Equity risk premium is a long-term prediction of how much the stock market will outperform risk-free debt instruments.
Recall the three steps of calculating the risk premium:
- Estimate the expected return on stocks.
- Estimate the expected return on risk-free bonds.
- Subtract the difference to get the equity risk premium.
In this article, we take a deeper look at the assumptions and validity of the risk premium by looking at the calculation process in action with actual data.
Key Takeaways
- Equity risk premium predicts how much a stock might outperform risk-free investments over the long term.
- Calculating the risk premium can be done by taking the estimated expected returns on stocks and subtracting them from the estimated expected return on risk-free bonds.
- Estimating future stock returns is difficult, but it can be done through an earnings-based or dividend-based approach, or by using the price/earnings-to-growth (PEG) ratio.
- Calculating the risk premium requires some assumptions that run from safe to dubious.
Step 1: Estimate the Expected Total Return on Stocks
Estimating future stock returns is the most difficult (if not impossible) step. Here are a few methods of forecasting long-term stock returns:
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Plugging into the Earnings Model
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The earnings-based model shows that the expected return is equal to the earnings yield. In the graph above, we show the S&P 500 earnings per share (EPS) and the (via an exchange-traded fund (ETF) that tracks the index: SPY). Following the 2020 pandemic dip, we see the S&P 500 Index rebound in a steady upward movement, while the EPS graph shows an extreme upside spike, taking some of the index’s stocks into overvalued territory. Note that the EPS begins to decline from overvalued territory before the S&P 500 Index stalls out and begins to move lower. This indication of EPS slowing before the overall market suggests that stocks had indeed become overvalued on an EPS basis.
To get the earnings yield, we can divide the S&P 500 Index level by the EPS level (392.47 ÷ 19.17 = 20.47 = price-to-earnings (P/E) ratio). As the index finished the year with a P/E ratio of 20.47, the earnings yield was 4.89% (1 ÷ 20.47 = 0.0488). According to the earnings-based approach, the expected nominal return—before inflation—was, therefore, 4.89%. The underlying intuitive idea is mean reversion—the theory that P/E multiples cannot get too high or too low before they revert to some natural middle ground. Consequently, a high P/E ratio implies lower future returns and a low P/E ratio implies higher future returns.
Equity risk premium and market risk premium are often used interchangeably; however, the former refers to stocks while the latter refers to all financial instruments.
Plugging into the Dividend Model
The dividend model says that expected return equals dividend yield plus growth in dividends. This is all expressed as a percentage.The index ended 2022 with a dividend yield of about 1.68%. We only need to add a long-term forecast of growth in the markets’ dividends per share. One way to do this is to assume dividend growth will track with economic growth. And we have several economic measures to choose from, including gross national product (GNP), per-capita gross domestic product (GDP), and per-capita GNP.
:max_bytes(150000):strip_icc()/SPYDivYield-3e43eac9ec644cc2ac9ab38e625a94c1.jpg "Calculating the Equity Risk Premium (3)")
Let’s take real GDP at 4% for example. To use this measure for estimating future equity returns, we need to acknowledge a realistic relationship between it and dividend growth. It is a big leap to assume that 4% real GDP growth will translate into 4% growth in dividends per share. Dividend growth has rarely, if ever, kept pace with GDP growth—and there are two good reasons why.
First, private entrepreneurs create a disproportionate share of economic growth—the public markets often do not participate in the economy’s most rapid growth. Second, the dividend yield approach is concerned with per-share growth, and there is a leakage because companies dilute their share base by issuing stock options. While it is true that stock buybacks have an offsetting effect, they rarely compensate for stock options dilution. Publicly traded companies are, therefore, remarkably consistent net diluters.
History tells us that real GDP growth of 4% translates, at best, into roughly 2% growth in real dividends per share—or 3%, if we are optimistic. If we add our growth forecast to the dividend yield, we get about 3.7% to 4.7% (1.68% + 2% to 3% = 3.7% to 4.7%). We happen to match the roughly 4% predicted by the earnings model, and both numbers are expressed in nominal terms before adjusting for inflation.
Using the PEG Ratio
The price/earnings-to-growth (PEG) ratio is a stock’sprice-to-earnings(P/E) ratio divided by the growth rate of its earnings for a specified time period. The PEG ratio is used to determine a stock’s value while also factoring in the company’s expected earnings growth, and it is thought to provide a more complete picture than the more standard P/E ratio.
The PEG ratio enhances the P/E ratio by adding expected earnings growth into the calculation. However, that means, just as with other methods of valuing stocks, the PEG ratio also relies on assumptions and projections, which are inherently unreliable.
Step 2: Estimate the Expected ‘Risk-Free’ Rate
The nearest thing to a safe long-term investment are Treasury Inflation-Protected Securities (TIPS). Because the coupon payments and principal are adjusted semiannually for inflation, the TIPS yield is already a real yield. TIPS are not truly risk free—if interest rates move up or down, their price moves, respectively, down or up. However, if you hold a TIPS bond to maturity, you can lock in a real rate of return.
:max_bytes(150000):strip_icc()/10yearyields-8dac0e71d97747719306ab7d78b00409.jpg "Calculating the Equity Risk Premium (4)")
In the chart above, we show two versions of inflation-adjusted 10-year bond yields—the TIPS 10-year bond yield (blue), and the real 10-year Treasury rate (gold)—to give us an idea where inflation-adjusted interest rates may be in the future. The range is 1.20% to 2.23%, leaving us with an average 10-year inflation-adjusted risk-free yield of about 1.7%.
