A Second Look at the Role of Hedge Funds In a Balanced Portfolio Jean L.P. Brunel, C.F.A The CFA...

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


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%


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%


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%


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




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


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


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


Similarly, it totally

ignores traditional equities to “pile” into

equity hedge

strategies, despite the

tail risk …

Note the lack of allocation to traditional equities


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:


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


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


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%


Target Risk 6.76% 7.75% 8.75% 9.75% 10.75%


Total 100% 100% 100% 100% 100%


S&P 500 Greater than


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%


Target Risk 1.02% 3.50% 6.00% 8.50% 11.00%


Total 100% 100% 100% 100% 100%


S&P 500 Between


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%


Total 100% 100% 100% 100% 100%

S&P 500 Negative


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%


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%


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




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 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


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


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


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


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


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 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


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


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


R Squared 0.295 0.000 0.400 0.003


Alpha 0.0086 0.0027 0.0041 0.0038t-stat 4.9377 1.7653 3.8249 1.0720


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




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

A Second Look at the Role of Hedge Funds In a Balanced Portfolio Jean L.P. Brunel, C.F.A The CFA...

Documents

Transcript of A Second Look at the Role of Hedge Funds In a Balanced Portfolio Jean L.P. Brunel, C.F.A The CFA...