What it means
An equity premium compares equity returns with returns on an appropriate relatively safe asset, and the puzzle asks why that difference has historically been so large relative to what a particular model can explain. Rajnish Mehra and Edward Prescott first posed the puzzle in 1985.
The model, dataset and safe-asset comparison must be identified before interpreting the result. Stocks can fall sharply and expose investors to uncertain wealth, so a positive premium can be consistent with compensation for risk.
The puzzle is more specific: conventional consumption-based models have struggled to explain the observed magnitude without assumptions that may be difficult to reconcile with other economic behaviour. Consumption matters because these models connect investment payoffs to people's economic well-being, so a payoff when consumption is already high may be less valuable than an equal payoff during hardship.
Risk aversion measures how strongly investors dislike uncertain outcomes in the model, and raising it can increase the premium the model predicts. However, very high assumed values may create other problems, so a parameter should not be treated as a freely adjustable explanation without checking its implications elsewhere.
Explanations studied in the literature include changes to preferences, market participation, incomplete markets and unusually severe economic risks, but none is universally accepted as the single solution. Historical evidence is not a forward contract, because realised returns depend on the observation period, market and asset definition.
A large premium in one dataset does not promise that a new investor will receive that amount or that the same result holds for every country. Arithmetic and geometric averages also answer different questions, and mixing them can create an apparent disagreement before any economic theory is considered.
Mehra's review of the puzzle describes the discrepancy between standard intertemporal models and historical financial-market statistics, discusses attempts to improve the models and notes their limitations. Its historical analysis should not be converted into a precise current forecast for a portfolio or a corporate valuation.
Analysts may choose a forecast premium for valuation while acknowledging the underlying academic debate, and a practical assumption can be useful without proving that a theoretical model explains all the evidence. Distinguish a discount-rate input from an expected investment result, since a premium used in a valuation model is an assumption with sensitivity, not cash income already earned.
Show how changing that input affects a project's assessed value rather than citing the puzzle as evidence for one exact rate. For a non-finance manager, ask what returns were measured, which safe asset was used and which model is being challenged, and separate historical observation, theoretical explanation and forward-looking assumption.
In practice
Real-world examples.
Example
A valuation uses a historical stock-return premium as a forecast without explaining the sample. The reviewer asks for the period, market, benchmark and averaging method, then tests a range rather than treating the historical number as promised income. The final valuation shows results under a low, middle and high premium.
Example
Two analysts report different premiums because one compares shares with bills and the other with long-term bonds. They align the benchmark and return definitions before interpreting the difference as a disagreement about investor behaviour. Once aligned, most of the gap disappears.
Example
A manager says that shares must be low risk because their average premium was positive. Finance shows that average returns can coexist with severe losses and that the puzzle concerns model explanation, not the absence of investment risk. The manager revises the planning assumptions to include a bad-decade scenario.
Formula
Calculation
Realised equity premium = Equity return - Safe-asset return
Worked example. A 9% equity return compared with a 3% bill return gives a 9% - 3% = 6-percentage-point premium for that period. This subtraction describes an observation; explaining its historical magnitude through an economic model is the separate puzzle.
Sensitivity of a valuation to the premium assumption. A fictional project is expected to produce $90,000 a year indefinitely, with a bill rate of 3%.
- With a 6% premium the discount rate is 3% + 6% = 9%, and the value is $90,000 / 0.09 = $1,000,000.
- With a 3% premium the discount rate is 6%, and the value is $90,000 / 0.06 = $1,500,000.
The same cash flows are worth $500,000 more under the lower premium, which shows why the assumption deserves a range rather than a single figure.Case study
Seen in the real world.
Fictional case: A pension committee treats a long historical equity premium as a fixed future return. Its adviser explains the benchmark and model debate, then compares funding outcomes under lower and higher premiums and severe loss scenarios. The committee retains equity exposure but stops presenting its planning assumption as a certainty. The adviser also shows how contribution rates would need to change if the premium were lower than assumed, and what the scheme could tolerate if equities fell sharply early in the period.
The committee sets a range for its planning assumption and agrees to review it with each valuation. The illustrative outcome is a plan that keeps its equity allocation but is no longer built on a single historical number. The committee's papers now state the benchmark, the period and the averaging method behind every assumed return.
Watch out
Common mistakes.
- Treating the historical premium as a guaranteed future return.
- Confusing the equity premium puzzle with a claim that stocks carry no risk.
- Mixing benchmarks or average-return measures when comparing empirical results.
Questions
People also ask.
Does the puzzle mean equities should not earn a risk premium?
No. It concerns the magnitude relative to predictions from particular models.
Does a large historical premium guarantee future outperformance?
No. Future returns and the relevant investment horizon remain uncertain.
Is there one universally accepted explanation?
No. Different theories address parts of the evidence with their own assumptions and limits.
From the founder's library
Take it further with the book.
Build your financial confidence beyond this definition. Shihan's full-length guide, Accounting Fundamentals, takes the same plain-English approach and turns it into a complete, practical playbook for non-finance managers, business owners and students - with chapter-end quiz answers and presentation slides included.
25% off with code MMHQ25, applied at checkout. Priced in USD - checkout may show the equivalent in your local currency.
View the book and save 25%Related