SCHWESERNOTES™
FOR THE
FRM EXAM
FRM 2013
Book 4
Part II
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1
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4
£
<4
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Risk Management and Investment Management;
Current Issues in Financial Markets
2 0f 2
KAPLAN
SCHWESER
Topic 62
Cross Reference to GASP Assigned Reading
—
Consiantinides et ah* Chapter 17
KEY CONCEPTS
AIM 62.1
Hedge funds are private investments and have very little financial regulation. They tend to
he highly leveraged, and managers make large bets. On the other hand, mutual funds are
regulated and more structured.
AIM 62.2
There have heen major events affecting die hedge fund industry including large losses
following a change in Fed policy in 1994, the LTCM collapse in 199K, and die dot-com
collapse in 200 1.
AIM 62.3
Managed futures funds focus on investments in bond, equity, commodity futures, and
currency markets around the world. The payoff function of this strategy is similar co a
lookback straddle.
Global macro managers make large bets on directional movements in interest rates,
exchange races, commodities, and stock indices, and do better during extreme moves in die
currency markets.
Merger arbitrage funds bet on spreads related to proposed merger and acquisition
transactions, and perform poorly during major market declines.
Distressed hedge funds invest across the capital structure of firms that are under financial
or operational distress, or are in the middle of bankruptcy. The strategy tends to have a
long-bias. These hedge fund managers try co profit from an issuer’s ability to improve its
operation, or come out of a bankruptcy successfully
Fixed income arbitrage funds try to obtain profits by exploiting inefficiencies and price
anomalies between fixed income securities which are related. Their performance is
correlated to changes in the convertible bond default spread.
Convertible arbitrage funds attempt DO profit from the purchase of convertible securities and
the shorting of corresponding stock.
LongAshorc equity funds take both long and short positions in die equity markets,
diversifying or hedging across sectors, regions, or market capitalizations, and have
directional exposure to the overall market and also have exposure to long small-cap/short
large-cap positions.
Dedicated short bias funds tend to take net short positions in equities, and their returns are
negatively correlated with equities.
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©2013 Kaplan, Inc.
Cross Reference to GASP Assigned Reading
—
Topic 62
Consiantinides et aJ., Chapter 17
Emerging market funds invest in currencies, debt, equities, and other instruments in
countries with emerging or developing markets.
Equity market neutral funds attempt to achieve zero heta(s} against a broad, sec of equity
indices.
AIM 62.4
The cop 50 hedge funds demonstrated statistically .significant alpha relative to the DJCSI
and HFR1 hedge fund indices. The strategy of buying large hedge funds appears to deliver
superior performance, compared to just investing in hedge fund indices. Hedge fund
managers are still delivering alpha relative to peers, and also have low exposure to the
U.S. equity market.
AIM 62.5
Diversification among hedge fund strategies may not always be effective due to the
convergence of risk during times of extreme market stress, There is significant credit-driven
tail risk in a hedge fund portfolio. The use of managed futures may be a partial solution it
has been a strategy with a convex performance profile relative to other hedge fund strategies.
Hedge fund investors need to consider portfolio risks associated with dramatic market
—
events.
AIM 62.6
In the hedge fund industry, risk sharing asymmetry between the principal (investor) and the
(fund manager) is a concern due to variable compensation schemes.
agent
AIM 62.7
Institutional investors flocked to hedge funds beginning in 2000. With the increase of
institutional investment came greater demands on hedge fund management for operational
integrity and governance.
©2013 Kaplan, Inc.
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Topic 62
Cross Reference to GARP Assigned Reading Constantinides et al., Chapter 1?
-
CONCEPT CHECKERS
1.
What critical iliifc occurred in the hedge fund industry following die collapse of
Long-Term Capital Management (LTCM) in 199H and the dot-com bubble burst in
2001?
A. There was a significant drop in assets under management in the hedge fund
industry.
B. There was a large influx of institutional investors investing in hedge funds.
C. Reporting within the hedge fund industry became more regulated dian mutual
funds.
D. There was a significant increase in hedge fund failures.
2,
Which of die following hedge fund strategies would he characterized as an “asset
allocation” strategy that performs hest during extreme moves in the currency
markets?
A. Global macro.
B. Risk arbitrage.
C. Dedicated short bias.
D* Long/short equity.
3.
Comparing hedge fund performance during the time period 2002-2010 to earlier
time periods, how would monthly alpha compare, if looking at large hedge firuds?
A. Alpha was higher in the 2002-2010 rime period.
B. Alpha remained constant over both time periods.
C. A “foresight-assisted” portfolio did not have a statistically significant alpha
during the 2002-2010 rime period.
D. There was a decline in alpha in the 2002-2010 rime period.
4.
Jamie Chen, FRM, is considering investing a client into distressed hedge funds.
Which of die following investments would serve as the best proxy for the types of
returns to expect?
A. Convertible bonds.
B. .Small-cap equities.
C. Managed futures.
D. High-yield bonds.
5.
What would he an ideal approach for a hedge fund investor who is concerned about
die prohlem of risk sharing asymmetry between principals and agents within die
hedge fund industry?
A. Focus on investing in funds for which the fund managers have a good portion of
their own wealth invested.
B. Focus on diversifying among the various niche hedge fund strategies.
C. Focus on funds with improved operational efficiency and transparent corporate
governance.
D. Focus on large funds from the “foresight-assisted” group.
For additional Book 4, Topic 62 practice questions see:
Self- Test Questions: # 6 (page 254)
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©2013 Kaplan, Inc.
Cross Reference
to
Topic 62
CARP Assigned Reading Constantin ides et aJ., Chapter 17
-
CONCEPT CHECKER ANSWERS
1.
B
During the time period fallowing the dot-com collapseÿ hedge funds outperformed the
S&lP 500 with a lower standard deviation, which attracted institutional investment,
2,
A
A global macro fund docs better if there arc extreme moves in the currency markets,
Along with managed futures, global macro is an asset allocation strategy. Managers tafcc
opportunistic bets in different markets. The strategy has a low correladon to equities,
3,
D Comparing the two different time periods, there was a decline in alpha due to more
competition in the hedge fund industry,
4,
D
Distressed hedge funds have Jong exposure to credit risk of corporations with low credit
ratings. Puhlicly traded high-yield bonds are a good proxy for the returns to expect.
