Is Alpha-Beta Analysis Useful for Constructing
Fund of Hedge Funds Portfolio?
Martin Lee
Some background
•
Of the approximately USD 1.0 trillion being managed by hedged
funds (including privately managed accounts), about USD 540 billion
is managed through fund of hedge funds.
•
Traditionally, private HNW segment has accounted for most of the
hedge fund AUM
•
More recently, institutions have started to allocate into hedge funds
(approx. 60 billion as of Sep 2004 – according to a survey
conducted by Bank of NY and Casey, Quirk & Associates)
•
1
Will the institutions demand a more formal investment process?
Some background
•
The management of fund of hedge funds have tended to emphasize
manager selection
- Hedge fund returns are mostly alpha(?)
- Indices are not reliable, not style pure, and difficult to replicate
- Fund exposures (beta) are not stable
- Reluctance to make frequent changes to portfolio
•
On the other hand, academic research indicate significant systematic
components in hedge fund returns
- Fung and Hsieh (1997,2002), Agarwal and Naik (2001)
- In fact, indications are that beta component outweighs the alpha component
for many of the hedge fund strategies
- Implies that, in theory, asset allocation process can be useful
2
What do we mean by beta?
•
Security level aggregation – factor model
- Represents a snapshot exposure of a portfolio
- Useful for risk measurement, but not to understand return process
•
Traditional style analysis (Sharpe, 1992)
- Use traditional asset returns (long & short) to model fund returns
- Ignores trading P&L
•
again, not very useful for hedge funds
Alternative style analysis(Fung & Hsieh, Agarwal & Naik)
- Incorporate dynamic trading strategies as factors
- Factors are harder to interpret (return on options, implied volatility, etc.)
- Useful for alpha forecasting, but difficult to use in asset allocation
3
Peer-group beta
•
Using composite index of manager returns as style factor
- HFR, Tremont, MSCI, S&P, etc.
•
Cons
- Index is not style pure - ad hoc fund categorization (beta consistency)
- Funds exhibit style drifts and style proliferation (beta stability)
- Statistical issues: reporting biases, serial correlation
•
Pros
- Represents an average of ALL return generation process
(exposure + trading) and it is adaptive
- Simple, easy to interpret, and practical
- Style factor same as performance benchmark
4
Stylized model of investment process
Process Steps
Inputs
Strategic Portfolio Benchmark
(strategy allocation)
Estimate Strategy Returns
and Covariance Matrix
(Long Horizon)
Tactical Portfolio
Forecast Strategy Returns
over Tactical Horizon
Model Portfolio
Manager Universe +
Estimate of Manager
Alpha and Beta
Final Portfolio
Product and
implementation constraints
Can this work in fund of hedge funds?
5
Does asset allocation matter in hedge funds?
Convertible
Distressed
Eq Hedged US
Eq Hedged US (MSCI)
1997
1.7%
0.8%
0.9%
-1.5%
1998
7.8%
-4.2%
16.0%
10.6%
2.6%
3.3%
4.8%
4.3%
28.4%
0.2%
6.7%
2.4%
13.5%
8.3%
1.7%
7.2%
10.1%
2.5%
-10.3%
-3.6%
8.1%
16.5%
Eq Hedged Europe (MSCI)
Eq Hedged Japan (MSCI)
EMN
Event
Merger Arbitrage
Stat Arbitrage
Short Sellers
Fixed Income
Macro Discretionary
Macro Systematic
High - Low Dispersion
1999
14.4%
16.9%
44.2%
48.5%
48.0%
44.2%
7.1%
24.3%
14.3%
-0.2%
-1.1%
7.4%
5.8%
-3.7%
48.6%
2000
14.5%
2.8%
9.1%
16.9%
26.3%
6.6%
14.6%
6.7%
18.0%
8.9%
30.0%
4.8%
11.7%
9.9%
20.1%
2001
13.4%
13.3%
0.4%
5.1%
1.8%
11.7%
6.7%
12.2%
2.8%
1.6%
4.1%
4.8%
18.4%
3.0%
13.4%
2002
9.1%
5.3%
-4.7%
-7.4%
-2.4%
11.1%
1.0%
-4.3%
-0.9%
-3.2%
31.8%
8.8%
14.7%
12.1%
25.0%
Cross-strategy dispersions are large
6
2003
9.9%
29.6%
20.5%
25.4%
8.3%
22.0%
2.5%
25.3%
7.5%
3.4%
-36.1%
9.4%
18.0%
8.7%
36.8%
2004
-0.1%
20.7%
9.3%
10.4%
10.7%
14.4%
5.8%
16.4%
4.8%
4.8%
-2.8%
7.3%
10.8%
-2.8%
19.1%
Example – Asset Allocation
Cash
Convertible
Distressed
Eq Hedged US
Eq Hedged Europe (MSCI)
Eq Hedged Japan (MSCI)
EMN
Event
Merger Arbitrage
Stat Arbitrage
Short Sellers
Fixed Income
Macro Discretionary
Macro Systematic
Total
Strategic
Weights
Tactical
Weights
Active vs.
