**Why Does It Matter?**

The equity premium helps to set portfolio return expectations and determine asset allocation policy. A higher premium, for instance, implies that you would invest a greater share of your portfolio into stocks. Also, the capital asset pricing relates a stock's expected return to the equity premium: a stock that is riskier than the market - as measured by its beta - should offer excess return above the equity premium.

**Greater Expectations**

Compared to bonds, we expect extra return from stocks due to the following risks:

- Dividends can fluctuate, unlike predictable bond coupon payments.
- When it comes to corporate earnings, bond holders 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).

But history is one thing, and what we really want to know is tomorrow's equity premium. Specifically, how much extra above a safe investment should we expect for the stock market going forward? Academic studies tend to arrive at lower equity risk premium estimations - in the neighborhood of 2-3%, or even lower! Later in this article, we'll explain why this is always the conclusion of an academic study, whereas 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:

**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 (bond).
- Find the difference: expected return on stocks minus risk-free return equals the equity risk premium.

By 'real', we mean net of inflation. Even if we estimated the stock and bond returns in nominal terms, inflation would fall out of the subtraction anyhow. And by 'compound', we mean to ignore the ancient question of whether forecasted returns ought to be calculated as arithmetic or geometric (time-weighed) averages.

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 therefore expect equity returns of 7%. Say we earn the risk-free rate entirely in bond coupons taxed at ordinary income tax rates 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

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. 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, at the end of 2003, the P/E 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: 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. Arnott and 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 sub-par 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. Lately 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 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 earnings yield have reciprocal valuation multiples:

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 - and, for that matter, earnings or EPS growth - 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. Therefore, 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.

**Conclusion**

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; and step three is to try to arrive at a reasonable equity risk premium.