Transcript Chapter20 File

Chapter 20
Hedge Funds
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
20.1 Hedge Funds Versus
Mutual Funds
20-2
Hedge Funds vs Mutual Funds
Transparency
Mutual Funds
Hedge Funds
• Public info on
portfolio
composition
• Info provided only to
investors
• Unlimited
• < 100, high dollar
minimums
Investors
Strategies
• Must adhere to
prospectus, limited
short selling &
leverage, limited
derivatives usage
• No limitations
20-3
Hedge Funds vs Mutual Funds
Mutual Funds
Liquidity
Fees
Hedge Funds
• Multiple year lock
• Redeem
up periods typical
shares on
demand
• Fixed percentage
• Fixed
of assets; typically
percentage of
1% to 2% plus
assets;
incentive fee =
typically 0.5%
20% of gains
to 2%
above threshold
return
20-4
20.2 Hedge Fund Strategies
20-5
Directional & Non-Directional
Strategies
• Directional strategies
– A position that benefits if one sector of the
market outperforms another, an unhedged bet
on a price movement
– For example, buy bonds in anticipation of an
interest rate decline
20-6
Directional & Non-Directional
Strategies
• Non-Directional strategies
– Attempt to arbitrage a perceived mispricing
• Typically a risky arbitrage
• For example, spread between corporates and
Treasuries is believed to be too large so you buy
the corporates and short the Treasuries.
• Market neutral with respect to overall interest
rates.
• Which type of strategy is riskier,
Directional or Non-Directional?
20-7
Hedge Fund Styles
Insert Table 20.1 here
20-8
Convertible Bond Arbitrage
• Convertible bond arbitrage:
– If the fund thinks the convertible is
underpriced the fund would buy the
convertible and short the stock. Wait for the
mispricing to be fixed.
• Risky strategies, bets on particular
perceived mispricings, called “pure play”
bets
20-9
Statistical Arbitrage
• Statistical arbitrage
– Uses quantitative math models and often automated trading
strategies that attempt to identify small mispricings in multiple
securities.
– Involves placing small bets in hundreds of different securities for
short holding periods (minutes).
– Require fast trading and low transactions costs.
– “Pairs Trading”
• Find two ‘twin’ stocks; short the high priced one and buy the
low priced one.
• Do this for many pairs, rely on law of large numbers.
20-10
20.3 Portable Alpha
20-11
Fundamental risk and mispriced
securities
• Problem:
– A fund finds a positive alpha stock but expects
the overall market to fall.
• Solution:
– Buy the stock and sell stock index futures to
drive effective stock beta to zero,
– This is a ‘market neutral’ pure play,
– When combined with a passive strategy this is
called alpha transfer.
20-12
Pure Play Example
rportfolio  rf  (rM  rf )  e  
β  1.20; α  0.02; rf  0.01;S & P500 Index  800, futuresmultiplier  250
Hedge ratio 
$1,000,000
S0
 1.20  6 contracts
 
800  250
F0
Find a portfolio with P > 0, but rM < 0
The portfolio monthly return is
We wish to hedge by selling stock index futures. How many contracts
should we sell if we have a $1,000,000 portfolio?
