a second look at the role of hedge funds in a balanced portfolio jean l.p. brunel, c.f.a the cfa...
TRANSCRIPT
A Second Look at the Role of Hedge Funds
In a Balanced Portfolio
Jean L.P. Brunel, C.F.A
The CFA Society of VictoriaVictoria, BC
September 21st, 2010
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
-10.00%
-5.00%
0.00%
5.00%
10.00%
15.00%
20.00%
0.00% 5.00% 10.00% 15.00% 20.00% 25.00%
Volatility of Returns
Ave
rag
e R
etu
rns
Does this look as one
set of strategies or quite a
number of different
ones?
A wide risk spectrum …
Moving from a 5-year to a 15-year analysis does not
really change the picture that
much …
Last 15 Year Data - Risk/Return Scatter
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
20.00%
0.00% 5.00% 10.00% 15.00% 20.00% 25.00%
Volatility of Returns
Ave
rag
e R
etu
rns
Return volatility < 6% Return volatility > 6%
Market
Concentration
Model
Leverage
Valuation
MarketMarket
Model Model ModelModel
Leverage
What do these managers do?
Valuation Valuation Valuation
Concentrated Portfolios
Global MacroManagedFutures
Equity Long/Short
Sector
Convertible Merger/Risk
Statistical
Fixed IncomePair Trades
Market Neutral
ImpliedLeverage
ImpliedLeverage
There seems to be two clusters …
It looks as if one can
classify the various
strategies according
to whether they take
fixed income- or
equity-type risks …
Last 5 Year Data - Risk/Return ScatterAbsolute Return Strategies in Orange
-10.00%
-5.00%
0.00%
5.00%
10.00%
15.00%
20.00%
0.00% 5.00% 10.00% 15.00% 20.00% 25.00%
Volatility of Returns
Ave
rag
e R
etu
rns
There seems to be two clusters …
The 15-year
picture confirms
the insights gained
from the shorter
term time horizon …
Last 15 Year Data - Risk/Return ScatterAbsolute Return Strategies in Orange
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
20.00%
0.00% 5.00% 10.00% 15.00% 20.00% 25.00%
Volatility of Returns
Ave
rag
e R
etu
rns
These clusters make sense …
An analysis of risk and
return history within
traditional and non-
traditional clusters
shows the grouping
makes sense …
The fixed income cluster makes sense:o absolute return and bonds: similar volatilityo despite at times differing returns
The equity cluster similarly makes sense:
Return Volatility Return VolatilityAbsolute Return Cluster 7.49% 3.89% 10.24% 4.63%Traditional Fixed Income Cluster 7.15% 3.76% 5.53% 4.31%Semi-Directional Cluster 6.91% 12.48% 13.68% 13.86%Traditional Equity Cluster 9.85% 16.95% 5.73% 17.20%
Last 5 Years Last 15 Years
Cluster Risk/Return Averages
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 those that look like fixed incomeo 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 non-
traditional strategies are often
not normally
distributed…
Traditional returns are normally distributed
That is not true for non-traditional returns:o often showing a negative skewo often substantial excess kurtosis
Same return and volatility, and yet …
The high “manager”
risk incurred in
non-traditional strategies
disturbs the normal distributions we would
typically expect …
-10
0
10
20
30
40
50
60
-4.15% -1.66% 0.84% 3.34% 5.83%
Arbitrage
Normal Distribution
Both means = 0.84%Arbitrage = 1.29%Normal = 1.22%
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
-10
0
10
20
30
40
50
60
-4.15% -1.66% 0.84% 3.34% 5.83%
Arbitrage
Normal Distribution
Both means = 0.84%Arbitrage = 1.29%Normal = 1.22%
Arbitrage Skew = -2.71Normal Skew= -0.10
Then, how about excess kurtosis?
