1. Speculation and Price Indeterminacy in Financial Markets Shyam Sunder, Yale University (with Shinichi Hirota, Juergen Huber and Thomas Stoeckl) Asset Prices, Finance and Macroeconomics Barcelona GSE Summer Forum Barcelona, June 8-10, 2016

2. Based on Hirota, Shinichi and Shyam Sunder. “Price Bubbles sans Dividend Anchors: Evidence from Laboratory Stock Markets,” Journal of Economic Dynamics and Control vol.31, no. 6 (June 2007): 1875-1909.

3. The purpose of this paper To explore – How speculating traders cause price indeterminacy (deviations from fundamental values in financial markets) To focus on – Speculating investors (focused on capital gains) facing the difficult tasks of backward induction and forming rational expectations. To conduct – Laboratory experiments to get some answers 3

4. Main Findings In markets with speculating investors – Price deviations from fundamental value are larger – Price deviations increase as the holding periods get shorter (and frequency of security transfers increases) – Speculative trading creates upward (downward) pressure on prices when liquidity is high (low) – Price expectations are formed from forward induction from recent price changes, instead of backward induction from the fundamentals Conclusion: speculation causes price indeterminacy when dynamic formation of inter- temporal rational expectations in infeasible 4

5. Background Arguments for link between speculative trading inducing price volatility because valuation depends on future price expectations (noisy information, higher order expectations, recent price changes (Keynes 1936, Shiller 2000, Stiglitz 1989). Standard finance theory, all traders assumed to form rational expectations Even in a market dominated by speculating investors, backward induction is supposed to generate prices close to the fundamentals 5

6. 6 Critical assumption in finance theory 1.All generations of investors form rational expectations of future prices. 2.Rational expectation is common knowledge among all generations of investors By recursively forming REs, P t = F t is derivable as REE.

7. In practice, backward induction may not occur Some generations of investors may not form rational expectations. Even if all generations of investors do, rational expectation may not be common knowledge. Under such conditions, investors cannot backward induct from first and higher order expectations to the present value of securities. Prices are no longer anchored to the fundamental values and become indeterminate. We explore this possibility by conducting laboratory experiments. 7

8. 8 Fundamental Value vs. Price for a simple, single dividend security Fundamental value: Long-term Investor’s Valuation: (1) (2) Short-term Investor’s Valuation: (3) P t is not necessarily equal to F t

9. 9 For P t to be equal to F t Rational Expectation of P t+k Homogeneous Investors The Law of Iterated Expectations By recursive process, P t = F t is derivable by the backward induction.

10. 10 Difficulty of Backward Induction Backward Induction may fail. – Infinite maturity (rational bubbles) Blanchard and Watson (1982), Tirole (1985) – Infinite number of trading opportunities Allen and Gorton (1993) – Heterogeneous Information Froot, Scharfstein, and Stein (1992), Allen, Morris, and Shin (2002) – Rationality may not be common knowledge Delong et al. (1990a)(1990b), Dow and Gorton (1994)

11. 11 Price Bubble sans Dividend Anchors There are cases where short-term investors have difficulty in backward induction. Stock prices (P t ) form deviate from fundamentals (  F t ) No longer anchored by future dividends

12. 12 In an Earlier Experimental Study Hirota, Shinichi and Shyam Sunder. “Price Bubbles sans Dividend Anchors: Evidence from Laboratory Stock Markets,” Journal of Economic Dynamics and Control 31, no. 6 (June 2007): 1875-1909. What happens when short-term investors have difficulty in the backward induction? Two kinds of the lab markets – (1) Long-term Horizon Session (fundamental) – (2) Short-term Horizon Session (speculating) Bubbles (positive and negative) tend to arise in (2), but not in (1)

13. 13 Long-term Horizon Session Single terminal dividend at the end of period 15. An investor’s time horizon is equal to the security’s maturity. Prediction: P t = D Period 1Period 15 D (Trade)

14. 14 Short-term Horizon Session Single terminal dividend at the end of period 30. The session will “likely” be terminated earlier. If terminated earlier, the stock is liquidated at the following period predicted price. An investor’s time horizon is shorter than the maturity and it is difficult to backward induct. Prediction: P t  D Period 1 Period xPeriod 30 DE x (P x+1 ) (Trade)

