Capital Allocation Modeling In Hedge Funds Methods and Models

1
Capital Allocation Modeling In Hedge Funds
Methods and Models
Thomas Schneeweis Director/CISDM 3rd Annual
Hedge fund Performance and Risk Measurement Forum
April 17, 2007
Isenberg School of Management University of
Massachusetts, Amherst, MA 01003 Tel
413-577-3166, Fax [phone]
2
Capital Allocation Across Hedge Funds Methods
And Models

• The history of the race, and each individual's
  experiences, are thick with evidence that a truth
  is not hard to kill and a lie told well is
  immortal
• Mark Twain, Advice to Youth
• If It Were Easy They Would Hire A Monkey and Feed
  It Bananas
• Thomas Schneeweis, Advice to Students

3
Good News Bad News In AA

• Good News Asset allocation methodology
  approaches (e.g., Mean/Variance Optimization)
  which are useful for Mutual Funds can also be
  used for Hedge Funds.
• Really Good News Theoretical Models of
  Return/Risk Process for MF works for HF.
• Bad News The problems of parameter estimation
  and model determination in the use of various
  asset allocation models in traditional asset
  investments also impact their use for hedge
  funds.
• Really Bad News Potential Degree of Estimation,
  Error, Data Error, Model Error May Almost
  Eliminate Any Benefit of Decisions Based
  Primarily on Historical Data.

4
Robustness of Optimal Allocation

• Inputs to optimizations have to be estimated
• The resulting optimal allocation is just a point
  estimate of the true optimal allocation
• How good an estimate is it?
• Use re-sampling to test its robustness

5
The Four-Asset Class Efficient Frontier
The Re-sampled Frontier
Point Estimate of the Frontier
6
Robustness of Optimal Allocation

• Correlations among asset classes changes
  substantially when market conditions change.
• An allocation that is optimal during normal
  periods may not be optimal during turbulent
  periods.
• Optimal allocations have to be back tested under
  different economic environments

7
Robustness of Optimal AllocationAdding Hedge
Funds Increases Stability
8
Some Simulation Results

• We sampled 5 years of monthly returns from a
  normal distribution with a true Sharpe of 1.16
• About 2/3rds were between 0.7 and 1.6, 95
  between 0.2 and 2.1

9
Some Simulation Results

• We then sampled from a normal mixture
  distribution with a kurtosis of 4 moderate by
  hedge fund standards -- and a true Sharpe of
  1.16
• About 2/3rds were between 0.4 and 1.9, and 95
  between -0.3 and 2.7
• Even with 5 years of data, estimated Sharpe (and
  other risk-adjusted metrics) are subject to large
  estimation error.

10
Example of Potential Issues in Parameter
Estimate Data Makes A Difference
11
Data Makes A Difference Fund Composition Changes
Over Time Such That Historical Returns May Not
Reflect Current Return and Risk Attributes
12
Changing Composition (e.g. Non Strategy
Consistent) Makes Asset Allocation Based on
Tracking Historical EW Indices Difficult
1990
2004
Source HFR
13
Measuring Return

• Biases in Hedge Fund Databases
• Self-Selection bias size unknown
• Instant history (backfill) bias 2 per year for
  the first 5 years.
• Survivorship bias 2 per year.

14
Estimated Mean Return

• Graph shows distribution of estimates of mean
  return when
• 1 year
• 2 years
• 5 years
• 10 years
• 20 years
• of data are available

15
Estimated Return Process

• Auto-correlation may indicate that the underlying
  return process is more volatile than the observed
  process
• What is the impact of auto-correlation?

