Strategic Interaction between Hedge Funds and Prime Brokers

Transcription

1 Strategic Interaction between Hedge Funds and Prime Brokers Eric Jondeau UNIL & SFI EHL, June 30, 2016 Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

2 Motivation Hedge fund (HF): very reactive, large fluctuations, high leverage Leverage implies vulnerability Leverage is generated by prime brokers (borrowing) and off balance-sheet positions (derivatives) Prime broker (PB): very concentrated industry Top 3: 41.1% of HF 50% of HF have 1 PB, 3% of HF have more than 2 PB Prime brokers provide financing and services Interaction between HF and PB: mutually risky to each other Large loss of HF large loss of PB (asset liquidity risk) PB can withdraw capital from HF (funding liquidity risk) Main interaction: leverage decision Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

3 Motivation Model Interaction between PB decision and HF financing strategy 1 representative PB and 1 representative HF Both are risk neutral and maximize the expected RoE for next period HF obtains financing for long and short positions through margin account (collateralized) Model determines optimal decisions of HF and PB HF: amount of free cash and long/short balance PB: amount of free cash, margin rates, rehypothecation rate Equilibrium lending rate: risk-free rate + risk premium Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

4 Motivation Literature Performance of hedge funds and their service providers: Olaru (2006), Klaus and Rzepkowski (2009), Cumming et al. (2013), Hespeler and Witt (2014), Mirabile (2015), Chung and Kang (2016) Leverage of hedge funds: McGuire and Tsatsaronis (2008), Duffie et al. (2009), Dai and Sundaresan (2010), Ang et al. (2011), Lan et al. (2013), Buraschi et al. (2014), Farnsworth (2014) Leverage of intermediaries and funding liquidity risk: Adrian and Shin (2010), Dudley and Nimalendran (2011), Liu and Mello (2011), Adrian and Shin (2014), Adrian et al. (2014) Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

5 Motivation Financing HF Long Positions Reverse REPO collateral REPO rehyp. collateral Hedge Fund Prime Broker Money Market Fund security cash cash cash cash Security Market Bank Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

6 Motivation Financing HF Short Positions Securities Loaned cash Securities Borrowed cash Hedge Fund Prime Broker Security Lender cash security security cash security Security Market Bank Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

7 Motivation Framework HF optimization problem PB optimization problem Equilibrium lending rate Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

8 Hedge Fund Mechanics of Leveraging: Long Positions Main steps: HF buys n t + shares at price p t... with n t + µ + t of its own equity (margin: µ + t )... and n + t l t of PB loan Securities are deposited as collateral Balance sheet: L t = j n+ j,t p j,t: long position financed through buying on margin M + t = j n+ j,t µ+ j,t : margin account on long positions Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

9 Hedge Fund Mechanics of Leveraging: Short Positions Main steps: HF sells nt shares at price p t borrowed from the PB... with nt µ t of its own equity (margin: µ t ) HF sells the securities on market... and receives proceeds in cash, deposited as collateral Balance sheet: S t = j n j,t p j,t: short position M t = j n+ j,t µ j,t : margin account on short positions Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

10 Hedge Fund HF Balance Sheet Assets Liabilities and Equity Free cash (C t ) Debt (D t ) Cash proceeds (P t ) Short securities (S t ) Long securities (L t ) Equity (Nt H ) Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

11 Hedge Fund Margin account Long positions Initial margin: M + t = µ L,t L t = L t D t At t + 1: M + t+1 = L t+1 D t+1 Maintenance margin: M + t+1 m L,tL t+1 Short positions Initial margin: M t = µ S,t S t = P t S t At t + 1: Mt+1 = P t+1 S t+1 Maintenance margin: Mt+1 m S,tS t+1 Portfolio margining M t+1 = M t+1 + +M t+1 = max(l t+1 D t+1 +P t+1 S t+1, m L,t L t+1 +m S,t S t+1 ) Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