15. 15 Figure 4: Stock Prices and Efficiency of Allocations for Session 4 (Exogenous Terminal Payoff Session)

16. 16 Figure 5: Stock Prices and Efficiency of Allocations for Session 5 (Exogenous Terminal Payoff Session)

17. 17 Figure 6: Stock Prices for Session 6 (Exogenous Terminal Payoff Session)

18. 18 Figure 7: Stock Prices and Efficiency of Allocations for Session 7 (Exogenous Terminal Payoff Session)

19. 19 In Fundamental sessions Long-horizon Investors play a crucial role in assuring efficient pricing. – Their arbitrage brings prices to the fundamentals. Speculative trades do not seem to destabilize prices. – 39.0% of transactions were speculative trades. By contrast, in short horizon treatments:

20. 20 Figure 8: Stock Prices and Efficiency of Allocations for Session 1 (Endogenous Terminal Payoff Session)

21. 21 Figure 9: Stock Prices and Efficiency of Allocations for Session 2 (Endogenous Terminal Payoff Session)

22. 22 Figure 10: Stock Prices and Efficiency of Allocations for Session 8 (Endogenous Terminal Payoff Session)

23. 23 Figure 11: Stock Prices and Efficiency of Allocations for Session 9 (Endogenous Terminal Payoff Session)

24. 24 Figure 12: Stock Prices for Session 10 (Endogenous Terminal Payoff Session)

25. 25 Figure 13: Stock Prices for Session 11 (Endogenous Terminal Payoff Session)

26. 26 Discussion (speculating sessions) Price levels and paths are indeterminate. – Level Small Bubble (Session 1) Large Bubble (2, 8, 9, 10) Negative Bubble (11) – Path Stable Bubble (1, 11, 2 ?) – Rational Bubble Growing Bubble (8, 9, 10) – Amplification Mechanism, Positive Feedback

27. 27 Results In the fundamental sessions, price expectations are consistent with backward induction. In the speculating sessions, price expectations are consistent with forward induction.

28. 28 However, Objections to Design of the Short-Horizon Sessions Single terminal dividend at the end of period 30. The session will “likely” be terminated earlier. If terminated earlier, the stock is liquidated at the following period’s predicted price. Environment not fully specified In the current work, we use a fully specified overlapping generations structure Period 1 Period xPeriod 30 DE x (P x+1 ) (Trade)

29. Laboratory Experiment All markets have 16 periods of trading – Each period lasts for 120 seconds. Single kind of simple assets – Single, certain, common knowledge terminal dividend of 50 at the end of period 16 (Fundamental value = 50). Control the presence of speculating and fundamental traders by varying the length of stay in the economy – Overlapping generations structure (see the next slide). High / Low liquidity treatment – See the slide after next 29

30. Markets with Overlapping Generations of Traders Every period has two overlapping generations of five traders each in the market Only one initial generation is endowed with assets A single common knowledge dividend of 50 paid at maturity—end of period 16—to traders of the last entering generation only All other generations enter with cash, can buy assets from the “old” generation, and sell them when they become “old” to exit the market with cash Individuals may re-enter after sitting out the market for one or more (random number) of generations (in T4 and T8 only) Each session is repeated six times (independently with different subjects) Equilibrium transaction volume per session: 160

31. Overlapping Generations Experimental Design 31 Treat- ment Period # of Subjects 12345678910111213141516 End of 16 T1 5 G0 5 G1D T2 5 G0 5 G1 5 G2D T4 5 G0 5 G1 5 G2 5 G3 5 G4D T8 5 G0 5 G1 5 G2 5 G3 5 G4 5 G5 5 G6 5 G7 5 G8D Notes: D means that the last generation of investors receives terminal dividends (50) at the end of Period 16.

32. Table 2: Treatment Overview Liquidity Low (C/A ratio=2) High (C/A ratio=10) Number of entering generations 1 T1LT1H 2 T2LT2H 4 T4LT4H 8 T8LT8H

