Dynamics of the leverage cycle!

Transcription

1 Dynamics of the leverage cycle!! Newton Ins*tute August 26, 2014 J. Doyne Farmer Ins/tute for New Economic Thinking at the Oxford Mar/n School and Mathema/cal Ins/tute External professor, Santa Fe Ins*tute

2 Genno?e and Leland (1990) Danielsson et al (2001) Geanakoplos (2003, 2010) History Danielsson, Shin and Zigrand (2004, 2010) Fostel and Geanakoplos (2008) Adrian and Shin (2008, 2014) Brunnermeier and Pedersen (2008) Thurner, Farmer and Geanakoplos (2010) Gorton and Metrick (2010) Tasca and BaRston (2010) Adrian, Colla and Shin (2012) Corsi, Marmi and Lillo (2013) Poledna, Thurner, Farmer and Geanakoplos (2014) Caccioli, Shrestha, Moore, Farmer (2014) Aymanns and Farmer (2014) 2

3 Ability to dynamically adjust risk levels should be good, no? probability of contagion =0 = average diversification gamma is parameter allowing dynamic risk control: Bank anticipates problems. Caccioli, Shrestha, Moore and Farmer, 2014

4 Key fact When prices drop leverage goes up When prices rise leverage goes down!! λ = A A L

5 ! model of leveraged value investors! (Thurner, Farmer, Geanakoplos, Quantitative Finance 2011) (Poledna, Thurner, Farmer, Geanakoplos, J. Banking Finance 2014) Agents funds (value investors) noise traders reverting to a fundamental value investors choosing between fund and cash; base decisions on trailing performance of funds bank lending to funds Results clustered volatility, heavy tails better risk control can make things worse Explanation: Leverage causes positive feedback, banks recall loans, generating adverse price pressure

6 bank fund1 fund2 risky asset noise trader investors fund3

7 Value investor s demand 100 Investor heterogeneity in aggression =! variations in slope of demand function 50 D h (t)p(t) m(t) s.s. w.s.s.

8 Wealth & vol. vs. time 100 (a) β=5 β = β = 15 β = β = 25! β = β = 35 β = 40 20! β = 45 β = σ(t) 60 50! ^VIX 80 (b) !! t x 10 Hedge fund wealth fluctuates There are crashes, large volatility fluctuations Evolutionary pressure favors more aggressive funds

9 Main points When mispricing is small, funds act as simple value investors and lower volatility. When market is quiet, aggressive funds gain capital and average leverage increases market becomes more fragile. When mispricing is large funds hit max leverage. Negative price shocks force them to sell into falling market, which causes crashes and amplifies volatility. Realistic fat tails and clustered volatility. Extreme events caused by attempt to control risk. Dynamic leverage regulation (Basel II or III) can make things worse.

10 ABM reproduces time profile of volatility peaks 1 VIX peak profiles 0.5 k1=16.4 k2= (a) σ(t) peak profiles GARCH(1,1) peak profiles (b) k1=9.19 k2= 1.18 (c) time

11 Leverage causes power law tail for stock returns 10 0 (b) P(r>R m>0) " max =1 " max =10!= R P (r >R) R

12 Default vs. leverage <probability of default> unreg. basel perfect. h. (a) λ max

13 How do banks differ from funds? Funds create instabili*es when they are fully leveraged. Banks create instabili*es all the *me if prices drop, leverage goes up and banks sell if prices rise, leverage goes down and banks buy In addi*on, there is a leverage cycle, i.e. leverage varies endogenously due to collec*ve (systemic) effects of individual risk management. 13

14 Systemic effects of bank risk control (Dynamics of the leverage cycle, Aymanns and Farmer, 2014) Banks trade risky assets using leverage Several possible risk management strategies unconstrained: start at an ini*al leverage, let por[olios evolve constant leverage VaR (Basel II): Banks set leverage pro- cyclically based on EMA of asset vola*lity Countercyclical based on vola*lity Countercyclical based on price 14

15 Full agent based model 15

16 Risk management policy Target leverage vs. volatility λ t = α t ( σ 2 P,t + σ 0 ) b 16

17 Two dimensional model p(t) = (t)e 2 (t + 1) = (1 ) 2 (t)+ log p(t) p(t 1) 2, (t) = 2 (t)+ 0 b. With sigma_0 = 0 and b = -1/2: z 1 (t + 1) =(1 )z 1 (t)+ 4 log z 2 (t) z 1 (t) 2, z 2 (t + 1) = z 1 (t)

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19 Limita*ons of 2D model Fixed equity neglects an important component of stress on leveraged investors when prices fall. Model insensi*ve to alpha => independent of av. leverage. Symmetric in cyclicality parameter b. Cannot dis*nguish pro- cyclical and counter- cyclical leverage. 19

20 Leverage targeting Assume bank has a leverage target If current leverage λ under leverage target, borrows B and buys B of asset If over leverage target, sells Band pays back loan λ λ = A(t) A(t) L(t) λ = A(t)+ B A(t) L(t) Bank trades with noise trader = passive investor who maintains fixed fraction of asset

21 Five dimensional model (t) = (t) 2 b (t)+ 0, B(t) = (t)(a(t) L(t)) A(t) 2 (t + 1) =(1 ) 2 (t)+ log L(t + 1) = L(t)+ B(t), p(t) p(t 1) n(t + 1) = (w B (n(t)p(t + 1) + c B (t)+ B(t))) /p(t + 1), p(t + 1) = w B(c B (t)+ B(t)) + w N (t + 1)c N (t). (1 w B n(t) (1 n(t))w N (t)) 2,

22 6 D model with stochastic noise trader Noise trader is mean reverting dw N (t + 1) w N (t) =(0.5 w N (t)) + dw, w N (t + 1) = w N (t)+dw N (t + 1)

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25 Coefficient of varia*on vs. aggression and memory parameter 25

26 Coefficient of varia*on vs aggression and regulatory cyclicality 26

27 Countercyclical policy based on price Increase leverage when prices drop as suggested by Adrian and Shin (2008) d (t + 1) = ( 0 (t)) + q(t), (t + 1) = (t)+d (t + 1), q(t + 1) = (1 )q(t)+ log p(t) p(t 1)

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30 Impact adjusted accounting Caccioli, Bouchaud, Farmer, Risk (2012) Value portfolilo based on average asset price under full liquidation possible to do this because of law of market impact I = Kσ Q V

31 Q VaR Impact Adjusted P Price VaR Impact Adjusted Fabio Caccioli and Vincent Tan Equity VaR/ES (% Loss) VaR Impact Adjusted VaR Impact Adjusted Leverage VaR Impact Adjusted Time

32 Leverage limits 32

33 Conclusions Leverage targe*ng is inherently destabilizing. The existence of an endogenous leverage cycle makes this worse. Macropruden*al policies with dynamic risk limits can be effec*ve, but they should be used with cau*on as they can also be counterproduc*ve. 33