Part X · Edges, one by one · Chapter 10B

The equity risk premium

Why stocks pay more than bonds

Where we are

Chapter 10A placed four premia in the foundation category, and this chapter takes the first and largest of them: the equity risk premium. Chapter 1D set it up as the benchmark every strategy has to beat. Here it is an edge in its own right, with a mechanism, a price, a way of failing and a rule.

What you need first

Compounding, and the logarithms that turn it into addition (Chapter 1A).
A risk premium as payment for bad-times risk, and the island economy (Chapter 1G).
The equity risk premium as the benchmark, with its canonical studies and survivorship bias (Chapter 1D).
The rules for a foundation premium (Chapter 10A).

In plain terms

Equities pay a premium over bonds and cash because their cash flows are riskier in the states of the world that matter most to investors. Stocks pay least in recessions, when consumption is already low and every dollar is most needed, so investors demand compensation for holding them. A behavioral effect adds to the premium: people who check their holdings often feel each short-term loss more sharply than the long-term gain.

1 · A dollar from 1900

The premium looks small in any one year and enormous over a lifetime, as a single dollar shows.

Worked example: Two dollars invested in 1900

Step 1: the outcomes. In the United States, $1 invested in equities in 1900 grew to about $107,409 in nominal terms by 2024, and $1 in long bonds grew to about $268. Both were positive, yet the ratio between them is about 400 times over 125 years.

Step 2: the yearly rates. A sum that grows by a factor $G$ over $n$ years compounds at $G^{1/n} - 1$ a year (Chapter 1A). For equities, $\ln 107{,}409/125 = 0.0927$ , and $e^{0.0927} - 1 = 9.7\%$ a year. For bonds, $\ln 268/125 = 0.0447$ , or 4.6% a year.

Step 3: the gap, compounded. The yearly gap is $1.097/1.046 = 1.049$ , about 4.9%, and $1.049^{125} \approx 400$ , the ratio of Step 1. That ratio is the equity risk premium compounding.

The same arithmetic works in reverse: a small change in the expected premium makes a large difference to what a long-lived portfolio becomes.

2 · The formal object

The equity risk premium (ERP) is the expected return of equities above the risk-free rate. Chapter 1G wrote any risk premium as an exposure times a price of risk, and for equities the Edge Book adds a behavioral term:

\begin{aligned} \mathbb{E}[R_{\text{eq}}] - r &= \beta_{\text{eq}}\,\pi_{\text{cons}} \\ &\quad + \text{behavioral premia} \end{aligned}

(10B.1)

Here $R_{\text{eq}}$ is the return on equities and $r$ the risk-free rate. The exposure $\beta_{\text{eq}}$ measures how far equities carry consumption risk, the risk of paying least when households can spend least. The price $\pi_{\text{cons}}$ is what the market pays for each unit of that exposure. The behavioral premia are the extra return that biases such as myopic loss aversion add. With a hypothetical exposure of 1.0, a price of 4% and a behavioral term of 0.5%, the formula gives a premium of $1.0 \times 4\% + 0.5\% = 4.5\%$ a year.

The long-run realized US ERP is about 5% to 7% a year over bills and about 3% to 5% over long bonds. The two figures differ because long bonds pay their own premium over bills, the term premium of Chapter 1G. Forward-looking estimates come out lower: Damodaran's implied ERP for 2025 is about 4.3%, which suggests some compression against 20th-century averages.

An implied equity risk premium is read from today's prices rather than from past returns. Damodaran computes his with models in the style of the dividend discount model (DDM), which values an index as the present value of all the cash it is expected to pay out. Run backward, the model gives the return that today's price implies.

