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The Impact of Short-Selling Constraints on Financial Market - - PowerPoint PPT Presentation

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion The Impact of Short-Selling Constraints on Financial Market Stability Mikhail Anufriev Jan Tuinstra CeNDEF, University of Amsterdam

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

The Impact of Short-Selling Constraints on Financial Market Stability Mikhail Anufriev Jan Tuinstra

CeNDEF, University of Amsterdam

15th International Conference on Computing in Economics and Finance University of Technology, Sydney 16 July 2009

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Definition

If a mean-variance investor, who demands Ai,t(p) = Ei,t[pt+1 + yt+1] − (1 + rf )p ai Vi,t[pt+1 + yt+1] , expects positive return then Ai,t > 0, i.e. investor has “long” position expects negative return then Ai,t < 0, i.e. investor has “short” position

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Price Correction

Ai,t(p) = Ei,t[pt+1 + yt+1] − (1 + rf )p ai Vi,t[pt+1 + yt+1] , If price change is not expected Ai,t > 0 iff ¯ y > prf , i.e., when asset is undervalued Ai,t < 0 iff ¯ y < prf , i.e., when asset is overvalued Ai,t = 0 iff ¯ y = prf , i.e., when price is on the fundamental value Notice that if price responds to the change in demand/supply, then strategy “buy low, sell high” is self-reinforcing and leads to price correction.

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Mechanism

  • 1. investor’s broker “locates” stocks

◮ stock is borrowed ◮ stock is actually not borrowed

  • 2. security is sold and delivered to the buyer
  • 3. investor closes (“covers”) his position,

buying shares back

  • 4. investor return the shares

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Costs and risks of the short-selling strategy

◮ profit is limited, but loss are unlimited ◮ borrowing a stock might be difficult in an absence of a market

for it

◮ a borrowed stock can be recalled at any moment by the lender ◮ legal restrictions ◮ hostility from society

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Short Selling

◮ increases liquidity and informational efficiency, and eliminates

mis-pricing Theory: Miller (JF, 1977), Harrison and Kreps (QJE, 1978),

Diamond and Verrecchia (JFE, 1987), Gallmeyer and Hollifield (JF, 2008) Empirics: Jones and Lamont (JFE, 2002), Lamont and Thaler (JPE, 2003), Diether, Lee and Werner (RFS, 2008)

◮ increases volatility and may lead to market crashes

◮ Lecce, Lepone and Segara (WP, 2006), Setzu and Marchesi (WP,

2008)

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

This Paper

◮ Take a model with heterogeneous agents (Brock and Hommes,

JEDC, 1998)

◮ Introduce the short-selling constraints ¯

A > 0: Ai,t(p) = max

  • −¯

A, Ei,t[pt+1] + ¯ y − (1 + rf )p aσ2

  • ◮ Analyse stability of the fundamental steady-state and amplitude
  • f oscillations

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Dynamical model of financial market

  • 1. two assets

◮ riskless: risk-free interest rate rf ◮ risky: price pt and i.i.d. dividend yt with mean ¯

y supply per investor ¯ S fundamental price pf = (¯ y − aσ2¯ S)/rf

  • 2. mean-variance demand for the risky asset

zh,t = Eh,t

  • pt+1 + yt+1 − (1 + rf ) pt

a σ2

  • 3. heterogeneous expectations of agents

◮ fundamentalists: Ef,t[pt+1] = pf ◮ trend-followers: Ec,t[pt+1] = pf + g (pt−1 − pf ),

g ≥ 1

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Dynamical model of financial market

  • 4. market clears, price pt is determined

pt − pf = 1 1 + rf

H

  • h=1

nh,t Eh,t[pt+1 − pf ] = g 1 + rf n2,t(pt−1 − pf )

  • 5. performances are computed

Ah,t−1rt = Eh,t−1[xt] − (1 + rf )xt−1 a σ2 + ¯ S xt−(1+rf )xt−1+aσ2¯ S

  • Mikhail Anufriev, Jan Tuinstra

CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Evolutionary updating of types

  • 6. agents choose a new type for the next period

◮ past profits of two types

Uf,t = πf,t − C Uc,t = πc,t

◮ fraction of type h is computed as

nh,t+1 = exp[β Uh,t]

  • Zt, with Zt =
  • h exp[β Uh,t]

◮ β is the intensity of choice ◮

β = 0: equal distribution nf,t+1 = nc,t+1 = 0.5

◮

β = +∞: all traders use the optimal strategy

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Two regimes: stable and volatile

Zero Supply Positive Supply

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Two regimes: stable and volatile

◮ β < β∗ :

all agents have 0 assets

◮ β∗ < β < β∗∗ :

“optimistic” type is long, “pessimistic” is short

◮ β > β∗∗ :

fluctuations

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Two attractors: overvaluation and undervaluation

  • 2

2 20 30 40 50 60 70 Positions fundamentalists chartists 0.5 1 Fractions

  • 1.5
  • 1
  • 0.5

Return 98 100 102 Price

  • 2

2 20 30 40 50 60 70 Positions fundamentalists chartists 0.5 1 Fractions 0.5 1 1.5 Return 98 100 102 Price

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Short-Sell Constraints

Assume ¯ A > 0 and impose a restriction: Ai,t(pt) = max

  • − ¯

A, Ei,t[pt+1] + ¯ y − (1 + rf )pt a σ2

  • .

