Trading Under Uncertainty

Ankur Pareek

Yale School of Management

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

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.

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

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

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.

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

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

  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

  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

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.