5,
A
The incentive fee structure within the hedge fund industry has not really changed over the
years; and there is incentive for managers to take undue risks in order to earn fees. Thus,
there should he a focus on investing in funds for which the fund managers have a good
portion of their own wealth invested.
©2013 Kaplan, Inc.
Page 145
The fallowing is i review of the Risk Management. atid Invesunem Management principles designed in address
the AIM statements set forth hy GARP®. This topic Ls also covered in:
RISK MANAGEMENT FOR HEDGE FUNDS:
INTRODUCTION AND OVERVIEW
Topic 63
EXAM FOCUS
cools are required to capture risk exposures for a variety of dynamic
hedge fund strategies. The investment perspective of hedge fund managers is very different
from institutional investors. There is no position transparency or risk transparency with hedge
funds as they are not subject to the same degree of accountability or regulation requirements.
Traditional static risk measures such as value at risk (VaR); do not address die wide range of
risks associated with hedge funds. For example, VaR is an unconditional statistical measure of
risk, while hedge funds vary strategies based on changing economic conditions. Market VaR
does not capture time-varying risks, credit risks, liquidity risks, event risks, or factor exposure
risks. In addition to the lack of transparency, empirical studies of hedge funds are subject to
survivorship bias, because inactive funds are seldom included in databases for analysis. Phase¬
locking behavior and asymmetric correlations are furdier examples of nonlinear risks diat
traditional risk metrics do not capture. New metrics, such as the Q-statistic and the analysis of
serial autocorrelations, provide valuable insights regarding the underlying liquidity of hedge
funds.
New risk
measurement
INSTITUTIONAL INVESTORS
VS.
HEDGE FUND MANAGERS
AIM 63.1: Compare and contrast the investment perspectives between institutional
investors and hedge fund managers.
Hedge fund managers and institutional investors have very different investment
perspectives, but both desire superior investment performance. Institutional investors have
specific fiduciary responsibilities to understand and explain the investment process. Hedge
fund managers, on the other hand, determine the appropriate risk/ return tradeoff without
the same level of fiduciary disclosure since they do not operate under the same regulatory
constraints as institutional investors. They are instead allowed to protect proprietary
strategies by not revealing position transparency. Therefore, hedge fund managers enjoy die
freedom to switch asset allocation and trading strategies without a pre-disclosed risk/return
structure that institutional investors are required to maintain.
The primary and often only objective for hedge funds is to maximize return, while
institutional investors are typically concerned with return, risk, tracking error, benchmarks,
and peer comparisons. The unique nature of hedge funds creates challenges for risk
management due to the lack of risk transparency. Thus, risk management and risk
transparency are essential for institutional investors, but not for hedge funds. Five unique
aspects of risk management for hedge funds that create challenges for analysis are: (1)
survivorship hias, (2) dynamic risk analytics, (3) nonlinearities, (4} liquidity, and (5} risk
preferences.
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Topic 63
-
Cross Reference to GARP Assigned Reading Lo
Hedge funds are designed to avoid regulatory constraints and compliance issues. Conversely,
federal and state compliance laws are very restrictive lor pension plan sponsors and other
fiduciaries. Intellectual property is a valuable asset that is owned by the institution and is
a product of numerous managers. However, diere is little intellectual property with hedge
funds, where it is common for one manager to have sole responsibility for the fund.
Figure 1 illustrates how hedge fund managers differ from insdtudonal investors with respect
to the following six characteristics: (1) accountability, (2) trading strategies, (3) performance
objectives, (4) risk management, (5) regulatory environment, and (6) intellectual property.
Figure 1: Comparison of Hedge Fund Managers and Institutional Investors
Characteristic
Accountability
Hedge Fund Manager
Manager determines the
appropriate risk/rcturn tradeoff
Institutional Investors
Institutions hatvc fiduciary
responsibility to understand and
explain the investment process
Trading strategics
Proprietary and closely guarded
Managers must fully disclose
risk exposures to institutions
and must maintain strategics
consistent with the institutions
objectives
Performance objective
Return is the primary objective
Return, risk, tracking
error, benchmark, and peer
comparisons arc all important
objectives
Risk management
Non-essential
Risk management and risk
transparency arc essential
Regulatory environment
Fund is designed to avoid
regulatory constraints and
compliance issues
Highly regulated environment
subject to federal and state
compliance laws for pension plan
sponsors and other fiduciaries
Intellectual property
Little intellectual property since
general partner is the fund
Well-defined institutional
investment process that is not
dependent on arty one manager
GENERATING ALPHA WITH RISK MANAGEMENT
AIM 63.2: Explain how proper risk management can itself be a source of alpha for
a hedge fund.
Hedge fund managers often accept more risk in search of higher returns. However, a major
axiom of modern portfolio theory is die tradeoff between risk and return. Higher returns
are associated with higher risks. If die manager is able to truncate risk through proper risk
management, then alpha returns are possible. The following example illustrates how risk
management can be used to create alpha for a hedge fond.
©2013 Kaplan, Inc.
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Topic 63
Cross Reference to GARP Assigned Reading
- Lo
Suppose a hedge fund his an expected annual return of 10% and an annual standard
deviation of 50%. This hedge fund manager uses a risk management strategy that limits
downside returns to -10%. Assuming returns follow a lognormal distribution, we can
use a given table of lognormally distributed returns with various expectations, standard
deviations, and truncation points (i.e., return thresholds) to find die expected annual return
with the incorporation of the risk management strategy. We find that the expected return
when eliminating returns below -1 0% will actually increase to 18.9%, nearly double die
original expected return, which illus crates die value of managing risk.
An obvious downside to this risk management strategy is the cost of implementation. For
example, the cost of implementing a portfolio return floor of —20% by purchasing put
options could be estimated at 15.4% of total assets based on the Black-Scholes-Merton
model. This assumes the risk-free rate is 5%, die strike for the put is 20% out-of-themoney, and volatility is 75%. The more effective the risk management strategy, the more it
will contribute to the managers alpha return.
Professor's Note: You are not expected to know how to solve for the above values
on the exam (e.g., the expected return according to a lognormal distribution
given a return threshold). The figures are used illustration purposes only.
The calculation methodologies are not outlined in the assigned reading, nor are
for
they required by the AIM statement.
LIMITATIONS OP VAR WHEN ANALYZING HEDGE FUNDS
AIM 63.3: Explain the limitations of the VaR measure in capturing the spectrum of
hedge fund risks.