Dollar value of the stock portfolio in one month will be:
$1,000,0001 rportfolio   $1,000,000[.01 1.2(rM  .01)  .02  e]
Dollar Value  $1,018,000  $1,200,000rM  $1,000,000e
20-13
Pure Play Example
β  1.20; α  0.02; rf  0.01;S & P500 Index  800, futuresmultiplier  250
Dollar Value  $1,018,000  $1,200,000rM  $1,000,000e
Futures Position Value = 6 x 250 x (F0-F1)
F0 = 1.01S0 from spot futures parity model,
F1 = S1 because of convergence of spot and futures prices at contract maturity, substituting into the
Future’s Position Value formula:
6 x 250 x (1.01S0 – S1)
S1 = S0(1+rM) ; The market moves by rM so we now have:
6 x 250 x (1.01S0 – S0(1+rM))
1500 x (800(.01-rM) = $12,000 - $1,200,000rM
Spot futures position combined:
= 1500 x (S0(.01-rM)); recall S0 = 800 so
Hedged End Value  $1,030,000  $1,000,000e
$1,018,000  $1,200,000rM  $1,000,000e  $12,000  $1,200,000rM
20-14
Pure Play Example
β  1.20; α  0.02; rf  0.01;S & P500 Index  800, futuresmultiplier  250
Starting Dollar Value  $1,000,000
Hedged End Value  $1,030,000  $1,000,000e
$1,030,000  $1,000,000
Re turn 
 .03
$1,000,000
.03  rf  
.01  rf   (.02  )
We have captured the alpha and hedged out the
market risk. (Unsystematic risk remains.)
20-15
Pure Play Example
20-16
20.4 Style Analysis for
Hedge Funds
20-17
Style and Factor Loadings
• Many fund strategies are directional bets and
may be evaluated with style analysis (see
Chapter 18),
• Directional investments will have nonzero betas,
called “factor loadings,”
• Typical factors may include exposure to stock
markets, interest rates, credit conditions and
foreign exchange.
20-18
Style Analysis w/ Hedge Funds
20-19
20.5 Performance
Measurement for Hedge
Funds
20-20
Fund Alphas and Sharpe Ratios
• Hasanhodzic and Lo (2007) find that style adjusted
alphas and Sharpe ratios are significantly greater than
the measures for the S&P500 for a large sample of
hedge funds.
• This implies:
– Hedge fund managers are highly skilled OR
– Aragon (2007) controls for illiquidity of hedge funds
with lockup periods and other redemption restrictions
and finds the alphas become insignificant.
– Related work by Sadka (2008) shows that hedge
funds must generate significantly larger returns to
offset liquidity risk.
20-21
Illiquidity and Hedge Fund
Performance
Prices in illiquid markets tend to exhibit serial correlation.
– In illiquid markets funds estimate values of their
investments to calculate the fund’s share values and rates
of return to quote to investors,
• Funds estimate prices optimistically,
• Funds mark to market slowly instead of all at once,
• Serial correlation is strongly related to fund’s Sharpe
ratios. What does this imply?
– Higher Sharpe ratios are compensation for illiquidity
• The Santa effect:
– Hedge funds typically report results in December
and average returns are highest in December.
20-22
Serial Correlation and Sharpe
Ratios of Hedge Funds
20-23
Fund Performance and
Survivorship Bias
• Survivorship bias is a problem in performance
measurement of risky hedge funds
– Those that don’t survive don’t report results that are
used in estimating average performance.
• Backfill bias
– Hedge funds report returns to publishers only if they
choose to.
20-24
Fund Performance & Factor
Loadings
• Many performance measures assume constant risk levels and many
hedge funds have variable risk levels.
– This implies that the positive alphas may be due to
measurement error.
• Many funds hold options or perform like options
– Option positions make performance measurement more
challenging because options result in nonlinear performance but
most performance measures assume or fit a straight line to
return data.
20-25
Characteristic Line of a Timer
20-26
Characteristic Line of a Stock Portfolio
with Written Options
20-27
Returns on Broad Hedge Fund Index
vs S&P500, 1993-2008
20-28
Returns on Fixed-Income Arbitrage
Funds vs S&P500, 1993-2008
20-29
Returns on Event-Driven Funds vs
S&P500, 1993-2008
20-30
Tail Events and Performance
• Many hedge funds employ mathematical models that
rely on near term historical price data.
• Their strategies’ performance takes the form of a written
put option.
– Writing a put option is a way to capture the put
premium and is appropriate in low volatility markets.
– In high volatility markets they face large losses, out of
pocket if markets fall and large opportunity costs if
markets rise.