Excess kurtosis
mean that the return
distribution is “peaky” and that it
has “fat tails” …
-10
0
10
20
30
40
50
60
-4.15% -1.66% 0.84% 3.34% 5.83%
Arbitrage
Normal Distribution
Both means = 0.84%Arbitrage = 1.29%Normal = 1.22%
Arbitrage Skew = -2.71Normal Skew= -0.10
Arbitrage Kurtosis = 9.73Normal Kurtosis= -0.25
In plain English …
A look at third and
fourth statistical moments
helps make sense of the high Sharpe ratio of
non-traditional strategies
…
Strategies combining:o negative skew ando more highly positive kurtosis
Have a higher risk of bad surprises:
Which must be “compensated” by either:o higher expected returns, oro lower expected return volatility
Which mean-variance optimization misses …
Traditional optimization results …
The traditional
mean-variance
model over-
allocates to absolute
return strategies
and ignores
bonds …
Note the very low allocations to bonds:
Expected Return 4.53% 6.59% 9.21% 11.63% 11.85%Expected Risk 0.56% 1.02% 2.02% 3.02% 3.13%
Target Risk 0.56% 1.00% 2.00% 3.00% 4.00%
Portfolio CompositionCash 100% 70% 31% 0% 0%Bonds 0% 3% 9% 5% 0%Absolute Return Strategies 0% 27% 60% 95% 100%
Total 100% 100% 100% 100% 100%
Fixed Income - Like Universe
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
Expected Return 15.63% 16.65% 16.65% 16.65% 16.65%Expected Risk 8.58% 9.00% 9.05% 9.05% 9.05%
Target Risk 8.58% 9.00% 10.00% 11.00% 12.00%
Portfolio CompositionEquity 0% 0% 0% 0% 0%Equity Hedge 0% 99% 100% 100% 100%Equity Non-Hedge 0% 0% 0% 0% 0%Managed Futures 0% 0% 0% 0% 0%Global Macro 100% 1% 0% 0% 0%
Total 100% 100% 100% 100% 100%
Equity - Like Universe
Let us try and experiment …
A simple experiment
will helps us set early
ground rules
Let’s divide fixed income market history:o periods when bond returns were positiveo periods when bond returns were negative
Let’s divide equity market history:o periods when returns were higho periods when returns were “normal”o periods when returns were low
Let’s re-run the traditional optimization:
Traditional optimization results …
In periods when bond returns are positive, a
mean-variance
optimization model will not
shun bonds …
Note that the model CAN allocate to bonds:
Expected Return 4.58% 8.08% 13.00% 13.52%Expected Risk 0.60% 1.02% 2.03% 2.57%
Target Risk 0.60% 1.00% 2.00% 3.00%
Portfolio CompositionCash 100% 60% 3% 0%Bonds 0% 26% 62% 100%Absolute Return Strategies 0% 14% 35% 0%
Total 100% 100% 100% 100%
Bond Returns PositiveFixed Income - Like Universe
Traditional optimization results …
In periods when bond returns are negative, a
mean-variance
optimization model
will seemingly
shun bonds
Note also that the model can ignore bonds:
Expected Return 4.16% 4.96% 6.09% 7.10% 8.07% 8.87%Expected Risk 0.72% 1.00% 2.00% 3.00% 4.00% 4.83%
Target Risk 0.72% 1.00% 2.00% 3.00% 4.00% 5.00%
Portfolio CompositionCash 100% 83% 60% 38% 17% 0%Bonds 0% 0% 0% 0% 0% 0%Absolute Return Strategies 0% 17% 40% 62% 83% 100%
Total 100% 100% 100% 100% 100% 100%
Bond Returns NegativeFixed Income - Like Universe
Traditional optimization results …
In periods when
equity returns are
high, a mean-
variance optimizatio
n model will not
shun traditional equities …
