A Second Look at the Role of Hedge Funds
In a Balanced Portfolio
The CFA Society of Victoria
Victoria, BC
September 21st, 2010
Jean L.P. Brunel, C.F.A
Three main points …
A highly heterogeneous universe
Different optimization needs
What about leverage
A highly heterogeneous universe
The term
hedge fund
is misleading
as it does
not cover a
well-defined
universe.
Rather, it
describes
many
differing
strategies …
A very wide risk spectrum
Justified by a wide variety of strategies
Looking for a better classification
Recognizing differing return distributions
A wide risk spectrum …
Last 5 Year Data - Risk/Return Scatter
20.00%
Average Returns
Does this
look as one
set of
strategies or
quite a
number of
different
ones?
15.00%
10.00%
5.00%
0.00%
-5.00%
-10.00%
0.00%
5.00%
10.00%
15.00%
Volatility of Returns
20.00%
25.00%
A wide risk spectrum …
Last 15 Year Data - Risk/Return Scatter
20.00%
18.00%
16.00%
Average Returns
Moving from
a 5-year to a
15-year
analysis
does not
really
change the
picture that
much …
14.00%
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
0.00%
5.00%
10.00%
15.00%
Volatility of Returns
20.00%
25.00%
What do these managers do?
Convertible
Merger/Risk
Statistical
Fixed Income
Pair Trades
Market Neutral
Equity
Long/Short
Sector
Leverage
Implied
Leverage
Implied
Leverage
Concentrated
Portfolios
Global Macro
Managed
Futures
Leverage
Concentration
Model
Market
Market
Market
Valuation
Valuation
Valuation
Valuation
Model
Model
Model
Model
Return volatility < 6%
Return volatility > 6%
There seems to be two clusters …
Last 5 Year Data - Risk/Return Scatter
Absolute Return Strategies in Orange
20.00%
15.00%
Average Returns
It looks as if
one can
classify the
various
strategies
according to
whether they
take fixed
income- or
equity-type
risks …
10.00%
5.00%
0.00%
-5.00%
-10.00%
0.00%
5.00%
10.00%
15.00%
Volatility of Returns
20.00%
25.00%
There seems to be two clusters …
Last 15 Year Data - Risk/Return Scatter
Absolute Return Strategies in Orange
20.00%
18.00%
Average Returns
The 15-year
picture
confirms the
insights
gained from
the shorter
term time
horizon …
16.00%
14.00%
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
0.00%
5.00%
10.00%
15.00%
Volatility of Returns
20.00%
25.00%
These clusters make sense …
An analysis
of risk and
return history
within
traditional
and nontraditional
clusters
shows the
grouping
makes sense
…
The fixed income cluster makes sense:
o absolute return and bonds: similar volatility
o despite at times differing returns
The equity cluster similarly makes sense:
Cluster Risk/Return Averages
Absolute Return Cluster
Traditional Fixed Income Cluster
Semi-Directional Cluster
Traditional Equity Cluster
Last 5 Years
Return Volatility
7.49%
3.89%
7.15%
3.76%
6.91%
12.48%
9.85%
16.95%
Last 15 Years
Return Volatility
10.24%
4.63%
5.53%
4.31%
13.68%
13.86%
5.73%
17.20%
In short …
The term
hedge fund
is misleading
as it does
not cover a
well-defined
universe.
Rather, it
describes
many
differing
strategies …
The universe is indeed highly heterogeneous
The strategy risk spectrum is very wide …
… because managers do very different things
It makes sense to classify hedge funds as:
o
o
those that look like fixed income
those that look like equities
… and use that to build balanced portfolios
Three main points …
A highly heterogeneous universe
Different optimization needs
What about leverage
Important differences …
The returns
on nontraditional
strategies
are often not
normally
distributed…
Traditional returns are normally distributed
That is not true for non-traditional returns:
o
o
often showing a negative skew
often substantial excess kurtosis
Same return and volatility, and yet …
The high
“manager”
risk incurred
in nontraditional
strategies
disturbs the
normal
distributions
we would
typically
expect …
60
50
Both means = 0.84%
Arbitrage  = 1.29%
Normal = 1.22%
Arbitrage
Normal Distribution
40
30
20
10
0
-4.15%
-10
-1.66%
0.84%
3.34%
5.83%
First, consider negative skew …
Negative
skew means
more points
right of the
mean, but
also a wider
range on the
left (i.e.
down) side
of it as well
60
50
Both means = 0.84%
Arbitrage  = 1.29%
Normal = 1.22%
Arbitrage
Normal Distribution
40
Arbitrage Skew = -2.71
Normal Skew = -0.10
30
20
10
0
-4.15%
-10
-1.66%
0.84%
3.34%
5.83%
Then, how about excess kurtosis?
