Limits to arbitrage and behavioral finance

Question 1

Behavioral finance (assumptions):

Answer 1

1) Some agents are not fully rational.
2) Asset prices systematically deviate from fundamental values.
3) Impact on corporate finance decisions, investments and asset prices.

Question 2

Main areas of behavioral finance application

Answer 2

1) Asset princing:
- Aggregate stock market, bond market, real estate. - Performance of various stock market strategies.
- Bubbles.
2) Investor behavior:
- Portfolios that investors hold.
- Trading activity over time.
3) Corporate finance:
- Security issuance.
- Capital structure.
- Investment decisions.
- M&A activity.

Question 3

Rational choice meets four criteria:

Answer 3

1) It is based on decision maker’s current assets.
2) Based on the possible consequences of the choice (no effect of framing).
3) Agents make choices consistent with the expected utility framework.
- Consider different possible future outcomes.
- Decide how good or bad each outcome will make him feel.
- Weight each outcome by its probability and sum up.
4) When agents receive new information, they update their expectations correctly, as described by Bayes law.

Question 4

Market efficiency:

Answer 4

An efficient market is one in which prices equal fundamental value:

• Prices equal the discounted sum of expected future cash flows.
• The discount rate is consistent with a normatively acceptable preference specification.
• Prices incorporate all relevant available information.

Question 5

Forms of market efficiency:

Answer 5

1) Strong form - prices incorporate all public and private information.
2) Semi-strong form - prices incorporate all public information.
3) Weak form - prices incorporate only past public information.

Question 6

Behavioral finance

Answer 6

1) Some agents are not fully rational:
Fail to update beliefs correctly (fail to incorporate all available information). - Make choices that are normatively unacceptable.
2) Limits to arbitrage:
- Rational agents cannot always correct the irrationality of other investors.
- Irrationality (mispricing) can have substantial and long impact.
3) Behavioral biases (psychology):
- The irrational decisions are not random.
- Systematic form of irrationality that creates a mispricing.
- Belief formation - how agents form expectations.
- Decision-making (preferences) - how agents evaluate risky decisions.

Question 7

Limits to arbitrage

Answer 7

Even when an asset is wildly mispriced, strategies designed to correct the mispricing can be both risky and costly, rendering them unattractive.

Question 8

Risks and costs allowing the mispricing to survive:

Answer 8

1) Fundamental risk:
- The risk that the asset held by an investor loses value.
- Finding a perfect hedge (substitute) is usually impossible.
2) Noise trader risk:
- Mispricing worsens further in the short run due to investor sentiment. - Can force arbitrageurs to liquidate their positions prematurely.
3) Implementation costs:
- All costs that make it less attractive to exploit the mispricing. - Transaction costs, short-sale constrains, and information costs. - Horizon risk.

Question 9

Sufficient conditions to limit the arbitrage:

Answer 9

1) Arbitrageurs are risk averse and have short horizons.
- Arbitrageurs cannot afford to be patient.
- Creditors and investors evaluate the arbitrageur based on his returns. - Forced closure of a short position.
2) Noise trader risk is systematic.
- Whatever investor sentiment is causing one asset to be undervalued relative to the other, it could also cause the mispricing to increase in the short term.

Question 10

Examples of limits to arbitrage?

Answer 10

1) Index inclusions of stocks (S&P500, Russell 1000):
- When a stock is added to the index, it jumps even though its fundamental value does not change.
- Fundamental risk and noise trader risk.
2) Closed-end funds:
- Mutual funds that issue a fixed number of shares that are traded on exchanges. - Fund share prices differs from the net asset value (NAV).
- Mainly noise trader risk.
- Lee, Shleifer and Thaler (1991).
3) Bubbles:
- Limited short-selling (implementation costs) during the DotCom bubble. - Housing bubble - short selling is not directly possible.
- Griffin, Harris, Shu and Topaloglu (2011).
4) Equity carve-outs:
5) Twin Shares

Question 11

What is an Equity carve-outs?

Answer 11

Equity carve-out (partial public offering) - IPO for shares, usually minority stake, in a subsidiary company; partial divestiture of a business unit.
Spinoff - the parent firm gives remaining shares in the subsidiary to the parent’s shareholders; the parent distributes the entire ownership interest in the subsidiary as a stock dividend to existing shareholders and no money changes hands.

Question 12

What is a Stub?

Answer 12

Stub - residual security that is left over after removing the carve-outed subsidiary from the parent security.
Constructing stubs:
s0 = (P0P-xP0S)/P0P

Question 13

What happened to 3Com/Palm stub values?

Answer 13

1) The stub remains negative for longer than two months.

2) The announcement of IRS approval and distribution date cause the stub to go from negative to positive.