Note that the model CAN allocate to equities:
1.17%
Expected Return 32.55% 22.54% 42.98% 42.83% 46.93%Expected Risk 6.76% 7.75% 8.75% 8.94% 7.58%
Target Risk 6.76% 7.75% 8.75% 9.75% 10.75%
Portfolio CompositionEquity 63% 37% 3% 0% 100%Equity Hedge 0% 0% 0% 0% 0%Equity Non-Hedge 0% 0% 97% 100% 0%Managed Futures 37% 63% 0% 0% 0%Global Macro 0% 0% 0% 0% 0%
Total 100% 100% 100% 100% 100%
Equity - Like Universe
S&P 500 Greater than
Traditional optimization results …
In periods when bond returns are normal, the
mean-variance
optimization model
seems to ignore
traditional equities …
The model mostly ignores equities:
0.00% 1.17%
Expected Return 8.51% 15.17% 18.29% 17.45% 16.94%Expected Risk 1.02% 3.50% 6.00% 8.50% 10.60%
Target Risk 1.02% 3.50% 6.00% 8.50% 11.00%
Portfolio CompositionEquity 100% 20% 0% 0% 0%Equity Hedge 0% 68% 0% 0% 0%Equity Non-Hedge 0% 10% 76% 25% 0%Managed Futures 0% 0% 0% 0% 0%Global Macro 0% 2% 24% 75% 100%
Total 100% 100% 100% 100% 100%
Equity - Like Universe
S&P 500 Between
Traditional optimization results …
In periods when
equity returns are
negative, the model
does not want to
hear about them …
The model still ignores equities:
Expected Return 1.08% -12.02% -16.21% -22.31% -27.83%Expected Risk 7.37% 8.49% 9.75% 11.00% 12.24%
Target Risk 7.37% 8.48% 9.73% 10.98% 12.23%
Portfolio CompositionEquity 0% 0% 0% 0% 0%Equity Hedge 0% 0% 58% 30% 6%Equity Non-Hedge 0% 44% 42% 70% 94%Managed Futures 0% 0% 0% 0% 0%Global Macro 100% 56% 0% 0% 0%
Total 100% 100% 100% 100% 100%
S&P 500 Negative
Equity - Like Universe
What have we learned?
The optimizer does not like losses!!!
It can allocate to bonds:o When they offer competitive returnso But not when they are “normal”
It can allocate to equities:o When they offer competitive returnso 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 return and risk expectations, and …o … covariance among each pair of assets
Let’s design a different model:o return and risk observationso skew and kurtosis observations”o implicit preferences for skew and kurtosiso the same covariance matrix
Let’s re-run the optimization:
The goals for that model would be ...
Rather than
focusing on mean-
variance, we
calculate a “Z-Score”
which incorporate
s all four moments
…
On the one hand:o to capture as much return as possibleo while avoiding as much risk as possible
At the same time, we would like:o to minimize the risk of negative surpriseso minimizing negative skew”o minimizing excess kurtosis
In “Greek” our “Z-Score” will be:o Max (E[r] - + *skew - *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:
Monthly DataReturn 0.37% 0.46% 0.52% 0.55% 0.63%Volatility 0.16% 0.41% 0.66% 0.81% 1.13%Skew -0.24 -0.46 -0.47 -0.47 -0.46Kurtosis -0.57 1.01 0.90 0.84 0.75
Target Risk 0.16% 0.41% 0.66% 0.81% 1.13%
Portfolio CompositionCash 100% 67% 44% 30% 0%Bonds 0% 33% 56% 70% 100%Absolute Return Strategies 0% 0% 0% 0% 0%
Total 100% 100% 100% 100% 100%
Fixed Income - Like Universe and0.01)
Z-Score fixed income optimization:
These results are
much more intuitively satisfying,
with a better
balance between
traditional and non-
traditional strategies .
.