Excess
kurtosis
mean that
the return
distribution is
“peaky” and
that it has
“fat tails” …
60
50
Both means = 0.84%
Arbitrage  = 1.29%
Normal = 1.22%
Arbitrage
Normal Distribution
40
Arbitrage Skew = -2.71
Normal Skew= -0.10
30
Arbitrage Kurtosis = 9.73
Normal Kurtosis = -0.25
20
10
0
-4.15%
-10
-1.66%
0.84%
3.34%
5.83%
In plain English …
A look at
third and
fourth
statistical
moments
helps make
sense of the
high Sharpe
ratio of nontraditional
strategies …
Strategies combining:
o
o
negative skew and
more highly positive kurtosis
Have a higher risk of bad surprises:
Which must be “compensated” by either:
o
o
higher expected returns, or
lower expected return volatility
Which mean-variance optimization misses …
Traditional optimization results …
The
traditional
meanvariance
model overallocates to
absolute
return
strategies
and ignores
bonds …
Note the very low allocations to bonds:
Fixed Income - Like Universe
Expected Return
Expected Risk
4.53%
0.56%
6.59%
1.02%
9.21%
2.02%
11.63%
3.02%
11.85%
3.13%
Target Risk
0.56%
1.00%
2.00%
3.00%
4.00%
Portfolio Composition
Cash
Bonds
Absolute Return Strategies
Total
100%
0%
0%
100%
70%
3%
27%
100%
31%
9%
60%
100%
0%
5%
95%
100%
0%
0%
100%
100%
Traditional optimization results …
Similarly, it
totally
ignores
traditional
equities to
“pile” into
equity hedge
strategies,
despite the
tail risk …
Note the lack of allocation to traditional equities
Equity - Like Universe
15.63%
8.58%
16.65%
9.00%
16.65%
9.05%
16.65%
9.05%
16.65%
9.05%
Target Risk
8.58%
9.00%
10.00%
11.00%
12.00%
Portfolio Composition
Equity
Equity Hedge
Equity Non-Hedge
Managed Futures
Global Macro
Total
0%
0%
0%
0%
100%
100%
0%
99%
0%
0%
1%
100%
0%
100%
0%
0%
0%
100%
0%
100%
0%
0%
0%
100%
0%
100%
0%
0%
0%
100%
Expected Return
Expected Risk
Let us try and experiment …
A simple
experiment
will helps us
set early
ground rules
Let’s divide fixed income market history:
o
o
periods when bond returns were positive
periods when bond returns were negative
Let’s divide equity market history:
o
o
o
periods when returns were high
periods when returns were “normal”
periods when returns were low
Let’s re-run the traditional optimization:
Traditional optimization results …
In periods
when bond
returns are
positive, a
meanvariance
optimization
model will
not shun
bonds …
Note that the model CAN allocate to bonds:
Bond Returns Positive
Fixed Income - Like Universe
Expected Return
Expected Risk
4.58%
0.60%
8.08%
1.02%
13.00%
2.03%
13.52%
2.57%
Target Risk
0.60%
1.00%
2.00%
3.00%
Portfolio Composition
Cash
Bonds
Absolute Return Strategies
Total
100%
0%
0%
100%
60%
26%
14%
100%
3%
62%
35%
100%
0%
100%
0%
100%
Traditional optimization results …
In periods
when bond
returns are
negative, a
meanvariance
optimization
model will
seemingly
shun bonds
Note also that the model can ignore bonds:
Bond Returns Negative
Fixed Income - Like Universe
