Chapters 7 & 8 — Bodie, Kane & Marcus
Monmouth University
Risk-return in U.S. markets, random walks, and why prices are hard to predict
Assumptions, CML, SML, beta, alpha — the workhorse pricing model
APT, multifactor models, Fama-French, and CAPM's real-world limitations
Three forms, anomalies, active vs. passive management, and market efficiency
Big picture: Chapter 6 told us how to build efficient portfolios. Chapter 7 asks: if everyone does this, what happens to prices? Chapter 8 asks: do prices actually behave that way?
What does the data actually look like?
Historical annual data (1927–2020) shows the fundamental tradeoff:
| Asset Class | Avg Return | Std Dev |
|---|---|---|
| T-Bills | 3.3% | 3.1% |
| T-Bonds | 5.6% | 7.7% |
| Corporate Bonds | 6.4% | 7.0% |
| Large Stocks | 11.7% | 20.0% |
| Small Stocks | 16.3% | 31.7% |
Key insight: Higher risk → higher average return. But is this relationship linear? CAPM says yes.
Stock price changes are independently and identically distributed (i.i.d.) over time.
Analogy: If you knew a stock would rise tomorrow, you'd buy today — pushing the price up today instead. The opportunity self-destructs.
On Jan 28, 1986, the Challenger exploded. Within minutes, the market correctly identified Morton Thiokol (O-ring maker) as responsible — its stock dropped 12% while other contractors barely moved.
Implication: Markets process information extremely fast. By the time you read the news, the price has already adjusted.
Scatterplots of returntoday vs. returnyesterday look like random blobs — no upward or downward slope.
| Data | Correlation |
|---|---|
| IBM Daily (1927–2016) | ≈ 0.01 |
| S&P Monthly (1927–2020) | ≈ 0.03 |
| IBM vs. Market | ≈ 0.55 |
Serial correlation ≈ 0 means past returns don't predict future returns. But cross-sectional correlation (stock vs. market) is very real — that's beta.
What return should you expect for bearing risk?
Reality check: These assumptions are obviously unrealistic. But CAPM's value isn't in its assumptions — it's in its predictions. If the SML approximately holds, the model is useful even if assumptions are violated.
The CML is the efficient frontier when a risk-free asset exists. Its slope is the market's Sharpe ratio.
Separation theorem: The investment decision (pick the market portfolio) is separate from the financing decision (how much to borrow/lend at rf).
Conservative investors hold more rf and less M. Aggressive investors lever up beyond 100% in M.
Unlike the CML (which plots σ), the SML plots beta on the x-axis. It prices any asset, not just efficient portfolios.
α > 0: Asset plots above SML → underpriced, buy
α < 0: Asset plots below SML → overpriced, sell
α = 0: Asset is fairly priced by CAPM
Given β, compute the hurdle rate for any asset:
Discount project cash flows at CAPM rate to find NPV:
Alpha = actual return minus CAPM-predicted return:
A project has β = 1.7, rf = 9%, E(rM) = 19%. Cash flows: −$20M today, $10M in years 1–3.
Step 1: k = 9% + 1.7(19% − 9%) = 9% + 17% = 26%
Step 2: NPV = 10/1.26 + 10/1.26² + 10/1.26³ − 20 = 7.94 + 6.30 + 5.00 − 20 = −$0.75M
Decision: NPV < 0 → Reject the project.
Given the information below:
| Parameter | Value |
|---|---|
| E(rM) | 14% |
| rf | 5% |
| Portfolio A β | 1.5 |
| Portfolio A actual return | 20% |
E(r) = rf + β × [E(rM) − rf]
α = Actual − Expected
1. E(r) = 5 + 1.5 × (14 − 5) = 5 + 13.5 = 18.5%
2. α = 20 − 18.5 = 1.5% (positive alpha → outperformed CAPM prediction)
APT, multifactor models, and real-world limitations
| Line | X-axis | Y-axis | Applies to | Purpose |
|---|---|---|---|---|
| CML | σ (total risk) | E(r) | Efficient portfolios only | Optimal risk-return tradeoff |
| SML | β (systematic risk) | E(r) | All assets | Pricing / fair return |
| SCL | rM − rf | ri − rf | Single asset | Estimate α and β via regression |
| CAL | σ | E(r) | Any risky + rf | Investor's portfolio line |
Key distinction: CML uses total risk (σ) — only efficient portfolios lie on it. SML uses systematic risk (β) — every asset should lie on it if CAPM holds.