With a lesser manager risk aversion, the model allocates to absolute return strategies:
Monthly DataReturn 0.37% 0.46% 0.52% 0.79% 0.63%Volatility 0.16% 0.41% 0.66% 0.81% 1.13%Skew -0.24 -0.46 -0.47 -0.57 -0.47Kurtosis -0.57 1.01 0.90 0.47 0.75
Target Risk 0.16% 0.41% 0.66% 0.81% 1.13%
Portfolio CompositionCash 100% 67% 44% 0% 0%Bonds 0% 33% 56% 55% 100%Absolute Return Strategies 0% 0% 0% 45% 0%
Total 100% 100% 100% 100% 100%
Fixed Income - Like Universe and= 0.005
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 ,)1()1()1( 431
dddZ
Subject to ,][ *111
~
ZdxRXE n
,)}][({ *33
3~~
ZdRERXE
,])}[({ *44
4~~
ZdRERXE
XIx
X
VXX
ddd
n
1
;0
;1
,0,,
1
431
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
…
S&P 500 +
S&P 500R Square 0.566 0.469 0.753 0.762
Coefficient 0.4615 0.4228 0.4098 0.084t-stat 13.6955 11.2878 20.949 2.3415
Coefficient 0.364t-stat 13.2614
Alpha 0.0075 0.008 0.0079 0.0075t-stat 5.202 4.979 7.2946 6.9984
1995-2007
Russell 3000
Russell 2000
Russell 2000
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
…
S&P 500 +
S&P 500R Square 0.637 0.567 0.807 0.808
Coefficient 0.3857 0.3672 0.3167 0.0282t-stat 10.0114 8.6322 15.4409 0.5705
Coefficient 0.3001t-stat 8.3979
Alpha 0.0048 0.0053 0.0041 0.0041t-stat 3.4208 3.4322 3.9655 3.9448
2002-2007
Russell 3000
Russell 2000
Russell 2000
Leverage and manager alpha …
Now the idea is to test the alpha of
managers in rising
and falling
markets against
the benchmar
k
Managers can add value in two ways:
o Market timing: varying market exposureo Bottom up security selection
If managers are great market timers:
o positive and strong correlation in up marketso 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…
S&P 500 +Russell
3000 S&P 500Russell
2000Russell
2000R Square 0.031 0.067 0.056 0.153
Coefficient -0.1169 -0.1627 0.0995 -0.2004t-stat -1.7206 -2.6047 2.3503 -3.2803
Coefficient 0.1265t-stat 3.0761
Alpha 0.0091 0.0106 0.0013 0.0069t-stat 3.2867 4.1174 0.5784 2.5345
Rising Markets – Russell 30001995-2007
In rising markets…
Whatever relationship there is
now appear a
bit stronger,
but still weak and
in the wrong
direction …
S&P 500 +Russell
3000 S&P 500Russell
2000Russell
2000R Square 0.324 0.361 0.086 0.375
Coefficient -0.2598 -0.2702 -0.087 -0.3144t-stat -4.2713 -4.6341 -1.8962 -4.1332
Coefficient 0.0454t-stat 0.9082
Alpha 0.0069 0.0067 0.0032 0.0061t-stat 3.3859 3.5639 1.4415 3.0766
2002-2007Rising Markets – Russell 3000
How about falling markets?
There appears to be virtually
no relationshi
p in view of the very
low R Squares, and the
direction is mostly
wrong…
S&P 500 +Russell
3000 S&P 500Russell
2000Russell
2000R Square 0.000 0.000 0.008 0.186
Coefficient 0.0016 -0.0078 0.0207 -0.1591t-stat 0.0255 -0.1380 0.6137 -3.2775
Coefficient 0.0646t-stat 1.8333
Alpha 0.0058 0.0061 0.0051 0.0031t-stat 2.0665 2.3723 2.7529 1.6127
Falling Markets – Russell 30001995-2007
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…
S&P 500 +Russell
3000 S&P 500Russell
2000Russell
2000R Square 0.2640 0.3100 0.0250 0.3320
Coefficient -0.1660 -0.1709 -0.0407 -0.1981t-stat -2.6818 -2.9949 -0.7215 -2.9500
Coefficient 0.0441t-stat 0.7895
Alpha 0.0017 0.0017 0.0052 0.0026t-stat 0.6915 0.7166 1.818 0.9844
2002-2007 Falling Markets – Russell 3000
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
…
Russell 90 Day Salomon Merrill Average HY
3000 Treasuries B I G High Yield SpreadsR Squared 0.358 0.064 0.001 0.306 0.038
Coefficient 0.1248 1.457 0.0221 0.2498 -0.0007t-stat 8.9554 3.1254 0.3242 7.9606 -2.3737
Alpha 0.0076 0.0039 0.0087 0.0071 0.0128t-stat 12.6132 2.2366 10.5385 11.1245 7.0065
1995-2007
Russell 90 Day Salomon Merrill Average HY3000 Treasuries B I G High Yield Spreads
R Squared 0.356 0.024 0.003 0.376 0.096
Coefficient 0.1264 0.9158 -0.0371 0.2331 -0.0009t-stat 5.7537 1.2044 -0.4182 6.0122 -2.5263
Alpha 0.0055 0.0043 0.0064 0.0043 0.011t-stat 6.9108 2.3284 6.1611 5.2466 5.2646
2002-2007
Is there a static mix?
