“That which is static and repetitive is boring. That which is dynamic and random is confusing. In between lies art.” John Locke – English Philosopher (1632 – 1704)

A dynamic universe

The hedge fund world since 1990 has seen some impressive moves, with the number of hedge funds and funds of hedge funds rising from 610 to 9,767 and the number of assets under management rising from US$39 billion to US$1,745 trillion1. All of this is against a backdrop of world markets that has seen the MSCI World index achieve annualised returns of 6.5%2 and the Citi World Government Bond Index deliver annualised returns of 7.1%2 from December 1989. The HFRI Fund of Funds index performance has annualised at 10.05%2 for the period.

When looking at the performance of hedge funds in the top five bear markets for equities and bonds, hedge funds consistently deliver downside protection. When added to a balanced portfolio as seen in Fig.1,2 & 3, hedge funds boost performance and manage portfolio risk by providing diversification.

There is no doubt that hedge funds have a place in the line up of potential investments, yet when considering how to construct optimal portfolios it is hard to predict results in this fast moving universe.

This makes the function of quantitative analysis a critical element in bringing some order to the randomness of the hedge fund data and providing a structure to help active managers determine optimal portfolio allocation.

By using a mix of qualitative and quantitative analysis it is possible to determine a level of order and predictability in the hedge fund universe.

However, creating funds of hedge fund portfolios with specific target returns and with volatility ranges takes a systematic and rigorous process which evolves over time and is synthesised with experience. By working through investment and portfolio management committees it is possible to bring multiple perspectives to the process yet this portfolio management style requires a clear framework for decision making and a disciplined approach to implementation. Quantitative analysis is able to provide the parameters or framework for these committees, through a level of numerical results and historic analysis.

Systematic processes

When beginning to navigate the hedge fund universe it helps to consider strategies and their relationships with each other rather like the alignment of the planets and the sun. Each strategy has certain characteristics, including a level of volatility and these factors may be affected by another strategy’s gravitational pull much the same as the moons around Jupiter. By defining the profile of each strategy it is possible to define the future building blocks of a portfolio allocation and by choosing a range of measurable data for all the strategies it is possible to set parameters within which results for the group can be tracked, with unusual data being quickly distinguished as falling outside of an expected range. Importantly this also provides the peer groups against which individual managers can be positioned in analysis at the portfolio level.

Once the characteristics of the strategies have been established it starts to become possible to consider the use of simple quantitative modelling to create a rough outline of a portfolio. This can then be fine-tuned to address specific requirements or restrictions at a future date, but operates in the first instance as a starting point that reflects the input from the macro level, and brings together the component parts, without any of the finesse of a final portfolio. Typically at this stage target returns and risk parameters begin to set the framework for the construction, including risk parameters to enable exceptions, limits and specialities to emerge. Although there are almost an infinite range of hedge fund types, it is useful to group them under 10 main classifications.

Portfolio strategy allocation methodology

Creating a working strategy allocation methodology begins by understanding what level of risk/return a fund is prepared to take on. Where an investment into a fund of hedge fund sits on the risk/return spectrum will dictate the characteristics of that portfolio and the types of strategies that will deliver the required level of risk/return. For example:

* PORTFOLIO 1 – RELATIVE VALUE

Low volatility, low correlation and low likelihood of drawdown
Need strong diversification and low allocation to directional strategies

* PORTFOLIO 2 – GENERAL

Low volatility and relatively low correlation to traditional equity markets
Need strong diversification and potential for larger allocation to strategies with better fundamental attributes

* PORTFOLIO 3 – OPPORTUNITY DRIVEN

Return focused with greater tolerance of short-term volatility and correlation
Need more concentration with aggressive allocations possible in those strategies with stronger fundamental attributes.

The level of risk that is taken on determines the strategy allocation profile for that portfolio. In constructing a portfolio, parameters should be set for the weighting allocations of each of the ten major strategies. The weighting parameters are set as percentage ‘bands’ within which the actual allocation to each strategy will fall for the individual portfolios at any given time. The size of these bands is based on a view of the fundamental attributes of each strategy. Each of the ten broad hedge fund strategies can be analysed to determine its rating against a set of fundamental attributes or criteria.

