Behavioural finance and limits to aribitrage

Question 1

What are we going to look at today?

Answer 1

Psychological biases that lead to under and over reaction
Then limits to arbitrage ( implementation costs, Noise trader risk and riding the sentiment wave)

Question 2

What is under reaction and over reaction and which one is a reason for momentum and which one is a reason for reversals?

Answer 2

Underreaction: Insufficient market response to new information. This may lead to momentum, where asset prices continue to move in the same direction as investors gradually adjust.

Overreaction: Excessive market response to new information. This can result in reversals, where asset prices eventually correct, moving in the opposite direction after the initial overreaction.

Question 3

There are 3 models that simultaneously account for investors under and over reaction to news by who?

Answer 3

DHS ( 1998)
BSV ( 1998)
Hong and Stein ( HS)
These are initials of names by the way.
They all argue that momentum and reversal are due to behavioural biases in the process of interpreting information.

Question 4

What did we say caused undereaction and what did we say cause overreaction?

Answer 4

Under reaction - conservatism and limited attention

Overreaction - Representativeness. ( BSV 1998 say investors over-extrapolate from a sequence of growing earnings )

Question 5

What is the main summary of DHS (1998) model?

Answer 5

In summary, the DHS model demonstrates that investor overconfidence and self-attribution bias can lead to stock prices initially underreacting to news and later overreacting as reliance on private information increases and hence explain momentum and reversal.

Question 6

Provide a detailed step by step theory of DHS model ?

Answer 6

• Investors interpret good news as further evidence of their skills and attribute bad news to external errors or sabotage. When investors receive confirming news, their confidence in the private signal rises too much; when they receive disconfirming news, confidence declines too little.
• Suppose, they get good private signal and buy stocks at date 1. If later they receive good news they buy even more; if they receive bad news, they do not sell much; hence, on average, the price increases.
• The reaction to a favorable initial shock (the private information signal) is hump-shaped. Price on average rises further as public information arrives, because confidence about the private signal on average grows => short-lag positive autocorrelation; more accumulated evidence forces investors back to a more reasonable expectation => reversal at long horizons.

Question 7

What does this show?

Answer 7

Solid line = overeconfidence but not have self attribution bias
Dashed line = overconfidence and self attribution bias
Positive price - Overconfidence generates reversal - because investors are overconfident in their private signal, they push prices over fundamental value, when they receive bad public signals, they revise their private signal is wrong and gradually correct their bias. Self attribution bias generates momentum, but eventually when they keep getting bad public signals they are forced to revise their private signals and gradually correct bias.

Similar intuition for loser stocks.

Question 8

Now we are going to move to BSV(1998 ) Model which summarises to what?

Answer 8

BSV model explains how investor psychology, specifically the principles of representativeness and conservatism, can cause stock prices to under- and overreact to news.

Question 9

Provide a detailed step by step theory to explain reversal of BSV model?

Answer 9

1) Investors receive stock news, such as earnings reports or company announcements.

2) They form expectations about future performance based on the news.

3) Representativeness leads to over-extrapolation, causing overreaction and a rising stock price. A positive shock following this pattern yields small positive returns, as investors trade to eliminate predictability.

4) A negative shock in the next period surprises investors, leading to a large negative return and a reversal of long-term returns.

Question 10

Provide a detailed step by step theory to explain momentum of BSV model?

Answer 10

1) Investors receive stock news and form expectations about future performance.

2) Representativeness leads to over-extrapolation, causing overreaction and momentum when stocks perform well.
3) Continued positive news strengthens momentum.

4) Conservatism delays belief updates when new information contradicts established patterns, prolonging momentum.

5) When patterns change or overvaluation is recognized, momentum fades, and stock prices revert to fundamental values.

Question 11

What is the model summary of Hong and Stein ( HS) 2000? about?

Answer 11

The HS model highlights how the interaction between news watchers and momentum traders can contribute to market anomalies and inefficiencies, such as underreaction, momentum, and overreaction

Question 12

Provide a detailed step by step of the model by HS 2000

Answer 12

1) News watchers follow and react to stock news, sharing their beliefs while ignoring price information.

2) When news is released, only news watchers react, causing underreaction due to the fact they ignore information on prices, so its slow.

3) As the stock price reflects the news, momentum traders follow the trend, buying stocks with positive momentum and selling those with negative momentum.

4) Momentum traders’ actions ( buying stocks) reinforce the price movement, leading to a momentum effect and pushing the stock price further in the direction of the initial news.

