MBUS 813 — Session 6

Risk, Return & Market Theory

Queen's Smith AMBA 2026 · Exam-Ready Prep
Portfolios & MPT Efficient Market Hypothesis Behavioural Finance Anomalies
Block 1 — Risk, Return & Portfolio Theory

Holding Period Return (HPR)

The foundational single-period return measure capturing both income and capital gain/loss.

HPR = [ I + (P₁ − P₀) ] ÷ P₀
I = income (coupon or dividend) · P₁ = ending price · P₀ = beginning price
Worked Example

Bond: Coupon = 8%, YTM = 8%, N = 30 years, P₀ = $1,000

Interest rates fall → P₁ = $1,050

HPR = [ 80 + (1,050 − 1,000) ] ÷ 1,000 = 130 ÷ 1,000

HPR = 13%

8% coupon yield + 5% capital gain. Rates fell → price rose — the Session 2 inverse relationship in action.

Exam watch: HPR decomposition matters. If rates rise, P₁ falls and HPR may be below coupon yield or even negative despite receiving coupons.

Risk = Standard Deviation

Standard deviation (σ) measures how much returns deviate from the mean — the course's primary risk proxy.

68.3%
of returns within ±1σ
95.4%
of returns within ±2σ
99.7%
of returns within ±3σ

Canadian Historical Returns (1957–2009)

Asset Avg Annual Return Std Dev (Risk) Key Point
Common Stocks 10.70% 17.05% Highest return, highest risk
Long Bonds 8.52% 9.80% Intermediate risk/return
Treasury Bills ★ 6.35% 3.67% Risk-free rate proxy
Inflation 4.01% 3.18% Real return benchmark
Equity Risk Premium = Stock return − T-Bill rate = 10.70% − 6.35% = 4.35%. This is the extra compensation investors demand for bearing stock market risk.

Modern Portfolio Theory (MPT) & Correlation

The core insight of MPT: Portfolio return is a weighted average of individual returns — but portfolio risk is NOT.

r̄ₚ = w₁r̄₁ + w₂r̄₂
Portfolio expected return = simple weighted average
σₚ < w₁σ₁ + w₂σ₂
Portfolio risk is LESS than the weighted average — as long as ρ < +1

The Correlation Coefficient (ρ)

Correlation is the engine of diversification. It ranges from −1 to +1.

ρ ValueRelationshipDiversification Benefit
+1.0 Perfect positive None — portfolio risk = weighted average
0 to +1 Partial positive Moderate — most real-world asset pairs
~0 No relationship Substantial
−1.0 Perfect negative Maximum — theoretically riskless portfolio possible (basis for hedging)

Real-World Correlations (Canada, 1938–2011)

Asset PairρImplication
Canadian vs. U.S. Stocks 0.686 Moderate positive — some diversification benefit from going international
Canadian Stocks vs. T-Bills −0.077 Near zero (slightly negative) — excellent diversifier; holding some T-bills dramatically cuts portfolio risk
Rule: The lower the correlation, the greater the diversification benefit. Choose assets that don't move together.
Diversification & Risk Decomposition

Total Risk = Two Components

Market (Systematic) Risk — CANNOT diversify away
Unique (Non-Systematic) Risk — CAN diversify away
TypeAlso CalledDiversifiable?Examples
Market Risk Systematic, Non-diversifiable No ✗ Recessions, interest rate changes, inflation shocks
Unique Risk Non-systematic, Diversifiable, Idiosyncratic Yes ✓ CEO departure, product recall, lawsuit, fire at plant
As you add more stocks, unique risk falls rapidly then flattens. The floor you hit is market risk — it cannot be eliminated regardless of how many securities you hold.

How Many Stocks Are Enough?

SourceRecommended NumberRationale
Benjamin Graham (1949) 10–30 stocks Adequate diversification; beyond this, transaction costs offset marginal benefit
Modern studies 50–100+ More recent data shows higher number needed for true diversification
Practical advice (Bernstein) Broad index funds Low cost, hundreds/thousands of stocks, eliminates selection risk

International Diversification

Adding international stocks to a domestic-only portfolio lowers the systematic risk floor further — domestic-only portfolios plateau at a higher risk level than globally diversified portfolios.

Note: Global market integration has increased correlations between country markets since 2000 (especially during crises), reducing but not eliminating the international diversification benefit.
Efficient Market Hypothesis (EMH)

Three Forms of Market Efficiency

Definition: An efficient market is one where prices quickly and relatively accurately reflect all relevant available information, so prices are correct on average.

Form 1

Weak Form

Prices reflect all past market data — price history and volume.

Technical analysis (chart patterns) is useless.