Key fundamental attributes for each strategy include;

• Longevity – How long has the strategy been in existence, do managers tend to be highly experienced or is it a leading edge strategy?
• Depth – How many managers are there within the strategy, how significant are the underlying funds, how much concentration is there?
• Correlation – Is there strong diversification of returns and risk from the managers within the strategy, to what extent is it an alpha generating strategy?
• Liquidity – Do the underlying investments for this strategy require long-term capital or is there strong liquidity across the market cycle?
• Transparency – Do managers generally within the strategy provide good transparency? Is this transparency useful from a Fund of Funds portfolio manager or is it a snap shot that rapidly becomes meaningless?
• Complexity – How complex is the strategy and the instruments used? Are managers adopting straightforward investment techniques that have been tried and tested over whole economic cycle or is this something relatively new?
• Directionality – Do managers tend to have significant directionality at certain points in the cycle?
• Leverage – How much leverage is used within this strategy and how vulnerable does that make it to market shifts?

In assessing the appropriateness over a given strategy for a portfolio, these attributes should be assessed and given a rating, say positive (+ve), negative (-ve) or equal/neutral (=) (Table 1). The resulting ‘score’ for all eight criteria can then provide an indication of what band to set for the strategy within each investment mandate style. Each strategy is risk graded with respect to the view on their standing within these fundamental attributes. Importantly, certain attributes are more relevant for certain types of portfolios and these will be emphasised when considering the bands.

The final ‘score’ or summary view determines which weighting band the strategy is allocated within a particular risk/return level that a fund wishes to take on.

In the above worked example for Capital Structure/ Credit Arbitrage the fundamental attributes are not overwhelmingly attractive and consequently would have a relatively tight weighting band regardless of the level of risk/return a fund would take on.

Optimal portfolio allocations

The actual allocation to these strategies for each portfolio can be debated in the ‘current context’ of the allocation given two considerations:

• The latest outlook for the strategy (risk and return)
• The availability of managers and funds which are suitable

Table 2 shows the strategy weighting bands that may be applicable for the three general risk/return level portfolios outlined earlier. For each portfolio there should be differing band widths applied for each strategy. In a dynamic world, these bands should be reviewed at least annually and more frequently if there has been a significant change in market dynamics.

Any changes to the portfolios’ sector allocations reflect changes in the outlook both in terms of risk and return for each sector. It is possible that one or more strategies may be excluded if the return profile is not attractive or is likely to become asymmetrically biased to the downside.

Constructing a new portfolio

In a dynamic world, the construction and management of a new fund of hedge fund portfolio should reflect the current views on the:

• Macro economic environment
• Potential future performance of hedge fund strategies and
• Best approved managers within each of the strategies

When constructing a new portfolio the initial requirement is to determine what level of targeted return and risk is applicable and then to apply the investment guidelines including restrictions, liquidity targets (subscription/redemption timings) and portfolio objectives to create an outline. The outline is then populated by individual funds. However the composition of underlying funds in each portfolio is in turn dependent on various conditions, including accessibility, suitability, intra-portfolio correlation and an on-going assessment of the manager’s risk profile. In addition, just before constructing the portfolio, the latest analysis of macro trends and market environment must be undertaken covering macro market drivers and any sector specific issues to ensure that the strategy allocations are adjusted appropriately within the bands.

From the bottom-up, funds can then be selected from a short list of managers who have been thoroughly researched and analysed. These should comprise the best managers within each of the strategies at a given time. Further consideration should be given to the liquidity of the underlying funds since some are less liquid than others. Cash flow issues will also influence which funds are best used to correctly match the client’s liquidity requirements.

The importance of diversification in constructing an overall portfolio should not be overlooked. A portfolio should include managers with non-overlapping investment strategies, risk profiles and return horizons. Based on experience the most suitable number of holdings is between 20-30 hedge fund holdings with exposure to 6-10 different strategies. Below 20 managers in a portfolio there is a danger of over concentration and the portfolio is at an increased level of risk of exposure to any one manager. However, above 30 funds means that there is a large level of dispersion and holdings become less meaningful, so good performance becomes diluted and will have less of an impact. Populating each strategy ‘band’ in a new portfolio is not just a qualitative exercise. Once an ‘initial’ portfolio of the preferred mix of strategies and underlying funds has been identified it should also undergo a series of quantitative tests using historic data. This analysis should include portfolio optimisation, portfolio simulation and expected return analysis, correlation analysis (internal, external and overall portfolio correlation figures), efficiency evaluation and particularly in a dynamic world, rigorous stress testing.