16
Impact of Auto-Correlation
17
However, empirical research has shown those
studies which emphasize price smoothing (e.g.,
correlation impacts) to be time specific.
18
Trend in Historical Volatility
19
Historical Trend in Correlations
20
Skewness is time varying.
21
Impact of Number of Managers on Portfolio
Characteristics
22
Risk In Different Market Conditions

• Hedge funds have changing risk exposure

23
Do Parameter Estimates Differ if Daily, Weekly,
or Monthly Data is Used? Interval Effects
24
Examples Of Model Risk

• Is modern portfolio theory too simplistic to deal
  with hedge funds?
• Models of Var Estimation
• Models of Conditional VaR

25
Is modern portfolio theory too simplistic to deal
with hedge funds?
Modern portfolio theory has a number of issues in
providing a basis for forecasting expected risk
and return relationships 1) return estimates
dominate results where do you get them from, 2)
most programs are based on mean and variance if
assets non-normal or if investor has different
risk concerns (liquidity) results may not
reflect investor needs, 3) the number of assets
in a portfolio. Your model needs flexibility in
capturing these issues.
26
Are Hedge Fund of Funds Constructed to Minimize
Risk or Maximize Return?
One can create a fund of funds from hedge funds
which differ in market sensitivity and therefore
with reduced risk or one in which the underlying
returns of the various managers are more closely
align. The first offers the potential for
positive return over varying markets but with
little certainty of when it will perform well.
The second offers greater return consistency but
in certain market environments, lower return.
27
Style purity is required for consistent market
sensitivities of the funds.
28
Variation in Var Estimates
29
Variation in VaR Estimates Hedge Equity
30
Constraints Based on Situational Portfolio

• Investments could be used as
• Risk diversifiers
• Return enhancers
• Both
• Their role depends on which asset class
  dominates the investors portfolio

31
Relative Market Performance
32
Relative Market Performance
33
Multi-Factor Models Alternative Betas Alphas

• Using a single-factor benchmark (e.g., MSCI
  World), most hedge funds appear to have positive
  alpha.
• Using a multi-factor model, most hedge fund
  managers (about 75) fail to deliver alpha on a
  consistent basis.
• Sources of returns for most hedge fund managers
  are from alternative betas (e.g., various types
  of credit, volatility, currency, commodity,
  illiquidity risks), rather than skill.

34
Alternative forms of Return Analysis

• Use univariate and multivariate regression.
• Use Generalized Method of Moments
• Nests multivariate regression
• Imposes few restrictions on the data
• Very suitable when volatility is changing and
  returns may be autocorrelated

35
Alpha Levels
36
Institutional Use of Alternative Investments Use
of Expected Returns in Asset Allocation Framework
37
Institutional Use of Alternative Investments
Similar Exposure to Market and Economic Factors
Bullet Point Portfolio can be created which
includes alternative assets and which still
retains primary market and economic factor
sensitivity of original portfolio
38
Investible Indices and Fund of Funds

• Index Products
• Single Strategy FOF Diversification of Judgment
  (Multiple Managers)
• Multi-Strategy Diversification of Style
• Performance Characteristics
• Style Purity
• Performance Consistency

39
Reason for the Creation of Manager Style Pure
Comparison
Similar Patterns of Ranking by Composite Average,
but For Hedge Funds Insure Data Set Is Style Pure
(e.g., no Asia Hedge Equity In Set Of US Hedge
Equity)
40
Diversification of Style (Across Strategies)

• Bullet Point
• FOF Can Be Created In Which Funds Differ in
  Factor Sensitivity Or Are Similar
• Fund with the highest standard deviations drive
  risk parameter in FOF

41
Diversification of Style (Across Strategies)
Correlations

• Bullet Point
• FOF Can Be Created In Which Funds Differ in
  Factor Sensitivity Or Are Similar
• Fund with the highest standard deviations drive
  risk parameter in FOF

42
Importance of Selecting Style Pure Managers

• Fewer managers can replicate the return process
  of the larger set
• Have well understood sources of risk return
• Returns are more predictable given market
  conditions
• Have more stable relationship with traditional
  assets

43
Hedge Funds to Substitute for Traditional Assets
44
Manager Based Hedge Funds can be used Replicate
Russell Index used in Asset Allocation
Hedge Funds to Track Traditional Indices
45
Hedge Fund Indices in Portfolio Asset Re
Allocation
46
Relative VAR
47
Hedge Fund Portfolio With Similar Factor Exposure
of Original Portfolio
48
Hedge Fund Portfolio With Similar Factor Exposure
of Original Portfolio
49
Hedge Fund Portfolio With Similar Factor Exposure
of Original Portfolio
50
Strategic Allocation Value at Risk