Well Supported ✓
Form 2

Semi-Strong Form

Prices reflect all publicly available information — earnings, dividends, filings, news.

Fundamental analysis cannot generate consistent excess returns.

Largely Supported (with exceptions) ⚠
Form 3

Strong Form

Prices reflect all information — including private/inside information.

Even insiders cannot earn abnormal returns.

Not Supported ✗
The three forms are cumulative: semi-strong encompasses weak form; strong form encompasses both. If semi-strong holds, weak form must also hold.

Four Assumptions Underlying Efficient Markets

  1. Large number of rational, profit-maximizing investors actively analyzing securities
  2. Information is costless and widely available to all participants simultaneously
  3. Information arrives randomly; announcements are not predictable
  4. Investors react quickly and fully to new information → reflected in prices
Key caveat — Grossman-Stiglitz Paradox: If markets were perfectly efficient, there would be no incentive to gather information (since prices already reflect it). But if no one gathers information, prices cannot reflect it. Therefore, markets must be slightly inefficient to reward information gathering. Efficiency is a matter of degree, not binary.

Evidence Summary

FormEmpirical VerdictKey Evidence
Weak Well supported Serial correlation tests; price changes largely independent; technical rules don't outperform buy-and-hold after costs
Semi-Strong Largely supported Active fund managers underperform passive benchmarks by 50–200 bps after fees; event studies show rapid price adjustment
Strong Not supported Insiders earn abnormal returns; insider trading laws exist to prevent exploitation of private information (e.g., Galleon hedge fund: CEO jailed 11 years)
Market Anomalies — Exceptions to EMH

Key Documented Anomalies

Anomalies are exceptions to market efficiency — patterns that persist and could theoretically be exploited. Most violate semi-strong form EMH since they use publicly available information.

Momentum Effect

Stocks with high returns in the past 3–12 months tend to continue outperforming in the subsequent 3–12 months. "Winners keep winning."

Canadian data: Top 30 momentum → 20.76% vs TSX 6.10% (1980–99, 6-month HPR)

Contrarian / Reversal

Over longer horizons (3–5 years), prior losers outperform prior winners — stock prices mean revert. Opposite of momentum. Note: Does not hold in Canadian markets (Kryzanowski & Zhang).

Value Effect

Low P/E, low Market-to-Book, high dividend yield stocks ("value stocks") consistently outperform high P/E, high M/B growth stocks — even after risk adjustment. Anomalous because ratios are publicly available.

Size Effect

Small-cap stocks outperform large-cap stocks even after adjusting for risk. Interacts with January effect (up to 50% of size premium occurs in January).

January Effect (Santa Claus Rally)

Returns statistically higher in January, especially for small caps. Driven by tax-loss selling in December + "window dressing" by fund managers. Evidence suggests this has weakened as investors have traded it away.

Earnings Surprise Drift

Stock prices continue drifting after positive earnings surprises — the market underreacts to new information. Prices should adjust instantly in semi-strong efficient markets.

Fischer Black's caution: "Most so-called anomalies don't seem anomalous to me at all. They seem like nuggets from a gold mine, found by one of thousands of miners all over the world." Many anomalies are products of data mining and disappear after accounting for transaction costs, risk adjustments, and time period selection.
Behavioural Finance

Traditional Finance vs. Behavioural Finance

Traditional Finance (EMH)

  • Investors are rational
  • All information is processed correctly
  • Decisions maximize utility
  • Prices always correct on average
  • No persistent exploitable patterns

Behavioural Finance

  • Investors make systematic errors
  • Psychological biases distort decisions
  • Emotion overrides logic
  • Group think and herding create mispricings
  • Anomalies are real and persistent
Key behavioural insight from David Dreman: "Investors pay too much for trendy, fashionable stocks and too little for companies that are out-of-favour. Emotion overrides logic time after time." This explains why value stocks persistently outperform — they're boring, not fashionable.

Why Anomalies Persist — The Behavioural Explanation

If mispricing were recognized and exploited, it should be arbitraged away. But behavioural biases are systematic — they don't disappear with experience. Investors:

