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Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
The Mathematics of Hedge Fund Fees
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders(University of Waterloo), Mohammad Shakourifar (Sigma Analysis &
Management Ltd.), Luis Seco.
May 10, 2016
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
Outline
1 Hedge FundsDefinitionHedge Fund FeesA new investment paradigm
2 The First Loss ModelDefinitionOption pricing framework
3 Consequences of the derivative pricing frameworkGraphical analysisBeyond pricing
4 Recap
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionHedge Fund FeesA new investment paradigm
A snow swap
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionHedge Fund FeesA new investment paradigm
Is this a good investment?
Consider a portfolio of two swaps:
A swap with the City, were $10M are exchanged as a function of snowprecipitation in the City.
A swap with the ski resort, where $10M are exchanged as a functionof snow precipitation at the resort.
We charge 10% of the flow ($200,000) as risk premium. We assume a50% correlation between snow fall in the two locations.
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionHedge Fund FeesA new investment paradigm
Is this a good investment?
Our cashflows are:
We post $2M as collateral
We receive $200,000 as a fee
With 75% probability, the two swaps cancel each other’s cash flows
With 12.5% probability, we receive $1M from both the city and theresort
With 12.5% probability, we have to pay $1M to both the city and theresort
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionHedge Fund FeesA new investment paradigm
Is this a good investment?
The investment parameters are:
The expected return is 10%.
The standard deviation is
σ =√
0.125 ∗ [(2M − 200k)2 + (2M + 200k)2] + 0.75 ∗ (200k)2
≈ 50%
Its Sharpe ratio is 0.2
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionHedge Fund FeesA new investment paradigm
The snow fund
We perform 100 similar swaps, with 100 different cities and ski resorts, forexample:
Blue Mountain (Toronto)
Mountain Creek (New Jersey)
Panorama Mountain Village (Calgary)
Snowshoe Mountain (West Virginia)
Steamboat Ski Resort (Hayden, Denver)
Stratton Mountain Resort (Vermont)
Tremblant (Montreal)
Whistler Blackcomb (Vancouver)
etc.
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionHedge Fund FeesA new investment paradigm
The snow fund
With $2Bn, we can then create a very interesting hedge fund:
10% expected return
5% standard deviation
Sharpe ratio of 2.
Since we do not like to work for free, we will charge our investors 1% ofthe AUM, and 20% of the net profits.
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionHedge Fund FeesA new investment paradigm
Hedge Funds
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionHedge Fund FeesA new investment paradigm
Hedge fund economics
Investor Hedge Fund
Gross Profit from Investments $200M 0
Management Fee - $20M $20M
Performance Fee -$36M $36M
Total 7.2% $56M
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionHedge Fund FeesA new investment paradigm
Hedge Fund Fees
Hedge Funds are pooled investment vehicles managed by a managementcompany.
Hedge funds pay the management company two types of fees (2/20):
Fixed management fees, ranging from 1% to 2% of assets or higher
Performance fee, most commonly equal to 20% of net profitsobtained by the fund
Management fees are usually paid quarterly or monthly, whereasperformance fees are usually paid annually.
This fee structure is asymmetric: only the investor has downside.
The business value delivered to the manager is strictly positive.
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionHedge Fund FeesA new investment paradigm
The CalPers syndrome
Calpers announced in 2014 that they were exiting hedge fund investments.One of the reasons quoted was high fees
Are hedge fund fees too high?
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionHedge Fund FeesA new investment paradigm
A new investment paradigm
One of the major forces to restructure the finance world is the shift ofbalance between buy-side and sell-side.
The past: Sell side ruled the finance sector
The future: Investors (buy-side, asset owners), are gaining marketpower
The present: a battle of wits between buy and sell side
Hedge funds: we are moving towards a more symmetric compensationstructure.
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionHedge Fund FeesA new investment paradigm
Innovation in hedge fund economics
Back in our snow-fund example:
In 2008, Intrawest filed for bankruptcy
26 of our swap counterparties therefore are in default
Assume a cold, snowy winter: $260M of lost swap revenue
Investor Hedge Fund
Gross Profit from Investments -$60M 0
Management Fee -$20M $20M
Performance Fee $0M $0M
Total -4% $20M
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionOption pricing framework
First loss models
A new investment model:
The investor provides an investment to the fund X0.Example $100M
The fund manager will absorb the first loss up to a fixed percentageamount c of the initial investment.Example 10 %.