Value at risk (VaR) it a commonly used risk measurement technique that estimates the
amount of loss for a specific time period. The estimates are typically calculated using
volatilities and correlations from historical data. In this section, we will discuss che
limitations of using the VaR technique when measuring hedge fund risks.
The first limitation of VaR as a risk measure for hedge funds is related to the fact that hedge
funds exhibit a wide spectrum of risks. Key components of hedge funds can vary gready,
which contributes to the heterogeneity of risks for hedge funds. For example, consider the
differences that can exist between die risks of a long/short equity hedge fund and a fixed
income hedge fund.
Key components of a typical long/short hedge fund strategy include die following:
Investment style (value, growth, blended, etc.)*
Fundamental analysis (earnings, forecasts, accounting techniques).
*
Estimation of factor exposures (market indices, industries, characteristics).
*
Portfolio optimization {mean-variance analysis, market neutrality).
*
Short-selling limitations (hard-to-horrow securities, short squeezes).
*
Execution
costs (price impact, expenses, borrowing rate, short rebate).
•
Benchmarks and tracking errors (S&P 500 or T-bill rate).
*
*
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Topic 63
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-
Key components of a typical Used-income hedge fund strategy include the following:
Yield curve models (arbitrage or equilibrium}.
Prepayment models (used for mortgage-backed securities).
*
• Option features (call, convertible, put).
Credit risk (default, interest race risk, price risk).
*
• Inflationary pressures and central bank decisions.
Macroeconomic events and factors impacting fixed income instruments.
*
*
As you can see, the key components and risks for these two types of hedge funds vary
greatly. Compounding these differences, hedge fund managers have much greater freedom
in managing their investments compared to institutional asset managers.
A second limitation is that VaR is purely a statistical measure of risk that does not capture
unique risks associated with different underlying economic structures. VaR was originally
designed to measure the risk exposure of portfolios consisting of derivatives in terms of the
amount of loss corresponding to a 5% tail probability. Thus, VaR may not apply ro other
rypes of investments common to hedge funds (e.g., emerging market debt, risk arbitrage, or
convertible bond arbitrage}. Hedge fund managers often use dynamic trading strategies that
vary with different market conditions. Market VaR does not capture these time-varying risks
or other types of risks, such as liquidity risk, event risk, and credit risk.
Professor's Note: As you will encounter in other parts of the curriculum, VaR
has been adapted to measure risks other than market risk. As such, you will
see how to calculate liquidity-adjusted VaR, operational VaR, and credit VaR.
However,
references to VaR by itself typically only refer to the impact of market
risk on the value of assets.
A dfird limitation is chat VaR Is difficult to estimate due to die uncertainty of tail exposure
for differing economic structures. Tail events happen infrequendy and are therefore difficult
LO associate with accurate probabilities. Historical data captures only a few events, and this
sample size is often too small for reliable esdmares. Anodier problem related to tail events
occurs when VaR is used as a risk measure under the assumption that returns are normally
distributed. In this case, tail events are estimated based on the mean and standard deviation
of the underlying distribution rather than the occurrence of rare events. This is problematic
since hedge fund returns are not normally distributed. They are often highly skewed and
asymmetrically distributed with fat tails that imply a greater probability of die occurrence of
rare tail events.
A fourth limitation to VaR is that it is an unconditional measure of risk. The term
unconditional references the underlying distribution. This is a drawback, because hedge
funds are often actively managed based on conditional measures. For example, suppose
the VaR measure for a portfolio over die next week is $2Q million under normal economic
conditions. Alternatively, a conditional probability measure based on changing underlying
market conditions yields a VaR of $ 100 million. Historical data suggests that asset classes
are more highly correlated in market crises (referred to as asymmetric correlations).
Clearly, VaR was not designed to measure the risks associated with hedge funds. Thus,
traditional risk measures designed for static or conditional environments have many
limitations with respect to hedge fund analysis. The unique characteristics of hedge funds
require new risk measurement tools to address dynamic strategies and conditions.
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Topic 63
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—
SURVIVORSHIP BIAS
AIM 63.4: Explain how survivorship bias poses a challenge for hedge fond return
analysis.
Historical data is used to analyze the risk of portfolios and strategies. However, after a
hedge fund is closed, the historical data of that hedge fund is seldom included in data for
future studies. Tire reason for the hedge fund's removal it twofold, first, investors desire
the analysis of funds diat are investible. Second, hinds that are shut down do not wish to
disclose data for legal reasons* The exclusion of data from funds that are no longer active is
known as survivorship bias. A few studies that have included data from inactive funds have
found significantly different results when survivorship bias is not present.
To illustrate the importance of survivorship bias, suppose there are n funds with returns Jf
through J?n. Excess returns per unit of risk are defined using the Sharpe ratio as follows:
,
Rj ~RF
aj
where:
Rp = risk-free race of return
o, standard deviation of returns for asset j
=
In addition, assume that die returns are independently and identically distributed (i.i.d.)
widi distribution function F(X).
Suppose a group of hedge fund portfolio managers are ranked based on their portfolio’s
actual realized performance. In addition, assume that none of these managers possess
superior selection skills {i.e., no alpha is gained). This implies that the expected excess
return per unit of risk for all funds equals zero [E(X+) = 0]. The hest-performing fund is no
better than die worst-performing fund, because there is no alpha. Selection bias will occur
if we falsely assume that one of these managers has superior selection skills.
A fund may he ranked as superior based solely on die realized performance of the fund
without considering the fact that we selected it from a population of funds. Figure 2 further
illustrates the concept of selection bias. The means and standard deviations of die realized
excess return per unit of risk, X*, are reported for the best performing funds out of a sample
of n funds. Assume
are standard normal random variables. Hie selection bias for a
five
funds
of
sample only
implies an excess return per unit of risk ratio of 1.163. As the
sample size is increased, the bias increases to 2.0428 for a sample of 30 funds.
Figure 2: Selection Bias of Manager Performance
n
mv
fTjÿ
1
0.0000
1.0000
5
1.1630
1.5388
1 .8675
2.0428
0.6690
0.5868
0.5251
10
20
30
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Topic 63
—
Cross Reference to CARP Assigned Reading Lo
If we assume no manager possesses superior skills and no alpha is present, then the historical
performance is entirely random and the best performing fund going forward is unknown.