  • Overreact to recent information (drives momentum and contrarian patterns)
  • Anchor to reference prices (slows adjustment to new information)
  • Herd with the crowd ("group think") — better to fail conventionally than succeed unconventionally (Keynes)
  • Display loss aversion — losses hurt more than equivalent gains feel good
Keynes on group think (1936): Professional investors are "mainly concerned with foreseeing changes in the conventional basis of valuation a short time ahead of the general public." They care less about intrinsic value than about what the market will value something at in three months. This destabilizes rather than corrects prices.
Likely Exam & Discussion Questions
Q1: Why does portfolio standard deviation fall below the weighted average of individual standard deviations?
Because assets are not perfectly positively correlated (ρ < +1). When one asset declines, another may not decline by the same proportion — losses are partially offset. The key variable is the correlation coefficient. The lower the correlation, the greater the risk reduction relative to the weighted average. Only when ρ = +1 does portfolio risk equal the weighted average.
Q2: What risk cannot be diversified away, and why?
Systematic (market) risk cannot be diversified away because it affects all securities simultaneously. Events like recessions, interest rate increases, or inflation shocks move the entire market. There is no offsetting asset — all stocks are exposed. Total risk = Systematic risk + Unique risk. Adding more stocks eliminates unique risk but leaves systematic risk untouched. This is why investors earn an equity risk premium — compensation for bearing unavoidable systematic risk.
Q3: If markets are semi-strong efficient, what is the value of financial analysts?
This is the Grossman-Stiglitz paradox. If markets are perfectly efficient, analysis adds no value (prices already reflect everything). But if no one analyzes, prices cannot be efficient. Therefore some inefficiency must exist to reward analytical effort. In practice: most active fund managers underperform passive benchmarks by 50–200 bps after fees — the strongest evidence for semi-strong efficiency. Analysts may add value at the margin, but as a group they cannot consistently beat the market.
Q4: Why does the strong form of EMH fail?
Strong form requires prices to reflect all information — including private (insider) information. This is demonstrably false: insiders consistently earn abnormal returns using non-public information. This is precisely why securities law prohibits insider trading. The Galleon hedge fund case (Raj Rajaratnam, jailed 11 years) is a textbook example — he built a network of insiders to exploit non-public information and generated substantial abnormal returns, directly refuting strong form EMH.
Q5: How does the value effect challenge EMH, and what do both sides argue?
Value stocks (low P/E, low M/B) consistently outperform growth stocks using publicly available information — this violates semi-strong EMH. EMH defenders argue value stocks carry higher risk not captured by standard measures (beta), so the excess return is rational compensation. Behavioural finance argues investors irrationally overpay for growth stocks (excitement/fashion) and underpay for boring value stocks. The persistence of the effect despite widespread recognition is troubling for EMH — if it were a risk premium, it should be priced in once identified.
Session Connections — Building the Course Framework

How Session 6 Links to Prior & Future Sessions

← Session 2 (Bonds)

HPR directly extends bond pricing. When rates fall, P₁ rises → HPR exceeds coupon yield. The inverse price-yield relationship drives the capital gain component of HPR.

← Session 3 (WACC/DCF)

T-bill rate (risk-free) and the equity risk premium (stocks − T-bills = 4.35%) are inputs into cost of equity. Session 6 explains WHY investors demand this premium — compensation for systematic risk.

→ Session 7 (CAPM — likely)

Beta (β) is the formal measure of a stock's systematic risk. CAPM prices that risk: E(r) = Rf + β × (Rm − Rf). Everything in Session 6 — systematic risk, market risk premium, diversification — is the foundation for CAPM.

← Sessions 4 & 5 (Comps & M&A)

Market efficiency assumptions underpin public market comparables. If markets are semi-strong efficient, trading multiples are fair signals of value — making comp analysis a valid valuation tool.

← Session 1 (Financial System)

Operational, allocational, and informational efficiency — introduced in Session 1 — reappear here as the three components of market efficiency. Informational efficiency is the EMH focus.

Exam Integration

Session 6 is a conceptual bridge. Expect exam questions that test whether you can connect risk measurement → portfolio theory → EMH → why WACC/DCF/comps are valid or invalid valuation tools.

Formula Sheet — Session 6
Holding Period Return
HPR = [ I + (P₁ − P₀) ] ÷ P₀
I = income; P₁ = end price; P₀ = start price. Captures both yield and capital gain.
Portfolio Expected Return
r̄ₚ = Σ (wᵢ × r̄ᵢ)
Simple weighted average. No diversification effect on expected return — only on risk.
MPT Portfolio Risk Inequality
σₚ < Σ (wᵢ × σᵢ)
Holds whenever ρ < +1. The gap between sides grows as correlation falls.
Total Risk Decomposition
σ_total = σ_market + σ_unique
σ_unique → 0 with diversification. σ_market is irreducible — it's the floor.
Equity Risk Premium
ERP = r_stocks − r_f
Historical Canada: 10.70% − 6.35% = 4.35%. Compensation for systematic risk.
Correlation Coefficient Range
−1 ≤ ρ ≤ +1
ρ = −1: perfect hedge possible. ρ = 0: uncorrelated. ρ = +1: no diversification benefit.
MBUS 813 · Session 6 Prep · Queen's Smith AMBA 2026