• Criteria for Portfolio Optimization
• Maximize Expected Return Subject to
• Probability of Return lt -VaR ?
• Adjustment for Non-Normality of Return
• VaR can be adjusted for Skewness and Kurtosis of
  returns.
• Allocation will be different than the M-V model
• Delta VaR can tell us how much each investment
  will add to a portfolios VaR

51
VaR Implications for Asset Allocation

• Annual Standard Deviation 6.93 and Annual Mean
  Return of 9.48
• Value at Risk of this Portfolio
• 4.1 for 1-month Horizon at 5 Sig. Level

52
VaR Implications for Asset Allocation

• Annual Standard Deviation 6.93 and Annual Mean
  Return of 13.4 
• Value at Risk of this Portfolio
• 2.9 for 1-month Horizon at 5 Sig. Level

53
Frontier in Asset Allocation

• Security Based Hedge Fund Tracking
• Convexity Drives Conditional VAR Find Hedge
  Fund Managers With Convexity
• Find Funds with Strategy Timing Ability

54
Security Based Tracking
55
Relative Tracker Performance
56
Hedge Fund Based Tracking Of Hedge Fund Indices
57
Tactical Asset Allocation

• Certain Financial Variables Lead Returns on
  Various Strategies

Change in Credit Risk Premium
All Dates
Medium
High
Low
Min
Max
Min
Max
Min
Max
-0.25
-0.02
-0.02
0.02
0.02
0.20
Mean
Mean
Mean
Mean
HFRI Equity Hedge Index
20.06
4.04
-4.18
0.41
HFRI Relative Value Arbitrage Index
13.30
4.01
-4.43
0.68
HFRI Macro Index
17.84
-0.58
-4.65
5.19
HFRI Fund of Funds Index
11.16
3.33
-5.59
2.48
0.85
-0.53
-0.26
HFRI Equity Market Neutral Index
11.01
HFRI Convertible Arbitrage Index
11.90
2.26
-2.11
0.00
HFRI Fixed Income Arbitrage Index
8.62
2.20
-0.29
-1.76
SP500 Return
15.39
2.63
-9.33
2.50
Lehman Aggregate Bond Index
7.84
0.76
0.36
-0.84
58
Tactical Asset Allocation

• Using Leading Indicator Can Lead to Improved
  Performance
• An Example of Tactical Asset Allocation Using
  Model Portfolios

59
Convexity A Question Of Strategy/Mgr Timing

• Timing Can Occur at Two Levels
• Across Strategies InterStrategy Timing
  Picking the strategy that will outperform others
• Within Strategies IntraStrategy Timing or
  Manager Selection
• Increasing Exposure to Managers during periods
  when that strategy is profitable
• Selecting Managers that themselves will have more
  exposure during favorable markets, and less
  during unfavorable markets

60
Analyzing Strategy Timing

• Timing ability implies a convex relationship
  between manager returns and the benchmark
• A simple and intuitive way of specifying that
  convexity
• ReturnsAlphaBeta1BenchmarkBeta2Max(Benchmark,
  0)
• Type of analysis due to Robert Merton
• One can think of the successful timing
  relationship as adding a free call option to
  portfolio exposure.

61
Multiple Asset Model Portfolios

• Allocation was switched between Model Portfolios
  II, III, and IV depending on our predictions.
• Performance is compared to that of Model
  Portfolio III

62
Dynamic Strategies Returns Distribution
63
Other Dynamic Trading Strategy
The Strategy is designed to Protect the Value of
Portfolio to 90 of the Initial Investment
Value of a 100 investment
64
Conclusions

• Bad News Knowledge of Potential Estimation
  Error, Model Error, Data Error May Reduce
  Reliance Solely on Quantitative Driven Processes
• Good News Knowledge of Potential Estimation
  Error, Model Error, Data Error May Focus HF
  Selection Process and Asset Allocation Process on
  Tractable Factors (Style Purity, Manager
  Consistency) Which May Allow for A Level of Risk
  Management and Forecastable Factor Sensitivities.