The Limits To Arbitrage Theory in Finance

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In order for us to understand the limits of arbitrage theory, and what the restrictions/risks are, we need to take a dive into neo-classical economics, the efficient market hypothesis and behavioral finance beforehand.

The Modern Quantitative Approach to Finance and Neo-Classical Economics

The modern quantitative approach to finance has its original roots in neo-classical economics.

Neo-classical economics is am approach to the field of economics that believes in an idealized world in which markets work smoothly without impediments such as irrationality, asymmetrical information, and etc.

Assumptions of the neo-classical theory include the following:

  • People are rational (homo economicus)
  • People follow prospect theory
  • People have perfect information (all information is available, accessible and transparent)
  • People discard sunk costs
  • People can objectively measure value
  • People respond to incentives

Essentially, the market is always right.

Behavioral Finance & Efficient Market Hypothesis

Behavioral finance is a new approach to financial markets that has emerged. This is in response to the problems of the traditional finance paradigm rooted in neo-classical economics.

In the traditional framework of finance, individuals within the market are rational and there are no frictions. A security’s price equals its fundamental value. This is also known as the intrinsic value. This is calculated by taking the discounted sum of expected future cash flows.

The Efficient Market Hypothesis states that the prices are right, you can’t beat the market and these prices are set by individuals who understand Bayes’ Law.

However, Behavioral Finance argues that some features of asset prices are most plausibly interpreted as deviations from fundamental value (intrinsic value), and that these deviations are brought about by the presence of traders who are not fully rational.

One of the objections to this viewpoint goes back to a line of argument made by economist, Milton Friedman. He argues that rational traders (arbitrageurs) will quickly undo any dislocations caused by irrational traders (noise traders).

This argument is based on two assertions:

  • As soon as there is a deviation from the fundamental value (mispricing), an attractive investment opportunity is created.
  • Rational traders will immediately snap up the opportunity, correcting the mispricing or deviation from the fundamental value.

The issue isn’t with the second assertion, but the first. Even when an asset is wildly mispriced, strategies designed to correct the mispricing can be risky and costly. This renders them ineffective, and as a result, the mispricing will continue within the market.

Arbitrage and Arbitrageurs

Arbitrage is the strategy of taking advantage of price differences in different markets for the same asset.

Arbitrageurs are rational investors who exploit market inefficiencies of any kind. They are necessary to ensure that inefficiencies between markets are ironed out or remain at a minimum.

A noise trader is an individual who trades/invests based on incomplete or inaccurate data, often irrationally.

For an arbitrage to take place, there must be a situation of at least two equivalent assets with differing prices.

The simplest form of arbitrage is purchasing an asset in the market where the price is lower and simultaneously selling the asset in the market where the asset’s price is higher.

Arbitrage may occur if the following conditions are met:

  1. In different markets, the same asset is traded at different prices.
  2. Assets with similar cash flows are traded at different prices.
  3. An asset with a known future price currently traded at a price different from the expected value of the future cash flows.

In theory, arbitrage is done by an infinite number of small risk-neutral investors. This leads to a direct price adjustment that Milton Friedman was asserting with the Efficient Market Hypothesis.

In reality, arbitrage is done by a small number of highly specialized risk averse institutional investors. This results in a slower price adjustment. This increases risks and costs.

Limits To Arbitrage

The theory of limits to arbitrage says that these unbalanced asset prices may stay unbalanced for a significant period of time due to restrictions/limits on funds. Without these restrictions, arbitrageurs would fix this unbalance.

There are three main limits on arbitrage:

  1. Fundamental risk —The most obvious risk an arbitrageur faces if he buy’s Ford’s stock at $15 is that a piece of bad news about Ford’s fundamental value causes the stock to fall further, leading to losses. Of course, arbitrageurs are well aware of this risk, which is why they short a substitute security such as GM at the same time that they buy stocks of Ford. The problem is that substitute securities are rarely ever perfect, making it impossible to remove all the fundamental risk.
  2. Noise trader risk — This is the risk that the mispricing that is being exploited by the arbitrageur worsens in the short run. Even if GM is a perfect substitute security for Ford, the arbitrageur still faces the risk that the pessimistic investor causing Ford to be undervalued will become further pessimistic, driving the price down further. This risk can force arbitrageurs to liquidate their position.
  3. Implementation cost —Well understood transaction costs such as commissions, bid-ask spreads, and price impact can make it less attractive to exploit a mispricing. There are also legal constraints to be included within this. Many pension funds and hedge funds are legally not allowed to short-shell.

As a result of the limits to arbitrage, prices might not always reflect the fundamental value.