A government asset such as a bond is considered a risk-free asset because the government is unlikely to default on the interest.
Step 3: Subtract the Estimated Bond Return from the Estimated Stock Return
When we subtract our forecast of expected bond returns from projected stock returns, we get an estimated equity risk premium of +2.0% to 3.0%. That means your stock investments need to gain at least 2% to 3% to justify the risk of owning equities vs. staying parked in risk-free investments.
| Step | Estimated Long-Term Return |
|---|---|
| 1. Real stock returns | 3.7% to 4.7% |
| 2. Subtract real bond returns | -1.7% |
| 3. Estimated equity risk premium | +2.0% to 3.0% |
All Sorts of Assumptions
The model attempts a forecast and therefore requires assumptions—enough for some experts to reject the model entirely. However, some assumptions are safer than others. If you reject the model and its outcome, it is important to understand exactly where and why you disagree with it. There are three kinds of assumptions, ranging from safe to dubious.
First, the model does assume that the entire stock market will outperform risk-free securities over the long term. But we could say this is a safe assumption because it allows for the varying returns of different sectors and the short-term vagaries of the market. Take calendar year 2021 for an example: The S&P 500 jumped 26% while experiencing a modest decline in the P/E multiple.
No equity risk premium model would have predicted such a jump, but this jump does not invalidate the model. It was caused largely by phenomena that cannot be sustained over the long haul: a 17% increase in the combined forward EPS (i.e., EPS estimates for four future quarters) and an almost-unbelievable 60+% increase in trailing EPS (according to the S&P, from $27.60 to $45.20).
Second, the model requires that real growth in dividends per share—or EPS, for that matter—be limited to very low single-digit growth rates in the long run. This assumption seems secure but is reasonably debated. On the one hand, any serious study of historical returns (like those by Robert Arnott, Peter Bernstein, or Jeremy Siegel) proves the sad fact that such growth rarely gets above 2% for a sustained period.
Optimists, on the other hand, allow for the possibility that technology could unleash a discontinuous leap in productivity that could lead to higher growth rates. After all, maybe the new economy is just around the bend. But even if this happens, the benefits will surely accrue to selected sectors of the market rather than to all stocks. Also, it is plausible that publicly traded companies could reverse their historical conduct, executing more share buybacks, granting fewer stock options, and reversing the eroding effects of dilution.
Finally, the model’s dubious assumption is that current valuation levels are approximately correct. We’ve assumed that, at the end of 2022, the P/E multiple of 25 and the price-to-dividend yield of 65 (1 ÷ 1.5% dividend yield) is going to hold going forward. Clearly, this is just a guess! If we could predict valuation changes, the full form of the equity risk premium model would read as follows:
:max_bytes(150000):strip_icc()/dotdash_Final_Calculating_the_Equity_Risk_Premium_Dec_2020-06-acd73a07b27f4ea38d124481e271fe49.jpg "Calculating the Equity Risk Premium (5)")
Which is the best method to forecast future stock earnings growth?
While each of the three methods of forecasting future earnings growth has its merits, they all inherently rely on forecasts and assumptions, leaving many an investor scratching their heads.
If we had to pick one, it would be the forward price/earnings-to-growth (PEG) ratio, because it allows an investor the ability to compare dozens of analysts’ ratings and forecasts over future growth potential, and to get a good idea where the smart money thinks future earnings growth is headed.
Why do I need to calculate equity risk premium in the first place?
Two main reasons:
- To avail yourself of stocks that are undervalued, offering a potential bargain buying opportunity
- To avoid stocks that are overvalued by the many metrics outlined above
You might have the right stock in mind, but wouldn’t it be great if you had some statistical background to catch it at the right level (undervalued) as opposed to the wrong level (overvalued)?
What happens if the growth rate of my selected stock fails to beat the risk-free rate?
If you’re lucky, the stock you picked is still in positive territory, though not above the risk-free rate. Even if you’re not lucky, unless there’s some really bad news behind your company’s current performance, it more than likely will pick back up above the risk-free rate in the future. That’s the nature of the stock market—do your research and select your stocks carefully, and you should be able to eventually come out ahead of the risk-free rate.
The Bottom Line
Equity risk premium is calculated as the difference between the estimated real return on stocks and the estimated real return on safe bonds—that is, by subtracting the risk-free return from the expected asset return (the model makes a key assumption that current valuation multiples are roughly correct).
The U.S. Treasury bill (T-bill) rate is most often used as the risk-free rate. The risk-free rate is merely hypothetical, as all investments have some risk of loss. However, the T-bill rate is a good measure since they are very liquid assets, easy to understand, and the U.S. government has never defaulted on its debt obligations.
When the dividend yield on stocks is close enough to the TIPS yield, the subtraction conveniently reduces the premium to a single number—the long-term growth rate of dividends paid per share.
The equity risk premium can provide some guidance to investors in evaluating a stock, but it attempts to forecast the future return of a stock based on its past performance. The assumptions about stock returns can be problematic because predicting future returns can be difficult. The equity risk premium assumes the market will always provide greater returns than the risk-free rate, which may not be a valid assumption. The equity risk premium can provide a guide for investors, but it is a tool with significant limitations.