A majority of databases of hedge funds only include currently active funds. This implies a
survivorship bias, because the funds are ranked based on historical realized returns of only
the surviving funds. The performance of inactive funds is ignored and survivorship bias is
compounded over rime as only the hest funds are selected to be included in data analysis.
Thus, the investor must adjust for survivorship bias to construct an optimal portfolio when
including hedge funds.
MEASURING RISK OF DYNAMIC INVESTMENT STRATEGIES
AIM 63.5: Describe how dynamic investment strategies complicate the risk
measurement process for hedge funds.
Hedge fund managers incorporate a variety of strategies due to the freedom from regulatory
constraints. They are able to use leverage, trade actively, adjust asset allocations, and switch
strategies fnequendy. These dynamic investment strategies create constantly changing risk
exposures. As you have learned, modern portfolio theory evaluates systematic risk based on
the beta measure, which is designed to only explain risks for static investments. However,
with dynamic investment strategies, no single risk measure can explain the inherent risk
exposure used by hedge fund managers. To confound the problem of accurately measuring
risk, there is no required position transparency with hedge fund strategies. Thus, hedge fund
managers are able to protect dteir proprietary trading strategies.
A hypothetical hedge fund can be used to illustrate how difficult it is to measure the risk
for various strategies by comparing the results of a trading strategy and the S&P 500 index.
Suppose a hedge funds strategy is shorting S&P 500 (SPX) put options with strike prices
that are 7% out-of-the-money and have maturity dates less than or equal to three months
for each monthly expiration date.
Figure 3 compares the short put hedge fund strategy with the S&P 500 index using
monthly results. The first impression from Figure 3 suggests impressive results for the
hedge fund strategy, which has a monthly mean return of 3.7% compared to the LS&P
500 monthly mean return of 1.4%. The annual Sharpe ratio for the hedge fund is 1*94
compared to 0.98 for the S&P 500 index. If this strategy was implemented from January
1, 1992 to December 31, 1999, the total returns for the hedge fond would be 2,721.3%
compared to 367.1% for the S&P 500 index.
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Topic 63
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-
Figure 3: Performance of Short SPX Put Hedge Fund and S&P 500
Statistics are Based on Monthly Returns
Mean
Standard- deviation
Minimum monthly return
Maximum monthly return
Annual Sharpe ratio
Number of months with negative returns
(total months for period is 96)
Correlation with SAP 500
Total return (1 992—1999)
Short Pal Strategy
S&P500
37%
5-8%
-183%
27-0%
L4%
3-6%
-8-9%
14,0%
1,94
0,98
6
36
0-599
1
2,721-3%
367,1%
As noted earlier, traditional risk measures do not capture the correct risk exposure for
hedge funds- Hedge funds are not required to disclose their trading strategies, which
is problematic since some managers may actually implement a simplistic strategy. It is
douhtfol that investors would pay a hedge fund manager performance feet for following
such a simple strategy. However, due to the lack of transparency for most hedge fund
strategies, investors are not able to detect such behavior without measures chat capture more
dynamic risk exposures.
Consider another example of a hypodietical hedge fund using a delta-hedging strategy. A
delta-hedging strategy synthedcally replicates short posidons. Suppose a hedge fund creates
a synthetic European put option for $l(),O00,0O0 in shares ofXYZ expiring in two years.
Also, assume the synthetic put has a strike price of $25 and die initial stock price Is $40.
As you can see, this strategy involves deep out-of- die-money put options, Titus, this is
a contrarian strategy, where the position in XYZ is increased (decreased) when the price
declines (increases).
Now suppose that a hedge fond manager duplicates this delta-hedging strategy for 500
fundi. This strategy would require a significant amount of leverage; however, without
additional risk analysis chat addresses the dynamic nature of this strategy, it would he
impossible for an investor to truly understand the strategy's risks. Even if the fund disclosed
total position transparency, the underlying risks would .still not be clear,
As discussed, traditional mean-variance risk measures based on static strategies are not
applicable for dynamic trading strategies, -such as shorting out-of-the-money put options
or delta-hedging deep out-of-the-money synthetic puts. Hedge funds that short out-of-themoney put options will result in positive returns that are greater than the S&P 500 index
most of die time. However, as Figure 3 indicates, when the returns are negative, they are
signiheandy lower for the put strategy. That is, the standard deviation does not capture the
amount of tail risk from diis strategy. Therefore, die standard risk measurement tools used
by the hedge fond industry are not sufficient for capturing the risks of dynamic strategies.
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Topic 63
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NONLINEARITIES IN HEDGE FUND RETURNS
AJM 63.6: Describe haw the phase- Locking phenomenon and nonlineaiities in
hedge fund returns can he incorporated into risk models.
“Phase-locking” behavior occurs with events that cause normally uncorrelaced actions to
become highly correlated. For example, in the summer of 199&, the Russian government
defaulted on its debt. This default event started a global crisis where assets that normally
had a correlation of 0 moved together with a correlation of close to 1. It is necessary co
explicidy allow die occurrence of phase-locking events in risk models in order to capture
their impact on hedge funds. Suppose returns are generated by the following two-factor
model:
Rit = “i +
+ 1,2,. + eit
(1)
where:
Rÿt = return on fund i at time t
- fund intercept
(3. - fund sensitivity to the market
M,
= market component
ejf
= idiosyncradc risk (error term)
I,Z, - phase-locking component or catastrophic market event
In addition, assume that
Zt, and ejt are independent and identically distributed
(i.i.d.) variables and the following expected returns and variances apply:
EIMJ.PM
Var[MJ = crÿ
E[eit] = 0
Var[£it] =
4
E[Zt] = 0
Var[2,] =
4
The phase-locking event indicator, 7(, can be defined as:
1 widi probability p
0 with
probability L
—
p
When die probability of a phase-locking event is very small, then the expected return
for the fund is comprised of just o j + PjMt . However, when a phase-locking event is
more probable, then the third component, Z, impacts the expected return for the fund.
The common factor, Z(, will dominate the expected return when there is phase-locking
behavior (i.e., I, = 1) and the volatility of the common factor is significantly larger than the
volatilities of die market factor and the error term.
