Limits to Arbitrage and Behavioral Asset Pricing

“No free lunch” and “the price is right” are different claims

The efficient-markets hypothesis is often stated as one idea, and it is really two. The first is **no free lunch**: it is hard to earn returns above the market after costs and risk, consistently. The second is **the price is right**: prices equal the best estimate of fundamental value. The evidence for the first is strong — most professionals fail to beat their benchmarks (PF8) — and the first does not imply the second. A price can be wrong and still offer no free lunch, if nobody can safely make money correcting it. The mechanism that is supposed to keep prices right is **arbitrage**. In the classic argument, made by Milton Friedman among others, irrational traders who push a price away from value will lose money to rational ones who trade against them, and in doing so the rational traders push the price back. If arbitrage were costless and riskless, that argument would be airtight, and mispricings would last seconds. Real arbitrage is neither costless nor riskless, and the gap between the textbook and the trading desk is where behavioral finance found its evidence. When correcting a mispricing is limited, the prices that result reflect both the fundamental value and the demand of whoever is trading on something else — sentiment, stories, constraints — and that mix can last for years. • No free lunch: hard to beat the market after costs and risk — strongly supported. • The price is right: price equals fundamental value — a separate, weaker claim. • Arbitrage is the mechanism meant to enforce the second. • When arbitrage is limited, sentiment can move prices for a long time. Two claims, two kinds of evidence — No free lunch: Most active funds trail their benchmarks — strong support · The price is right: Contradicted when identical assets trade at different prices ← · What links them: Arbitrage — and how limited it is

Four reasons smart money cannot always fix a price

**Fundamental risk.** Most arbitrage is not between identical assets but close substitutes, and the substitute can move for its own reasons. Shorting an overpriced bank and buying a cheaper one still leaves you exposed to news about either bank. **Noise-trader risk.** De Long, Shleifer, Summers and Waldmann showed that the same irrational demand that created a mispricing can widen it before it closes, so an arbitrageur with a limited horizon can be forced out at a loss precisely because the price became more wrong. **Implementation costs.** Shorting requires borrowing shares, which can cost a great deal, can be impossible for hard-to-borrow stocks, and can be recalled at the worst moment; transaction costs and margin requirements eat into small gaps. **The limits of capital.** Shleifer and Vishny pointed out that professional arbitrageurs invest other people’s money. When a trade moves against them, their clients see losses and withdraw — so capital leaves exactly when the mispricing is largest and the opportunity best. Long-Term Capital Management is the case study for the last two. Its convergence trades were, by many accounts, right about where prices would eventually end up. But in 1998, after Russia’s default, the spreads it had bet would narrow widened instead, its leverage turned losses into a crisis, and a group of banks organised by the Federal Reserve Bank of New York put $3.6 billion into the fund to wind it down in an orderly way. The line usually attributed to Keynes — that markets can stay irrational longer than you can stay solvent — is the summary every arbitrageur learns. • Fundamental risk: the substitute is not identical. • Noise-trader risk: mispricing can widen before it closes. • Implementation costs: borrowing, recalls, margin and trading costs. • Limits of capital: clients withdraw when the trade looks worst and is best. LTCM, 1998: right about the destination, ruined by the path — The bet: Spreads between similar bonds would narrow · What happened: After Russia’s default they widened sharply ← · The amplifier: Very high leverage turned losses into a crisis · The end: A $3.6 billion bank-funded rescue to wind the fund down

The cases: twins, stubs and closed-end funds

**Royal Dutch and Shell.** For decades two companies, Royal Dutch Petroleum and Shell Transport and Trading, shared the cash flows of one business in a fixed 60:40 split, so Royal Dutch shares should always have been worth one and a half times Shell shares. Froot and Dabora found the ratio wandered far from parity — by up to about a third — and stayed away for long periods, apparently because each share was owned mainly in a different country by different investors. Identical cash flows, different prices, and no safe way to profit, because the gap could widen for years. **3Com and Palm.** The stub in this lesson’s prediction is the starkest example: the market valued 3Com’s non-Palm assets at about −$22 billion on the day of Palm’s IPO, and the gap closed only gradually. The trade that would fix it — buy 3Com, short Palm — needed Palm shares to borrow, and there were very few; the cost of borrowing them was extreme. **Closed-end funds** add a quieter puzzle: funds holding ordinary listed shares often trade at discounts, sometimes premiums, to the value of what they own, and Lee, Shleifer and Thaler found those discounts move with measures of individual-investor sentiment. Each case has the same structure: a price that is demonstrably wrong, and a friction that stops the correction. That is why the right question about any apparent mispricing is not “is it wrong?” but “what stops the people who could fix it?” • Royal Dutch/Shell: should trade at 1.5 : 1; wandered up to about a third away for years. • 3Com/Palm: a stub worth about −$22 billion, sustained by the impossibility of shorting Palm. • Closed-end funds: discounts to their own holdings that move with retail sentiment. • For any mispricing, ask what stops the correction. Wrong prices, and what kept them wrong — Royal Dutch and Shell: Different home markets and investors; the gap could widen · 3Com and Palm: Palm almost impossible to borrow and short ← · Closed-end fund discounts: Sentiment; no way to force the fund to liquidate

