Chapter 2: Market Efficiency & Arbitrage
This chapter covers the Efficient Markets Hypothesis (EMH), the role of information in pricing, factor investing, and the mechanics and risks of short selling and arbitrage.
1. Core Concepts and Definitions
Efficient Markets Hypothesis (EMH): Formulated by Eugene Fama, EMH states that rational asset prices should equal the present value of expected future payoffs. Expectations are formed conditional on available information and perceived risk. A key implication is that systematic risk-adjusted abnormal profits (alpha) are hard to achieve.
Random Walk Hypothesis: A consequence of EMH stating that the best estimate of tomorrow's price is today's price. Price changes between today and tomorrow are unpredictable because prices immediately incorporate new information.
Post Earnings Announcement Drift (PEAD): An empirical anomaly where stock prices continue to drift in the direction of an earnings surprise (up for positive, down for negative) for weeks or months after the announcement. This suggests market underreaction to information, challenging the strict form of EMH.
Factor: A systematic source of return across many assets, captured by a portfolio constructed using a simple rule. A factor serves two roles: as an investment strategy (earning a premium) and as a pricing factor (explaining returns across assets).
Arbitrage: The simultaneous purchase and sale of an asset to profit from an imbalance in the price. It is a trade that profits by exploiting the price differences of identical or similar financial instruments on different markets or in different forms.
Short Selling: The practice of borrowing an asset (like a stock) and selling it immediately, with the intention of buying it back later at a lower price to return to the lender, profiting from the decline in price.
Short Squeeze: A situation where a heavily shorted stock or asset suddenly increases in price. Short sellers are forced to buy back the asset to cover their positions and limit losses, which drives the price even higher, creating a feedback loop.
2. Key Formulas and Mechanics
Short Run vs. Long Run Pricing
According to EMH, price behavior differs depending on the horizon:
Short Run (Random Walk):
Pt+1 = Pt + et+1
Expected returns are approximately zero; price changes are dominated by unpredictable shocks (et+1).
Long Run (Risk Compensation):
Pt+1 = Pt(1 + r) + et+1
Expected returns (r) are positive; prices drift upward to compensate investors for risk.
Margin Account Mechanics (Short Selling)
When short selling, an investor must maintain a margin account to cover potential losses if the asset price rises.
Initial Margin Requirement: Typically 50% of the short sale value.
Maintenance Margin Requirement: Typically 30% of the current market value of the shorted asset.
Total Margin Requirement: Current Market Value of Short + Maintenance Margin.
Margin Call: Triggered when the account equity falls below the Total Margin Requirement. The investor must deposit additional funds to meet the requirement.
3. Comparative Analyses of Intersecting Terms
Value Factor vs. Momentum Factor
| Feature |
Value Factor |
Momentum Factor |
| Definition |
Going long on stocks with low prices relative to accounting fundamentals (value stocks) and shorting growth stocks. |
Going long on recent winners (assets that have performed well) and shorting recent losers. |
| Information Used |
Prices relative to accounting fundamentals (e.g., Book-to-Market ratio). |
Past returns over medium horizons (e.g., 1 year). |
| Risk Profile |
Volatile, with long periods of underperformance. |
Subject to rare but severe crashes, especially during market rebounds. |
Public vs. Private Information
| Feature |
Public Information |
Private Information |
| Accessibility |
Available to all market participants (e.g., earnings reports, news). |
Known only to a select few (e.g., corporate insiders). |
| Market Reaction (EMH) |
Quickly reflected in prices. Using easily accessible public data should not generate abnormal profits (alpha = 0). |
Not reflected in prices until it becomes public or is traded upon heavily. Can generate significant abnormal profits. |
| Nuance |
Some public information is costly, slow, or difficult to process, behaving more like private information in competitive markets. |
Trading on material non-public information is often illegal (insider trading). |
4. Limits to Arbitrage and Risks
While arbitrage theoretically offers risk-free profits, real-world frictions create significant risks, as illustrated by the Twin Coin and GameStop cases.
- Widening Gap: The mispricing (gap) between two assets can widen before it converges, causing mark-to-market losses and potential margin calls.
- Liquidity Risk: The "cheap" asset in an arbitrage pair is often illiquid. If forced to unwind the position early, the arbitrageur may face severe price impact, worsening the losses.
- Predatory Trading: Other traders, knowing an arbitrageur is distressed and facing margin calls, may take the opposite position to force liquidation at unfavorable prices (a short squeeze).
- Funding Risk: "Markets can remain irrational longer than you can remain solvent." Arbitrageurs rely on capital (often from investors with lock-up periods). If investors withdraw funds or brokers demand higher margins, the arbitrageur may be forced to close the position at a loss.
Please review this chapter. Once confirmed, I will proceed to generate Chapter 3: Investors & Performance.