The conditional correlation coefficient for two funds t andy when there are no phase¬
locking events occurring (i.e*, I, = 0) is shown below. The betas for the two funds, (1
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Topic 63
Cross Reference to GARP Assigned Reading
- Lo
and 3-j axe assumed to be approximately equal at 0 in order
characteristic of most hedge funds.
reflect the market-neutral
PiPjÿM
Corr(R3t,Rjt 1 1, =0) =
Conversely, die conditional correlation coef ficient for
when phase-locking events are present (Le., I( = 1).
Corr(Rjt,Rjt|It = l) =
to
two
funds i andÿ can also he defined
PjPjÿM+4
+ <4 + <4
+ <4 + °lj
If the volatility of the common factor, Ze is significandy larger than the volatilities of the
idiosyncratic risks for bodi funds, and p. and p. are both approximately zero, then the
previous correlation equation will equal roughly 1. "When catastrophic events occur, the
volatility of the catastrophe component will most likely be very high. This will result in
increasing the correlation to a point that is close to 1 for the two funds chat, under normal
conditions, would have a correlation close to 0.
The corneladon measure most commonly used for VaR calculations, portfolio optimization,
and risk reports is known as the unconditional correlation. This measure is formulated
by the unconditional covariance divided by the product of the square roots of the
unconditional variances. One of die hidden implicadons of Equation 1 is that die
unconditional correlation is very small. However, it will tend to increase as the variance of
the phase-locking component increases.
For example, if the variance of the phase-locking component is ten times greater than the
variance of the residuals, then the unconditional correlation is approximately equal to 0.01.
If the variance of the phase-locking component is 10G times greater than the variance of the
residuals, dien die unconditional correlation is approximately equal to 0.10. The explicit
risk model defined by Equation 1, allows for the detection of a phase-locking component
from standard correlation coefficients. Widiour such a risk model, the phase-locking
component is virtually impossible to detect.
Asymmetric correlation refers to the notion diat heta coefficients are more highly correlated
with the market index in down markets dian diey ate in up markets. Thus, asymmetric
correlation creates another nonlinearity risk that traditional risk measurement models do
not capture. This concept is illustrated by the following regression model:
R-it =
+ Pÿ
+ Pi
+ eit
where:
Mt>0
MTH{6Mcotherwise
Mt ifMt<0
M7 = {0 Otherwise
it
Mt = return on the S&P 500 index
Pi = fund i sensitivity to the market
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-
The market return for the LS&P 500 is separated into an up-market return, M+, and
down-market return,
If fund f$ market returns and betas are identical in up-anddown markets, then it will be a special case, which is equivalent to a standard linear
regression model.
L
This regression was specifically used to analyze hedge funds for the period January 19%
to November 1999* Monthly hedge fund returns were separated into positive and negative
returns and analyzed using the S&P 500 as the market index. Figure 4 illustrates the impact
of nonlinearities of two hedge fund strategies. Results for the emerging market equities
index and the option arbitrage index illustrate that beta asymmetries are in fact present
during diis time period. The emerging market equities hedge fund had an up-market heta
of 0.16 and a down-market beta of 1 .49. The relative-value opdon arbitrage index had an
up-market beta of-0.78 and a down-market beta of 0.33. Numerous other types of hedge
funds were tested using the same methodology and yielded similar results. These examples
suggest the hedge funds examined are not truly market-neutral.
Figure 4: Nonlinearities in Hedge Fund Strategies
If
Hedge fund Strategy
—
Emerging market equity
Relative value - option arbitrage
3.78
4.48
0.16
1.49
0.11
-0.78
0.33
0.07
Empirical results suggest the need for dynamic risk measurement models that can account
for phase-locking behavior, asymmetries in factor exposures, and other nojilinearities
that occur with active hedge fund strategies. Nonlinear risk models for all types of hedge
funds should address the following factors: credit, liquidity, market index returns, sectors,
investment style, volatility, and macroeconomic indicators.
MEASURING ASSET LIQUIDITY
AIM 63.7: Explain how autocorrelation of returns can be used as a measure of
liquidity" of the asset.
Consider an unrealistic extreme version of market efficiency where all market movements
are totally random. The martingale model is one of the earliest asset pricing models where
asset returns are assumed to he serially uncorrelated. In other words, the correlations for
all assets have a correlation of 0 with one another. If markets are efficient with respect
to information, then price changes cannot he forecasted. Thus, as markets become
more efficient with respect to information, price changes become more random. Market
inefficiencies that could result in profits are more quickly discovered as the number of
market participants seeking inefficiencies increases.
En the real-world market, frictions exist in the form of transactions costs, borrowing
constraints, information costs, and institutional restrictions. These market imperfections
cause asset returns to exhibit serial autocorrelations. Illiquidity is one of the most common
forms of market friction. Thus, autocorrelations are a useful indicator of liquidity for die
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underlying asset* The degree of serial autocorrelation in an
of ill iquidity friction chat: is present,
asset s returns is a
proxy for die
amount
More liquid assets should exhibit less serial autocorrelation than illiquid assets. For example,
residential real estate investments are very illiquid, and historical returns exhibit much
higher autocorrelations than the returns of the S&P 500 index* In 1965, Samuelson1
suggested that predictability in asset returns will he exploited and eliminated only to the
extent allowed by market frictions. Therefore, even if residential real estate returns are
highly predictable, it is not easy to profit from these predictions. The high transactions
costs associated widi real estate transactions, die inability to short sell properties, and other
market frictions make it difficult to profit from predictions in the real estate market.
Another reason autocorrelations are an important proxy for estimating liquidity is related
to the calculation of a hedge fund’s net asset value (NAV)* A market price is difficult to
determine for assets that are not frequently traded. This illiquidity allows a hedge fund
manager considerable discretion in determining the portfolio’s value at the end of each
mondi, which is used to calculate the fund’s NAV. Hedge fund managers have an incentive
to smooth their returns over time hecause dieir compensation contracts are based on
performance. Smoothing returns over time also decreases die volatility of die fund, which in
turn increases the Sharpe ratio.
When hedge funds smooth returns over time, die smoothing process creates serial
correlation. Ljung and Box2 proposed the following statistic as a summary measure of the
overall statistical significance of the autocorrelations:
=T(k)
Q„=T(T+2)y; T-k
t-1
This statistical measure is approximately chi-squared distributed with m degrees of
freedom in large samples under die null hypothesis of no autocorrelations. The Q-statistie
(sometimes referred to as the Ljung-Box Q-statistic) reflects the absolute magnitudes of the
correlations, because it sums the squared autocorrelations. Thus, die signs do not cancel
each other out, and funds with large positive or negative autocorrelation coefficients will
result in large Q-statistics.