• When the more rare large market moves (tail events) do
occur hedge fund performance is not likely to appear as
strong and they may suffer large losses.
20-31
20.6 Fee Structure in Hedge
Funds
20-32
Evaluating Hedge Fund Fees
• Typical hedge fund fees includes a fixed
management fee between 1% and 2% of assets
plus an incentive fee usually equal to 20% or
more of investment profits above a benchmark
performance return.
• Incentive fees are analogous to call options on
the portfolio with a strike price equal to the
current portfolio value x (1+ benchmark return).
20-33
Incentive Fees as a Call Option
20-34
Black-Scholes Value of
Incentive Fee
•
•
•
•
•
•
•
Suppose a hedge fund’s returns have an annual  =30%
The annual incentive fee is 20% of the return over the risk free money
market rate.
The fund has a net asset value of $100 per share and the annual risk free
rate is 5%.
The implicit exercise price of the incentive fee is $100 x 1.05 = $105
The Black-Scholes value of a call option with S0 = $100,
X = $105,  =30% ,T = 1 year, & rf = LN 1.05 = 4.88% is $11.92. (See
Chapter 16 for details on option prices)
Incentive fee is equal to only 20% of the value over $105 so the current
value of the incentive fee = 20% x $11.92 = $2.38 per share or 2.38% of
net asset value.
Coupled with 2% management fee yields total fees of 4.38%, much larger
than mutual funds.
20-35
Fees and the High Water Mark
• High Water Mark
– Funds that experience losses in one period
may not be able to charge any incentive fee
until the prior period losses are regained.
– This complicates estimating the value of the
incentive.
– Gives managers an incentive to close the
fund and start over when large losses occur.
20-36
Funds of Funds
• Funds of funds invest in one or more other hedge funds.
– Serve as ‘feeder funds’ to ultimate hedge fund
– Allows investors to easily diversify across hedge
funds.
– May be a bad deal because of extra layer of fees.
– Earned a bad reputation when it became apparent
that many large fund of funds were major investors in
Bernard Madoff’s $50 billion Ponzi scheme.
20-37
Fees and Funds of Funds
•
Suppose a fund of funds has $1 million invested in each of three hedge funds.
For simplicity assume the hurdle rate to earn incentive fees is a zero rate of
return (no losses) and the normal fixed asset management fee is zero.
Start of year (M$)
End of year (M$)
Gross
rate
of
return
Incentive fee (M$)
End of year value,
net of fee
Net rate of return
•
•
Fund of
Fund 3 Funds
$1.00
$3.00
$0.25
$2.85
Fund 1
$1.00
$1.20
Fund 2
$1.00
$1.40
20%
$0.04
40%
$0.08
-75%
$0
-5%
$0.12
$1.16
16%
$1.32
32%
$0.25
-75%
$2.73
-9%
The fund of funds must pay incentive fees even though it realized a net loss.
The fund of funds normally charges a lower incentive fee to its own investors, but
still another layer of fees.
20-38
The $50 Billion Madoff Scandal
• Madoff operated a $50 billion Ponzi Scheme
– In a Ponzi scheme the con artist (Madoff) promises and
initially pays high returns to investors. The large returns
are generated by paying out to old clients some of the
money paid in by new clients.
• The con also skims some of the money for his or her own
purposes. The scheme can work for some time until the
fund stops growing.
• Madoff was a respected individual, former chairman of
NASDAQ with prestigious client book.
20-39
The $50 Billion Madoff Scandal
• In 2008 redemptions began as clients needed money, scheme
unwound.
• Lack of reporting requirements made the fraud possible but
there were several warning signs:
– Returns were too stable for too long,
– Fund fee structure was too generous,
– Audit firm was not a major auditor,
– All assets were kept in house rather than with a custodian,
– No evidence of option investments Madoff claimed to be
making,
– SEC received a letter in 2000 stating that the fund was a
Ponzi scheme.
20-40