33. Table 3: Treatment Parameters TreatmentT1LT1HT2LT2HT4LT4HT8LT8H Market setup No. of generations22335599 Terminal dividend50 Initial No. assets/trader G032 16 8844 Initial No. assets G(i)00000000 Total assets outstanding160 80 40 20 Total value of assets8,000 4,000 2,000 1,000 Initial cash/trader G000000000 Initial cash/trader G(i)3,20016,0001,6008,0008004,0004002,000 Total cash16,00080,0008,00040,0004,00020,0002,00010,000 Cash-asset-ratio (C/A-ratio)2102 2 2 Invited subj. (3n+3)15 a 18 Participating subjects90 108 Exchange rates (Taler/€) Generation 0 (G0)100 Transition generations 100500100500100500 Last generation2001,0002001,0002001,0002001,000 Predictors133 Exp. payout/subject (euros)16 NOTES: The following parameters are identical across all treatments: Number of traders/generation (5); number of active generations (2); market size (10 traders); period length (120 sec.); total number of periods (16); number of markets per treatment (6); number of expected transactions (160). a In treatments T1LH we invited 15 subjects instead of 18 as no subject pool for future generations is needed. However we invited five subjects to serve as predictors.

34. Continuous double auction markets 34 Trader: Information about your task (trader), period you leave the market, current Share and Taler holdings. Predictors: Information about your task (predictior) and your forecast. Current Market Price (of Stock) Price-Chart of current period SELL: You sell one unit, given the price with the blue background. BUY: You buy one unit, given the price with the blue background. List of all ASKS: from all traders - your own asks are written in blue. The ask with blue background is always the most attractive, because it is the cheapest for the buyer. List of all BIDS: from all traders - your own bids are written in blue. The bid with blue background is always the most attractive, yielding the highest revenues for the seller. ASK: seller’s analogue to BID - see above. BID: enter the price you are willing to pay for one unit. Trade does not take place until another participant accepts your bid!!!

35. Conducted Experiments Innsbruck-EconLab at University of Innsbruck September, October and November 2013 A total of 828 University of Innsbruck students (bachelor and master from different fields). 35

36. Hypotheses I Hypothesis I 0 (REE): Deviations of prices from the fundamental value are the same during periods when only speculating investors are present compared to periods when dividend-collecting investors are present in the market. Hypothesis I A : Deviations of prices from the fundamental value are larger during periods when only speculating investors are present compared to periods when dividend-collecting investors are present in the market. 36

37. Hypotheses II Hypothesis II 0 (REE): For a security of a given maturity, the deviation of prices from the fundamental value is not affected by the length of investors’ holding period. Hypothesis II A : For a security of a given maturity, the deviation of prices from the fundamental value increases as the length of investors’ holding period becomes shorter. 37

38. Hypothesis III Hypothesis III: Prices are the same irrespective of the total amount of cash in the market. Hypothesis IIIA: Prices are higher when the total amount of cash in the market is higher. 38

39. Experimental Results 39

41. 41 G0 G1

42. 42 G0 G1 G2

43. 43 G0 G1 G2 G3 G4

44. 44 G0 G1 G2 G3 G4 G5 G6 G7 G8

45. Summary of results (high Liquidity) 45

46. 46 G0 G1

47. 47 G0 G1 G2

48. 48 G0 G1 G2 G3 G4

49. 49 G0 G1 G2 G3 G4 G5 G6 G7 G8

50. Summary of results (low Liquidity) 50

51. Figure 2: High Liquidity Treatments

52. Table 4: Formulae for market efficiency measures

53. Analyses of the Price Deviations Measure of mis-pricing Relative Absolute Deviation (RAD): Stoeckl, Huber and Kirchler (2010) RAD = Period-RAD = = 53

54. 54 Table 3: Average Period-RAD for each period Panel A: High-liquidity session Panel B: Low-liquidity session Period 12345678910111213141516 T1 1.4230.5820.3540.2930.3290.3010.3210.3900.3740.3820.3960.3030.3230.2860.3870.259 T2 1.8251.0160.3100.4060.4670.5360.5410.4770.6760.8650.7050.3130.2320.4680.2320.179 T4 1.5521.4711.3421.0381.1820.9600.7980.4990.6970.5090.4700.5590.3250.2100.1670.040 T8 1.8791.2491.3731.3921.4091.4981.1770.9911.1081.0821.6071.7331.0190.6470.5500.273 Period 12345678910111213141516 T1 1.4230.5820.3540.2930.3290.3010.3210.3900.3740.3820.3960.3030.3230.2860.3870.259 T2 1.8251.0160.3100.4060.4670.5360.5410.4770.6760.8650.7050.3130.2320.4680.2320.179 T4 1.5521.4711.3421.0381.1820.9600.7980.4990.6970.5090.4700.5590.3250.2100.1670.040 T8 1.8791.2491.3731.3921.4091.4981.1770.9911.1081.0821.6071.7331.0190.6470.5500.273

