Over the 90 years from 1889 to 1978, two types of investments told very different stories.[1]
Stocks — ownership in American companies — earned an average real return of about 7% per year.
Treasury bills — short-term loans to the government, about the safest investment possible — earned only about 1% per year.
The gap between them — roughly 6 percentage points every year, for nine decades — is called the equity premium.[1]
Six percent compounded over decades is enormous. A dollar invested in stocks in 1889 would be worth many times more than a dollar in bonds over the same period.
Mehra and Prescott's Table 1 shows returns across ten decades.[1] The equity premium fluctuates, but persists in every sub-period. Select a metric to highlight:
| Period | Consumption Growth | Risk-Free Rate | Risk Premium | S&P 500 |
|---|
The question is simple: why is this gap so large?
Economics has a standard explanation for why riskier investments earn higher returns. Mehra and Prescott tested whether it could account for the 6% gap.[1]
Imagine you are deciding between stocks and bonds. Stocks are riskier — their returns bounce around. Bonds are safe and predictable. Stocks must offer a higher average return to compensate for that risk. Otherwise everyone would sell stocks, and prices would fall until expected returns rose enough to attract buyers back.
How much extra return is "enough"? That depends on how risk-averse the typical investor is — and specifically, on how much the return on stocks moves together with the investor's overall consumption.[4][5]
Answer five quick gambles. Your choices will reveal your implied coefficient of relative risk aversion (α).
An asset that pays well when times are already good is not valuable as insurance. You do not need extra money when you are already comfortable.
Stocks tend to do well when the economy is booming — exactly when people are consuming more. They do badly during recessions, when people are already cutting back.
Because stocks pay off in good times but fail in bad times, they are a poor hedge against consumption risk. Investors need a higher return to hold them. The bigger the covariance between stock returns and consumption growth, and the more risk-averse the investor, the higher the required premium.[4]
This intuition is captured by the Consumption-CAPM:[4]
Expected equity premium ≈ α × Cov(stock returns, consumption growth)
Here, α is the coefficient of relative risk aversion. The higher it is, the more compensation investors demand.
Mehra and Prescott build an economy with one representative agent who has power utility preferences. They calibrate to U.S. data — average consumption growth of 1.83% per year with a standard deviation of 3.57% — and ask: for what values of α can this economy produce a 6% equity premium?[1]
The answer: it cannot. Not for any plausible value of risk aversion.[1]
With α in the plausible range (1 to 10), the model produces at most 0.35% — more than 17 times smaller than the observed 6.18%.[1]
You can push α to extreme values and eventually match the premium. But at those levels, the investor would pay absurd amounts to avoid tiny gambles. No real person behaves this way.[3]
There is a second problem. As α rises, the predicted risk-free rate also climbs far above the observed 0.8%.[2]
The root cause: aggregate consumption is remarkably smooth. Year-to-year per capita consumption barely moves — its standard deviation is only 3.57%.[1]
If consumption does not swing much, then from the representative investor's perspective, stocks are barely riskier than bonds in terms of what actually matters (their impact on consumption). The covariance between stock returns and consumption growth is small.
A small covariance multiplied by a reasonable α gives a small equity premium. To make it 6%, you need an enormous α — one that implies behavior nobody actually displays.
This is the equity premium puzzle.[1]
Four years later, Philippe Weil asked: what if the problem is that standard utility ties two unrelated things together?[2]
In power utility, the parameter α controls two things at once:
1. Risk aversion — how much you dislike gambles
2. Intertemporal elasticity of substitution (IES) — how willing you are to shift consumption between today and tomorrow
These are locked as inverses: IES = 1/α. Raising α to explain the equity premium automatically makes the investor want very smooth consumption over time (low IES), which has devastating consequences for the risk-free rate.[2]
Weil uses Epstein-Zin preferences (also called Kreps-Porteus preferences), which give two independent knobs:[6]
γ — controls risk aversion only
1/ρ — controls intertemporal substitution only
The hope: set γ high to explain the equity premium, and set 1/ρ independently to keep the risk-free rate reasonable.
Weil proves that the equity premium depends almost entirely on risk aversion alone.[2] The IES knob barely affects it. When consumption growth is i.i.d., the IES is exactly irrelevant to the equity premium.
Moving the IES slider barely changes the equity premium — it just makes the risk-free rate problem better or worse. The extra degree of freedom does not help.[2]
The table below reproduces Weil's Table 1 (β = 0.95).[2] Each cell shows the model's predicted equity premium and risk-free rate for a combination of risk aversion (γ) and IES (1/ρ). Toggle between views:
| IES \ CRRA | γ = 0.5 | γ = 1 | γ = 5 | γ = 10 |
|---|
Weil does not solve the equity premium puzzle. He discovers a second puzzle hiding behind it.[2]
Matching the large equity premium requires high risk aversion (γ around 40+). That has not changed from Mehra and Prescott.[1]
In a growing economy (U.S. consumption grows ~1.83%/year), if investors strongly prefer smooth consumption over time, they need a high interest rate to persuade them to save and allow consumption to grow. Low IES means "I refuse to have different consumption levels in different years."
Empirical estimates suggest people do have a low IES. But the observed risk-free rate is only 0.8%. The model predicts it should be much higher (10–25%). Why are people saving so much at such a low interest rate?
This is the risk-free rate puzzle.[2]
The two puzzles are two sides of the same coin. The equity premium puzzle demands high risk aversion. High risk aversion forces low IES. Low IES means a high predicted risk-free rate. But the observed risk-free rate is low. No parameter combination makes both facts fit.[3]
In the decade after Mehra and Prescott, economists tried every available avenue. Kocherlakota surveyed them all.[3]
Badges show whether the approach can explain the equity premium (EP) and the risk-free rate (RF).
The idea: Separate risk aversion from intertemporal substitution, giving the model two independent knobs instead of one.[6][2]
On the risk-free rate: It works. By setting IES independently, the model can match the low observed risk-free rate.
The idea: Happiness depends on past consumption as a reference point. If you drove a BMW last year, going back to a cheaper car feels painful. This habit formation effectively amplifies risk aversion.[7]
The idea: People care about how they compare to everyone else. If everyone's consumption falls, you feel extra pain beyond your own loss.[8]
The idea: Real people cannot insure against everything — job loss, health shocks, divorce. Individual consumption is more volatile than aggregate. Maybe the representative agent misses this extra risk.[9]
The idea: If people cannot borrow against future income, they hold extra safe assets as a buffer, pushing the risk-free rate down.
The idea: Stocks are more expensive to trade than bonds (brokerage fees, bid-ask spreads). Part of the equity premium compensates for these costs, not for risk.[11]
The idea: Investors fear catastrophe — a Great Depression, a war. Even if these events did not occur in the 90-year sample, the fear could justify a high equity premium.[12]
The idea: We study the U.S. because it survived and thrived. Collapsed markets (Russia 1917, Germany 1945) are absent from the data. The observed equity premium may overstate the true expected premium.[13]
Aggregate consumption is too smooth relative to stock returns for any reasonably risk-averse investor to demand a 6% premium for holding stocks over bonds. Every modification to preferences, market structure, or statistical assumptions tried over the first decade of research failed to convincingly change this arithmetic.[3]
The puzzle matters beyond finance. The risk-free rate puzzle means we do not fully understand why people save. The equity premium puzzle means we do not understand how people perceive and price aggregate risk. Until these are resolved, our models of the macroeconomy have a gap at their center.[3]