Behavioral asset pricing: who sets the price when arbitrage is limited

If arbitrage cannot always correct prices, then prices reflect a mix of fundamental value and the demand of investors trading for other reasons — sentiment, stories, rules and constraints. That is the core of behavioral asset pricing, and it explains where the famous return anomalies tend to live. Patterns such as momentum, the post-earnings-announcement drift and the long-run underperformance of the most speculative stocks are usually strongest among small, illiquid, hard-to-short and hard-to-value companies — exactly where the limits to arbitrage bite hardest, and where Baker and Wurgler found sentiment matters most (T15). The same insight disciplines anyone who finds an anomaly in a backtest (T17). A pattern that ignores borrowing costs, trading costs and the size the trade can actually reach may be real and still unexploitable: the friction that lets it exist is the same friction that eats its return. Professional capacity is limited too, so an anomaly that is profitable at a small size can disappear once enough money chases it. For an ordinary investor the practical lesson is asymmetric. You rarely need to bet against a mispricing — which means shorting, with all four frictions working against you. You can always simply not own the overpriced side, and you can tilt modestly toward assets that look cheap without betting the plan on a correction arriving on time. Avoiding the bad side of a mispricing is cheap; profiting from it is not. • With limited arbitrage, prices mix fundamental value and sentiment demand. • Anomalies concentrate where arbitrage is hardest: small, illiquid, hard-to-short stocks. • A backtested anomaly may be real and still unexploitable after costs and capacity. • Avoiding the overpriced side is cheap; betting against it is expensive. What a mispricing means for you — You own the overpriced asset: Reduce it — you never need permission to sell what you own · You want to bet against it: Every limit to arbitrage now works against you ← · You found it in a backtest: Check borrow costs, trading costs and capacity before believing it A price that is obviously wrong is a reason to ask what stops the correction. Usually the answer is a cost or a risk that would land on you too.

Demand curves slope down: what index inclusion shows

In textbook finance a stock’s price is set by its expected cash flows and risk, and the demand curve for it is flat: if one investor wants more shares, arbitrageurs supply them at the same price, because perfect substitutes exist. Index inclusion is a natural experiment that tests the claim. When a company is added to the S&P 500, nothing about its business changes — but every fund that tracks the index has to buy it. Andrei Shleifer found in 1986 that additions earned abnormal returns of a few percent around the announcement, and that the gain did not reverse: buying pressure alone moved the price, which means the demand curve slopes down. Tesla’s addition in 2020 is the most dramatic modern example. Between the announcement in November and the inclusion in December the stock rose by more than half, as index funds and everyone anticipating them prepared to buy one of the largest additions in the index’s history; on the day it joined, it fell. The business had not changed in five weeks; the buyers had. The effect has shrunk as it became famous — traders now buy ahead of likely additions, and index providers have spread the trades out — which is itself the lesson in miniature. A mispricing that depends on predictable, forced demand attracts arbitrage until the remaining gap is roughly what the costs and risks of exploiting it allow. The effect does not vanish because markets became perfectly efficient; it shrinks to the size the limits to arbitrage permit. • Index inclusion changes demand, not the business — a clean test of whether demand moves prices. • Shleifer (1986): additions earned abnormal returns of a few percent that did not reverse. • Tesla, 2020: up more than half between announcement and inclusion, then down on the day. • The effect has shrunk as traders anticipate it — to the size the limits to arbitrage allow. Index inclusion as a natural experiment — What changes: Forced buying by index funds · What does not change: The company’s cash flows and risk ← · What the price does: Rises on the demand — the demand curve slopes down · Why the effect shrank: Anticipation and arbitrage, up to the limit of their costs

Sources

• The limits of arbitrageShleifer & Vishny, “The Limits of Arbitrage” (Journal of Finance, 1997)
• Noise-trader riskDe Long, Shleifer, Summers & Waldmann, “Noise Trader Risk in Financial Markets” (Journal of Political Economy, 1990)
• 3Com and PalmLamont & Thaler, “Can the Market Add and Subtract? Mispricing in Tech Stock Carve-Outs” (Journal of Political Economy, 2003)
• Royal Dutch and ShellFroot & Dabora, “How Are Stock Prices Affected by the Location of Trade?” (Journal of Financial Economics, 1999)
• Closed-end fund discountsLee, Shleifer & Thaler, “Investor Sentiment and the Closed-End Fund Puzzle” (Journal of Finance, 1991)