where RPj = risk premium for factor j
| CAPM | APT | |
|---|---|---|
| Factors | 1 (market) | Multiple |
| Assumptions | Strong | Weaker |
| Identifies factors? | Yes (market) | No |
| Testable? | Joint test issue | Same issue |
APT weakness: It doesn't tell you which factors matter. CAPM at least identifies the market portfolio.
Same as CAPM — reward for bearing market risk
Size premium: small stocks tend to outperform large stocks
Value premium: high book-to-market (value) stocks outperform growth stocks
Factor risk premiums: Industrial Production = 6%, Inflation = −2%
Stock X: βIP = 1.0, βINF = 0.4, rf = 6%
E(r) = 6 + 1.0(6) + 0.4(−2) = 6 + 6 − 0.8 = 11.2%
Bottom line: CAPM is like Newtonian physics — it's wrong in detail (Einstein was more accurate), but it's simple, intuitive, and good enough for most practical purposes. Most of finance still uses it as a first approximation.
A project has β = 1.7, rf = 9%, E(rM) = 19%. Cash flows (in $M):
| Year | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| CF | −$20 | $10 | $10 | $10 |
k = rf + β(E(rM)−rf)
PV of CFs − initial cost
Hint: at what k does NPV=0?
1. k = 9 + 1.7(19−9) = 9 + 17 = 26%
2. NPV = 10/1.26 + 10/1.26² + 10/1.26³ − 20 = 7.94 + 6.30 + 5.00 − 20 = −$0.75M → Reject
3. IRR ≈ 23.4% (from 10/1.234 + 10/1.234² + 10/1.234³ = 20). βmax = (23.4 − 9)/10 = 1.44
Are markets smarter than you?
A market is efficient with respect to an information set if it is impossible to make economic profits by trading on that information.
Prices reflect all past trading data (prices, volume, short interest).
Implication: Technical analysis is useless.
Prices reflect all publicly available information (financials, news, analyst reports).
Implication: Fundamental analysis is useless.
Prices reflect all information, including private/insider info.
Implication: Even insiders can't profit.
Hierarchy: Strong ⊃ Semi-Strong ⊃ Weak. Evidence generally supports weak and semi-strong forms; strong form is rejected (insiders do earn abnormal returns).
If a company announces higher-than-expected earnings and the stock doesn't move, which form of EMH does this support?
Semi-strong form. The earnings announcement is public information. If the price doesn't move, it means the market had already incorporated this information before the announcement (perhaps from analyst estimates, industry trends, or management guidance).
This does not support strong form — it's about public info, not insider info.
Small-cap stocks earn ~3% more per year than large-cap (1927–2020). Has weakened since discovery.
High book-to-market (value) stocks outperform low B/M (growth) by ~4% per year.
Past winners continue to win for 3–12 months; past losers continue to lose.
Are these real? Debate continues: (1) Data mining / look-ahead bias? (2) Risk premiums for bearing these exposures? (3) Behavioral mispricing? Fama argues risk; Shiller argues behavior.
Uses past price patterns, volume, momentum indicators to predict future prices.
EMH says: Useless if weak form holds. Past prices already reflected in current price.
Uses financial data (earnings, growth, valuation ratios) to find mispriced stocks.
EMH says: Useless if semi-strong form holds. Public info already in price.