Strategic
0.0%
10.0%
8.6%
13.8%
8.6%
9.0%
9.9%
11.7%
0.0%
0.0%
4.8%
9.7%
10.1%
4.0%
100.0%
0.0%
4.9%
6.6%
9.8%
8.9%
11.7%
11.7%
16.7%
0.0%
0.0%
5.0%
12.0%
6.3%
6.3%
100%
0.0%
-5.1%
-2.0%
-3.9%
0.3%
2.8%
1.8%
5.0%
0.0%
0.0%
0.2%
2.3%
-3.8%
2.3%
0.0%
Can we reflect this allocation with actual hedge fund managers?
7
What do we need to establish?
•
Is asset allocation useful in fund of hedge fund portfolios?
- Is there really a systematic component? Otherwise, strategic and
tactical model portfolios are pointless.
- How well is the systematic component reflected by the indices?
- How many managers required to reflect a tactical allocation?
•
Efficacy of using alpha-(peer)beta analysis
- Advantage of using alpha-beta over equal weighted portfolio
- Does a stable beta exist?
- Portfolio construction using alpha-beta analysis
8
Dataset and methodology
•
Study conducted using data on individual hedge funds
- Proprietary hedge fund data that is a compilation of many index
providers plus group’s own data collection
- Duplications have been removed
- Only managers with > 50 million in AUM included in the study
- HFR indices used for strategy index
•
Methodology
- Simulation based on creating multiple randomly-selected (without
replacement for each sample) portfolios of hedge funds
- Most of the analysis uses data from 01/2002 – 12/2004
- Initial study on systematic component was conducted using equalweighted portfolios
9
Is there a systematic component?
Manager Portfolio Diversification
Convertible Arbitrage
4.0%
+1 STD
3.5%
3.0%
2.5%
-1STD
2.0%
1.5%
theoretical pure alpha curve
1.0%
0.5%
0.0%
2
6
10
14
18
22
26
30
Number of Managers
10
34
38
42
46
50
Is there a systematic component?
Manager Portfolio Diversification
Macro Discretionary
16.0%
14.0%
+1 STD
12.0%
10.0%
8.0%
6.0%
4.0%
-1 STD
2.0%
theoretical pure alpha curve
0.0%
0
4
8
12
16
20
24
28
Number of Managers
11
32
36
40
44
48
Is there a systematic component?