Figure 5 contrasts serial autocorrelations and Q-statistics for the monthly returns of a
sample of mutual funds and hedge funds. The figure reports number of months, T, mean,
fit , standard deviation, cr , autocorrelations pj to p6, and /ÿ-values for the Q-statistic
calculated using the sum of the squared first six autocorrelations. The statistics for two
mutual funds and two hedge funds are reported in Panels A and B, respectively. The results
suggjest diat serial autocorrelations are very low for mutual funds, and the Q-statistics ate
not significant at the 5% level* Conversely, Panel B reflects high serial autocorrelations for
hedge funds, with Q-statistics that are significant at the 5% level.
Samuelson, P 1965. ‘‘Proof That Properly Anticipated Prices Fluctuate Randomly.” Induslriat
Management Review, vof* 6, no. 2 (Spring): 41—49.
2. Ljung, G., and G, Box. 1978, “On a Measure of Lack of Fit in Time Series Models,”
Bwmetrika, Vol. 65, No. 2, 299-315,
1.
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Figure 5: Autocorrelation % of Monthly Returns for Mutual and Hedge Funds
Fund
T
p
(7
Pi
Pi
h
k
h
A
p'VdIit£
°f
A: Mutual Funds
Vanguard 500
286 1.30
4.27 -3.99 -6.60 -4.94
-6.38
10.14
-3.63
31.85
Fidelity Magellan
402 1.73 6.23 12.37 -2-31 -0.35
0.65
7.13
3.14
17.81
Convertible/
option arbitrage
104 1.63 0.97 42.59 28.97 21.35
2.91
-5.89 -9.72
Relative value
97
B: Hedge Funds
0.66
0.21
25.90 19.23 -2.13 -16.39 -6.24
1.36
0.00
3.32
Large mutual funds typically invest in highly liquid securities. Therefore, it is not surprising
that die serial autocorrelations for mutual funds are low. In addition, SEC regulations,
detailed prospectuses, and daily NAV calculations prevent price manipulation or smoothing
of returns. Conversely, the hedge fund sample reveals significant autocorrelations and
Q-statistics that are reflective of potential return smoothing and illiquidity of the underlying
securities. Thus, the results suggest autocorrelations, and Q-statistics provide valuahle risk
metrics for liquidity exposures in hedge funds.
Other Issues to Consider
Risk preferences are important from both die manager’s and investor s perspective.
Hedge fund managers are often compensated with nonlinear payoffs based on fixed and
performance incentives. Thus, there is an incentive for excessive risk-taking on die part of
the manager. In addition, the behavior of investors also influences hedge fond managers.
Hedge fund investments are sometimes referred to as “hot money,” which may encourage
hedge fond managers to be more aggressive in taking on risks. Furthermore, lock-up periods
are often imposed to prevent investors from panicking and running in periods of poor
performance. Risk management tools should also consider these risk preferences of both
managers and investors.
Opera cionnl risks refer to organizational characteristics, such as back-office operations, legal
infrastructure, accounting practices, personnel, trading, and management practices. These
risks, while difficult to quantify, should not be ignored.
Institutional investors, such as pension funds, may find that hedge funds are good fits
for their optimal risk portfolios. However, fiduciary responsibilities require better risk
measurements that reflect risk transparency of the hedge funds. For example, plan sponsors
manage pension fund assets to minimize the risk of defaulting on the plan's liabilities.
However, a completely immunized portfolio against defaults is often too costly to obtain.
Thus, managers maintain a “surplus1’ of assets to liabilities to help control tills risk It is not
clear how much surplus there should be and what is an acceptable level of default risk for
different time horizons, such as one, five, or twenty years. Better risk measurements that
capture these dynamic aspects of pension funds ate required for finding the optimal risk
exposure for pension portfolios that include hedge funds.
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KEY CONCEPTS
AIM 63.1
The investment perspectives of hedge fund managers are very different than those of
institutional investors. This difference is largely due to the lack of position transparency
and risk transparency. Thus, major differences are reflected in the following characteristics:
accountability, trading strategies, performance objectives, risk management, regulatory
environment, and intellectual property.
AIM 63.2
If returns follow a lognormal return distribution, then hedge fond managers maybe able
alpha returns by truncating downside risks.
to
create
AIM 63.3
The following are limitations of VaR as a risk measure for hedge funds:
*
*
*
*
Hedge funds are exposed to a wide variety of risks that VaR cannot measure.
VaR does not capture unique risks for varying economic conditions.
VaR is difficult to estimate because of uncertainty related to tail events.
VaR is an unconditional measure of risk, buL hedge funds use conditional strategies.
AIM 63.4
Survivorship bias refers
to
the exclusion of data from inactive funds in hedge fond data and
analysis.
AIM 63.5
Standard risk measurement cools do not accurately reflect the risks of certain hedge fond
strategies that are not required to reveal positions or strategies. For example, shorting outof-the-money put options or delta-hedging strategies can create impressive, but misleading
performance results using traditional risk measures.
AIM 63.6
“Phase-locking1’ behavior refers to the phenomenon where an event causes assets that
normally have zero correlation to become highly correlated. Asymmetric correlation refers
to another type of nonlinear risk in which correlation coefficients approach one when die
U.S. market Is in a down market.
AIM 63.7
The Q-statisdc Is an absolute measure of correlations, because it sums the squared
autocorrelations. Q-statistics and serial autocorrelations are very useful in measuring the
liquidity risk for a hedge fond.
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CONCEPT CHECKERS
1.
Which of the following statements is not characteristic of hedge funds in general?
Hedge funds:
A. are not subject to a highly regulator)' environment or federal and state
compliance laws.
B. have limited risk transparency as managers desire to protect proprietary
strategies.
C. are equally concerned with risk management and return performance.
D. have little intellectual property as die fond typically relies on one individual.
2.
Constructing optimal hedgie fund portfolios based on analysis of only active hedge
funds results in;
A. riskier portfolios.
B. survivorship bias.
C. excess returns or alpha.
D. lower Sharpe rados.
3.
Creating synthetic put opdons on deep out-of-the-money European securities is a
strategy referred
to
as:
A. market-neutral.
B. synthetic-hedging.
C. delta-hedging.
D. a long/short strategy.
4.