The investor pays a management fee m and performance fee α to themanager.Example: 1% and 50%
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionOption pricing framework
First loss economics
Back in our snow-fund example:
Investor ND HF ND Investor D HF D
Investment Profit $200M 0 0 -$60M
Management Fee -$20M $20M 0 0
Performance Fee -$90M $90M 0 0
Total 4.5% $110M 0 -$60M
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionOption pricing framework
A start-up model
Hedge fund start-ups have become more difficult in recent times
New comers, and funds who seek to introduce new strategies, can optfor a first-loss model to achieve:
SizeTrack recordReputationAim for high grade, institutional investors
Also popular in trading houses, who are looking for young tradingtalent
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionOption pricing framework
A game-theoretic framework
He and Kou (2013) consider a liquidation barrier, adopting aninvestor viewpoint.
Hodder and Jackwerth (2007) adopt a liquidation decision from themanager’s viewpoint.
Goetzmann et al (2003) consider random liquidations andbarrier-driven liquidations
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionOption pricing framework
The first-loss value model
A new game-theoretic situation:
The fact that the manager risks the deposit c to compensate theinvestor for losses delivers value to the investor
The relationship between X0, c , m and α will determine whether theinvestor, or the manager, is the net winner of value add.
We will use the option pricing framework to determine the net businessvalue delivered to investor and manager.
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionOption pricing framework
Buy side vs. sell side
Question: Given values X0, c , m and α, and an investment horizon T , ...
...who wins?
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionOption pricing framework
The option pricing framework
The fund value Xt is split between the Investors It and the Manager Mt
Xt = It + Mt .
The manager receives a management fee equal to m · X0.
The performance fee is valued as a call option on the underlying valueαXt with strike price αX0, payable at time T .
The first-loss guarantee is valued as a (covered) put option, payableto the investor,
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionOption pricing framework
The option pricing framework
The value of the investment to the investor at time T is:
IT =
XT − α(XT − X0) −mX0 when XT ≥ X0
(1 −m)X0 when (1 − c)X0 ≤ XT ≤ X0
XT + (c −m)X0 when XT ≤ X0
and the value to the manager is MT = XT − IT .It is easy to check that
IT = XT −mX0 (pays a management fee)−α(XT − X0)+ (pays a performance fee)
+(X0 − XT )+ − ((1 − c)X0 − XT )+ (receives a guarantee)
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionOption pricing framework
Management Income
Equivalently, the manager’s income will be
MT = mX0 (receives a management fee)+α(XT − X0)+ (receives a performance fee)
−(X0 − XT )+ + ((1 − c)X0 − XT )+ (provides a guarantee)
The performance fee is a call option.
The guarantee is a (short) covered put option.
The net income to the management company is now no longerguaranteed to be positive.
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionOption pricing framework
The price of investing in a hedge fund
An interesting array of new possibilities:
When the investor subscribes to a first-loss fund structure, there is anexchange of options between the investor and the manager:
The investor pays a call option to the manager (the performance fee)and the investor provides a covered put option to the investor (theguarantee).
If c is high enough relative to m and α, it is possible that themanager pays the investor for the privilege of managing her money.
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
DefinitionOption pricing framework
Pricing fees as a derivative
If we assume a fund value process for Xt given by
dXt = rXt dt + σ Xt dWt ,
we can obtain a valuation of the investor fee expenses or manager income,in a risk-neutral valuation framework.
Issues
Lock-ups
Frequency of fee payments
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
Graphical analysisBeyond pricing
Payoff structure comparison
The investor owns 90% of the fund, the manager owns 10%.
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
Graphical analysisBeyond pricing
Sensitivity to Volatility
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
Graphical analysisBeyond pricing
Maturity sensitivity
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
Graphical analysisBeyond pricing
Other topics of interest
Dynamic allocation
Investment redemption
Impact of the fee on portfolio construction
Fund shut-down
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees
Hedge FundsThe First Loss Model
Consequences of the derivative pricing frameworkRecap
Recap
The world is changing: buy-side is gaining power with respect to thesell-side
Hedge fund start-ups are becoming more difficult
Some managers offer a first loss structure to investors
The option pricing framework allows us to perform a cost/benefitanalysis of a particular fee structure
Ben Djerroud (Sigma Analysis & Management Ltd.), David Saunders (University of Waterloo), Mohammad Shakourifar (Sigma Analysis & Management Ltd.), Luis Seco.The Mathematics of Hedge Fund Fees