Expected Return
Expected Risk
4.16%
0.72%
4.96%
1.00%
6.09%
2.00%
7.10%
3.00%
8.07%
4.00%
8.87%
4.83%
Target Risk
0.72%
1.00%
2.00%
3.00%
4.00%
5.00%
Portfolio Composition
Cash
Bonds
Absolute Return Strategies
Total
100%
0%
0%
100%
83%
0%
17%
100%
60%
0%
40%
100%
38%
0%
62%
100%
17%
0%
83%
100%
0%
0%
100%
100%
Traditional optimization results …
In periods
when equity
returns are
high, a
meanvariance
optimization
model will
not shun
traditional
equities …
Note that the model CAN allocate to equities:
S&P 500 Greater than
1.17%
Equity - Like Universe
32.55%
6.76%
22.54%
7.75%
42.98%
8.75%
42.83%
8.94%
46.93%
7.58%
Target Risk
6.76%
7.75%
8.75%
9.75%
10.75%
Portfolio Composition
Equity
Equity Hedge
Equity Non-Hedge
Managed Futures
Global Macro
Total
63%
0%
0%
37%
0%
100%
37%
0%
0%
63%
0%
100%
3%
0%
97%
0%
0%
100%
0%
0%
100%
0%
0%
100%
100%
0%
0%
0%
0%
100%
Expected Return
Expected Risk
Traditional optimization results …
In periods
when bond
returns are
normal, the
meanvariance
optimization
model
seems to
ignore
traditional
equities …
The model mostly ignores equities:
S&P 500 Between
0.00%
1.17%
Equity - Like Universe
Expected Return
Expected Risk
8.51%
1.02%
15.17%
3.50%
18.29%
6.00%
17.45%
8.50%
16.94%
10.60%
Target Risk
1.02%
3.50%
6.00%
8.50%
11.00%
Portfolio Composition
Equity
Equity Hedge
Equity Non-Hedge
Managed Futures
Global Macro
Total
100%
0%
0%
0%
0%
100%
20%
68%
10%
0%
2%
100%
0%
0%
76%
0%
24%
100%
0%
0%
25%
0%
75%
100%
0%
0%
0%
0%
100%
100%
Traditional optimization results …
In periods
when equity
returns are
negative, the
model does
not want to
hear about
them …
The model still ignores equities:
S&P 500 Negative
Equity - Like Universe
Expected Return
Expected Risk
1.08%
7.37%
-12.02%
8.49%
-16.21%
9.75%
-22.31%
11.00%
-27.83%
12.24%
Target Risk
7.37%
8.48%
9.73%
10.98%
12.23%
Portfolio Composition
Equity
Equity Hedge
Equity Non-Hedge
Managed Futures
Global Macro
Total
0%
0%
0%
0%
100%
100%
0%
0%
44%
0%
56%
100%
0%
58%
42%
0%
0%
100%
0%
30%
70%
0%
0%
100%
0%
6%
94%
0%
0%
100%
What have we learned?
The optimizer does not like losses!!!
It can allocate to bonds:
o When they offer competitive returns
o But not when they are “normal”
It can allocate to equities:
o When they offer competitive returns
o Or when they are the lowest risk choice
These strategies do not always make sense
Let us try a final experiment …
Though this
experiment
is not a
“solver,” but
a calculator,
it can help
demonstrate
the power of
a more
detailed
model …
Mean-variance optimization only uses:
o
o
return and risk expectations, and …
… covariance among each pair of assets
Let’s design a different model:
o
o
o
o
return and risk observations
skew and kurtosis observations”
implicit preferences for skew and kurtosis
the same covariance matrix
Let’s re-run the optimization:
The goals for that model would be ...