The aim of the analysis is to fully understand and confirm the profile of the new portfolio. These tests should also be applied to existing portfolios in the stages of active portfolio management in response to dynamic market conditions.

Quantitative analysis

Quantitative tools should be used to help in the creation of optimal portfolios, and not just be blindly applied. The results of quantitative analysis, including strategy attribution and risk budgeting can bring practical insights to the risk management of portfolios, including optimal strategy portfolios, and proposed new portfolios. Quantitative inputs at the macro level that impact the top down structure could include:

• data on the world markets eg stock market indices
• views on the wider global economy (gained from access to an international banking network)
• the predetermined investment mandate or portfolio limitations and constraints (as discussed above in strategy allocation methodology)

To provide an accurate comparative context it is important to have manager peer groups as determined by strategy indices that create a universe tailored to the particular investment style of the firm. These are similar to indices in the long only world, but are hard to establish in hedge funds where data is often tricky to source and is often only available over short time periods. Indices arealso subject to concerns with survivorship bias, where poorly performing managers stop reporting numbers, as well as questions regarding the validity of the self-reported numbers. From the bottom up (ie. at the individual manager and fund level) other data inputs include performance monitoring and, within the context of the portfolio, the individual portfolio manager allocations and performance statistics. Further concerns also include whether the data tends to have non-normal and auto-correlated return distributions that will render the traditional mean-variance framework based performance analysis inadequate. Low transparency within hedge funds and issues regarding the frequency of performance data for underlying managers generally render performance statistics less robust.

The commitment to delivering absolute returns versus passive or relative returns means that consideration is needed of active total risk management rather than tracking risk management. Finally, non-linear asymmetric exposure to risk factors means traditional factor modeling-based risk analysis and VaR based approaches are of limited use.

Within the fund of hedge fund portfolio construction and management process, the over-riding objective of quantitative analysis is to stimulate regular debate amongst those applying qualitative judgement by highlighting any patterns or trends that may remain hidden when looking at data ‘on the face of it’. Using quantitative analysis establishes a numeric context for decisions and enables a level of consistency to be achieved within a decision making framework by setting ‘normal’ parameters and enabling items to either fall within or outside these boundaries.

In a practical context, to keep the allocations optimal and to manage risk there are several tools that can be utilised including, portfolio optimisation and forward looking portfolio simulations (combining historic information with predictive likelihoods of possible trends to consider possible outcomes), as well as stress tests, scenario analysis and monitoring.

Portfolio strategy optimisation and simulation

Portfolio strategy optimisation is a top down process that looks at the strategy levels (or bandwidths) within the portfolio and determines the optimal percentage of capital allocation. After defining strategy bands it is still important to know where to start within the context of the bandwidth and the appropriate investment mandate style. Significantly, portfolio optimisation results can then be tested through portfolio simulation and incorporating any qualitative views to ask whether the allocation makes sense intuitively as there may be qualitative reasons why a suggested optimisation level is inappropriate that can not be quantified. This analysis can stimulate the qualitative debate and provides a basis for attribution analysis.

This methodology is in contrast to traditional allocation methods where decisions are made on the basis of past performance and allocating to maximum and minimum constraints. When trying to forecast optimal allocations for the coming months or years, some level of prediction is required. These predictions, or expected return outcomes, can then be combined with historic manager performance and appropriately adjusted historical data to incorporate future market views.

Proposed strategy allocations and ultimately the final recommendation can then be made in the context of the overall qualitative view and confidence in future market environments for each strategy. After formalising the qualitative view into expectations as to future average returns they can be combined with historic distribution of returns to account for natural dispersion.

Future views

There are two steps that can be taken to quantify the future views. Firstly, an interpretation of positive, neutral and negative outcomes should be made. The neutral outcome should represent the historic average performance whilst a positive and negative outcome can also be derived subjectively to quantify ranges ofoutcome away from the neutral position (see Fig.5 below). This implies that for positive and negative expected returns the distribution is a shift of historic distribution and the magnitude of the shift expresses the degree of improvement or deterioration expected.