The dividend discount model, and the return it implies

Suppose the index pays cash $D_1$ next year, growing at a steady rate $g$ a year, and investors require a return $k$ . The price is the sum of every payment discounted at $k$ :

P = \frac{D_1}{1+k} + \frac{D_1(1+g)}{(1+k)^2} + \dots

(10B.2)

Each term is the one before multiplied by $(1+g)/(1+k)$ . For $k > g$ this is a geometric series, whose sum is the first term divided by one minus the ratio:

\begin{aligned} P &= \frac{D_1/(1+k)}{1 - (1+g)/(1+k)} \\ &= \frac{D_1}{k - g} \end{aligned}

(10B.3)

Solving for $k$ gives the return the price implies, and subtracting the risk-free rate gives the implied premium:

k = \frac{D_1}{P} + g, \qquad \text{ERP} = k - r

(10B.4)

Worked example: An implied premium from three inputs

Step 1: the premium. Suppose, hypothetically, that the index pays out cash worth 2.0% of its price over the next year, that the payout grows at 6.0% a year, and that the risk-free rate is 3.7%. By (10B.4), the implied return is $k = 2.0\% + 6.0\% = 8.0\%$ , and the implied ERP is $8.0\% - 3.7\% = 4.3\%$ . These inputs are illustrations, not Damodaran's.

Step 2: the effect of price. If the price rose 25% with the same cash and growth, the payout yield would fall to $2.0\%/1.25 = 1.6\%$ and the implied premium to 3.9%. Higher starting prices mean lower forward returns, which is why the forward premium has compressed.

3 · The evidence

Three bodies of evidence support the premium, and Chapter 1D gives the first two in more detail:

Mehra and Prescott (1985), in the Journal of Monetary Economics (JME), named the equity premium puzzle: the observed ERP was too large to fit standard models of utility.
The Dimson-Marsh-Staunton UBS Global Investment Returns Yearbook of 2025 covers 35 markets, 23 of them with a full history from 1900 to 2024. It puts the world equity real return at about 5.2% a year, against about 1.7% for bonds.
Damodaran updates the implied ERP regularly, using DDM-style models.

A real return is a return after inflation: $(1 + \text{nominal return})/(1 + \text{inflation}) - 1$ . The Yearbook's two world figures imply a real premium of equities over bonds of about $1.052/1.017 - 1 = 3.4\%$ a year, inside the range of 3% to 5% over long bonds given for the United States.

4 · Why it exists

The ERP is a compensated risk premium, Source 1 of Chapter 1G. Equities have systematic exposure to consumption risk: they pay less in bad times, when a dollar is worth most. The island economy of Chapter 1G showed how that pushes a stock's price down and its expected return up.

A behavioral addition comes from Benartzi and Thaler (1995), who called it myopic loss aversion: investors evaluate equity returns annually, so they overweight short-term losses. The more often you look, the more often a look shows a loss. Suppose, hypothetically, that equity log returns are normal with a mean of 7% a year and a volatility of 16%. A loss then comes in 33% of years (0.44 standard deviations below the mean), 45% of months and 8% of decades, and an investor who checks often demands more to bear it.

The figure draws the same hypothetical model. Stretch the horizon from a month to twenty years and watch the shaded loss area shrink.

horizon 1 year

mean 7%

volatility 16%

a look shows a loss: 33%

zero is 0.44 sd below the mean

losing looks in 20 years: 6.6 of 20

The more often you look, the more often a look shows a loss. Equity log returns are modeled as normal, with the chapter's hypothetical mean of 7% a year and volatility of 16%. Above, the return per year over one look at the chosen horizon, with the part below zero, a loss, shaded. Below, the chance that a look shows a loss against the horizon, with a month, a year and a decade marked. Lengthen the horizon: the spread narrows around the mean, and the loss area shrinks from 45% of months to 8% of decades.

5 · In practice

In practice

Vehicles. Use SPY or VOO for the United States, VXUS or IXUS for markets outside it, and VT for a single global all-country fund.
The haircut. It is small: a Sharpe ratio of 0.4 to 0.5 academically, 0.4 to 0.5 in a live ETF and 0.35 to 0.50 in your account (Chapter 13A). A broad exchange-traded fund trades rarely and tracks its index closely, so little is lost between paper and account.
Tax. In a taxable account, prefer tax-efficient ETFs. For leveraged exposure, use ES, the E-mini S&P 500 future of Chapter 2A, taxed as a Section 1256 contract at 60/40.
Diversification. Dimson and his coauthors argue strongly for global diversification. A US-only portfolio is simpler, but risks overweighting one market's lucky century.

6 · When it fails

When it fails

Multi-decade negative real returns are real: Japan from 1989 to 2010 and beyond, Germany from 1900 to 1955, and the United States from 1929 to 1949. Forward returns also depend on starting valuations, and periods with a high CAPE ratio have historically produced lower 10-year returns. A foundation premium pays on average across decades, and a single decade can hold none of it.