Rather than
focusing on
meanvariance, we
calculate a
“Z-Score”
which
incorporates
all four
moments …
On the one hand:
o
o
to capture as much return as possible
while avoiding as much risk as possible
At the same time, we would like:
o
o
o
to minimize the risk of negative surprises
minimizing negative skew”
minimizing excess kurtosis
In “Greek” our “Z-Score” will be:
o
Max (E[r] -  + l*skew - g*Kurtosis)
Z-Score fixed income optimization:
This model
produces
results that
ignore
absolute
return
strategies if
the aversion
to manager
risk is set at
a high level
The model ignores absolute return strategies:
Fixed Income - Like Universe landg0.01)
Monthly Data
Return
Volatility
Skew
Kurtosis
0.37%
0.16%
-0.24
-0.57
0.46%
0.41%
-0.46
1.01
0.52%
0.66%
-0.47
0.90
0.55%
0.81%
-0.47
0.84
0.63%
1.13%
-0.46
0.75
Target Risk
0.16%
0.41%
0.66%
0.81%
1.13%
Portfolio Composition
Cash
Bonds
Absolute Return Strategies
Total
100%
0%
0%
100%
67%
33%
0%
100%
44%
56%
0%
100%
30%
70%
0%
100%
0%
100%
0%
100%
Z-Score fixed income optimization:
These
results are
much more
intuitively
satisfying,
with a better
balance
between
traditional
and nontraditional
strategies ..
With a lesser manager risk aversion, the
model allocates to absolute return strategies:
Fixed Income - Like Universe landg= 0.005
Monthly Data
Return
Volatility
Skew
Kurtosis
0.37%
0.16%
-0.24
-0.57
0.46%
0.41%
-0.46
1.01
0.52%
0.66%
-0.47
0.90
0.79%
0.81%
-0.57
0.47
0.63%
1.13%
-0.47
0.75
Target Risk
0.16%
0.41%
0.66%
0.81%
1.13%
Portfolio Composition
Cash
Bonds
Absolute Return Strategies
Total
100%
0%
0%
100%
67%
33%
0%
100%
44%
56%
0%
100%
0%
55%
45%
100%
0%
100%
0%
100%
A much better potential formulation
This model
has the
potential to
address our
problem, but
it still needs
to be tested
on balanced
portfolios ...
Neil Davies, Harry Kat and Sa Lu have
proposed an interesting “solver” formulation:
Minimize
a
b
g
Z (1 +d1 ) +(1 +d3 ) +(1 +d4 ) ,
Subject to
E[X R] +xn +1 t +d1 Z1* ,
T
T
~
~
~
3
*
E{X (R -E[R])} +d3 Z3 ,
~
~
-E{X T (R -E[R])}4 +d4  -Z4* ,
d1 , d3 , d4 0,
T
X VX 1;
X 0;
T
xn +1 1 -I X
Three main points …
A highly heterogeneous universe
Different optimization needs
What about leverage
Naïve expectations for L/S …
We can
dispense
with the
detailed
analysis of
statistical
results and
rather look at
how similar
or not these
are to naïve
expectations
If systematic leverage is the key, on should
o
Find a relatively high R Square
o
A Beta coefficient greater than 1
o
A negative Alpha coefficient
Equity L/S vs. equity indexes …
In fact, the R
Squares are
relatively
low, the
betas are
very low and
significant
and the
alphas are
all positive
and
significant …
1995-2007
R Square
Coefficient
t-stat
Coefficient
t-stat
Alpha
t-stat
Russell
3000
0.566
S&P 500
0.469
Russell
2000
0.753
0.4615
13.6955
0.4228
11.2878
0.4098
20.949
0.0075
5.202
0.008
4.979
0.0079
7.2946
S&P 500 +
Russell
2000
0.762
0.084
2.3415
0.364
13.2614
0.0075
6.9984
Equity L/S vs. equity indexes …
Again, the R
Squares are
relatively
low, the
betas are
very low and
significant
and the
alphas are
all positive
and
significant …
2002-2007
R Square
Coefficient
t-stat
Coefficient
t-stat
Alpha
t-stat
Russell
3000
0.637
S&P 500
0.567
Russell
2000
0.807
0.3857
10.0114
0.3672
8.6322
0.3167
15.4409
0.0048
3.4208
0.0053
3.4322
0.0041
3.9655
S&P 500 +
Russell
2000
0.808
0.0282
0.5705
0.3001
