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, 2016
1 / 31
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
I
I
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
I
I
I
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, 2016
2 / 31
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, 2016
3 / 31
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, 2016
4 / 31
Motivation
Financing HF Long Positions
Reverse REPO
REPO
rehyp. collateral
collateral
Hedge Fund
cash
cash
security
cash
Security Market
Nataliya Gerasimova and Eric Jondeau
Money Market Fund
Prime Broker
cash
Bank
Hedge Funds and Prime Brokers
EHL, June 30, 2016
5 / 31
Motivation
Financing HF Short Positions
Securities Loaned
Securities Borrowed
cash
Hedge Fund
cash
security
security
cash
security
Security Market
Nataliya Gerasimova and Eric Jondeau
Security Lender
Prime Broker
cash
Bank
Hedge Funds and Prime Brokers
EHL, June 30, 2016
6 / 31
Motivation
Framework
HF optimization problem
PB optimization problem
Equilibrium lending rate
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
7 / 31
Hedge Fund
Mechanics of Leveraging: Long Positions
Main steps:
HF buys nt+ shares at price pt
+
... with nt+ µ+
t of its own equity (margin: µt )
... and nt+ lt of PB loan
Securities are deposited as collateral
Balance sheet:
P +
Lt = j nj,t
pj,t : long position financed through buying on margin
P + +
+
Mt = j nj,t µj,t : margin account on long positions
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
8 / 31
Hedge Fund
Mechanics of Leveraging: Short Positions
Main steps:
HF sells nt− shares at price pt borrowed from the PB
−
... with nt− µ−
t of its own equity (margin: µt )
HF sells the securities on market
... and receives proceeds in cash, deposited as collateral
Balance sheet:
P −
St = j nj,t
pj,t : short position
P + −
−
Mt = j nj,t µj,t : margin account on short positions
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
9 / 31
Hedge Fund
HF Balance Sheet
Liabilities and Equity
Assets
Free cash
(Ct )
Debt
(Dt )
Cash proceeds
(Pt )
Short securities
(St )
Long securities
(Lt )
Equity
(NtH )
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
10 / 31
Hedge Fund
Margin account
Long positions
Initial margin: Mt+ = µL,t Lt = Lt − Dt
+
At t + 1: Mt+1
= Lt+1 − Dt+1
+
Maintenance margin: Mt+1
≥ mL,t Lt+1
Short positions
Initial margin: Mt− = µS,t St = Pt − St
−
At t + 1: Mt+1
= Pt+1 − St+1
−
Maintenance margin: Mt+1
≥ mS,t St+1
Portfolio margining
+
−
Mt+1 = Mt+1
+Mt+1
= max(Lt+1 −Dt+1 +Pt+1 −St+1 , mL,t Lt+1 +mS,t St+1 )
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
11 / 31
Hedge Fund
HF Optimization Program
H /N H − 1
risk neutral ⇒ max RoE, rNH,t+1 = Nt+1
t
control variables
I
cash holdings: (1 − αt )NtH
I
risky strategy:
F
long position: αt γt NtH
F
short position: αt (1 − γt )NtH
simple investment strategy: exposition to market risk
I
rL,t+1 = βL rM,t+1
I
rS,t+1 = βS rM,t+1
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
12 / 31
Hedge Fund
Parametrized HF Balance Sheet
Assets
(rF )
(rF )
(rL )
Free cash
Cash proceeds
Long securities
Liabilities and Equity
(1 − αt )
αt (1 −
1
1+µ
γt ) µS,tS,t
αt γt µL,t
1−µL,t
µL,t
Margin debt
αt γt
(rD )
Short securities
1
αt (1 − γt ) µS,t
(rS )
Equity
1
(rNH )
- Free cash
- Long account
- Short account
(1 − αt )
αt γt
αt (1 − γt )
(scaled by NtH )
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
13 / 31
Hedge Fund
Impact of a Market Crash
When market goes down, sequence of HF actions (increasing cost):
0
-10
-20
Regular margin call
-30
Using free cash only
Buying back short positions
-40
-50
Selling long positions
-60
Default
-70
Hedge fund rN H
(M C )
r7M
(F C )
r7M
(SS)
r7M
(DE)
r7M
-80
-90
-100
-40
-35
-30
-25
-20
-15
-10
-5
0
rM (in %)