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Short-selling constraints: ¯ A = 1

◮ primary bifurcation is not affected ◮ asymmetry between upper and lower attractors emerges ◮ the mispricing (amplitude of oscillations) increases

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Adjusted demand and supply

  • 2
  • 1

1 2 3 4 2 4 6 8 10 12 14 Price Deviation Adjusted Quantity EU xc Fundamentalists Chartists Aggregate

  • 2
  • 1

1 2 3 4 2 4 6 8 10 12 14 Price Deviation Adjusted Quantity EU EC xc A+S Fundamentalists Chartists Aggregate

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Effect of short-selling constraints on upper trend

  • 2

2 20 30 40 50 60 70 Positions fundamentalists chartists 0.5 1 Fractions

  • 1.5
  • 1
  • 0.5

Return 98 100 102 Price

  • 2

2 20 30 40 50 60 70 Positions fundamentalists chartists 0.5 1 Fractions

  • 1.5
  • 1
  • 0.5

Return 98 100 102 Price

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Short-selling constraints vs. No constraints

When the short sell constraints are binding:

◮ level of price becomes higher

֋ smaller liquidity

◮ level of return is higher (smaller in absolute value)

֋ capital gain

◮ fundamentalists’ performance worsens w.r. to chartists’

֋ (Af,t−1 − Ac,t−1)rt

◮ fraction of fundamentalists is lower

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Effect of short-selling constraints on crash

  • 2

2 20 30 40 50 60 70 Positions fundamentalists chartists 0.5 1 Fractions

  • 1.5
  • 1
  • 0.5

Return 98 100 102 Price 20 40 60 20 30 40 50 60 70 80 90 100 Positions fundamentalists chartists 0.5 1 Fractions

  • 50
  • 30
  • 10

Return 100 120 140 160 Price

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Short-selling constraints vs. No constraints

When the crash takes place under short-sell constraints:

◮ level of price is higher ◮ return is extremely low ◮ fractions of fundamentalists is much higher

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Recall Lower Attractor vs. Upper Attractor

  • 2

2 20 30 40 50 60 70 Positions fundamentalists chartists 0.5 1 Fractions 0.5 1 1.5 Return 98 100 102 Price

  • 2

2 20 30 40 50 60 70 Positions fundamentalists chartists 0.5 1 Fractions

  • 1.5
  • 1
  • 0.5

Return 98 100 102 Price

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Lower Attractor without and with Crash

  • 2

2 20 30 40 50 60 70 Positions fundamentalists chartists 0.5 1 Fractions 0.5 1 1.5 Return 98 100 102 Price

  • 2

2 20 30 40 50 60 70 Positions fundamentalists chartists 0.5 1 Fractions 0.5 1 1.5 Return 98 100 102 Price

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Summary

Under short-sell constraints

◮ primary bifurcation (of the fundamental steady-state) is not

affected (local stability is a local property, and the restrictions at the fundamental steady-state are not binding)

◮ there is an asymmetry between upper and lower attractors

(constrained investors are present there in different proportions)

◮ amplitude of oscillations on the upper attractor increases

(investors who try to eliminate mis-pricing are short)

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Dependence on ¯ A for zero and positive supply

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Fundamentalists vs. Contrarians

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Fundamentalists vs. Sophisticated Trend Followers

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Fundamentalists vs. Sophisticated Trend Followers

95 100 105 110 115 120 125 130 20 40 60 80 100 contsrained at t = 40, A = 7 no constraints

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Fundamentalists vs. Sophisticated Trend Followers

95 100 105 110 115 120 125 130 20 40 60 80 100 contsrained at t = 40, A = 7 no constraints 95 100 105 110 115 120 125 130 20 40 60 80 100 contsrained at t = 40, A = 7 constrained at t = 50, A = 5 no constraints

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Conclusion

◮ Short-sell constraints affect the amplitude of cycle and drive

price up

◮ liquidity effect ◮ “composition” of the ecology effect

◮ Short-sell constraints do not affect the local stability properties

  • f the fundamental steady-state

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Fundamentalists vs. Sophisticated Trend Followers

  • 6
  • 3

3 6 30 40 50 60 70 80 Positions fundamentalists chartists 0.5 1 Fractions

  • 5
  • 2.5

2.5 5 Return 94 97 100 103 106 Price

  • 6
  • 3

3 6 30 40 50 60 70 80 Positions fundamentalists chartists 0.5 1 Fractions

  • 5
  • 2.5

2.5 5 Return 94 97 100 103 106 Price

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability

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Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion

Fundamentalists vs. Contrarians

  • 0.5

0.5 20 25 30 35 40 Positions fundamentalists chartists 0.5 1 Fractions

  • 1
  • 0.5

0.5 1 Return 99 100 101 Price

  • 0.5

0.5 20 25 30 35 40 Positions fundamentalists chartists 0.5 1 Fractions

  • 1
  • 0.5

0.5 1 Return 99 100 101 Price

Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability