fin 355 behavioral finance. - unc charlotte pages...arbitrageurs lead to limited arbitrage; theory...

FIN 355 Behavioral Finance.Class 1. Limits to Arbitrage

Dmitry A Shapiro

University of Mannheim

Spring 2017

Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 1 / 23

Traditional Approach

Traditional approach:

No Frictions:Agents are rational:

Beliefs are updated correctly;Decisions are made consistently with SEUWeaker than rational expectations.

We relax the second assumption −→ “Behavioral Finance”



Traditional approach does not mean that there are no irrationalagents.It says that the effect of irrational agents is negligible and will beimmediately counter-acted by rational agents.Friedman (1953) said that noise traders cannot have substantialimpact on prices because:

Friedman-I): if p 6= FV rational traders will jump in and fix themispricing;Friedman-II): even if I) doesn’t work noise traders will make lessmoney and die out.


What’s wrong with Friedman’s arguments?

Even if noise traders were able to create mispricing, rationaltraders would see it as an attractive opportunity and exploited ituntil the mispricing is fixed.

Noise traders fight back.

Rational traders start fixing the mispricingNow for noise traders it becomes an attractive opportunityThey start to exploit it. Not clear who wins.

Noise traders don’t fight back (e.g. just do something randomly)

There are many risks that can prevent rational traders from fixing themispricing.These risks create limits to arbitrage.

Friedman-II is sort of true but

it can be very slow;ignores arrival of new noise traders;BUT computer trading;



From the Friedman argument if mispricing exists (p 6= FV) then

It creates an attractive investment opportunity;Rational traders come and fix the mispricing.

In other words No Free Lunch⇒ EM and p = FV.One of the biggest success of the behavioral finance was todocument many instances when mispricing does not necessarilycreate Free Lunch!Limits to arbitrage (irrationals can affect the price!).


Risks limiting arbitrage

Fundamental Risk - mispriced security will suffer adversefundamental news;

Can deal with by shorting “substitute security”Not always available;Thus fundamental risk limits the arbitrage only if it isnon-diversifiable

Noise trader risk (DSSW 1990, SV 1997)— mispricing can getworse in short run;

Money managers manage money of other people.Mispricing gets worse then clients can withdraw their moneyThus managers tend to be more cautious.


Risks limiting arbitrage

Horizon Risk - mispricing can take so long to correct that it’s notworth it:

Returns can be less than risky returns;Matters even if invest own money;

Model Risk - uncertainty that something is mispriced.Transaction costs

bid/ask spreads, price impact;short-sale constraints;cost of discovering mispricing.


Furthermore

Rational traders may trade in the same direction as irrational

Positive feedback traders buy everything that went up last monthUpward price pressureRational should do the sameBrunnermeier and Nagel (JF, 2004) showed that hedge funds hadhigher than average weight of apparently overpriced stocks in latenineties.


Examples of limits to arbitrage

Equity carve-outs. Mitchell, Pulvino, Stafford (JF, 2002)

70 cases where the parent worth less than subsidiary.Each case is evidence of limits to arbitrage.The risks involved are:

Fundamental: many cases terminated because 3rd party bought asubsidiary;Noise trader risk: mis-pricing was getting worse in SR.Horizon Risk: one situation took 3000 days to correct and often therate is less than risk-free;NO model risk: it’s obvious;Implementation cost on average not very high;


Examples of limits to arbitrage

Equity carve-outs with spin-offs: Lamont, Thaler (JPE, 2003);Used sub-sample of MPS data for which parents declared spin-offinitiation;Idea is that limits of arbitrage would be different;Before FR, NTR, HR - big; Implementation cost - small.LT claim the opposite;

True for Implementation cost: huge fees for short-selling;Another evidence: Put-call parity violations;FR: hard to judge since the sample is small;NTR should be actually high since lots of trade: Turnover insubsidiary shares was very high ≈ 37% per day.


Examples of limits to arbitrage. Index Inclusion.

Denis, McConnell, Ovtchinnikov and Yu (JF, 2003).

S&P500 wants to make the index representative of the USeconomy;No judgement about its investment appeal;The day when the stock is included in SP500 there is unreversiblejump up.This is mispricing because no fundamental news is released.


Index Inclusion

Index inclusion Denis, McConnell, Ovtchinnikov and Yu (JF, 2003).

What are the risks:

FR: some. Hard to find good substitute;NTR: some.HR: Yes. Takes long time to correct.MR: may be, not everyone thinks there is mis-pricing.ICosts: minor. Stocks are very liquid.

Prediction: If this is mispricing then more FR leads to highermis-pricing (Wurgler/Zhuravskaya (JB, 2002)).FR level is determined from availability of good substitute;Result: When FR is high (lower R2) price jump is bigger.


Index Inclusion.

May be inclusion actually increases FV?