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
14 / 31
Hedge Fund
HF Decisions as a Function of µM
1
Margin multiplier (,$ )
1
0.9
0.9
0.8
0.8
0.7
0.01
20
0.015
0.02
0.025
0.03
0.035
Return on equity (in %)
0.7
0.01
0.8
Fraction of long positions (. $ )
0.015
0.02
0.025
0.03
0.035
Probability of default (in %)
0.6
15
0.4
10
5
0.01
0.2
0.015
0.02
0.025
0.03
0.035
Gross leverage
4
0
0.01
0.015
2
3
0.02
0.025
0.03
0.035
Lending rate (in %)
1.8
2
1.6
1
0
0.01
0.015
0.02
0.025
0.03
0.035
1.4
0.01
0.015
7M
Nataliya Gerasimova and Eric Jondeau
0.02
0.025
0.03
0.035
7M
Hedge Funds and Prime Brokers
EHL, June 30, 2016
15 / 31
Hedge Fund
HF Decisions as a Function of σM
1
Margin multiplier (,$ )
1
0.9
0.9
0.8
0.8
0.7
0.2
14
0.22
0.24
0.26
0.28
Return on equity (in %)
0.7
0.2
3
12
2
10
1
8
0.2
0.22
0.24
0.26
0.28
Gross leverage
4
0
0.2
Fraction of long positions (. $ )
0.22
0.22
0.26
0.28
0.24
0.26
0.28
Lending rate (in %)
2
3
0.24
Probability of default (in %)
1.8
2
1.6
1
0
0.2
0.22
0.24
0.26
0.28
1.4
0.2
0.22
<M
Nataliya Gerasimova and Eric Jondeau
0.24
0.26
0.28
<M
Hedge Funds and Prime Brokers
EHL, June 30, 2016
16 / 31
Hedge Fund
HF Decisions as a Function of µL = µS
1
Margin multiplier (,$ )
1
0.9
0.9
0.8
0.8
0.7
0.2
12
0.3
0.4
0.5
Return on equity (in %)
0.7
0.2
0.3
11
Fraction of long positions (. $ )
0.3
0.4
0.5
Probability of default (in %)
0.2
10
0.1
9
8
0.2
4
0.3
0.4
0.5
Gross leverage
0
0.2
2
3
0.3
0.4
0.5
Lending rate (in %)
1.8
2
1.6
1
0
0.2
0.3
0.4
0.5
1.4
0.2
7L = 7S
Nataliya Gerasimova and Eric Jondeau
0.3
0.4
0.5
7L = 7S
Hedge Funds and Prime Brokers
EHL, June 30, 2016
17 / 31
Hedge Fund
HF Decisions as a Function of mL = mS
1
Margin multiplier (,$ )
1
0.9
0.9
0.8
0.8
0.7
0.15
12
0.2
0.25
0.3
Return on equity (in %)
Fraction of long positions (. $ )
0.7
0.15
0.8
0.2
0.25
0.3
Probability of default (in %)
0.6
11
0.4
10
9
0.15
4
0.2
0.2
0.25
0.3
Gross leverage
0
0.15
2
3
0.2
0.25
0.3
Lending rate (in %)
1.8
2
1.6
1
0
0.15
0.2
0.25
0.3
1.4
0.15
mL = mS
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
0.2
0.25
0.3
mL = mS
EHL, June 30, 2016
18 / 31
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, 2016
19 / 31
Prime Broker
PB Actions
Buying on margin
PB provides [αt γt (1 − µL,t )/µL,t ]NtH of cash to the HF
Its own financing:
I
I
[ρt αt γt (1 − µPL,t )/µL,t ]NtH from rehypothecation
[αt γt ((1 − µL,t ) − ρt (1 − µPL,t ))/µL,t ]NtH from the (unsecured)
interbank market
Short selling
PB borrows securities from another broker and deposits
[αt (1 − γt )(1 − µPS,t )/µS,t ]NtH as collateral
It lends the securities to the HF and receives
[αt (1 − γt )(1 − µS,t )/µS,t ]NtH as collateral (cash proceeds)
The difference, [αt (1 − γt )(µS,t − µPS,t )/µS,t ]NtH , is invested on the
(unsecured) interbank market.
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
20 / 31
Prime Broker
PB Optimization Program
P /N P − 1
risk neutral ⇒ max RoE, rNP,t+1 = Nt+1
t
control variables
I
cash holdings: (1 − αtP )NtP
I
rehypothecation rate: ρt
I
margin rates: µL,t , µS,t , mL,t , mS,t
I
own securities: APt
NtP 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, 2016
21 / 31
Prime Broker
PB Balance Sheet
Liabilities and Equity
Unsecured borrowing
Assets
Unsecured cash
(rI )
αt (1 − γt )
µS,t −µP
S,t
µS,t
P
NtH + (1 − αP
t )Nt
Collateralized Agreements:
(Securities borrowed)
(rF )
αt (1 − γt )
1+µP
S,t
µS,t
NtH
Receivables from HF:
(Reverse repo)
1−µL,t
µL,t
αt γt
1−µL,t −ρt (1−µP
L,t )
NtH
µL,t
Collateralized Financings:
(Securities loaned)
αt (1 − γt )
ρt αt γt
Own securities portfolio
Equity
P
P
AP
t = αt N t
NtP
αt γt
(rM )
1+µS,t
µS,t
1−µP
L,t
µL,t
- Free cash
- Other
Nataliya Gerasimova and Eric Jondeau
NtH
(rF )
Payables to MMF:
(Repo)
NtH
(rD )
(rI )
Hedge Funds and Prime Brokers
NtH
