Title: Limits to Arbitrage in Rational Investing: Risks and Real-world Examples

Introduction: The concept of limits to arbitrage, established by Andre Shleifer and Robert Vishny, forms a crucial aspect of behavioral finance theory. This theory explores the challenges faced by rational investors engaging in arbitrage transactions due to constraints and costs, leading to the persistence of mispricing in financial assets caused by the actions of irrational investors. This essay delves into the risks encountered by arbitrage investors, focusing on fundamental risk and noise trader risk, and examines real-world instances supporting the concept of limits to arbitrage.

Body:

1. Fundamental Risk: One primary risk faced by rational investors engaged in arbitrage is fundamental risk. Consider a scenario where a stock's mispricing causes its price to fall below the fair value. While rational investors can exploit this mispricing through arbitrage transactions, the fundamental risk arises when the fair value of the stock fluctuates over time. If the fair value declines further over time, exceeding the initial mispricing, rational investors who entered the arbitrage at the mispricing point may incur losses. This risk is known as fundamental risk, reflecting the potential decline in the fair value of financial assets [5].

2. Noise Trader Risk: Similarly, mispricing-induced arbitrage transactions face the challenge of noise trader risk. Even when rational investors react to mispricing and expect profits from arbitrage, irrational noise traders with pessimistic market views may exacerbate the degree of mispricing in the short term. Noise trader risk highlights the possibility that mispricing in financial assets expands due to the actions of irrational traders, known as noise traders [6]. This risk was introduced by DeLong, Shleifer, Summers, and Waldmann [4] and plays a significant role in the theory developed by Shleifer and Vishny [1].

3. Shleifer and Vishny's Limits to Arbitrage Mechanism: Shleifer and Vishny's central idea revolves around the constraints faced by arbitrage investors, such as hedge funds, due to limitations on the funds they manage. The mechanism suggests that these constraints hinder sufficient arbitrage transactions in response to mispricing caused by noise traders, allowing mispricing to persist and potentially worsen in the short term. The fear of market reactions to losses incurred in attempting to correct mispricing may lead to clients withdrawing funds, further limiting the ability of arbitrage investors to execute arbitrage transactions. Shleifer and Vishny termed this phenomenon as the "limits to arbitrage" [1].

Real-world Examples Supporting Limits to Arbitrage:

• LTCM and the Russian Financial Crisis: Shleifer cites the case of Long-Term Capital Management (LTCM) during the Russian financial crisis as consistent with the theoretical model. Despite having potentially profitable arbitrage positions, LTCM faced extensive losses during the crisis. The fear of a hard landing and its impact on the economy led to coordinated efforts to rescue LTCM, demonstrating that even seemingly lucrative arbitrage positions can be liquidated during financial crises [9].

• Royal Dutch and Shell Stock Prices: Another example illustrating the limits to arbitrage is the historical deviation between the stock prices of Royal Dutch and Shell. Despite theoretical expectations, where a market-neutral strategy would converge the prices to a 6:4 ratio, the actual prices deviated persistently. This deviation suggests that noise trader risk, leading to short-term losses for investors attempting arbitrage, may have limited the effectiveness of arbitrage in correcting the prices [10] [11].

Conclusion: In conclusion, the risks associated with arbitrage transactions, namely fundamental risk and noise trader risk, underscore the challenges faced by rational investors in correcting mispricing in financial assets. Real-world examples, such as the LTCM crisis and the divergence in Royal Dutch and Shell stock prices, provide empirical support for the concept of limits to arbitrage. Understanding these risks is crucial for investors and researchers alike, contributing to the broader field of behavioral finance.