56. 56 This supports Hypothesis I A, rather than I 0. REE does not hold in our laboratory Table 4: Comparison of average Period-RAD between periods with long-horizon investors and periods with only short-horizon investors (1)Periods with long-horizon investors (2) Periods with only short- horizon investors Difference (2) - (1) High-liquidity session (H) 0.401 (177) 1.024 (204) 0.623*** Low-liquidity session (L) 0.140 (178) 0.502 (203) 0.362***

57. 57 Average Period-RAD Conditional on Number of Entering Generations Left in High-Low Liquidity

58. 58 This supports Hypothesis II A, rather than II 0. The shorter the investment horizons, the more price deviation from the fundamentals. Table 5: Investment horizons and average Period-RAD Treatment (Average investment horizon) T1 (16.0 periods) T2 (10.7 periods) T4 (6.4 periods) T8 (3.6 periods) High-liquidity session (H) 0.421 (95) 0.586 (94) 0.739 (96) 1.187 (96) Low-liquidity session (L) 0.116 (94) 0.355 (96) 0.429 (96) 0.429 (95)

60. Liquidity Supply and Mispricing Prices tend to be above fundamental value in high- liquidity sessions, but below the fundamental value in the low liquidity sessions.  consistent with previous experiments Period-RD = The average of Period-RD = 0.534 in H, -0.222 in L This liquidity effect on prices is larger when there are only short-horizon investors in the market. 60

61. 61 With high liquidity, short-horizon investors magnify the overpricing (bubbles). With shortage of liquidity, short-horizon investors magnify the undervaluation (liquidity crisis). Table 6: Comparison of average Period-RD between periods with dividend collecting investors and periods with only speculating investors (1)Periods with dividend collecting investors (2) Periods with only speculating investors Difference (2) - (1) High-liquidity session (H) 0.295 (177) 0.741 (204) 0.446*** Low-liquidity session (L) - 0.087 (178) - 0.340 (203) - 0.253***

62. Price Expectations Short-horizon investors have difficulty in forming RE of future prices. Then, how do they expect future prices? The fundamental model The trend model The combined model 62

63. Price Predictions/Expectations Hirota and Sunder (2007): results show that when subjects cannot do backward induction, they resort to forward induction, and simply project past data in forming their expectations about the future In long-horizon sessions, future price expectations are formed by fundamentals. – Speculation stabilizes prices. In short-term sessions, future price expectations are formed by their own or actual prices. – Speculation may destabilize prices.

64. 64 High- liquidity Session Periods with dividend collecting investors Periods with speculating investors FUNDTRENDCOMBINEDFUNDTRENDCOMBINED Const.1.672**-0.7091.733**4.159**-2.611*0.515 (0.622)(1.595)(0.620)(1.895)(1.310)(1.449) (F t - P t )0.197***0.211***0.109*0.078 (0.043)(0.053)(0.061)(0.057) (P t - P t-1 )0.0200.067-0.301***-0.270*** (0.031)(0.044)(0.049)(0.043) N173167 186168 F20.960.428.093.1937.7125.16 p0.0000.5220.0020.0920.000 adj. R20.380.000.390.140.300.36 Table 7: Price expectations model estimates

65. 65 Low- liquidity Session Periods with long-horizon investorsPeriods with short-horizon investors FUNDTRENDCOMBINEDFUNDTRENDCOMBINED Const. -2.275***1.054-2.543**-0.804-0.248-1.636** (0.684)(0.737)(0.742)(0.524)(0.399)(0.671) (F t - P t ) 0.401***0.419***0.070***0.065** (0.092)(0.096)(0.017)(0.024) (P t - P t-1 ) -0.088-0.016-0.162*-0.180** (0.079)(0.031)(0.081)(0.074) N 171162 186168 F 19.361.2610.1016.253.95 5.82 p 0.0000.2740.001 0.0630.012 adj. R2 0.430.010.430.08 0.13

66. Conclusions Our experimental results showed that speculating investors cause price indeterminacy in financial markets. – Deviations of prices from fundamental values increase significantly when only speculating investors are present in the market. – Prices are more likely to depart from the fundamentals as the presence of speculators. – Price expectations are formed not based on fundamentals but based on recent price changes. – Speculation creates upward pressure on prices when liquidity is high and downward pressure when liquidity is low. 66

