Week 6 - Behavioural finance & limits to arbitrage

Question 1

Discuss how overconfidence and self-attribution biases can lead to momentum and reversal in the model of Daniel, Hirshleifer, and Subrahmanyam (1998).

[2019, 2016, 5m]

Answer 1

1. 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.
2. Suppose, they get good private signal and buy stocks at date.
   - 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.
3. 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.
4. Similarly for an unfavorable shock.

Question 2

What is performance-based arbitrage?
Explain why arbitrageurs may face capital constraints (such as fund outflows) at times when their investments have the best prospects, e.g., when the mispricing they bet against deepens.

[2019 paper, 4m]

Answer 2

1. Outside investors do not have full understanding of the manager’s strategies.
2. 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”).
3. Responsiveness of funds under management to past performance is called performance based arbitrage.
4. This means that the arbitrageurs may face capital constraints precisely when their investments have the best prospects, i.e. when the mispricing they bet against initially deepens.
5. Anticipating these potential capital constraints, rational arbitrageurs will be less aggressive in their initial bets against mispricing.
6. As a result, arbitrage may not fully enforce market efficiency.

Question 3

Explain how NOISE TRADER RISK creates limits to arbitrage for active portfolio managers.

[2022, 4m]
[2018, 5m]

Answer 3

1. Doing arbitrage often involves taking short positions.
2. However, before the prices of
   securities converge, they may diverge even more in the short term due to the activity of noise traders.
3. As a result, the arbitrageurs may need to liquidate their positions at a loss.
4. Therefore, the arbitrageurs have incentives to invest only limited amount of money into arbitrage strategies.