8.3979
0.0041
3.9448
Leverage and manager alpha …
Now the
idea is to
test the
alpha of
managers
in rising
and falling
markets
against the
benchmark
Managers can add value in two ways:
o
o
Market timing: varying market exposure
Bottom up security selection
If managers are great market timers:
o
o
positive and strong correlation in up markets
negative and equally strong in down markets
Caveat: multiple sources of alpha …
In rising markets…
Whatever
relationship
there is does
appear quite
weak and in
the wrong
direction:
managers
find it harder
to add value
in up
markets…
R Square
Coefficient
t-stat
Coefficient
t-stat
Alpha
t-stat
Rising Markets – Russell 3000
1995-2007
S&P 500 +
Russell
Russell
Russell
S&P 500
3000
2000
2000
0.031
0.067
0.056
0.153
-0.1169
-1.7206
-0.1627
-2.6047
0.0995
2.3503
0.0091
3.2867
0.0106
4.1174
0.0013
0.5784
-0.2004
-3.2803
0.1265
3.0761
0.0069
2.5345
In rising markets…
Whatever
relationship
there is now
appear a bit
stronger, but
still weak
and in the
wrong
direction …
R Square
Coefficient
t-stat
Coefficient
t-stat
Alpha
t-stat
Rising Markets – Russell 3000
2002-2007
S&P 500 +
Russell
Russell
Russell
S&P 500
3000
2000
2000
0.324
0.361
0.086
0.375
-0.2598
-4.2713
-0.2702
-4.6341
-0.087
-1.8962
0.0069
3.3859
0.0067
3.5639
0.0032
1.4415
-0.3144
-4.1332
0.0454
0.9082
0.0061
3.0766
How about falling markets?
There
appears to
be virtually
no
relationship
in view of the
very low R
Squares,
and the
direction is
mostly
wrong…
R Square
Coefficient
t-stat
Coefficient
t-stat
Alpha
t-stat
Falling Markets – Russell 3000
1995-2007
S&P 500 +
Russell
Russell
Russell
S&P 500
3000
2000
2000
0.000
0.000
0.008
0.186
0.0016
0.0255
-0.0078
-0.1380
0.0207
0.6137
0.0058
2.0665
0.0061
2.3723
0.0051
2.7529
-0.1591
-3.2775
0.0646
1.8333
0.0031
1.6127
How about falling markets?
There
appears to
be a bit more
of a
relationship
(still weak
though) and
the sign is in
the right
direction at
least…
R Square
Coefficient
t-stat
Coefficient
t-stat
Alpha
t-stat
Falling Markets – Russell 3000
2002-2007
S&P 500 +
Russell
Russell
Russell
S&P 500
3000
2000
2000
0.2640
0.3100
0.0250
0.3320
-0.1660
-2.6818
-0.1709
-2.9949
-0.0407
-0.7215
0.0017
0.6915
0.0017
0.7166
0.0052
1.818
-0.1981
-2.9500
0.0441
0.7895
0.0026
0.9844
Naïve expectations for A/R …
Though the
test variables
will be
different, the
naïve
expectations
we form are
the same as
in the case
of long/short
managers …
If systematic leverage is the key, one should
o
Find a relatively high R Square
o
A Beta coefficient greater than 1
o
A negative Alpha coefficient
Absolute return vs. benchmarks …
In fact, the R
Squares are
quite low, the
betas are
very low and
mostly
significant
and the
alphas are
all positive
and
significant …
R Squared
Russell
3000
0.358
Coefficient
t-stat
Alpha
t-stat
0.1248
8.9554
0.0076
12.6132
R Squared
Russell
3000
0.356
Coefficient
t-stat
Alpha
t-stat
0.1264
5.7537
0.0055
6.9108
90 Day
Treasuries
0.064
1.457
3.1254
0.0039
2.2366
90 Day
Treasuries
0.024
0.9158
1.2044
0.0043
2.3284
1995-2007
Salomon
Merrill
BIG
High Yield
0.001
0.306
0.0221
0.3242
0.0087
10.5385
0.2498
7.9606
0.0071
11.1245
2002-2007
Salomon
Merrill
BIG
High Yield
0.003
0.376
-0.0371
-0.4182
0.0064
6.1611
0.2331
6.0122
0.0043
5.2466
Average HY
Spreads
0.038
-0.0007
-2.3737
0.0128
7.0065
Average HY
Spreads
0.096
-0.0009
-2.5263
0.011
5.2646
Is there a static mix?
