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Trading Under Uncertainty
Ankur Pareek
Yale School of Management
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Motivation
• To study the interaction between arbitrageurs and uninformed investors and measure the ex-ante allocation efficiency of the market.
• Provide some insight into validity of some of the theories behind the dotcom bubble: – Ofek and Richardson(2003)- short sales restrictions with
heterogeneous beliefs explain the internet stock bubble– Pastor and Veronesi (2006)- high uncertainty in future earnings
growth rate explained the existing prices of tech stocks in late 90s– Lamont and Stein (2004) – less arbitrage capital for short-selling in
rising overvalued market
• Understanding the behavior of arbitrageurs under uncertainty
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Experimental Design
• Create market for stocks of a technology firm Sysco which is based on single technology still in R&D phase
• Three sets of traders with different information sets– Arbitrageurs with perfect information about the final dividend
realization– Traders with partial/noisy information about the final dividend.– Uninformed traders
• Arbitrageurs faced with uncertainty about when the arbitrage window will close (end of period 4 or period 5)
• Three sessions with 4 or 5 periods which vary in final dividend and signal received by partially informed traders.
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Time 0No information
Time 14 traders givenNoisy info
Time 24 traders givenPerfect info
Time 3Public announcementNoisy info.announced
Time 4 or 5Dividend paidand trading ends
Timeline for a Trading Session
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Experimental Results
• Prices did not converge to fundamental values when there was overvaluation in the market in session 1 and session 3– Consistent with Ofek and Richardson (2003): short sell
constraints and heterogeneous beliefs
• Traders with noisy private information trade on it aggressively immediately after receiving it but don’t trade on it or reverse some of their trades later
• Prices converge close to fundamental value when dividend is high
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Experimental Results (contd’)
• Arbitrageurs did not sell all their securities before the end of period 4 in low dividend sessions 1 and 3– Action inconsistent with risk aversion/ risk neutrality of
arbitrageurs.– Can be explained by risk loving preferences like prospect theory
with convex utility over losses w.r.t some benchmark target profit
• Arbitrageurs did not indulge in speculative behavior in most of the cases.
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S toc k P ric es and E ffic ienc y of Alloc ation for S es s ion 2
0
100
200
300
400
500
600
700
800
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77
T rade number
Pri
ce/P
erce
nta
ge
TransactionP rice
E quilibriumPrice
AllocationEfficiency
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S toc k P ric es and E ffic ienc y of Alloc ation for S es s ion 3
0
100
200
300
400
500
600
700
800
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57
T ra de numbe r
Pri
ce/
Per
cen
tag
e
E quilibriumP rice
Trans actionP rice
AllocationEfficiency
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Informed Partial info. Uninformed
Initial Stocks 20 20 35
Final Stocks 7 29 39
Aggregate Profit 8600 1255 5145
Profit/Trader 2150 313.75 735.00
Exante Exp Profit 3400 -280 360
Expected number of stocks 0 31 44
Informed Partial info. Uninformed
Initial Stocks 20 20 35
Final Stocks 30 15 30
Aggregate Profit 15291 17513 27196
Profit/Trader 3822.75 4378.25 3885.14
Exante max Exp Profit 5525 3400 3075
Expected number of stocks 75 0 0
Session 1 summary statistics
Session 2 summary statistics
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Informed Partial info. Uninformed
Initial Stocks 20 20 35
Final Stocks 17 14 44
Aggregate Profit 5200 6500 3531
Profit/Trader 1300.00 1625.00 504.43
Exante max Exp Profit 2047.22 866.67 477.78
Expected number of stocks 0 24 51
Session 3 summary statistics
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Conclusion
• Heterogeneous investors combined with short-sales constraints could lead to persistence of overpricing.
• Perfectly informed arbitrageurs more risk-loving compared to investors with noisy information sets.– Investors with partial information risk-averse as shown by their
trading behavior.– Arbitrageurs risk taking in final period can only be justified by
risk-loving behavior
• Difficult for under pricing to persist in a market with arbitrageurs with perfect information.
• Future experiments could help in resolving the debates about the existence and reasons behind the dot-com bubble of 1990s.