatile (although this is less true the longer the holding period).

And history validates theory. If you are willing to consider holding periods of at least 10 or 15 years, U.S. stocks have outperformed Treasuries over any such interval in the past 200-plus years.

But history is one thing, and what we really want to know is tomorrow's equity premium. Specifically, how much extra return should we expect the stock market to give us going forward?

Academic studies tend to arrive at lower estimations of equity risk premiums—in the neighborhood of 2% to 3%, or even lower. Later in this article, we'll explain why this is, while money managers often point to recent history and arrive at higher estimations of premiums.

## Getting at the Premium

Here are the four ways to estimate the future equity risk premium:

What a range of outcomes! Opinion surveys naturally produce optimistic estimates, as do extrapolations of recent market returns. But extrapolation is a dangerous business. First, it depends on the time horizon selected, and second, we cannot know that history will repeat itself. As Professor William Goetzmann of Yale has cautioned, "History, after all, is a series of accidents; the existence of the time series since 1926 might itself be an accident."

For example, one widely accepted historical accident concerns the abnormally low long-term returns to bondholders that started right after World War II (and subsequently low bond returns increased the observed equity premium). Bond returns were low in part because bond buyers in the 1940s and 1950s—misunderstanding government monetary policy—clearly did not anticipate inflation.

## Building a Supply-Side Model

Let's review the most popular approach, which is to build a supply-side model. There are three steps:

- Estimate the expected total return on stocks.
- Estimate the expected risk-free return (on bonds).
- Find the difference: expected return on stocks minus risk-free return equals the equity risk premium.

We'll keep it simple and sidestep a few technical issues. Specifically, we are looking at expected returns that are long-term, real, compound, and pre-tax. By "long-term," we mean something like 10 years, as short horizons raise questions of market timing. (That is, it is understood that markets will be overvalued or undervalued in the short run.)

By "real," we mean net of inflation. And by "compound," we mean to ignore the ancient question of whether forecasted returns ought to be calculated as arithmetic or geometric (time-weighted) averages.

### Taxes Make a Difference

Finally, although it is convenient to refer to pre-tax returns, as do virtually all academic studies, individual investors should care about after-tax returns. Taxes make a difference.

Let's say the risk-free rate is 3% and the expected equity premium is 4%. We thus expect equity returns of 7%. Say we earn the risk-free rate entirely in bond coupons taxed at an income tax rate of 35%, whereas equities may be deferred entirely into a capital gains rate of 15% (i.e., no dividends). The after-tax picture, in this case, makes equities look even better.

## Step One: Estimate the Expected Total Return on Stocks

### Dividend-Based Approach

The two leading supply-side approaches start with either dividends or earnings. The dividend-based approach says that returns are a function of dividends and their future growth. Consider an example with a single stock that today is priced at $100, pays a constant 3% dividend yield (dividend per share divided by stock price), but for which we also expect the dividend—in dollar terms—to grow at 5% per year.

In this example, you can see that if we grow the dividend at 5% per year and insist on a constant dividend yield, the stock price must go up 5% per year, too. The key assumption is that the stock price is fixed as a multiple of the dividend.

If you like to think in terms of P/E ratios, it is equivalent to assuming that 5% earnings growth and a fixed P/E multiple must push the stock price up 5% per year. At the end of five years, our 3% dividend yield naturally gives us a 3% return ($19.14 if the dividends are reinvested). And the growth in dividends has pushed the stock price to $127.63, which gives us an additional 5% return. Together, we get a total return of 8%.

That's the idea behind the dividend-based approach: The dividend yield plus the expected growth in dividends equals the expected total return. In formulaic terms, it is just a re-working of the Gordon Growth Model, which says that the fair price of a stock (P) is a function of the dividend per share (D), growth in the dividend (g) and the required or expected rate of return (k):

### Earnings-Based Approach

Another approach looks at the price-to-earnings (P/E) ratio and its reciprocal, the earnings yield (earnings per share ÷ stock price). The idea is that the market's expected long-run real return is equal to the current earnings yield. For example, if at the end of the year, the P/E ratio for the S&P 500 was almost 25, this theory says that the expected return is equal to the earnings yield of 4% (1 ÷ 25 = 4%). If that seems low, remember it's a real return. Add a rate of inflation to get a nominal return.

Here is the math that gets you the earnings-based approach:

Whereas the dividend-based approach explicitly adds a growth factor, growth is implicit to the earnings model. It assumes the P/E multiple already impounds future growth. For example, if a company has a 4% earnings yield but doesn't pay dividends, then the model assumes the earnings are profitably reinvested at 4%.

Even experts disagree here. Some "rev up" the earnings model on the idea that, at higher P/E multiples, companies can use high-priced equity to make progressively more profitable investments. Robert Arnott and Peter Bernstein—authors of perhaps the definitive study—prefer the dividend approach precisely for the opposite reason. They show that, as companies grow, the retained earnings they often opt to reinvest result in only subpar returns. In other words, the retained earnings should have instead been distributed as dividends.

## Handle With Care

Let's remember that the equity premium refers to a long-term estimate for the entire market of publicly traded stocks. Several studies have cautioned that we should expect a fairly conservative premium in the future.

There are two reasons why academic studies, regardless of when they are conducted, are almost certain to produce low equity risk premiums.

The first is that they make an assumption that the market is correctly valued. In both the dividend-based approach and earnings-based approach, the dividend yield and the earnings yield have reciprocal valuation multiples:

Both models assume that the valuation multiples—the price-to-dividend and P/E ratio—are correct in the present and will not change going forward. This is understandable, for what else can these models do? It is notoriously difficult to predict an expansion or contraction of the market's valuation multiple. The earnings model might forecast 4% based on a P/E ratio of 25. And earnings may grow at 4%, but if the P/E multiple expands, for example, to 30 in the next year, then the total market return will be 25%, where multiple expansion alone contributes 20% (30/25 -1 = +20%).

The second reason low equity premiums tend to characterize academic estimates is that the total market growth is limited over the long term. You'll recall that we have a factor for dividend growth in the dividend-based approach. Academic studies assume that dividend growth for the overall market cannot exceed the total economy's growth over the long term.

If the economy—as measured by gross domestic product (GDP) or national income—grows at 4%, then studies assume that markets cannot collectively outpace this growth rate. So, if you start with an assumption that the market's current valuation is approximately correct and you set the economy's growth as a limit on long-term dividend growth (or earnings or earnings per share growth), a real equity premium of 4% or 5% is pretty much impossible to exceed.

## The Bottom Line

Now that we have explored the risk premium models and their challenges, it is time to look at them with actual data. The first step is to find a reasonable range of expected equity returns. Step two is to deduct a risk-free rate of return, and step three is to try to arrive at a reasonable equity risk premium.