Manager Portfolio Diversification
16.0%
14.0%
12.0%
Convertible
Distressed
10.0%
EMN
Event
8.0%
Fixed Income
Hedge Equity
6.0%
Macro Discretionary
Macro Systematic
4.0%
2.0%
0.0%
0
4
8
12
16
20
24
28
32
36
40
44
48
Number of Managers
Anywhere from 6-20 managers required to reach full diversification
12
Characterizing the systematic component
Systematic
Vol (N=50)
Total - Syst Strategy Factor
Var Ratio
R-square
Mean
Std
Convertible
7.2%
4.4%
2.9%
43.3%
47.9%
Distressed
16.1%
7.1%
4.5%
39.1%
40.4%
4.4%
6.3%
2.1%
11.1%
10.4%
Event Driven
11.9%
9.1%
6.5%
50.8%
50.3%
Fixed Income
6.7%
3.8%
1.6%
17.8%
10.8%
US Hedged Equities
9.8%
13.7%
8.6%
39.9%
43.0%
Macro Discretionary
9.8%
11.8%
4.2%
12.8%
6.1%
Macro Systematic
9.8%
17.3%
11.5%
44.6%
50.7%
EMN
Generally high systematic components in many of the strategies
Except: EMN, Fixed Income, Macro Discretionary; possibly
indicates existence of distinct sub-strategies
13
Significance of strategy index factor has varied over time
01/02 - 12/04
01/99 - 12/01
01/96 - 12/98
01/94 - 12/95
Convertible
47.9%
23.9%
30.9%
18.5%
Distressed
40.4%
32.8%
56.3%
26.6%
EMN
10.4%
12.8%
16.8%
18.4%
Event Driven
50.3%
30.0%
51.7%
29.1%
Fixed Income
10.8%
5.3%
49.4%
11.4%
US Hedged Equities
43.0%
36.2%
48.1%
33.8%
Macro Discretionary
6.1%
6.3%
13.1%
17.9%
Macro Systematic
50.7%
37.8%
47.2%
49.2%
14
High systematic component – but also high mean dispersion
Cross-sectional Return Dispersion
(Distressed, 01/02 - 12/04)
18
16
14
12
10
8
6
4
2
0
0%
5%
10%
15%
20%
25%
So opportunities for manager selection still exists
15
30%
Decomposing manager returns
no diversification
(corr = 1)
partial diversification
(0 < corr < 1)
full diversification
(corr = 0)
ri, j = r f + α i, j + β iS, j ( R Bj , S − r f ) + β iM, j ( R Fj − rf ) + ε i, j
R Bj, S = strategy benchmark return ; R Fj = sytematic factor change
β iS, j = beta of fund i to strategy j return;
β iF, j = fund specific beta (sub - strategies)
Not clear that strategy indices necessary capture well the
systematic components of a given portfolio
16
Test: performance of index replicating portfolio
Manager Portfolio Diversification
8.0%
7.0%
6.0%
Convertible
Distressed
5.0%
EMN
Event
4.0%
Fixed Income
Hedge Equity
3.0%
Macro Discretionary
Macro Systematic
2.0%
1.0%
0.0%
0
4
8
12
16
20
24
28
32
36
40
44
48
Number of Managers
Diversification occur at different speed depending on factor composition
17
Constructing the total portfolio
•
Despite the fact that the ratio of systematic components are high in
many of the strategies, it appears that portfolios containing a
significant number of managers (6-20) is required to adequately track
each individual strategy
- Implies a fund of fund portfolio of 80 –90 managers to specifically track
each strategy
- It is generally not practical to run such large number of managers
•
We require a compromise solution: track the tactical model portfolio at
the total portfolio level – not individual strategies separately
- Requires that the idiosyncratic components of each strategy portfolios
diversify well across strategies
18
Tracking error at the total portfolio level
Total Portfolio Tracking Error
(tracking an equal-weighted tactical model represented by indices)
6.0%
5.0%
4.0%
3.0%
+1 STD
2.0%
-1 STD
1.0%
0.0%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Number of managers per strategy
The idiosyncratic components of manager portfolios does diversify
across different strategies – significantly fewer manager is required
19
Dispersion of manager portfolio return
Total Portfolio Std Dev of Mean Return
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
1
2
3
4
5
6
7
8
9
10
Number of managers per strategy
20
11
12
13
14
15
Number of managers
Contribution to Total Tracking Error
4.0%
3.5%
3.0%
2.5%
Total TE
2.0%
Tactical TE
Manager Select TE
1.5%
1.0%
0.5%
0.0%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Number of managers per strategy
Number of managers determine the relative risk allocation between
tactical asset allocation and manager selection
21
What have we discovered so far?
•
Hedge fund returns have significant systematic components for most
strategies
- EMN, Fixed-income, and Discretionary Macro are notable exceptions
- The systematic components converge to the index returns
•
This implies that beta is a useful concept for manager return factor model
•
It is difficult to construct a portfolio that tracks each strategy independently
- Instead, it is more practical to construct a portfolio that tracks the tactical
model portfolio – on average.