Fig.5 shows three lines, representing the historic returns distribution for a particular manager. The line to the left shows the returns if the result is negative (-6% in this example) the line to the right shows the returns if they are positive (+6%). These two possible outcomes are then subjected to the views analysis.

The most likely view for each strategy is determined as explained previously as positive, neutral or negative. Secondly, an interpretation of risk assessment is required in which risk reflects the level of confidence in the chosen view for a particular manager or strategy. Subjectively, probabilities of an outcome can be assigned to the positive, neutral and negative views. Following on from the risk assessment (eg +3%) the expected outcome must always be the most likely (highest percentage), however, the higher the risk, the greater the probability of the unexpected, so also raising the likelihood of the opposite to occur. If there is a low risk attached to a strategy then there is a high likelihood of the expected outcome being realised. If there is uncertainty or dichotomy of views then the risk is high.

Table 3 shows how risk assessment can be combined with a chosen view, when the subjective outlook is positive.

Optimisation

Having specified future views as probability distributions of returns, optimised allocations can be calculated using these views. Typically, a portfolio optimisation algorithm which belongs to a class of random sampling or stochastic global optimisation models can be employed to solve non-linear optimisation formulations.

It is clearly preferable to use global optimisation search techniques, as opposed to local optimisation search methods, as the aim is to find a globally optimal solution. The local search methods perform poorly when there are multiple local optima, which is usually the case in most of the real-life applications vis. portfolio optimisation, process control, engineering design etc. Simply put, you should not “confuse the foothills with the mountain peaks.”

Three types of objectives should be defined in an optimiser to reflect the fund’s requirements.

1. Maximise returns, subject to constraints on volatility and drawdown.
2. Minimise volatility subject to constraints on minimum return and maximum drawdown.
3. Minimise drawdown subject to constraints on minimum return and maximum volatility.

In addition to the constraints defined above, minimum and maximum allocation bounds can be defined for each of the underlying assets (hedge fund strategies or hedge fund managers). The frequency distribution of returns for each asset class, which are used by an optimiser to bootstrap time series of returns for each asset class, can be built from a modified empirical returns series of the asset classes. The historical time series for the asset classes should be modified in order to express exogenously defined expected return and risk views as defined.

The portfolio optimiser can then generate a set of portfolio weights that meets the defined objective and satisfies the specified constraints. Over time, the current, subjective views should be constantly under review and alter according to market fluctuations. In addition, the time horizon of these views must be aligned with the liquidity of hedge funds. However there is a fundamental belief in the philosophy that quality hedge fund managers will compound returns, therefore future market expectations tend to lead to the refining of portfolio allocations rather than any dramatic portfolio rebalancing.

Simulation

Following the optimisation process, the optimised portfolio can be used together with the combination of views for a particular strategy or manager to simulate the returns for each manager and portfolio as a whole. The simulation builds on the strategy review work previously undertaken and recognises the subjective nature of the qualitative views. It also takes account of expected outcome and uncertainty. To provide an appropriately accurate level of information on each manager, portfolio simulation which uses a bootstrapping methodology to build the database of track records and data points should be adopted. With this information it will then be possible to consider potential future outcomes in assessing the portfolio’s performance.

Risk contribution and performance attribution

For a snapshot view of the performance of an active portfolio, with historic performance record over a period, it is possible to use return (or risk) contribution to measure the contribution of certain portfolio constituents (managers, strategies, geographies etc) to overall portfolio return (risk). The return contribution methodology ensures that in the case of multi-period contributions calculations the sum of the constituents’ contributions equals the portfolio’s overall return for the period.

Risk contributions are calculated as the weighted marginal contributions of the constituents to portfolio risk (portfolio variance). The sum of risk contributions of all constituents equals portfolio variance. In contrast to risk contribution, performance attribution seeks to explain the value added in an investment portfolio and is integral to maintaining an optimal portfolio allocation for an existing, invested portfolio. To do this analysis a simplified version of arithmetic multi-period attribution methodology based on the Brinson method can be adopted.

