Equity risk premium: how much more equities return and why it is a puzzle

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The equity risk premium is the amount by which equities return more than safe investments such as the money market or government bonds over the long run. It is the most important number in investing: it determines how much you can expect from regular investing in stocks, how companies calculate their cost of capital and how much risk is worth taking at all. At the same time, it is hard to measure, fluctuates with valuations and has historically been so high that economists speak of a puzzle.

Definition: a premium over what?

Depending on the comparison, you get different numbers: the premium over the money market is larger than over long-dated bonds, which themselves contain a term premium. A distinction is also made between the historical premium (how much more equities actually returned) and the expected premium (how much more they are likely to return in future). The historical premium can be measured, but it is only an estimate of the expected one, and a biased one if valuations changed sharply during the measurement period.

A third distinction concerns the mean: the arithmetic mean of the annual premiums is above the geometric mean (the average annual rate over many years). For wealth planning, the geometric mean is what matters; for the expectation for a single year, the arithmetic one.

What history shows

Long data series exist mainly for the US. Siegel (2014) traced the returns on equities, bonds, the money market and gold in the US back to the early 19th century; over long periods, equities were clearly ahead. Because the US turned out in hindsight to be the most successful large market, US data may overstate the premium. Dimson et al. (2002) therefore compiled returns over 101 years for many countries, including markets that went through wars and hyperinflation. In this broader view, too, equities returned more than bonds and the money market, albeit with large differences between countries.

Bessembinder (2018) points out an important caveat: the premium of the overall market comes from a small number of exceptionally successful companies; the majority of individual stocks did no better than money market instruments over their lifetime. The premium therefore belongs to those who diversify broadly, not automatically to those who hold individual stocks.

And what investors actually earned is lower still: using money-weighted returns, Dichev (2007) shows that, through the timing of their inflows and outflows, investors achieved less than buy-and-hold in almost all major markets, and concludes that the historical premium from investors' point of view was lower than often assumed (see time-weighted return).

The equity premium puzzle

Mehra and Prescott (1985) asked whether the historical premium can be explained by a standard economic model in which investors want to smooth their consumption over time. Their finding for the US from 1889 to 1978: the restrictions that such equilibrium models impose on the average returns of equities and short-term government paper are clearly violated by the data. With plausible risk aversion, equities ought to return far less extra, or the risk-free rate ought to be much higher. This is the equity premium puzzle.

A well-known explanation comes from behavioral economics. Benartzi and Thaler (1995) combine two assumptions: investors are loss-averse (losses hurt considerably more than gains of the same size please) and they check their portfolio frequently. This myopic loss aversion makes equities seem riskier than they are for a long-term investor. In their simulations, the size of the premium matches the well-known parameters of the prospect theory of Kahneman and Tversky (1979) if investors evaluate their portfolio about once a year.

For private investors, this contains a practical piece of advice: if you look at your portfolio less often, you experience fewer losses and are more likely to stick with equities. In doing so, you collect the premium that others leave on the table out of impatience.

Estimating the expected premium

Instead of looking at the past, you can derive the premium from today's prices. The simplest model is the dividend growth model: the expected equity return is the dividend yield plus the expected growth of dividends.

Fama and French (2002) used this approach to estimate the premium for the US from 1951 to 2000: dividend growth gives 2.55% and earnings growth 4.32%. Both are far below the 7.43% suggested by the average return over the period. Their explanation: the high return of these 50 years came to a large extent from falling discount rates, i.e. from a revaluation that produced an unexpectedly large capital gain. Their conclusion: the average return of the last half-century was considerably higher than expected.

Valuation measures such as the Shiller P/E provide similar estimates for ten years. Their predictive power is limited, however: Welch and Goyal (2008) show that most well-known predictor variables for the equity premium were unreliable over decades, both in and out of sample, and would not have helped an investor with market timing.

For advanced readers: how certain is the premium over long periods?

A positive expected premium does not mean that equities are sure to come out ahead over any given period. If you assume that the log excess return has a mean of 3% a year and a volatility of 18%, then the probability that equities lag behind the safe asset over T years is:

The probability falls over time but does not disappear. At the same time, the possible shortfalls grow larger over long periods. This does not contradict the long-term superiority of equities; it is the reason why a premium exists at all: if it were certain over 20 years, nobody would pay it. The calculation assumes independent, normally distributed returns; with fat tails and fluctuating valuations, the picture is even more uncertain.

The premium in your own currency: over the money market and bonds

For an individual investor, the relevant premium is the excess return of a globally diversified equity portfolio in their own currency over that currency's money market or government bonds. A few special features change the calculation:

• Interest rate phases: with the same equity return, the premium over the money market is larger when interest rates are low; from 2014 to 2022, for example, the euro money market was even below zero. If interest rates rise, the premium falls when equity returns are unchanged.
• Currency: measured in US dollars, a world portfolio carries the currency risk of all its non-US holdings. This risk earns no reliable premium of its own in the long run, but it changes the return in individual years considerably (see currency risk).
• Term premium: the equity premium over long-dated government bonds is smaller than over the money market, because long-dated bonds themselves carry a premium for their interest rate risk.

What this means for planning

• Be conservative: for plans spanning decades, a premium below the historical average is more appropriate, especially when valuations are high.
• Plan geometrically: for final wealth, the geometric return counts, not the arithmetic one.
• Diversify broadly: the premium arises in the market as a whole; individual stocks carry a lot of risk without additional reward (see CAPM).
• Stay the course: the premium is only paid to those who stay invested through bad phases. If you sell after a crash, you swap the expected premium for a certain loss.

Ilmanen (2011) gives a comprehensive overview of the expected returns of all major asset classes and of how to sensibly combine historical and valuation-based estimates.

How Portfolio Lab calculates it

The Valuation page shows the Shiller P/E since 1881, its earnings yield 1/CAPE and the excess CAPE yield as an estimate of the real premium over bonds: the earnings yield minus the real interest rate, where the real interest rate is the ten-year bond yield less the average inflation of the last ten years. It also uses a regression with Newey-West standard errors to estimate which real return followed a given valuation level over the next 5, 10 or 15 years. In Monte Carlo and Financial goals, you can set the expected return more conservatively than the historical average. Details are in the valuation methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.