Which of the following statements does not accurately describe a limitation of using
VaR as a risk measure for hedgie funds? VaR is:
A. purely a statistical measure of risk that does not capture unique risks associated
with different underlying economic structures.
B. difficult to estimate due to the uncertainty of tail exposure for different
economic structures.
C. a conditional measure of risk.
D.
5.
not able to
address the wide spectrum of risks that hedge funds cover.
A useful measure for assessing liquidity risk for hedgie funds is die Q-statLstic.
Which of the following statements is true regarding the statistical significance of the
Q-statLstic measure?
A. Smaller
indicate chat autocorrelations are more starts dcally significant.
B. We will be 99% confident that we can reject the null hypothesis of no
correlation when the test statisdc has aÿ-value of 0.1,
C. The null hypothesis of posidve autocorrelations can be rejected when each
lagged autocorrelation is close to zero.
D. Larger /ÿvalues indicate chat autocorrelations are more statistically significant.
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CONCEPT CHECKER ANSWERS
1
L
2.
C
Hedge fund managers enjoy considerable freedom from regulations and compliance issues
compared to pension plan sponsors and other fiduciaries. They are not as concerned with risk
management, and there is little risk transparency as the fund return performance is the major
objective. The fund typically relies on the general partner who protects proprietary strategies.
B
Survivorship bias occurs when funds arc ranked based on historical realized returns of only
the currently active funds, excluding underperforming inactive funds. The Sharpe ratios, or
excess returns per unit of risk will be biased upward for the sample of funds selected from
onlv surviving funds.
3. G
Delta-hedging is a well-known strategy that creates synthetic pur options on deep
out-of-the-money European securities,
4. C
VaR is an unconditionalt measure of risk, referring to the unconditional underlying
distribution. It docs not capture risks associated with hedge funds that are often actively
managed based on conditional measures.
5. A The Q-statLstic reflects the absolute magnitudes of the correlations, because it sums the
squared autocorrelations. Thus, the signs do not cancel each other out, and funds with
large positive or negative autocorrelation coefficients will result in large Q-staristics. Fund
managers have an incentive for smoothing the returns of illiquid funds. This smoothing
process results in serial autocorrelations. As with most statistics, the smaller the
for the statistic, the greater our confidence in die inference made by rejecting the null
hypothesis.
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©2013 Kaplan, Inc.
The fbllowbig i-s i review of (he Risk Mali jÿeiuenL mJ Invesuitem Management principles designed
the ATM sniemenLS SCL forth by GART®. This topic is also covered in:
to
address
TRUST AND DELEGATION
Topic 64
EXAM FOCUS
This topic focuses on the role of due diligence in the delegated investment decision-making
process* Specifically, investors in hedge funds not only delegate decision-making to fund
managers, hut they also often do so with little information about die fund or fund managers.
The marker is non-transparent, and thus investors muse trust managers. However, some hedge
fund managers fail co report or mislead investors regarding past regulatory or legal prohlems.
Past problems, and more importantly, crying to hide past legal and regulatory problems
from investors, is a leading indicator of future operational risk Issues. Institutional investors
sometimes hire third- party due diligence firms to gadier and verify information about fund
managers. In the process, these firms uncover operational risk factors. Therefore, due diligence
is important for identifying inadequate or failed internal processes within hedge funds.
Investors in hedge funds delegate investment decision-making LO fund managers. Auditing
is expensive and markets are generally opaque. It is a classic principal-agent relationship
where the behavior of the agents, the hedge fund managers, is difficult to observe. As such,
the integrity of managers is critical.
Operational risk is defined by the Basel Committee on Banking Supervision1 as “the risk
of direct or indirect loss resulting from inadequate or failed internal processes, people, and
systems or from externa! events." The Basel Committee distinguishes operational risk from
market risk and insolvency risk. Several academic studies find that operational risk has
resulted in more hedge fund failures than had investment decisions and other types of risk.
DUE DILIGENCE IN THE INVESTMENT DECISION-MAKING PROCESS
AIM 64.1: Explain the role of third patty due diligence firms in the delegated
investment decision-making process.
Hedge fund investors are “sophisticated" and supposedly do not need die protection of
regulations that guard mutual fund investors. Therefore, with the exception of a brief
period in 2006, U.S. domiciled hedge funds have generally not been required to register
wirh the LSecurides and Exchange Commission (SEC). If they register, they generally do so
voluntarily.
1.
“Working Paper on the Regulatory Treatment of Operation al Risk," Basel Committee on Bank
Supervision, Working Paper # fl, September 2001.
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at al.
Professors Note: The Private Fund Investment Advisers Registration Act of
2010 wilt require hedge fundi with more than $100 million in atsets under
management to register with the SEC as investment advisors.
Public data services, such as the Lip per TASS database and the Center for International
Securities and Derivatives Markets (CISDM) hedge fund datahase, also rely on hedge funds
to voluntarily provide information regarding fees, performance, the use of leverage, and
hedge fund style.
As a result, there is litde publicly available information regarding the strategies,
performance, risk, organizational structure, and personnel of hedge funds. The fund
offering memoranda is viewed by potential investors but is not available to the general
public.
Several institutions have developed in response to the lack of information and transparency
regarding the character and actions of hedge fund managers. These include the following;
*
*
Third-party due diligence firms.
Independent auditors.
• Regulators.
*
Informal networks of investors transferring information via word-of-mouth.
Information is generated by these outside entities that eidier increases or diminishes the
perceived trustworthiness of a hedge fund manager.
Third-party due diligence firms are hired by hedge fund investors to gather and verify
information about the hedge fund. Funds-of-hedge-funds are typical clients; however,
investment banks or wealthy individuals may also hire these firms. The client is generally
interested in investing in the hedge fund but would like more informadon than is provided
by the fund in the prospectus and related documents.
The typical report provided by the third-party due diligence firm ranges from 100 to 200
pages hut may be several hundred pages in length. Along with the verification of fund
information regarding performance, fees, personnel, and style, red flags are raised by
die firm regarding potential operational risk factors. To gather information and identify
concerns,
die firm will do the following
• Thoroughly review offering documents and marketing materials provided by the fluid
manager.
*
*
•
*
*
Examine forms filled out in the due diligence process by fund managers.
Interview fund managers.
Attempt to verify the audit report with the funds auditor.
Verify operational controls, assets under management, and performance figures with the
fund administrator.
