In theory, stocks should provide a higher return than safer investments like Treasuries. The difference in return is called the equity risk premium and is what you can expect from the stock market in general over a risk-free return on bonds.

There is intense debate among experts about the methods used to calculate the capital premium and, of course, the resulting answers. In this article, we’ll take a look at these methods, in particular the popular supply-side model, and the debates.

Key takeaways

- The equity risk premium is the additional return investors should get from stocks versus bonds in exchange for taking the higher risk inherent in stocks.
- This return compensates investors for taking the greater risk of investing in stocks.
- There are four ways to calculate the risk premium for stocks, but experts disagree on which is the best.

## Why does that matter?

The equity risk premium helps set expectations of portfolio performance and determine asset allocation. A higher premium means that you would invest more of your portfolio in stocks.

The price of equity assets also relates the expected return on a share to the equity premium. A stock that is riskier than the broader market, as measured by its beta, should offer even higher returns than the equity premium.

## Higher expectations

Compared to bonds, we expect better returns on 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 common stock holders have a residual claim.
- Stock returns tend to be more volatile (although this is less true the longer the holding period is).

And the story validates the theory. If you’re willing to consider holding periods of at least 10 or 15 years, US stocks have outperformed Treasuries at any such interval in the last 200 years or more.

But history is one thing, and what we really want to know is tomorrow’s capital premium. Specifically, how much additional return should we expect the stock market to bring us in the future?

Academic studies tend to arrive at lower estimates of equity risk premiums, in the neighborhood of 2% to 3%, or even lower. Later in this article, we’ll explain why this happens, while money managers often point to recent history and come up with higher estimates of premiums.

## Get the Premium

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

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

For example, a widely accepted historical accident concerns abnormally low long-term returns for bondholders that began just after WWII (and, subsequently, low bond yields increased the observed equity premium) . Bond yields were low in part because bond buyers in the 1940s and 1950s — misunderstanding the government’s monetary policy — clearly did not anticipate inflation.

## Building a supply-side model

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

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

We’ll keep it simple and avoid some glitches. Specifically, we are looking at expected returns that are long-term, real, compounded, and before taxes. By “long term” we mean something like 10 years, as short horizons raise questions about market timing. (That is, it is understood that the markets will be overvalued or undervalued in the short term).

By “real” we mean net inflation. And by “composite” we want to ignore the old question of whether expected returns should be calculated as arithmetic or geometric (time-weighted) averages.

### Taxes make the difference

Finally, while it is convenient to refer to pre-tax returns, as virtually all academic studies do, individual investors should be concerned with after-tax returns. Taxes make the difference.

Let’s say the risk-free rate is 3% and the expected capital premium is 4%. Therefore, we expect a 7% return on equities. Suppose we earn the risk-free rate entirely on bond coupons taxed at an income tax rate of 35%, while stocks can be fully deferred at a capital gains rate of 15% (that is, without dividends). . The after-tax outlook, in this case, makes stocks look even better.

## Step One: Estimate the Expected Total Return of the Stock

### Dividend-based approach

The two main approaches to the supply side start with 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 the share price), but for which we also expect the dividend, in terms of dollars, grow at 5% per year.

In this example, you can see that if we increase the dividend to 5% per year and insist on a constant dividend yield, the stock price must also go up 5% per year. The key assumption is that the share price is set as a multiple of the dividend.

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

That’s the idea behind the dividend-based approach: the dividend yield plus the expected dividend growth equals the total expected return. In terms of formulas, it’s just a reworking of Gordon’s growth model, which says that the fair price of a share (P) is a function of the dividend per share (D), the dividend growth (g), and the rate of required or expected performance (k):

### Profit-based approach

Another approach looks at the price-earnings (P / E) ratio and its reciprocal, the earnings performance (earnings per share ÷ share price). The idea is that the expected long-term real return of the market equals the current return on earnings. 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 equals the return on earnings of 4% (1 ÷ 25 = 4%). If that seems low, remember that it is a true return. Add an inflation rate to get a nominal return.

Here is the math that gives you the profit-based approach:

While the dividend-based approach explicitly adds a growth factor, growth is implicit in the earnings model. Assume that the P / E multiple already accumulates future growth. For example, if a company has a 4% profit yield but does not pay dividends, then the model assumes that the profits are profitably reinvested at 4%.

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

## Handle with Care

Recall that the equity premium refers to a long-term estimate for the entire market for publicly traded stocks. Several studies have warned that we should expect a fairly conservative premium in the future.

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

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

Both models assume that the valuation multiples – the price-dividend and the P / E ratio – are correct in the present and will not change in the future. This is understandable, because what else can these models do? It is notoriously difficult to predict an expansion or contraction of the market valuation multiple. The earnings model could forecast 4% based on a P / E ratio of 25. And earnings can grow to 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 that low capital premiums tend to characterize academic estimates is that overall market growth is limited in the long run. You will recall that we have a factor for dividend growth in the dividend approach. Academic studies assume that dividend growth for the broader market cannot exceed growth for the total economy in the long run.

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

## The bottom line

Now that we’ve explored risk premium models and their challenges, it’s time to analyze them with real data. The first step is to find a reasonable range of expected returns on the stocks. The second step is to deduct a risk-free rate of return and the third step is to try to arrive at a reasonable equity risk premium.