(rC )
(rNP )
P
(1 − αP
t )Nt
P
αP
t Nt
EHL, June 30, 2016
22 / 31
Prime Broker
Impact of a Market Crash
0
-10
-20
-30
-40
-50
-60
-70
Hedge fund rN H
Prime broker rN P
(M C )
r7M
(F C )
r7M
(SS)
r7M
(DE)
r7M
-80
-90
-100
-40
-35
-30
-25
-20
-15
-10
-5
0
rM (in %)
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
23 / 31
Prime Broker
Equilibrium Lending Rate
Lending rate = risk-free rate + risk premium
rD,t = rF ,t + RPt
RPt covers the expected loss of the PB due to a HF default:
RPt
H
(1 + rD,t )DtH − (Dt+1
|HF default)
Et
DtH
[αt (1 − γt ) + µS,t (1 − αt γt )]µL,t
(1 + rD,t ) − (1 + rF ,t )
αt γt (1 − µL,t )µS,t
=
=
−
(1 +
(DE )
βL µM,t )
1−φ
(DE ) (1 + θ)αt (1 − γt )µL,t
(DE )
+ (1 + βS µM,t )
F (log(1 + r¯M,t ))
1 − µL,t
αt γt (1 − µL,t )µS,t
RPt depends on
I
HF decisions (α and γ)
I
PB decisions (µL and µS )
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
24 / 31
Results
Calibration
Symbol
Value
Liquidation cost for long positions
Liquidation cost for short positions
φ
θ
5%
2%
Sensitivity of long positions
Sensitivity of short positions
Prime broker
βL
βS
1.1
0.2
Liquidation cost for long positions
Liquidation cost for short positions
φ0
θ0
2.5%
1%
P
µP
L = µS
P
mL = mSP
20%
10%
ϑ
10
µM
σM
rF
rC
rI
2%
22.5%
1.5%
1.55%
1.75%
Hedge fund
Initial margin rate
Maintenance margin rate
Maximum leverage ratio
Market return and interest rates
Expected market return
Market volatility
Risk-free rate
General collateral rate
Short-term interbank rate
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
25 / 31
Results
Benchmark
ϑ = 10
σM = 22.5%
HF decision variables
α∗
γ∗
PB decision variables
0.923
0.902
µ∗L = µ∗S
mL∗ = mS∗
αP∗
ρ∗
Rates and expected returns
0.264
0.18
0.736
0.698
(% per year)
∗
rD,t
1.552
Et [rNH,t+1 ]
11.458
Et [rNP,t+1 ]
3.351
Probability of default (in %)
(DE )
Pr[rM,t+1 < r¯M,t+1 ]
Nataliya Gerasimova and Eric Jondeau
0.373
Hedge Funds and Prime Brokers
EHL, June 30, 2016
26 / 31
Results
Balance sheet of HF at equilibrium
Assets
Free cash
1153
Liabilities and Equity
Margin debt
34898
Cash proceeds
6498
Short securities
Long securities
47390
Total
Nataliya Gerasimova and Eric Jondeau
55040
5142
Equity
15000
- Free cash
- Long account
- Short account
1153
12492
1356
Total
55040
Hedge Funds and Prime Brokers
EHL, June 30, 2016
27 / 31
Results
Balance sheet of PB at equilibrium
Assets
Unsecured Cash
1246
Liabilities and Equity
Unsecured borrowing
1806
Securities borrowed
6171
Securities loaned
Receivables from HF
34898
Securities portfolio
Total
Nataliya Gerasimova and Eric Jondeau
2559
44873
6498
Payables to investor
26473
Equity
3478
- Free cash
- Other
3478
919
Total
Hedge Funds and Prime Brokers
44873
EHL, June 30, 2016
28 / 31
Results
Alternative parametrizations
Benchmark
ϑ = 10, σM = 22.5%
Hedge fund’s decision variables
Alternative 1
ϑ=5
Alternative 2
σM = 23%
α∗
0.923
γ∗
0.902
Prime broker’s decision variables
0.945
0.924
0.936
0.958
µ∗L = µ∗S
0.264
mL∗ = mS∗
0.180
αP∗
0.736
ρ∗
0.698
Rates and expected returns (% per year)
0.254
0.154
0.677
0.556
0.292
0.197
0.695
0.709
1.648
11.832
3.590
1.550
11.414
3.167
0.893
0.348
∗
rD,t
1.550
Et [rNH,t+1 ]
11.458
Et [rNP,t+1 ]
3.351
Probability of default (in %)
(DE )
Pr[rM,t+1 < r¯M,t+1 ]
Nataliya Gerasimova and Eric Jondeau
0.373
Hedge Funds and Prime Brokers
EHL, June 30, 2016
29 / 31
Results
Strategic Interaction
More regulation on PB (decrease ϑ)
I
PB reduces margin rate
I
HF increases leverage
I
Prob of default increases
⇒ More risk
Riskier market return (increase σ)
I
PB increases margin rates
I
HF decreases leverage
I
Prob of default decreases
⇒ Less risk
Nataliya Gerasimova and Eric Jondeau
Hedge Funds and Prime Brokers
EHL, June 30, 2016
30 / 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, 2016
31 / 31