Perform a background check on managers and other key hedge fund staff.
One of the goals of die diird- party due diligence process is to identify imperfect or failed
internal processes. The firm identifies discrepancies and misstatements made by fund
managers regarding performance and control processes by cross-checking information with
multiple sources.
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Topic 64
Brown et aJ.
In contrast to the TASS and CISDM databases, which focus primarily on quantitative
factors such as fees, assets, returns, and leverage, the due diligence report also reveals
qualitative factors such as:
*
*
*
*
The method by which asset/ portfolio values are determined.
How and by whom the day-to-day accounting of the hind is accomplished.
Substantiation of die accuracy of the data provided by the fund.
How control processes are performed.
Operational issues, which are not evident in public hedge fund data, could potentially be
revealed in third-party due diligence reports.
HEDGE FUND REPORTING ISSUES
AIM 64.2: Explain how past regulatory and legal problems with hedge fund
reporting relates to expected future operational events.
In a study of 444 due diligence reports compiled by a third-party due diligence firm,
Brown, Goetzmann, Liang, and Schwarz2 find that 4l% of the funds studied have had
some form of regulatory or legal problem. This is interesting in that it is more than twice
die percentage of funds self-reporting a problem in a study of the 2006 Form ADV flings
by Brown, Fraser, and Liang.3
Professor's Note: The Form ADV is the uniform form used by investment
advisors to register with the SEC and state securities regulators. Theform
requires thefund to provide information about the investment advisor's
business, ownership, clients, employees, business practices, affiliations, and
any disciplinary events of the advisor or the firm's employees. Firms might be
disinclined to provide information about regulatory or legal problems in a
publicly available medium, such as SEC registration forms. Some managers
who are less trustworthy may even misrepresent the extent ofpast problems or
deny them altogether. The third-party due diligence report should uncover such
discrepancies.
The third-party due diligence firm in the Brown et al. study compared self-reported
statements regarding past regulatory and/or legal problems to third-party records (such
as audit reports or discussions with prime brokers) and noted whether there were
discrepancies. In addition, Brown et al. separated problem funds (those funds dial have had
legal and/or regulatory problems) from non-problem funds and analyzed the characteristics
of the two groups.
2.
Stephen Brown, William Goetzmann, Bing Liang, Christopher Schwarz, “Trust and
Delegation,” May 28, 2010.
3. Stephen Brown, Thomas Fraser and Bing Liang, 2008, Hedge Fund Due Diligence: A Source of
Alpha in a Hedge Fund Portfolio Strategy,” Journal of Investment Management, 6, 23-33.
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CARP Assigned Reading Brown at d.
Based on univariate tests, common characteristics of problem funds include the following:
Generally more illiquid with longer lock-up and redemption periods.
Less likely to use independent pricing procedures for asset/ portfolio values (perhaps in
*
part due to die illiquidity of assets).
Less likely dian uon-prohlem funds to have a Big 4 auditor.
*
• More likely to switch data vendors.
Similar signature setups for transferring funds buL a higher level of verification problems
*
relative to non-problem funds.
• Generally larger than non-problem funds. This may simply indicate that there are more
opportunities to sue larger funds than smaller funds.
• Generally have poorer operational controls than non-problem funds.
*
In further analysis, Brown et al. uses a logistic model to examine the relationship between
past legal or regulatory problems and the operational risk of the fund. The findings support
the univariate results and indicate that funds with past legal/regulatory problems generally
have poor operational controls.
In addition, a lack of honesty from fund managers regarding past legal and regulatory
problems is a leading indicator of operational problems in the future. The failure to use a
Big 4 or well-known accounting firm is also an indicator of future operational problems.
The authors conclude that information verification, such as that provided by diird-party
due diligence firms, is important in lightly regulated industries, such as the hedge fund
industry.
Brown et al, also derive a direct measure of operational risk, referred to as the tu-score.
Again, supporting the above univariate results, they find that:
*
*
*
*
*
Funds widi better past performance have lower operational risk.
Funds with high quality managers have lower operational risk.
Funds with longer lock-up and redemption periods have higher operational risk
Smaller or newer funds generally have higher operational risk.
Funds with smoothed returns have higher operational risk
The authors find diat hedge funds with exposure to operational risk, as measured by the
w-score, have an increased chance of future poor performance. A to-score higher than die
median score, for a given time period, is an indicadon of high operadonal risk.
INDENTIFYING INADEQUATE OR FAILED PROCESSES
AIM 64.3: Explain the role of the due diligence process in successfully identifying
inadequate or foiled internal process.
The hedge fund industry is noted for its lack of transparency. Hedge fund managers are
reluctant to reveal details about the fund, especially if they engage in proprietary trading
strategies. Fund managers are not required to register with the SEC, though some funds do
so voluntarily. Even fund information reported in public databases, such as Lip per TASS
and CISDM, often include unverified, voluntarily provided information about specific
funds.
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In this environment, the due diligence process is critically important. Due diligence
identifies inadequate or failed internal processes by uncovering and verifying information.
As noted, third-party due diligence firms gather and verify information about the fund from
a numher of sources, including the offering documents of die fund, marketing materials,
interviews with fund managers, forms filled out by fund managers, background checks of
key employees, and interviews with prime brokers and administrators,
Firms who use one of the Big 4 accounting firms are subject to due diligence in the sense
that diese firms typically pre-screen managers for various operational risk factors before
caking the fund on as a client. One of the red flags in the Bernie Madoff Ponzi scheme
was the lack of a known auditing firm. MadofPs firm, which had billions of dollars under
management, was audited by Friehling and Horowitz, a three-person accounting firm
operating out of a strip mall.
By verifying and cross-checking information across sources, die due diligence process
can uncover failures in die internal processes of the fund, which in turn lead to increased
operational risk,
Professor’s Note: One would assume that would-be investors engage in due
diligence to uncover risk factors and either avoid the risk or price the risk into
©
the expected return. However, Brown et al. find, surprisingly, that investors
appear to chase past returns regardless of the operational risk characteristics
of the fund. Despite identifiable operational risk factors that surfaced in the
due diligence reports examined in the Brown et aL study, the flow of capital
into some problem hedge funds was unabated. In fact, the study finds that
there were higher investor flows after the due diligence report, indicating
that investors are comfortable investing in these funds despite the exposure to
operational risks uncovered by third-party due diligence providers.
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