Higher visibility may be good per se;Plus higher visibility may lead to improvement in corporateperformance;

Denis et al. measure changes in investor expectations:

Analysts forecast as proxy;After inclusion analysts are more likely to increase earning (i.e.forecast after minus before goes up).For included stock 42%↘, 56%↗;For “all” companies 56%↘, 40%↗;For same ISL (industry, size, liquidity) stock 50%↘ and 44%↗.

Expectations are rational: Realized earnings after minus forecastbefore is higher.


Index Inclusion.

Denis et al. (2003) showed that companies newly added to theIndex

experience increase in eps (earnings per share) forecasts;experience significant improvement in performance (realizedearnings).

Nonetheless: Kaul, Mehrote, Merck (JF, 2000)Toronto Stock Exchange: in 1996 weights of changed because ofbenign regulatory reasons;Stocks going up in weight are experiencing price jumps that arenot reversed.Not an information story: visibility did not change because stockswere in the index.(Weakly) suggests that some of the S&P500 story is mispricing.


Value Stocks

Value stocks (those with low P/E) have higher average returnsthan CAPM suggests.Probably they are undervalued. Why no arbitrage? Risks:


Value Stocks

Value stocks (those with low P/E) have higher average returnsthan CAPM suggests.Probably they are undervalued. Why no arbitrage? Risks:

FR: yes;NTR: yes;HR: yes;MR: yes (here it is an issue!)


Theory of Limits to Arbitrage

Theory I: Without perfect substitute, i.e. with FR:

Fama and French (JFE, 2007): non-diversified risk + risk-aversearbitrageurs lead to limited arbitrage;

Theory II: Perfect substitute (no FR) but NTR.

NTR and risk-averse arbitrageurs with short horizon then limitedarbitrage.DSSW (JPE 1990) is the first paper on NTR;Shleifer, Vishny (JF 1997) is one of the most influential papers onthe topic.


DSSW (1990)

Two assets:Safe asset that pays r in each period and available in perfectlyelastic supply;Unsafe asset: pays divided r and is in fixed supply of 1 (perfectsubstitute!).

There is µ noise traders and 1− µ rational traders;OLG structure:

Agents are born with the same endowment;In period 1 they buy portfolio;In period 2 they get profit;Convert safe asset into consumption good;Sell unsafe to new generation.

Rational people have correct expectations;Noise traders misperceive the expected price of unsafe asset byρt ∼ N(ρ∗, σ2

ρ);Utility is the same u = −e−2γw.


DSSW (1990)

Can separately solve for demands by sophisticated investors andnoise investors;The market-clearing price is

pt = 1 +µ(ρt − ρ∗)

1 + r+µρ∗

r− 2γ

µ2σ2ρ

r(1 + r)2Without NTR pt = 1.Second term captures the fluctuations in the price due to variationof noise traders misperceptions (p. 711).

If ρt = ρ∗ then the second term is zero.

Third captures the fact the average misperceptions by noisetraders are not zero.

If they are bullish on average the price goes up.

The last term is very interesting:Noise traders create risk and so rational traders should becompensated in order to hold the asset.Thus the price goes down and the return goes up.


DSSW (1990)

To sum up:

In this model there is no FR whatsoever;However, NTR is non-diversifiable;Short-horizon of rational traders is critical too: you must sell beforemispricing corrects.

DSSW (1990) claim that NT survive (if evolution is based on theexpected wealth);Sandroni (2000) shows that they do not;Blume and Easley (2001) show that they do if market areincomplete.


SV (1997)

DSSW (1990) showed that if arbitrageurs have short horizon thanNT can limit the arbitrage;SV (1997) also tell why arbitrageurs have short horizon.

Separation of brain and capital;Arbitrageurs manage money of other people (e.g. investors,lenders);If you have bad returns in short-run, investors and lenders will taketheir money.This makes arbitrageurs to be more careful.


Some of the Papers used for this class

Barberis and Thaler, survey, pp. 2-8Delong et al. (1990) - Friedman IIShleifer and Vishny (1997) — noise-trader riskOwen and Thaler (JPE, 2003) — equity carve-outsMitchell et al. (2002) — equity carve-outsDenis, McConnell, Ovchinnikov, Yu (JF, 2003) — index inclusion


Papers For The Next Class

Survey, pages 11-21Rabin (1998) “Psychology and Economics”Kahneman, Daniel, and Amos Tversky (1974), "Judgment UnderUncertainty: Heuristics and Biases"Kahneman, Daniel, and Amos Tversky (1979), "ProspectTheory:An Analysis of Decision Under Risk"Rabin, Matthew (2000), "Risk Aversion and Expected Utility,"Econometrica 68, 1281-1292.Brunnermeier, Parker, “Optimal expectations”, AER, 2005.Gilevich et al. (1985) Hothand effect in basketball


fin 355 behavioral finance. - unc charlotte pages...arbitrageurs lead to limited arbitrage; theory...

Documents