Risk & Portfolio Management
Lecture Notes: Expected Returns & Equity Risk Premium
Based on Fama & French (2002) | Advanced Portfolio Management
1. What Are Expected Returns & Why Do They Matter?
In finance, the expected return on an investment is the return you anticipate earning in the future.
This is one of the most fundamental — and frustratingly difficult — concepts in all of portfolio
management.
The Utility Formula
Your professor's slide shows this key equation:
Eu = Er - AV * sigma^2 + (higher moments)
Breaking it down:
• Eu = Expected Utility (how happy/satisfied you are with the investment outcome)
• Er = Expected Return (the average return you expect to earn)
• AV = Risk Aversion Coefficient (how much you hate risk — higher means you dislike risk
more)
• sigma^2 = Variance (the risk measure — how volatile/unpredictable returns are)
• = higher statistical moments like skewness (asymmetry) and kurtosis (fat tails)
You only invest in risky assets if the extra return (Er) compensates you enough for
KEY
the risk (sigma^2) scaled by how risk-averse you are (AV). This is the fundamental
INSIGHT
trade-off in all of investing.
Why Is This So Difficult?
We observe 'r' (actual realized returns) all the time in market data. But 'Er' (what we EXPECTED
before the fact) is unobservable — we can only estimate it. This makes pricing assets and computing
cost of capital extremely challenging.
• Cost of capital for firms depends on the expected return investors demand
• Portfolio allocation depends on expected returns of different assets
• The gap between expected and realized returns creates the entire puzzle this lecture
addresses
2. The Equity Risk Premium (ERP) — What Is It?
The Equity Risk Premium (ERP) is the extra return that investors demand for holding stocks instead
of a 'risk-free' asset like government bonds.
ERP = E(Rm) - Rf
, Where:
• E(Rm) = Expected return on the market (stocks)
• Rf = Risk-free rate (e.g., US Treasury yield)
This premium is compensation for the volatility and uncertainty of equity returns. If stocks weren't
riskier, no rational investor would need to be paid extra to hold them.
As of the slides (early 2026): The US ERP is estimated around 2.29%, which is
REAL
historically very LOW. The Eurozone ERP is around 5-6%. This gap matters
WORLD
enormously for asset allocation.
How Much Is The ERP? Experts Disagree Wildly
A 2001 survey of academics and practitioners showed ERP estimates ranging from 0% to 7% — a
massive spread. By 2021 the estimates shifted upward (3% to 6%+). This disagreement is not due to
incompetence; it reflects genuine difficulty in the measurement.
Period Source/Study ERP Estimate
2001 Arnott & Bernstein 0.0%
2001 Campbell & Shiller 0.0%
2001 Siegel 2.0%
2001 Graham & Harvey 4.0%
2001 Welch 6.0 – 7.0%
2001 Average of all 3.7%
2023 Siegel & McCaffrey (CFA) 3 – 6% range (shifted
right)
3. The Fama & French Approach (2001/2002)
Eugene Fama and Kenneth French (both Nobel-level researchers) wrote 'The Equity Premium' to
systematically estimate expected returns using market fundamentals rather than just averaging past
returns.
The Core Idea: Decompose Returns into Two Parts
The average stock return = dividend yield + capital gain. Formally:
A(Rt) = A(Dt/Pt-1) + A(GPt) ...(equation 1)
Where:
• A(Rt) = Average total return on stocks
• A(Dt/Pt-1) = Average dividend yield (dividends paid / previous price)
• A(GPt) = Average capital gain = (Pt - Pt-1) / Pt-1
Lecture Notes: Expected Returns & Equity Risk Premium
Based on Fama & French (2002) | Advanced Portfolio Management
1. What Are Expected Returns & Why Do They Matter?
In finance, the expected return on an investment is the return you anticipate earning in the future.
This is one of the most fundamental — and frustratingly difficult — concepts in all of portfolio
management.
The Utility Formula
Your professor's slide shows this key equation:
Eu = Er - AV * sigma^2 + (higher moments)
Breaking it down:
• Eu = Expected Utility (how happy/satisfied you are with the investment outcome)
• Er = Expected Return (the average return you expect to earn)
• AV = Risk Aversion Coefficient (how much you hate risk — higher means you dislike risk
more)
• sigma^2 = Variance (the risk measure — how volatile/unpredictable returns are)
• = higher statistical moments like skewness (asymmetry) and kurtosis (fat tails)
You only invest in risky assets if the extra return (Er) compensates you enough for
KEY
the risk (sigma^2) scaled by how risk-averse you are (AV). This is the fundamental
INSIGHT
trade-off in all of investing.
Why Is This So Difficult?
We observe 'r' (actual realized returns) all the time in market data. But 'Er' (what we EXPECTED
before the fact) is unobservable — we can only estimate it. This makes pricing assets and computing
cost of capital extremely challenging.
• Cost of capital for firms depends on the expected return investors demand
• Portfolio allocation depends on expected returns of different assets
• The gap between expected and realized returns creates the entire puzzle this lecture
addresses
2. The Equity Risk Premium (ERP) — What Is It?
The Equity Risk Premium (ERP) is the extra return that investors demand for holding stocks instead
of a 'risk-free' asset like government bonds.
ERP = E(Rm) - Rf
, Where:
• E(Rm) = Expected return on the market (stocks)
• Rf = Risk-free rate (e.g., US Treasury yield)
This premium is compensation for the volatility and uncertainty of equity returns. If stocks weren't
riskier, no rational investor would need to be paid extra to hold them.
As of the slides (early 2026): The US ERP is estimated around 2.29%, which is
REAL
historically very LOW. The Eurozone ERP is around 5-6%. This gap matters
WORLD
enormously for asset allocation.
How Much Is The ERP? Experts Disagree Wildly
A 2001 survey of academics and practitioners showed ERP estimates ranging from 0% to 7% — a
massive spread. By 2021 the estimates shifted upward (3% to 6%+). This disagreement is not due to
incompetence; it reflects genuine difficulty in the measurement.
Period Source/Study ERP Estimate
2001 Arnott & Bernstein 0.0%
2001 Campbell & Shiller 0.0%
2001 Siegel 2.0%
2001 Graham & Harvey 4.0%
2001 Welch 6.0 – 7.0%
2001 Average of all 3.7%
2023 Siegel & McCaffrey (CFA) 3 – 6% range (shifted
right)
3. The Fama & French Approach (2001/2002)
Eugene Fama and Kenneth French (both Nobel-level researchers) wrote 'The Equity Premium' to
systematically estimate expected returns using market fundamentals rather than just averaging past
returns.
The Core Idea: Decompose Returns into Two Parts
The average stock return = dividend yield + capital gain. Formally:
A(Rt) = A(Dt/Pt-1) + A(GPt) ...(equation 1)
Where:
• A(Rt) = Average total return on stocks
• A(Dt/Pt-1) = Average dividend yield (dividends paid / previous price)
• A(GPt) = Average capital gain = (Pt - Pt-1) / Pt-1
