Questions: Equity Risk Premium and Market Return Expectations

Question 1

An analyst uses the CAPM to value a stock with β = 2.0. The current risk-free rate is 3% and the equity risk premium is estimated at 5%. What expected return should she use?

• A. 8% — the risk-free rate plus the ERP, unadjusted for beta
• B. 10% — she should halve the ERP since beta exceeds 1.0
• C. 13% — the risk-free rate plus beta times the ERP
• D. 5% — only the ERP matters for equities, not the risk-free rate

Answer: (C)

The CAPM formula is E[R] = r_f + β × ERP = 3% + 2.0 × 5% = 13%. The ERP is the return premium for one unit of market risk (β = 1). A stock with β = 2.0 has twice the systematic risk of the market, so it earns twice the risk premium above the risk-free rate. Option A (8%) ignores beta entirely; this would only be correct for a stock with β = 1. The ERP is the slope of the security market line — multiply it by beta to get each stock's specific risk premium.

Question 2

When current price-to-earnings (P/E) ratios in the stock market are extremely high, what does the forward-looking equity risk premium estimate typically show?

• A. A higher-than-average ERP, because high prices signal high future returns
• B. A lower-than-average ERP, because the market has priced in optimistic expectations leaving little additional return
• C. An unchanged ERP, because the ERP is a long-run constant independent of current valuations
• D. A higher-than-average ERP, because high P/E ratios indicate elevated market risk

Answer: (B)

The forward-looking ERP uses E[R] = D₁/P₀ + g (Gordon Growth Model), then subtracts the risk-free rate. When prices (P₀) are high relative to earnings/dividends, the implied expected return falls, and so does the ERP. High valuations mean investors are paying a lot for each dollar of earnings — implying they accept a lower return going forward. This is the opposite of what option A claims: high past prices reflect past returns, not high future returns. The late 1990s dotcom bubble and 2020s valuations both showed compressed forward-looking ERPs.

Question 3

The equity risk premium is directly observable in real-time market data.

• T. True
• F. False

Answer: False

False. The ERP is expected future returns minus the risk-free rate — and expected future returns are unobservable. We can only estimate the ERP, using either historical realized returns (backward-looking) or current prices and earnings/dividend forecasts (forward-looking). Both approaches have significant limitations: historical estimates reflect luck and survivorship bias; forward-looking estimates depend on growth assumptions. This is why estimates of the ERP range from about 3% to 8% depending on method and time period, and why it remains a central source of uncertainty in valuation.

Question 4

In the CAPM framework, the equity risk premium equals the expected return of the market portfolio minus the risk-free rate.

• T. True
• F. False

Answer: True

True. In CAPM, the security market line is E[R_i] = r_f + β_i × (E[R_m] − r_f), where (E[R_m] − r_f) is the equity risk premium. The market portfolio by definition has β = 1, so its expected return is E[R_m] = r_f + 1 × ERP. The ERP is precisely the excess expected return of the market over the risk-free rate — the slope of the SML. Every other asset's expected return is scaled from this baseline by its beta.

Question 5

What is the equity premium puzzle, and why does it challenge standard consumption-based asset pricing models?

Model answer: The equity premium puzzle (Mehra and Prescott, 1985) is the observation that historical U.S. stock returns have exceeded risk-free returns by about 5–7% annually, while standard consumption-based models predict a premium of only 1–2%. In these models, investors care about consumption smoothing; to justify a 6% premium, investors would need implausibly high risk aversion coefficients. The puzzle matters because standard models cannot explain why equities demand so much compensation for their risk, suggesting that either the models are wrong (omitting habit formation, rare disaster risk, or market frictions) or that historical returns are not a reliable guide to future expectations.

The puzzle is not merely academic: whatever drives the ERP also determines the discount rate used to value every company and investment. If the ERP is explained by rare disaster risk, then the premium could vanish in a world with fewer catastrophic risks. If it reflects investor irrationality or limited participation, the implications for capital allocation differ entirely. The equity premium puzzle is one reason financial economists cannot simply look up the ERP — the right number depends on which theory of risk and compensation you believe.