The CAPE ratio, the cyclically adjusted price-to-earnings ratio, divides the index's price by the average of its last ten years of inflation-adjusted earnings. Averaging smooths out the boom and bust of a single year's profits. Its inverse is a cyclically adjusted earnings yield, the earnings you buy per dollar of price, so a CAPE of 25 is an earnings yield of $1/25 = 4\%$ .

7 · A decision rule

Decision rule

Allocate: the ERP is the foundation. Make tactical reductions in size, never exits, when either condition holds:

$1/\text{CAPE}$ minus the 10-year Treasury yield stays below −1% for a sustained period.
The VIX term structure is in backwardation and, at the same time, 12-month earnings growth turns negative.

Do not try to time exits. The cost of missing a few good years vastly exceeds the benefit of avoiding a few bad ones.

Common mistake: planning on the last century

The belief is that the US ERP has been about 7% real, so you should expect about 7% real going forward. The forward expected ERP is meaningfully lower than the ERP realized from 1900 to 2000. Starting valuations are higher, and nothing ensures that the "lucky" path of US 20th-century returns repeats. Use 4% to 5% real as a planning assumption, not 7%.

The difference is large over a working life. At 7% real, a sum grows $1.07^{30} = 7.6$ times in 30 years, while at 4.5% real it grows $1.045^{30} = 3.7$ times. A plan built on 7% saves about half of what it needs if 4.5% is what arrives.

Familiar ground

The United States was the winning market of the 20th century, chosen after the fact from 35. Planning on its premium is like powering a trial from the effect seen at the best-performing center of a multicenter pilot. That center's result is part effect and part luck, and the next trial regresses toward the pooled estimate. The global panel of Dimson, Marsh and Staunton is the pooled estimate.

What to carry forward

The ERP pays because equities fail investors in bad times, and myopic loss aversion adds to it. A gap of under 5 points a year turned $1 into $107,409, against $268 in bonds, from 1900 to 2024.
The realized US premium has been about 5% to 7% over bills and 3% to 5% over long bonds, while Damodaran's implied premium for 2025 is about 4.3%.
Plan on 4% to 5% real, not 7%, and diversify globally, because the US century was one market's luck as well as its premium.
Allocate, reduce size tactically when valuations or the regime warn, and do not time exits. Expect decades in which the premium pays nothing.

8 · Check yourself

Question 1

Why does the ERP exist?

Answer

It is a compensated risk premium. Equities have systematic exposure to consumption risk: they pay least in recessions, when consumption is already low and a dollar is worth most, so investors pay less for them and expect more from them. Myopic loss aversion (Benartzi and Thaler, 1995) adds to it, because investors who evaluate returns every year overweight short-term losses.

Question 2

What is the gap between the historical realized ERP and the forward expected ERP?

Answer

The realized US premium has been about 5% to 7% a year over bills and 3% to 5% over long bonds. Damodaran's forward-looking implied ERP for 2025 is about 4.3%, which suggests compression against 20th-century averages. Higher starting valuations are the reason: by (10B.4), a higher price for the same cash lowers the implied return. In real terms, plan on 4% to 5% rather than the 7% of the last century.

Question 3

Why do Dimson, Marsh and Staunton argue for global diversification?

Answer

A single market's history is a single draw, and the United States had a lucky century. Their Yearbook covers 35 markets, 23 with full histories from 1900 to 2024, and puts the world equity real return at about 5.2% against 1.7% for bonds. Single markets have had multi-decade negative real returns, as Japan did from 1989 and Germany from 1900 to 1955, and a global portfolio does not depend on any one of them.

Question 4

State a tactical sizing rule based on valuation, and apply it to a CAPE of 30 and a 10-year Treasury yield of 4.5%.

Answer

Reduce the equity sleeve's size, without exiting, when $1/\text{CAPE}$ minus the 10-year Treasury yield stays below −1% for a sustained period. At a CAPE of 30 the earnings yield is $1/30 = 3.3\%$ , and $3.3\% - 4.5\% = -1.2\%$ . The spread is below −1%, so if it persists the rule calls for a tactical reduction, not a sale.