We can test
this by
looking at
whether
absolute
return
strategy
returns can
be regressed
against the
same
variables…
1995-2007
R Square
Intercept
Russell 3000
90-Day T. Bills
Salomon BIG
Merrill High Yield
Average HY Spread
R Square
Intercept
Russell 3000
90-Day T. Bills
Salomon BIG
Merrill High Yield
2002-2007
Five Independent Variables
R Square
0.503
t-stats
Intercept
0.0019
0.9882
Russell 3000
0.0766
5.0432
90-Day T. Bills
1.5497
4.3023
Salomon BIG
-0.0749 -1.4093
Merrill High Yield
0.1791
5.2938
Average HY Spread
0
0.095
Four Independent Variables
R Square
0.503
t-stats
Intercept
0.002
1.5426
Russell 3000
0.0764
5.0865
90-Day T. Bills
1.5473
4.3215
Salomon BIG
-0.074
-1.4219
Merrill High Yield
0.1785
5.3652
0.507
0.0039
0.0702
0.8588
-0.0001
0.1629
-0.0002
t-stats
1.4808
2.5818
1.3929
-0.0017
3.5209
-0.7348
0.502
0.0023
0.0744
1.0448
-0.0078
0.1648
t-stats
1.5944
2.8088
1.8659
-0.1083
3.5824
Leverage and manager alpha …
Again, the
idea is to
test the
alpha of
managers
in rising
and falling
markets
against the
benchmark
Managers can add value in two ways:
o
o
Market timing: varying market exposure
Bottom up security selection
If managers are great market timers:
o
o
positive and strong correlation in up markets
negative and equally strong in down markets
Caveat: multiple sources of alpha …
Alphas in rising markets …
There is
virtually no
evident
relationship
and it is in
the wrong
direction for
half of the
variables
and often not
significant …
R Squared
Russell
3000
0.033
Coefficient
t-stat
Alpha
t-stat
0.0497
1.8146
0.0068
6.0728
R Squared
Russell
3000
0.128
Coefficient
t-stat
Alpha
t-stat
0.0936
2.3603
0.0046
3.4483
Rising Markets
1995-2007
Salomon
Merrill
BIG
High Yield
0.000
0.046
-0.0004
-0.0068
0.0085
11.9825
0.0901
2.1331
0.0073
8.8657
2002-2007
Salomon
Merrill
BIG
High Yield
0.008
0.088
-0.0471
-0.5646
0.0072
8.1597
0.1069
1.9157
0.0056
4.9323
Average HY
Spreads
0.009
-0.0003
-0.9205
0.0099
5.9715
Average HY
Spreads
0.034
-0.0005
-1.1532
0.0092
4.5032
Alphas in falling markets …
There is
virtually no
evident
relationship
and it is in
the wrong
direction
more often
than not. No
statistical
significance
save HY bds
R Squared
Russell
3000
0.295
Coefficient
t-stat
Alpha
t-stat
0.1660
4.4806
0.0086
4.9377
R Squared
Russell
3000
0.154
Coefficient
t-stat
Alpha
t-stat
0.1168
1.9097
0.0044
1.7806
Falling Markets
1995-2007
Salomon
Merrill
BIG
High Yield
0.000
0.400
-0.0169
-0.1322
0.0027
1.7653
0.2712
5.6596
0.0041
3.8249
2002-2007
Salomon
Merrill
BIG
High Yield
0.119
0.566
0.2436
1.6460
-0.0012
-0.6078
0.2500
5.1078
0.0013
1.1794
Average HY
Spreads
0.003
-0.0002
-0.3644
0.0038
1.0720
Average HY
Spreads
0.009
-0.0002
-0.4325
0.0024
0.5862
In short …
It is hard to
substantiate
the notion
that one can
replace nontraditional
managers
with
leveraged
long only
strategies …
In most instances, the observed alpha is:
o
o
not really related to market beta
not readily replicable with a static mix
More often than not, alpha is:
o
o
Statistically unrelated to market timing
The more recent past can be less clear-cut
Three main points …
A highly heterogeneous universe
Different optimization needs
What about leverage
Questions?
A Second Look at the Role of Hedge Funds
In a Balanced Portfolio
The CFA Society of Victoria
Victoria, BC
September 21st, 2010
Jean L.P. Brunel, C.F.A