- Implies that, if the tactical views change frequently, then it will be difficult to
distinguish between tactical allocation and manager selection
22
Why alpha-beta for portfolio construction?
•
All of the previous results can be implemented through equal-weighted or
equal-volatility weighted portfolios
- Simple to implement
- For the constructed portfolio, value is added only through manager selection
•
Alpha-beta analysis has the potential to add the following:
- Lower tracking error to the tactical model portfolio
- Higher return by varying the manager weights (optimize IR)
- Ability to change the characteristics of sector exposures from predominately
high alpha and low beta managers (bearish sector view) to predominately low
alpha and high beta managers (bullish sector view)
- Better understanding of return process of managers (manager selection)
23
Beta weighted portfolio vs. equal weighted portfolio
Total Portfolio Tracking Error
(tracking an equal-weighted tactical model represented by indices)
4.0%
3.5%
3.0%
2.5%
Equal Nominal
Equal Vol
2.0%
Beta Weighted
1.5%
1.0%
0.5%
0.0%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Number of managers per strategy
It is possible to achieve lower tracking error to tactical model portfolio
using beta-adjusted weights vs. equal (nominal or vol) weights
24
But is beta stable over time?
• Up to now, all of the analysis have used in-sample results
• How well does the beta estimated in ex-ante basis work ex-post?
- Hedge fund indices contain many statistical irregularities
- Conduct the following test:
1. Estimate the beta in an in-sample period
2. Calculate the implied alpha in the next period using estimated beta
3. Roll one period forward and repeat
4. Measure the correlation of implied alpha to strategy index
(ideally correlation should be 0)
25
Ex-post performance of estimated beta
Est. Beta
Resid Corr
Naïve Beta
Resid Corr
Avg Fund
Correlation
Convertible
0.21
0.28
0.65
Distressed
0.28
0.43
0.62
EMN
0.16
0.61
0.21
Event Driven
0.21
0.36
0.68
Fixed Income
0.22
0.43
0.17
US Hedged Equities
0.25
0.36
0.57
Macro Discretionary
0.28
0.34
0.15
Macro Systematic
0.21
0.34
0.59
• Estimated beta does a reasonably good job in ex-post period
• Tendency to underestimate beta. Probably due to the fact that beta
has increased during the past three years (capacity effect)
26
Some thoughts on enhancements to this framework
•
Introduce sub-strategy indices
- There are prominent sub-strategies making up the broader strategy index
(e.g. value/growth, large/small cap in hedge equities; credit-focus, mortgage
focus, and relative-value focus managers in fixed-income; etc.)
- Introducing these sub-strategies should improve the explanatory power and
the stability of the peer-group style factor
•
Incorporate Sharpe’s style analysis at the strategy portfolio level to control
the exposures to market factors in the portfolio construction
- Estimation errors in multi-factor models are probably too large in hedge funds
to be used directly for asset allocation
- Instead, utilize the analysis to impose constraints and general portfolio biases
27
Practical aspects of portfolio construction with hedge funds
•
Managers with short or non-existent track records
- requires semi-subjective parameter estimation
•
Lock-ups, gates and other liquidity constraints
- makes large and/or frequent asset allocation shifts difficult
•
Significant and rapid style migration by managers
•
Absolute – not relative – return focus
- For fund of hedge funds, we want to use alpha-beta approach as means of
achieving highest absolute return – not to blindly track the hedge fund indices
28
Conclusions
•
Traditional asset allocation approach can be adopted to fund of funds
- Systematic strategy returns exists and can be captured by a small (number)
portfolio of managers
- Adds transparency and structure to the investment process
- Opportunity to enhance returns
•
Estimation errors in multi-factor models are probably too large in hedge
funds to be used directly for asset allocation
•
Single peer-group factor (alpha-beta) approach reaches a compromise
between too little and too much
- There is sufficient explanatory power and stability with single factor approach
to adequately reflect the tactical model portfolio
29
Investcorp
30