In the performance attribution methodology the value added by active management, with respect to an optimised portfolio, is the sum of manager selection and asset allocation effects for a given month. Multi-period manager selection (or asset allocation) effect is then simply the arithmetic sum of monthly manager selection (or asset allocation) effects. Risk attribution can be calculated using a modified version of The Brinson-Hood-Beebower method, disaggregating the portfolio volatility into individual manager contributions. To demonstrate the application of this analysis, we have looked at the example of attribution for two managers. As illustrated by Fig.6 it is possible to see for each manager the three elements – returns, volatility and asset allocation. To focus on two examples:

Hedge Fund A shows a strong contributor of returns at approximately 15%, whilst only 5% of capital has been allocated. However the fund is a volatile fund and contributes nearly 10% to volatility therefore we can see greater return is a result of greater risk. This information can enable a fund of hedge funds to budget and allocate on the basis of risk rather than purely allocating capital on past performance.

Hedge Fund B shows another interesting example where the fund has the same allocation yet risk and return is significantly lower. The results of this snapshot could tell us where to focus any changes to the portfolio allocation, flagging both strong and weak managers.

At the portfolio level, over a two year period, Fig.7 demonstrates why active management adds value over and above an automated, optimised solution. In this example the portfolio shows active management ‘contributed’ approximately 3% to performance.

When looking at Fig.8, it details, for this portfolio, the attribution breakdown by strategy. It is possible to see that the manager selection contribution in five strategies is clearly positive, particularly in long/short equity. However, in the Capital Structure/Credit Arbitrage strategies themanager selection contribution appears to be negative. A review into these results indicated the likely cause to be a lack of high calibre managers within the strategy peer group. This type of analysis is essential in understanding where performance has been derived from.

Stress testing

Further analysis is undertaken through stress testing, in which the proposed portfolio is subjected to selected market scenarios to limit sensitivity to key risk factors. Stress tests are also carried out to determine the impact of extreme moves in the underlying risk factors on the portfolio. Taking the subjective views on the global macro environment and market outlooks, a scenario can be constructed. This scenario can be assigned a probability and compared against other scenarios. Other extreme scenarios may also be considered and when combined with the central estimate subjective view enables a more informed view of potential outcomes for the portfolio such as those listed below.

Extreme historic events:

• Interest rates shock of 1994
• Russian and Asian liquidity crisis of 1998
• Tech bubble burst and bear equity market of 2000

Future scenarios:

• Yield curve flattening/steepening
• Credit spread widening/narrowing
• Equity drawdown etc

Worst Case Situations: Constructing the worst case scenario uses a combination of quantitative and qualitative information. The quantitative information takes the form of sensitivity analysis and scenario building. These results are then compared with exposure analysis which has been generated using monthly information supplemented with direct contact with managers to form an exposure analysis.

Simple Quantitative Test: A test for a worst case scenario is to base analysis on the concept that an extreme negative event would cause managers to correlate. This analysis is simply calculated by considering each manager’s worst monthly performance sized by their portfolio weightings.

Conclusion

Undoubtedly creating the optimal portfolio strategy and allocation takes many sophisticated procedural stages in an investment process such as manager research, selection and due diligence.

However, the aim of this paper has been to focus on those stages where our experience has seen quantitative analysis provide a tool to organise data and to question or challenge the qualitative aspects of active portfolio management. By considering these quantifiable elements a fund can attempt to combine art with science and so attain a successful, consistent and scaleable investment process.

Whilst quantitative analysis is not always perfect (and it is good to remember that no matter how clever the analysis, if the data going in is inaccurate, then so to will the information coming out), highly skilled resources are able to maintain the integrity of the process by translating the data into useful statistical tools. This data provides a totally different perspective on constructing and managing the optimal portfolio. Experience has shown that the task of achieving target returns in the dynamic world of hedge fund investing is significantly enhanced through the use of practical quantitative solutions to produce intelligent analysis, which can then considered in a qualitative context to determine the next steps.

1. Source: HFR Industry Reports, © HFR, Inc. Second Quarter 2007

---

Biology

ANDREW GIBSON

Andrew joined IAM in 2001 and has over 18 years of investment experience. Andrew was formerly at Deutsche Bank (Director) as a member of the relative value fixed income sales team, responsible for hedge fund and proprietary trading accounts. Prior to that Andrew was Vice President at JP Morgan, head of institutional hedge fund team for Emerging Markets and previously a member of the hedge fund team covering European fixed income strategies. Andrew graduated from University of Washington.