We can test this by
looking at whether absolute
return strategy
returns can be
regressed against the
same variables…
R Square 0.503 R Square 0.507t-stats t-stats
Intercept 0.0019 0.9882 Intercept 0.0039 1.4808Russell 3000 0.0766 5.0432 Russell 3000 0.0702 2.581890-Day T. Bills 1.5497 4.3023 90-Day T. Bills 0.8588 1.3929Salomon BIG -0.0749 -1.4093 Salomon BIG -0.0001 -0.0017Merrill High Yield 0.1791 5.2938 Merrill High Yield 0.1629 3.5209Average HY Spread 0 0.095 Average HY Spread -0.0002 -0.7348
R Square 0.503 R Square 0.502t-stats t-stats
Intercept 0.002 1.5426 Intercept 0.0023 1.5944Russell 3000 0.0764 5.0865 Russell 3000 0.0744 2.808890-Day T. Bills 1.5473 4.3215 90-Day T. Bills 1.0448 1.8659Salomon BIG -0.074 -1.4219 Salomon BIG -0.0078 -0.1083Merrill High Yield 0.1785 5.3652 Merrill High Yield 0.1648 3.5824
Four Independent Variables
1995-2007 2002-2007
Five Independent Variables
Leverage and manager alpha …
Again, the idea is to test the alpha of
managers in rising
and falling
markets against
the benchmar
k
Managers can add value in two ways:
o Market timing: varying market exposureo Bottom up security selection
If managers are great market timers:
o positive and strong correlation in up marketso negative and equally strong in down markets
Caveat: multiple sources of alpha …
Alphas in rising markets …
Russell Salomon Merrill Average HY
3000 B I G High Yield SpreadsR Squared 0.033 0.000 0.046 0.009
Coefficient 0.0497 -0.0004 0.0901 -0.0003t-stat 1.8146 -0.0068 2.1331 -0.9205
Alpha 0.0068 0.0085 0.0073 0.0099t-stat 6.0728 11.9825 8.8657 5.9715
Russell Salomon Merrill Average HY3000 B I G High Yield Spreads
R Squared 0.128 0.008 0.088 0.034
Coefficient 0.0936 -0.0471 0.1069 -0.0005t-stat 2.3603 -0.5646 1.9157 -1.1532
Alpha 0.0046 0.0072 0.0056 0.0092t-stat 3.4483 8.1597 4.9323 4.5032
Rising Markets1995-2007
2002-2007
There is virtually no
evident relationship and it is
in the wrong
direction for half of
the variables and often
not significant
…
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
Russell Salomon Merrill Average HY3000 B I G High Yield Spreads
R Squared 0.295 0.000 0.400 0.003
Coefficient 0.1660 -0.0169 0.2712 -0.0002t-stat 4.4806 -0.1322 5.6596 -0.3644
Alpha 0.0086 0.0027 0.0041 0.0038t-stat 4.9377 1.7653 3.8249 1.0720
Russell Salomon Merrill Average HY3000 B I G High Yield Spreads
R Squared 0.154 0.119 0.566 0.009
Coefficient 0.1168 0.2436 0.2500 -0.0002t-stat 1.9097 1.6460 5.1078 -0.4325
Alpha 0.0044 -0.0012 0.0013 0.0024t-stat 1.7806 -0.6078 1.1794 0.5862
Falling Markets1995-2007
2002-2007
In short …
It is hard to substantiat
e the notion that
one can replace
non-traditional managers
with leveraged long only
strategies …
In most instances, the observed alpha is:
o not really related to market betao not readily replicable with a static mix
More often than not, alpha is:
o Statistically unrelated to market timingo 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
Jean L.P. Brunel, C.F.A
The CFA Society of VictoriaVictoria, BC
September 21st, 2010