Lecture 7 - Asset Market Bubbles and Crashes
1. Introduction: Financial Crises in Context
This lecture examines the economic mechanisms behind commonly occurring financial crises, beginning with asset market bubbles and crashes. The focus is not descriptive history but underlying economic logic.
Asset markets play a central role in modern economies because they allocate capital intertemporally. When these markets malfunction, distortions propagate into investment, banking stability, and macroeconomic performance.
Core questions
- How are asset prices determined?
- What do price changes signal?
- Are financial markets efficient?
- Why do bubbles and crashes occur?
The lecture builds from fundamental valuation logic to the random walk hypothesis and then challenges the Efficient Market Hypothesis using empirical evidence.
2. Asset Prices as Information Signals
In decentralised markets, prices coordinate economic activity. They convey dispersed information about:
- Demand conditions
- Supply constraints
- Expected future profitability
Financial asset prices are forward-looking. Unlike goods prices, they embed expectations about the future.
The key economic insight:
The price of a financial asset reflects expectations about future income streams.
This leads naturally to balance sheet valuation.
3. Book Value, Profits, and Market Value
January 1 Balance Sheet
The firm has:
- Assets: Cash = 1000, Fixed Assets = 4000
- Liabilities: Loans = 2000
- Equity = 3000
- Shares outstanding = 500
Book value per share:
Profit Scenario
Suppose profits of 1000 are generated during the year.
Two cases arise:
-
Profits paid as dividends
- Dividend per share = 2
- Balance sheet unchanged
- Book value remains 6
-
Profits retained
- Cash increases to 2000
- Equity increases to 4000
- Book value becomes:
Economic Interpretation
The key question is:
What determines the equilibrium market price on January 1?
The answer depends entirely on expectations.
4. Expectations and Market Pricing
Three cases illustrate valuation logic:
Case 1: No anticipated profits
Price = 6
Case 2: Profits anticipated, retained
Price = 8
Case 3: Profits anticipated, paid as dividend
Price = 8
The crucial result:
If investors fully anticipate profits, the price adjusts immediately.
Implication
Dividend policy does not affect firm value under perfect markets.
This illustrates the:
Modigliani–Miller Theorem (1958)
In frictionless markets:
- Firm value is independent of capital structure
- Firm value is independent of dividend policy
Value depends only on underlying cash flows.
This leads directly to the Efficient Market Hypothesis.
5. Efficient Market Hypothesis (EMH)
The EMH states:
Asset prices reflect all available information.
In competitive markets:
- Expected profits are immediately capitalised
- There are no systematic arbitrage opportunities
Prices therefore act as optimal forecasts.
6. The Random Walk Model
The statistical representation of EMH is:
where:
- Mean = 0
- Errors are random
Interpretation:
- The best predictor of tomorrow’s price is today’s price.
- New information arrives randomly.
This implies price changes are unpredictable.
7. Random Walk with Drift
Returns are normally distributed with:
- Mean
- Variance
Thus:
Economic intuition:
This framework underpins modern finance theory.
8. From Binomial Processes to the Normal Distribution
Pascal’s Triangle links discrete coin toss outcomes to the binomial distribution.
As the number of trials increases:
- The binomial distribution converges to the normal distribution.
This provides the statistical foundation for modelling asset returns as normally distributed.
9. The Bell Curve and Standardisation
Standard normal distribution:
Most observations cluster near the mean.
Extreme outcomes are very rare.
This is central to traditional financial risk modelling.
10. Fat Tails and Excess Volatility
Empirical data contradicts the normal distribution assumption.
Examples:
- Annual decline >10% predicted once every 500 years
- Observed once every 5 years
- Nine 20% crashes in a century
Implication:
- Financial returns exhibit fat tails
- Extreme events occur far more frequently than predicted
Why this matters
If markets were perfectly efficient and returns normally distributed:
- Large crashes should be extremely rare.
Observed volatility suggests:
- Prices deviate from fundamental values.
- Psychological or structural forces may amplify shocks.
11. Optimal Forecasting Principle
Revisit:
For optimal forecasting:
- Otherwise predictions could be improved
Fundamental principle:
The forecast must be less variable than the variable forecasted.
If stock prices are excessively volatile relative to fundamentals, this violates optimal forecasting logic.
12. Shiller’s Volatility Critique
Robert Shiller (1981) observed:
- The discounted present value of real dividends follows a relatively stable trend.
- Actual stock prices fluctuate dramatically.
This creates a paradox:
If prices are optimal forecasts of discounted dividends, why are they so volatile?
This challenges the simplest version of EMH.
13. Linking to Bubbles and Crashes
The lecture builds toward bubble logic:
- If prices deviate persistently from fundamentals
- And volatility exceeds justified levels
- Then speculative dynamics may be present
A bubble arises when:
- Prices rise due to expectations of further price increases
- Rather than underlying cash flow growth
A crash occurs when:
- Expectations reverse
- Price adjustments become discontinuous
Exam-Oriented Summary
Core Mechanisms
- Asset prices reflect expectations about future profits.
- Under EMH, prices follow a random walk.
- Forecast errors must be unpredictable.
- Empirical data shows excess volatility and fat tails.
Theoretical Tensions
- Modigliani–Miller implies valuation depends on fundamentals.
- Random walk implies unpredictability.
- Shiller shows volatility exceeds fundamental justification.
Key Equations
Book value:$$
\frac{\text{Equity}}{\text{Shares}}
p_{t+1} = p_t + \varepsilon_t
p_{t+1} = p_t + \mu + \varepsilon_t