67. Implications Frequently observed price bubbles (e.g., stock, gold, real estate) may arise from short trading horizons of investors. The excess price volatility (e.g. LeRoy and Porter 1981, Shiller 1981) in real stock markets may be caused by the existence of short-horizon investors. Market inefficiency, anomalies, and behavioral phenomena more likely to be observed in markets dominated by short-horizon investors. As the number of generations to maturity increases, forming rational expectations is more difficult and prices tend to deviate more from fundamentals. Duration of a security matters, raising questions about M&M. The results doubt on the validity of investors’ ability to form RE - a commonly applied assumption in finance literature. When backward induction becomes practically impossible, investors resort to forward induction from the past data (history is used for investment decisions) Monetary policy matters for stabilization of security markets 67

69. Table 5: Treatment averages for market efficiency measures Relative Absolute Deviation Relative Deviation Bid-Ask Spread Std. Dev. of Log Returns Share Turnover T1L11.43%-5.24%8.79%4.70%1.60 T2L35.47%-18.95%19.92%17.56%1.69 T4L42.92%-34.07%22.52%25.16%1.56 T8L43.03%-30.48%21.69%26.24%1.05 T1H41.99%37.39%29.61%14.08%2.01 T2H77.02%38.81%55.04%22.70%1.59 T4H73.86%52.11%23.37%17.72%1.57 T8H118.67%103.48%65.95%18.17%1.07

70. Table 6: Differences between averages across treatments, same Liquidity (RAD, RD, SPREAD, VOLA, and ST two-sided Mann-Whitney U) RADT2LT4LT8L T2HT4HT8H T1L 24.03%**31.48%***31.60%*** T1H 35.03%31.87%76.67%* T2L 7.45%7.56% T2H -3.16%41.64% T4L 0.11% T4H 35.03% RDT2LT4LT8L T2HT4HT8H T1L -13.70%**-28.83%***-25.23%** T1H 1.42%14.71%66.09% T2L -15.13%-11.53% T2H 13.29%64.67% T4L 3.60% T4H 51.38% SPREADT2LT4LT8L T2HT4HT8H T1L 11.13%*13.73%**12.90%** T1H 25.43%-6.24%36.34% T2L 2.59%1.76% T2H -31.67%10.91% T4L -0.83% T4H 42.58%** VOLAT2LT4LT8L T2HT4HT8H T1L 12.86%**20.46%***21.54%*** T1H 8.61%3.64%4.09% T2L 7.60%8.68%* T2H -4.98%-4.53% T4L 1.08% T4H 0.45% STT2LT4LT8L T2HT4HT8H T1L 0.09-0.03-0.55** T1H -0.43-0.44-0.94** T2L -0.12-0.64*** T2H -0.02-0.52** T4L -0.51 T4H -0.50**

71. Table 7: Differences between averages across treatments, different Liquidity (RAD, RD, SPREAD, VOLA, and ST two-sided Mann-Whitney U) H minus LRADRDSPREADVOLAST T1 30.56% ** 42.64% *** 20.82% ***9.39%*0.42 T241.56% 57.76% ** 35.12% *5.14%-0.10 T430.95% 86.18% ***0.86%-7.44%0.01 T8 75.64% * 133.96 %*** 44.26% **-8.07%0.02

72. Wrap Up Prices are close to the fundamental values when Investors have long-term horizons. Prices deviate from the fundamental values and become indeterminate when there are only short-term investors in the market. – Investors fail to backward induct to bring prices to the fundamental values. – The shorter the investment horizon (the larger number of generations), the more difficult the backward induction. – Prices in high liquidity treatments are higher and deviate more from fundamentals than those in low liquidity treatments. 72

73. Implications Bubbles are known to occur more often in markets for assets with – (i) longer maturity and duration – (ii) higher uncertainty Consistent with the lab data Inputs to expectation formation matter: – Dividend policy matters! Ex post, market inefficiency, anomalies, and behavioral phenomena more likely to be observed in markets dominated by short-horizon investors (difficulty of backward induction)

74. Thank You! Shyam.sunder@yale.edu http://faculty.som.yale.edu/shyamsunder/ research.html