The Impact of ShortSelling Constraints on Financial Market Stability


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1 The Impact of ShortSelling Constraints on Financial Market Stability Mikhail Anufriev Jan Tuinstra 5th International Conference on Computing in Economics and Finance University of Technology, Sydney 6 July 29
2 Definition If a meanvariance investor, who demands A i,t (p) = E i,t[p t+ + y t+ ] ( + r f )p a i V i,t [p t+ + y t+ ], expects positive return then A i,t >, i.e. investor has long position expects negative return then A i,t <, i.e. investor has short position
3 Price Correction A i,t (p) = E i,t[p t+ + y t+ ] ( + r f )p a i V i,t [p t+ + y t+ ] If price change is not expected A i,t > iff ȳ > pr f, i.e., when asset is undervalued A i,t < iff ȳ < pr f, i.e., when asset is overvalued A i,t = iff ȳ = 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 selfreinforcing and leads to price correction.,
4 Mechanism. 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
5 Costs and risks of the shortselling 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
6 Short Selling increases liquidity and informational efficiency, and eliminates mispricing Theory: Miller (JF, 977), Harrison and Kreps (QJE, 978), Diamond and Verrecchia (JFE, 987), Gallmeyer and Hollifield (JF, 28) Empirics: Jones and Lamont (JFE, 22), Lamont and Thaler (JPE, 23), Diether, Lee and Werner (RFS, 28) increases volatility and may lead to market crashes Lecce, Lepone and Segara (WP, 26), Setzu and Marchesi (WP, 28)
7 This Paper Take a model with heterogeneous agents (Brock and Hommes, JEDC, 998) Introduce the shortselling constraints Ā > : ( A i,t (p) = max Ā, E ) i,t[p t+ ] + ȳ ( + r f )p aσ 2 Analyse stability of the fundamental steadystate and amplitude of oscillations
8 Dynamical model of financial market. two assets riskless: riskfree interest rate r f risky: price p t and i.i.d. dividend y t with mean ȳ supply per investor S fundamental price p f = (ȳ aσ 2 S)/r f 2. meanvariance demand for the risky asset z h,t = E h,t [ pt+ + y t+ ( + r f ) p t ] / a σ 2 3. heterogeneous expectations of agents fundamentalists: Ef,t [p t+ ] = p f trendfollowers: E c,t [p t+ ] = p f + g (p t p f ), g
9 Dynamical model of financial market 4. market clears, price p t is determined p t p f = + r f H n h,t E h,t [p t+ p f ] = h= g + r f n 2,t (p t p f ) 5. performances are computed ( Eh,t [x t ] ( + r f )x t A h,t r t = a σ 2 ) ( + S 2 S) x t (+r f )x t +aσ
10 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+ = exp[β U h,t ] Z t, with Z t = exp[β U h,t] h β is the intensity of choice β = : equal distribution n f,t+ = n c,t+ =.5 β = + : all traders use the optimal strategy
11 Two regimes: stable and volatile Zero Supply Positive Supply
12 Two regimes: stable and volatile β < β : all agents have assets β < β < β : optimistic type is long, pessimistic is short β > β : fluctuations
13 Two attractors: overvaluation and undervaluation 2 2 Price Price 98 Return Return.5.5 Fractions.5 Fractions.5 2 fundamentalists chartists 2 fundamentalists chartists Positions Positions
14 ShortSell Constraints Assume Ā > and impose a restriction: { A i,t (p t ) = max Ā, E i,t[p t+ ] + ȳ ( + r f )p } t a σ 2.
15 Shortselling constraints: Ā = primary bifurcation is not affected asymmetry between upper and lower attractors emerges the mispricing (amplitude of oscillations) increases
16 Adjusted demand and supply 4 3 Fundamentalists Chartists Aggregate 4 3 Price Deviation x c 2 E U Price Deviation x c 2 E C E U Fundamentalists Chartists Aggregate Adjusted Quantity 2 A+S Adjusted Quantity
17 Effect of shortselling constraints on upper trend 2 2 Price Price Return .5 Return Fractions.5 Fractions.5 2 fundamentalists chartists 2 fundamentalists chartists Positions Positions
18 Shortselling 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 (A f,t A c,t )r t fraction of fundamentalists is lower
19 Effect of shortselling constraints on crash 2 6 Price Price Return Return 35 Fractions.5 Fractions.5 2 fundamentalists chartists 6 fundamentalists chartists Positions Positions
20 Shortselling constraints vs. No constraints When the crash takes place under shortsell constraints: level of price is higher return is extremely low fractions of fundamentalists is much higher
21 Recall Lower Attractor vs. Upper Attractor 2 2 Price Price 98 Return.5.5 Return Fractions.5 Fractions.5 2 fundamentalists chartists 2 fundamentalists chartists Positions Positions
22 Lower Attractor without and with Crash 2 2 Price Price Return.5 Return.5 Fractions.5 Fractions.5 2 fundamentalists chartists 2 fundamentalists chartists Positions Positions
23 Summary Under shortsell constraints primary bifurcation (of the fundamental steadystate) is not affected (local stability is a local property, and the restrictions at the fundamental steadystate 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 mispricing are short)
24 Dependence on Ā for zero and positive supply
25 Fundamentalists vs. Contrarians
26 Fundamentalists vs. Sophisticated Trend Followers
27 Fundamentalists vs. Sophisticated Trend Followers 3 25 contsrained at t = 4, A = 7 no constraints
28 Fundamentalists vs. Sophisticated Trend Followers 3 contsrained at t = 4, A = 7 no constraints 3 contsrained at t = 4, A = 7 constrained at t = 5, A = no constraints
29 Conclusion Shortsell constraints affect the amplitude of cycle and drive price up liquidity effect composition of the ecology effect Shortsell constraints do not affect the local stability properties of the fundamental steadystate
30 Fundamentalists vs. Sophisticated Trend Followers Price Price Return Return Fractions.5 Fractions.5 6 fundamentalists chartists 6 fundamentalists chartists Positions 33 Positions
31 Fundamentalists vs. Contrarians Price Price Return .5 Return Fractions.5 Fractions.5 fundamentalists chartists fundamentalists chartists.5.5 Positions Positions
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