Question 14

Risk and return from investing in stubs. Comment on strategy:

Answer 14

Investment strategy - long in the parent and short in the subsidiary:

1) Parents had 30/33 percent higher returns than subsidiaries.
2) The strategy delivers an alpha of 10 percent per month.
3) The Sharpe ratio of this strategy is around 0.7 per month. (sure thing)
4) The strategy can benefit from additional risks (canceled spin-off, takeover).

Question 15

What is short-sale constrains?

Answer 15

With irrational traders, short-sale constraints can cause some stocks to become overpriced.
Short sales constraints - costs and risks that make it less attractive for pessimistic investors to short stocks sufficiently and exploit the mispricing.
1. Shorting process:
- To be able to sell a stock short, one must first borrow it.
- The security lenders receive a fee.
- Rebate rate - interest rate paid to the deposit placed by the borrower. - Stocks held primarily by individual investors are difficult to short.
2) Short interest: the total amount of shares of stock that have been sold short relative to the total amount of shares outstanding.
Someone has to own the shares issued by the firm: the number of shares not lent out must equal the number of shares outstanding.

Increase over time in short interest for the subsidiaries:

1) It may take a while for investors to become aware of the mispricing.
2) The short-sale market works sluggishly.

Question 16

How to create synthetic short position with options?

Answer 16

Synthetic short: use options to simulate the payoff of a short stock position

• Buy at-the-money puts.
• Sell at-the-money calls.
• Borrow the present value of the strike price (price at which the option can be exercised).

Question 17

Tech stock carve-outs (Lamont and Thaler, 2003). Conclusions of it?

Answer 17

1) Negative stubs are blatant mispricings and gross violations of the law of one price.
2) They do not present exploitable arbitrage opportunities because of the costs of shorting the subsidiary.
3) Arbitrage does not always enforce rational pricing.
4) Limits of arbitrage can create market segmentation.
5) Systematic irrationality among a subset of investors can cause the prices to deviate from fundamental value for a longer period of time.

Question 18

How agents form expectations?(beliefs)

Answer 18

• Representativeness.
• Overconfidence and overoptimism (wishful thinking).
• Belief perseverance and confirmation bias.(Confirmation bias is the tendency to search for, interpret, favor, and recall information in a way that confirms or supports one’s prior beliefs or values.)
• Anchoring.(Anchoring is a behavioral finance term to describe an irrational bias towards an arbitrary benchmark figure. This benchmark then skews decision-making regarding a security by market participants, such as when to sell the investment.)
• Availability bias.(A distortion that arises from the use of information which is most readily available, rather than that which is necessarily most representative.)

Question 19

how agents evaluate risky decisions? (

Decision-making (preferences))

Answer 19

• Prospect theory. (The prospect theory says that investors value gains and losses differently, placing more weight on perceived gains versus perceived losses.)
• Ambiguity aversion.(Ambiguity aversion, or uncertainty aversion, is the tendency to favor the known over the unknown, including known risks over unknown risks.)

Question 20

What are the two biases generated by representativeness?

Answer 20

1) Sample size neglect, i.e. belief in the law of small numbers.
- People expect that even a small sample will reflect the properties of the model that generated it.
- Agents tend to infer the model on the basis of too few data points.
- Mistake - small sample typically is not enough to infer the overall model.
2) Base rate neglect.
- base rate fallacy is the tendency for people to erroneously judge the likelihood of a situation by not taking into account all relevant data. Instead, investors might focus more heavily on new information without acknowledging how this impacts original assumptions.

Question 21

Volatility puzzle?

Answer 21

The volatility of returns is higher than the volatility of earnings growth.
Variation in the price-earnings ratio can come from:
1) Variation in the expected earnings growth g.
2) Variation in the discount rate r.

Question 22

Potential explanations of the volatility puzzle?

Answer 22

1) Variation in the expected dividend growth g:
The P/E ratio should have predict cash-flow growth, but it does not! Rejected by Shiller (1981), research rewarded with a Nobel prize.
2) Variation in the discount rate r: Variation in expected future risk-free rate.
- But P/E ratio does not predict interest rates in time series. Changing forecast of risk.
- Also little evidence that P/E ratio predicts changes in risk. Changing risk aversion.
- The only remaining rational story.
- Campbell and Cochrane (1999) habit model.
3) Belief-based behavioral models:
Extrapolate trends: if the stock market has done well (poorly) in the past year
or two, some investors think it will keep doing well (poorly).
Such beliefs are incorrect… but can be justified by the law of small numbers.

Question 23

Kahneman and Tversky (1979) prospect theory:

Answer 23

• Descriptive model (how we actually behave?)

- Viewed as the best available summary of how people think about risk.

Question 24

Violations of expected utility framework?

Answer 24

1) Certainty effect. (The certainty effect is the psychological effect resulting from the reduction of probability from certain to probable)
2) Reflection effect. (having opposite preferences for gambles differing in the sign of the outcomes)
3) Isolation (framing) effect.(Frame dependance - choices between prospects are not determined solely by the probabilities of final stages.)