12 Hedge Fund HF Optimization Program risk neutral max RoE, r NH,t+1 = N H t+1 /NH t 1 control variables cash holdings: (1 αt )N H t risky strategy: long position: α tγ tn H t short position: α t(1 γ t)n H t simple investment strategy: exposition to market risk r L,t+1 = β L r M,t+1 rs,t+1 = β S r M,t+1 Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

13 Hedge Fund Parametrized HF Balance Sheet Assets Liabilities and Equity (r F ) Free cash (1 α t) Margin debt α tγ t 1 µ L,t µ L,t (r D ) (r F ) Cash proceeds α t(1 γ t) 1+µ S,t µ S,t Short securities α t(1 γ t) 1 µ S,t (r S ) (r L ) Long securities α tγ t 1 µ L,t Equity 1 (r NH ) - Free cash (1 α t) - Long account α tγ t - Short account α t(1 γ t) (scaled by N H t ) Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

14 Hedge Fund Impact of a Market Crash When market goes down, sequence of HF actions (increasing cost): 0-10 Regular margin call Using free cash only Buying back short positions Selling long positions Default Hedge fund rn H (M C) 7r M (F C) 7r M 7r (SS) M 7r (DE) M rm (in %) Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

15 Hedge Fund HF Decisions as a Function of µ M 1 Margin multiplier (, $ ) 1 Fraction of long positions (. $ ) Return on equity (in %) Gross leverage M Probability of default (in %) Lending rate (in %) M Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

16 Hedge Fund HF Decisions as a Function of σ M 1 Margin multiplier (, $ ) 1 Fraction of long positions (. $ ) Return on equity (in %) Gross leverage < M Probability of default (in %) Lending rate (in %) < M Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

17 Hedge Fund HF Decisions as a Function of µ L = µ S 1 Margin multiplier (, $ ) 1 Fraction of long positions (. $ ) Return on equity (in %) Gross leverage L = 7 S Probability of default (in %) Lending rate (in %) L = 7 S Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

18 Hedge Fund HF Decisions as a Function of m L = m S 1 Margin multiplier (, $ ) 1 Fraction of long positions (. $ ) Return on equity (in %) Gross leverage m L = m S Probability of default (in %) Lending rate (in %) m L = m S Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

19 Prime Broker Sources of PB Revenues PB makes money from HF through 3 channels: the difference between the borrowing rate and the lending rate for HF long positions the difference between cost and revenue of financing HF short positions the remuneration on the interbank market Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

20 Prime Broker PB Actions Buying on margin PB provides [α t γ t (1 µ L,t )/µ L,t ]Nt H Its own financing: Short selling of cash to the HF [ρt α t γ t (1 µ P L,t )/µ L,t]N H t from rehypothecation [α t γ t ((1 µ L,t ) ρ t (1 µ P L,t ))/µ L,t]N H t from the (unsecured) interbank market PB borrows securities from another broker and deposits [α t (1 γ t )(1 µ P S,t )/µ S,t]N H t as collateral It lends the securities to the HF and receives [α t (1 γ t )(1 µ S,t )/µ S,t ]N H t as collateral (cash proceeds) The difference, [α t (1 γ t )(µ S,t µ P S,t )/µ S,t]N H t, is invested on the (unsecured) interbank market. Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

21 Prime Broker PB Optimization Program risk neutral max RoE, r NP,t+1 = N P t+1 /NP t 1 control variables cash holdings: (1 α P t )Nt P rehypothecation rate: ρt margin rates: µ L,t, µ S,t, m L,t, m S,t own securities: A P t N P t determined by regulatory limit on leverage: Debt ϑ Equity If HF liquidates its positions, PB also has to liquidate (with a cost) Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