5) Price overshooting is corrected when news watchers learn all information, leading to reversal as all information is correctly incorporated into the stock price.

Question 13

Where going to look at empirical evidence of momentum which confirms the earlier evidence, who are people who investigate this?

Answer 13

Jegadeesh and Titman ( JT, 2001) aimed to test whether the momentum effect could be explained by differences in expected returns, underreaction, or overreaction to news, looking at what happens to winners and losers portfolio in the post holding period ( 13-60 months) in addition to confirm momentum still exists in the data.

Question 14

Lets look at differences in expected returns what did Jegadeesh and Titman find?

Answer 14

If the momentum effect were solely due to differences in expected returns, then the high past returns (winners) should persistently outperform the low past returns (losers) even beyond the holding periods. However ,they found that the momentum effect tended to reverse in the long run, indicating that the momentum effect was not solely driven by differences in expected returns.

Question 15

Lets look at underreaction and overreaction, what did Jegadeesh and Titman find?

Answer 15

Underreaction: The momentum effect could be due to underreaction, with the market slowly incorporating information into stock prices. The study found evidence for underreaction but couldn’t fully explain the effect’s persistence.

Overreaction: If momentum were due to overreaction, winners would eventually underperform and losers outperform as the market corrects. Jegadeesh and Titman found long-run reversals, indicating overreaction as a contributing factor to momentum.

Question 16

So we know investors have physiological biases, which can give rise to momentum and reversal but surely there should be investors that don’t have these biases, surely they should be able to trade on the irrationality of these investors and eliminate arbitrage opportunities but we still see that smart investors cannot eliminate this arbitrage? What are the 3 main explanations?

Answer 16

Implementation costs and noise trader risk

Alternative view: arbitrageurs may exaceberate misplacing, If mispriicng is predictable, they may find it optimal to ride a sentiment wave rather than correcting it.

Question 17

What is the implementation costs about why we don’t see arbitrageurs eliminate arbitrage opportunities?

Answer 17

short selling involves borrowing shares from a broker and selling them in the hope of buying them back at a lower price to make a profit. However, short selling also involves costs such as borrowing fees and margin requirements ( you have to post collateral in which its usually greater than stock value = margin requirement) which can be substantial, particularly in volatile markets. Also rebate, ( you get paid interest in short selling but its determined by supply and demand for short, hence rebate rate < Risk free rate ( haircut)
Also buy in risk ( the lender may recall the stock loan at any time, when price increase e.g., hence the short seller has to close position at a loss if he can’t find other shares to borrow)

Question 18

Explain the noise trader risk as a limit of arbitrage.

Answer 18

Noise traders buy and sell stocks for non-informational reasons e..g sell stocks to finance their expenses, hence stock prices reflect some noise.

For example, if an arbitrageur buys a security that is mispriced due to noise trader activity, they may be forced to hold the position for an extended period if the market does not immediately correct the mispricing. During this time, the arbitrageur may face further losses if the mispricing worsens, potentially leading to significant losses, especially if they cannot fund this.

Question 19

What is performance based arbitrage by Shelifer and Vishny ( SV 1997), hint it refines noise trader theory?

Answer 19

Outside investors do not have full understanding of the manager’s strategies. Hence, it may be rational for investors to allocate funds based on past performance of the manager and to withdraw some capital after poor performance (“performance based arbitrage”). Mispricing caused by noise traders may lead to bad performance, but investors may perceive it as a lack of skill by the manager. Arbitrageurs may face capital constraints when mispricings deepen ( arbitrage opportunity big), leading to less aggressive initial bets against mispricing.

Question 20

What behavioural explanation is there for dot com bubble ( that first)

Answer 20

Investors being overly optimistic about the prospect of internet companies ( hence extra polluted from this e.g. firms that added .com to their names managed to increase their stock price.

Question 21

We have a conventional view that rational arbitrageurs attack price bubbles, thus exerting a correcting force on prices, however we found that hedge funds rode technology bubble instead of attacking it, why? ( hint - consistent with another theory mentioned)

Answer 21

Attacking the bubble too early would have made them lose potential profit and clients, as in the SV 1997 model, clients see their funds withdrawing money from these stocks, at a time everyone keeps buying these stocks, thus might conclude the manager doesn’t have skills.

Also, If a bubble continues to inflate, the costs of holding a short position against the bubble may be high, making it difficult for arbitrageurs to maintain their position

Question 22

So to summarise what does SV 1997 TRY TO SAY ABOUT NOISE TRADER RISK?

Answer 22

Noise trader risk creates limits to arbitrage for active portfolio managers.