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Limits to Arbitrage 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 SEU Weaker than rational expectations. We relax the second assumption −!“Behavioral Finance” Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 2 / 23 Traditional Approach Traditional approach does not mean that there are no irrational agents. It says that the effect of irrational agents is negligible and will be immediately counter-acted by rational agents. Friedman (1953) said that noise traders cannot have substantial impact on prices because: Friedman-I): if p 6= FV rational traders will jump in and fix the mispricing; Friedman-II): even if I) doesn’t work noise traders will make less money and die out. Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 3 / 23 What’s wrong with Friedman’s arguments? Even if noise traders were able to create mispricing, rational traders would see it as an attractive opportunity and exploited it until the mispricing is fixed. Noise traders fight back. Rational traders start fixing the mispricing Now for noise traders it becomes an attractive opportunity They 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 the mispricing. 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; Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 4 / 23 Traditional Approach 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 to document many instances when mispricing does not necessarily create Free Lunch! Limits to arbitrage (irrationals can affect the price!). Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 5 / 23 Risks limiting arbitrage Fundamental Risk - mispriced security will suffer adverse fundamental news; Can deal with by shorting “substitute security” Not always available; Thus fundamental risk limits the arbitrage only if it is non-diversifiable Noise trader risk (DSSW 1990, SV 1997)— mispricing can get worse in short run; Money managers manage money of other people. Mispricing gets worse then clients can withdraw their money Thus managers tend to be more cautious. Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 6 / 23 Risks limiting arbitrage Horizon Risk - mispricing can take so long to correct that it’s not worth 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. Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 7 / 23 Furthermore Rational traders may trade in the same direction as irrational Positive feedback traders buy everything that went up last month Upward price pressure Rational should do the same Brunnermeier and Nagel (JF, 2004) showed that hedge funds had higher than average weight of apparently overpriced stocks in late nineties. Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 8 / 23 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 a subsidiary; Noise trader risk: mis-pricing was getting worse in SR. Horizon Risk: one situation took 3000 days to correct and often the rate is less than risk-free; NO model risk: it’s obvious; Implementation cost on average not very high; Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 9 / 23 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 a subsidiary; Noise trader risk: mis-pricing was getting worse in SR. Horizon Risk: one situation took 3000 days to correct and often the rate is less than risk-free; NO model risk: it’s obvious; Implementation cost on average not very high; Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 9 / 23 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-off initiation; 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 in subsidiary shares was very high ≈ 37% per day. Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 10 / 23 Examples of limits to arbitrage. Index Inclusion. Denis, McConnell, Ovtchinnikov and Yu (JF, 2003). S&P500 wants to make the index representative of the US economy; No judgement about its investment appeal; The day when the stock is included in SP500 there is unreversible jump up. This is mispricing because no fundamental news is released. Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 11 / 23 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 higher mis-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. Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 12 / 23 Index Inclusion. May be inclusion actually increases FV? Higher visibility may be good per se; Plus higher visibility may lead to improvement in corporate performance; 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 forecast before is higher. Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 13 / 23 Index Inclusion. Denis et al. (2003) showed that companies newly added to the Index experience increase in eps (earnings per share) forecasts; experience significant improvement in performance (realized earnings). Nonetheless: Kaul, Mehrote, Merck (JF, 2000) Toronto Stock Exchange: in 1996 weights of changed because of benign regulatory reasons; Stocks going up in weight are experiencing price jumps that are not reversed. Not an information story: visibility did not change because stocks were in the index. (Weakly) suggests that some of the S&P500 story is mispricing. Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 14 / 23 Value Stocks Value stocks (those with low P=E) have higher average returns than CAPM suggests. Probably they are undervalued. Why no arbitrage? Risks: Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 15 / 23 Value Stocks Value stocks (those with low P=E) have higher average returns than CAPM suggests. Probably they are undervalued. Why no arbitrage? Risks: FR: yes; NTR: yes; HR: yes; MR: yes (here it is an issue!) Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 16 / 23 Theory of Limits to Arbitrage Theory I: Without perfect substitute, i.e. with FR: Fama and French (JFE, 2007): non-diversified risk + risk-averse arbitrageurs lead to limited arbitrage; Theory II: Perfect substitute (no FR) but NTR. NTR and risk-averse arbitrageurs with short horizon then limited arbitrage. DSSW (JPE 1990) is the first paper on NTR; Shleifer, Vishny (JF 1997) is one of the most influential papers on the topic. Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 17 / 23 DSSW (1990) Two assets: Safe asset that pays r in each period and available in perfectly elastic supply; Unsafe asset: pays divided r and is in fixed supply of 1 (perfect substitute!). 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 by ∗ 2 ρt ∼ N(ρ ; σρ); Utility is the same u = −e−2γw. Dmitry A Shapiro (UNCC) Limits to Arbitrage Spring 2017 18 / 23 DSSW (1990) Can separately solve for demands by sophisticated investors and noise investors; The market-clearing price is µ(ρ − ρ∗) µρ∗ µ2σ2 p = 1 + t + − 2γ ρ t 1 + r r r(1 + r)2 Without NTR pt = 1. Second term captures the fluctuations in the price due to variation of noise traders misperceptions (p. 711). ∗ If ρt = ρ then the second term is zero. Third captures the fact the average misperceptions by noise traders 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 be compensated in order to hold the asset.
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