22 Prime Broker PB Balance Sheet Assets Unsecured cash Liabilities and Equity Unsecured borrowing (r I ) α t(1 γ t) µ S,t µ P S,t µ S,t N H t + (1 α P t )NP t α tγ t 1 µ L,t ρ t (1 µ P L,t ) µ L,t N H t (r I ) Collateralized Agreements: (Securities borrowed) Collateralized Financings: (Securities loaned) (r F ) α t(1 γ t) 1+µP S,t µ S,t N H t α t(1 γ t) 1+µ S,t µ S,t N H t (r F ) Receivables from HF: (Reverse repo) Payables to MMF: (Repo) (r D ) α tγ t 1 µ L,t µ L,t N H t ρ tα tγ t 1 µ P L,t µ L,t N H t (r C ) Own securities portfolio Equity (r M ) A P t = α P t N P t N P t (r NP ) - Free cash (1 α P t )NP t - Other α P t N P t Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

23 Prime Broker Impact of a Market Crash Hedge fund r N H Prime broker r N P (M C) 7r M (F C) 7r M 7r (SS) M 7r (DE) M r M (in %) Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

24 Prime Broker Equilibrium Lending Rate Lending rate = risk-free rate + risk premium r D,t = r F,t + RP t RP t covers the expected loss of the PB due to a HF default: [ ] (1 + rd,t )Dt H (D H RP t = E t+1 HF default) t = D H t [ (1 + r D,t ) (1 + r F,t ) [αt(1 γt) + µ S,t(1 α tγ t)]µ L,t α tγ t(1 µ L,t )µ S,t (1 + β L µ (DE) M,t ) 1 φ 1 µ L,t + (1 + β S µ (DE) M,t ) (1 + θ)αt(1 γt)µ L,t α tγ t(1 µ L,t )µ S,t ] F (log(1 + r (DE) M,t )) RP t depends on HF decisions (α and γ) PB decisions (µl and µ S ) Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

25 Results Calibration Hedge fund Symbol Value Liquidation cost for long positions φ 5% Liquidation cost for short positions θ 2% Sensitivity of long positions β L 1.1 Sensitivity of short positions β S 0.2 Prime broker Liquidation cost for long positions φ 2.5% Liquidation cost for short positions θ 1% Initial margin rate µ P L = µp S 20% Maintenance margin rate m P L = mp S 10% Maximum leverage ratio ϑ 10 Market return and interest rates Expected market return µ M 2% Market volatility σ M 22.5% Risk-free rate r F 1.5% General collateral rate r C 1.55% Short-term interbank rate r I 1.75% Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

26 Results Benchmark HF decision variables ϑ = 10 σ M = 22.5% α γ PB decision variables µ L = µ S ml = m S 0.18 α P ρ Rates and expected returns (% per year) rd,t E t [r NH,t+1 ] E t [r NP,t+1 ] Probability of default (in %) Pr[r M,t+1 < r (DE) M,t+1 ] Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

27 Results Balance sheet of HF at equilibrium Assets Liabilities and Equity Free cash 1153 Margin debt Cash proceeds 6498 Short securities 5142 Long securities Equity Free cash Long account Short account 1356 Total Total Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

28 Results Balance sheet of PB at equilibrium Assets Liabilities and Equity Unsecured Cash 1246 Unsecured borrowing 1806 Securities borrowed 6171 Securities loaned 6498 Receivables from HF Payables to investor Securities portfolio 2559 Equity Free cash Other 919 Total Total Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

29 Results Alternative parametrizations Benchmark Alternative 1 Alternative 2 ϑ = 10, σ M = 22.5% ϑ = 5 σ M = 23% Hedge fund s decision variables α γ Prime broker s decision variables µ L = µ S ml = m S α P ρ Rates and expected returns (% per year) rd,t E t [r NH,t+1 ] E t [r NP,t+1 ] Probability of default (in %) Pr[r M,t+1 < r (DE) M,t+1 ] Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

30 Results Strategic Interaction More regulation on PB (decrease ϑ) PB reduces margin rate HF increases leverage Prob of default increases More risk Riskier market return (increase σ) PB increases margin rates HF decreases leverage Prob of default decreases Less risk Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31

31 Results Extensions impact of Basel III ratios redemption risk from HF investors investment strategy of the HF... Nataliya Gerasimova and Eric Jondeau Hedge Funds and Prime Brokers EHL, June 30, / 31