Paradox: If nobody does fundamental analysis because markets are efficient... who keeps them efficient? Grossman-Stiglitz (1980) argued there must be enough profit to compensate analysts for the cost of research.
| Form | Test Method | Evidence | Verdict |
|---|---|---|---|
| Weak | Serial correlation, filter rules, trading rules | Autocorrelation ≈ 0; some short-term momentum | Mostly supported |
| Semi-Strong | Event studies (earnings, splits, M&A) | Prices adjust within minutes of announcements | Mostly supported |
| Strong | Insider trading studies, SEC filings | Insiders earn significant abnormal returns | Rejected |
The mutual fund test: ~50% of actively managed funds beat the S&P 500 in any given year — exactly what you'd expect from chance. And winners don't repeat consistently. This is strong evidence for semi-strong efficiency.
Bogle's insight: After fees and taxes, most active managers underperform the index.
The hurdle: An active manager charging 1% needs to generate >1% alpha consistently to justify their fee.
Even if you can't beat the market, portfolio management still adds value:
Eliminate firm-specific risk for free. The market doesn't reward unsystematic risk.
The split between stocks, bonds, and cash matters more than stock picking. Match risk to your horizon and risk aversion.
Tax-loss harvesting, asset location (taxable vs. tax-deferred accounts), and minimizing turnover.
Periodically restore target weights to maintain your desired risk level.
The efficient market investor: Hold a diversified index, choose an appropriate stock/bond mix, minimize taxes and fees, rebalance periodically. Simple — but most investors don't do it.
For each scenario, decide if it is consistent with or a violation of EMH:
A. Nearly half of professionally managed mutual funds beat the S&P 500 in a typical year.
B. Money managers who outperform one year are likely to outperform the next.
C. Stock prices are more volatile in January than other months.
D. Stocks announcing increased earnings in January outperform in February.
E. Stocks that perform well one week perform poorly the next.
A. Consistent. ~50% beating the index is what chance predicts. No skill required.
B. Violation. Persistent outperformance suggests skill, not luck — violates semi-strong EMH.
C. Consistent. Higher volatility ≠ predictable returns. Volatility clustering doesn't create profit opportunities.
D. Violation. If the earnings surprise is public in Jan, prices should adjust immediately — not drift into Feb (semi-strong violation).
E. Violation (weak form). This predictable reversal pattern could be exploited using past price data.
Markets are mostly efficient, most of the time. But:
The $100 bill on the sidewalk: An economist says "It can't be real — someone would have picked it up." A finance professor says "It might be real, but by the time you bend down, someone else will grab it." The truth: $100 bills do appear sometimes, but you can't build a reliable strategy around finding them.
| Formula | Name | Use |
|---|---|---|
| E(ri) = rf + βi[E(rM) − rf] | CAPM / SML | Expected return given beta |
| αi = ri − {rf + βi[rM − rf]} | Jensen's Alpha | Abnormal return vs. CAPM |
| E(rC) = rf + [E(rM)−rf]/σM × σC | CML | Efficient portfolio pricing |
| E(ri) = rf + Σ βijRPj | APT / Multifactor | Multi-factor expected return |
| E(r)−rf = βM(rM−rf) + βSSMB + βVHML | Fama-French 3-Factor | Size + value adjusted return |
Given: rf = 3%, E(rM) = 11%, Stock X has β = 1.4 and actual return = 15%
CAPM expected return
α = actual − expected
Overpriced, Underpriced, or Fair?
1. E(r) = 3 + 1.4(11−3) = 3 + 11.2 = 14.2%
2. α = 15 − 14.2 = 0.8%
3. α > 0 → stock plots above SML → Underpriced (buy signal)
Given: rf = 5%, Factor premiums: Industrial Production RP = 8%, Inflation RP = −3%
Stock Y: βIP = 1.2, βINF = 0.6. Actual return = 16%.
E(r) = rf + βIP·RPIP + βINF·RPINF
α = actual − expected
1. E(r) = 5 + 1.2(8) + 0.6(−3) = 5 + 9.6 − 1.8 = 12.8%
2. α = 16 − 12.8 = 3.2%