Question 25

Stages in the prospect theory

Answer 25

1) Editing and framing stage: Reference point:
- Status quo.
- Aspiration level.
- Security level or survival point.
- Break-even point.
2) Evaluation stage:
Value function.
Decision weight function.
U(x1, p1; x2, p2; x3, p3) = π(p1)ν(x1) + π(p2)ν(x2) + π(p3)ν(x3)

Question 26

Prospect theory decision weighting function.

Answer 26

Characteristics of the decision weighting function:

1) Near the zero point the curve is steep (lottery tickets).
2) The crossover point at about 0.20 on the objective probability dimension.
3) The curve is “too flat” at the central portion (super-additive weights).
4) Certainty effect at the high end (Allais paradox).

Question 27

Prospect theory summary

Answer 27

1) Most economic models of the stock market assume that investors evaluate risk according to the expected utility framework.
- but the predictions of these models have received mixed empirical support.
2) A model of the stock market in which investors evaluate risk according to prospect theory seems to do better.
- Value function (gains vs losses; loss aversion). - Decision (probability) weighting function.

Question 28

What are applications of Ambiguity aversion?

Answer 28

Equity premium puzzle. 
Insufficient diversification:
- Familiarity bias.
- Local (home) bias.
- Investing in company (employers) stocks.

Question 29

Equity premium puzzle

Answer 29

Equity premium puzzle:
The stock market return has historically earned a high excess rate of return. Typical estimation of equity premium are between 4.0% and 6.0%.
This risk premia cannot be explained with plausible levels of risk aversion

Question 30

What is the explanation for Equity premium puzzle?

Answer 30

Myopic loss aversion:
1) Loss aversion from prospect theory:
Agents are more sensitive to reductions in their wealth than to increases.
2) Frequent evaluation and narrow framing:
Based on mental accounting and can be motivated by:
- Regret.
- Bounded rationality.
- Temporal narrow framing (information presentation).
An investor evaluates the portfolio typically every year. Even long-term investors have a short evaluation horizon.

Question 31

Prospect theory decision weighting function explanation

Answer 31

1) The aggregate market has negatively skewed returns - occasional crashes.
2) Prospect theory agents overweight occasional crashes by using the decision weight function, and demand higher risk premia for the higher perceived risk.
3) Under probability weighting the equity market should therefore have a high average return.
4) Availability bias offers a similar explanation.

Question 32

Why investors like dividends? (Dividend puzzle)

Answer 32

1) Historically, dividends have been taxed at a higher rate than capital gains.
2) Taxes on dividends are paid immediately and investor loses the potential compounding of those taxes over time.
At least some shareholders would be better off with capital gains instead of dividends.

Question 33

Explaining investor preference for cash dividends:

Answer 33

1) Self-control - dividends provide a natural rule to prevent overconsumption.
2) Prospect theory and mental accounting:
- Segregate two gains.
- Integrate two losses.
- Integrate small loss and small gain.
- Segregate large loss and small gain (silver lining).
3) Regret aversion - frustration that people feel when they imagine having taken an action that would have led to a more desirable outcome.
- Stronger for errors in which people acted and took responsibility. - Weaker for errors when people followed the rule or failed to act.

Question 34

Results: Elicited risk tolerance

Answer 34

1) Stock market returns experienced in the past have a significant and positive effect on reported risk tolerance.
2) More recent returns are weighted more heavily.
3) But returns experienced far in the past still affect households’ level of risk tolerance.

Question 35

Results: Stock and bond market participation

Answer 35

• A change from the 10th to the 90th percentile of experienced stock returns implies a 10.2 pp increase in the probability of stock market participation.
• Experienced bond returns have a positive effect on bond market participation.

Question 36

Results: Counterfactual stock market participation rates

Answer 36

The gap between actual and counterfactual participation rates reaches up to 7 pp, suggesting that return experiences may have a considerable effect on overall stock market participation rates.

Question 37

Results: Fraction of liquid assets invested in stocks

Answer 37

• Experience hypothesis: an investor will increase her investment in stocks relative to bonds only if stocks performed better than bonds over her lifetime so far.
• Experienced excess returns explain households’ allocation to stocks as well as real stock returns.

Question 38

Aggregate results: Experienced stock returns and P/E ratio

Answer 38

• Periods of high experienced returns (and hence high risk taking) coincide with periods of high P/E ratios.
• The correlation is around 0.60.

Question 39

Conclusions on Personal experience

Answer 39

• Risky asset returns experienced over the course of an individual’s life have a significant effect on the willingness to take financial risks.
• Individuals put more weight on recent returns than on more distant realizations…
• …but experiences many years ago still have some impact on current risk taking