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
Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion Definition If a mean-variance investor, who demands A i , t ( p ) = E i , t [ p t + 1 + y t + 1 ] − ( 1 + r f ) p , a i V i , t [ p t + 1 + y t + 1 ] expects positive return then A i , t > 0, i.e. investor has “long” position expects negative return then A i , 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
Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion Price Correction A i , t ( p ) = E i , t [ p t + 1 + y t + 1 ] − ( 1 + r f ) p , a i V i , t [ p t + 1 + y t + 1 ] If price change is not expected A i , t > 0 iff ¯ y > pr f , i.e., when asset is undervalued A i , t < 0 iff ¯ y < pr f , i.e., when asset is overvalued A i , t = 0 iff ¯ y = pr f , 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
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
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
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
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: � A , E i , t [ p t + 1 ] + ¯ y − ( 1 + r f ) p � − ¯ A i , t ( p ) = max a σ 2 ◮ Analyse stability of the fundamental steady-state and amplitude of oscillations Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability
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 r f ◮ risky: price p t and i.i.d. dividend y t with mean ¯ y S fundamental price p f = (¯ supply per investor ¯ y − a σ 2 ¯ S ) / r f 2. mean-variance demand for the risky asset � � a σ 2 � z h , t = E h , t p t + 1 + y t + 1 − ( 1 + r f ) p t 3. heterogeneous expectations of agents ◮ fundamentalists: E f , t [ p t + 1 ] = p f ◮ trend-followers: E c , t [ p t + 1 ] = p f + g ( p t − 1 − p f ) , g ≥ 1 Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability
Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion Dynamical model of financial market 4. market clears, price p t is determined H 1 g p t − p f = n h , t E h , t [ p t + 1 − p f ] = n 2 , t ( p t − 1 − p f ) � 1 + r f 1 + r f h = 1 5. performances are computed � E h , t − 1 [ x t ] − ( 1 + r f ) x t − 1 � � � + ¯ x t − ( 1 + r f ) x t − 1 + a σ 2 ¯ A h , t − 1 r t = S S a σ 2 Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability
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 U f , t = π f , t − C U c , t = π c , t ◮ fraction of type h is computed as � � n h , t + 1 = exp [ β U h , t ] Z t , with Z t = h exp [ β U h , t ] ◮ β is the intensity of choice β = 0: equal distribution n f , t + 1 = n c , 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
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
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
Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion Two attractors: overvaluation and undervaluation 102 102 100 Price Price 100 98 98 1.5 0 1 -0.5 Return Return 0.5 -1 0 -1.5 1 1 Fractions Fractions 0.5 0.5 0 0 fundamentalists chartists fundamentalists chartists 2 2 Positions Positions 0 0 -2 -2 20 30 40 50 60 70 20 30 40 50 60 70 Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability
Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion Short-Sell Constraints Assume ¯ A > 0 and impose a restriction: A , E i , t [ p t + 1 ] + ¯ y − ( 1 + r f ) p t � � − ¯ A i , t ( p t ) = max . a σ 2 Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability
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
Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion Adjusted demand and supply 4 4 Fundamentalists Chartists Aggregate 3 3 x c x c 2 2 Fundamentalists Price Deviation Price Deviation E C Chartists E U E U Aggregate 1 1 0 0 -1 -1 -2 -2 A+S 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 Adjusted Quantity Adjusted Quantity Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability
Short Selling Heterogeneous Expectations Model Effect of Short Selling Restrictions Robustness Conclusion Effect of short-selling constraints on upper trend 102 102 Price Price 100 100 98 98 0 0 -0.5 -0.5 Return Return -1 -1 -1.5 -1.5 1 1 Fractions Fractions 0.5 0.5 0 0 fundamentalists chartists fundamentalists chartists 2 2 Positions Positions 0 0 -2 -2 20 30 40 50 60 70 20 30 40 50 60 70 Mikhail Anufriev, Jan Tuinstra CeNDEF, University of Amsterdam The Impact of Short-Selling Constraints on Financial Market Stability
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