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Tuning risk to client expectations

Whereas risk analysis is all about the risks run in a predefined portfolio, portfolio construction is about the general shape a portfolio should take to assume predefined risks.
The risk analysis problem is fairly well defined. Software packages are continually being built to dissect portfolios in novel ways and the debate about risk analysis has moved on from whether the job can be done, to whether it can be done better using different algorithms.
Portfolio construction, on the other hand, has been largely treated heuristically by the investment community. Experienced fund managers write specifications for funds by considering the competition and use their combined years of wisdom to set how aggressive a portfolio needs to be and how to implement that aggression.
This work has been undertaken to help us provide a more objective framework for designing funds, from benchmark setting through to position taking. This framework leads to a ‘flight envelope’ for the fund – a term specifically chosen to evoke images of how test pilots assess the safe regimes for flying aircraft, which can then be used by other pilots responsible for the safety of hundreds of passengers.
This provides clients with evidence that their monies are being managed carefully. After all, if too little risk is put into a client fund, then we end up with disappointed clients, who feel they were sold something that was not delivered. If too much risk is put into a fund, we get wild performance swings as part of the natural way of doing business and we can get a scared (or worse – litigious) client. The risk has to be tuned to the return expectations of the client.
So how do we set the benchmark? The asset allocation decision is often made in the context of the industry, but how much risk should be taken at this level? How much risk should be delegated to the stock selectors? For a given level of risk within an asset class (say UK equity), how many stocks should be in the portfolio? What industry and stock bets should be permitted? If we predict returns, how heavily should these views be supported, to achieve a given level of risk?
Let us address these questions.
o What do we mean by risk and how is it measured? To turn the risk analysis problem on its head, we first need a good understanding of how to assess risk in client funds. Clearly retail clients (or more generally, end-users) have cash as a benchmark. Volatility is the key risk measure that is appropriate here, since it dictates how much money can be lost in a period. Within a volatility class, though, tracking error becomes the dominant risk.
There are two types of tracking error, historical and system-estimated. The first is the ‘truth’ – the actual out-turns from investment decisions – suitably statistically processed. The second is an approximation, based on the link from position taking, through a covariance matrix, to the likely performance deviations from benchmark.
The covariance matrix has to be approximated to be tractable, and many systems have emerged designed to approximate in sensible ways. However, when approximations get made, they can be wrong (spectacularly so in the case of the internet bubble in 1999–2000.)
o How do we set a benchmark? In well-developed markets, it is usual to find industry norms appearing. For example, the UK pensions industry has defined a competitive portfolio split of asset classes. In other areas, the field is more open and we have the opportunity to influence the setting of an appropriate benchmark. We have to take each problem as it comes, but several classes appear amenable to standard approaches. Broadly benchmark setting is all about discussing suitable asset mixes to solve the original investment problem.
Often this reduces to visualising data about performance. For example, every quantitative analyst is comfortable with efficient frontiers, but we noticed that ternary diagrams from chemical engineering may be used to visualise more dimensions. Some elements of benchmark setting are about hedging particular risks. This might be immediate in that mark-to-market liabilities need hedging with mark-to-market assets, or more long term, such as the current debate about the replacement for the minimum funding requirement.
o How should risk be allocated to the various risk-taking activities in the fund? This is a tough problem. The overall asset allocation context can be defined with reference to the competition (although suitable care needs to be taken to exclude outliers for the sample to avoid distortion of the sample averages). This defines the tracking error taken at asset allocation level, which can then be married to the abilities of the various decision-taking groups to turn risk into return.
In 1998, we built a non-linear optimiser based on Lagrange multipliers that can be used to allocate tracking error optimally to the various teams. We have been using this technology to help with non-standard mandates for over three years. Approaches such as this appear to be becoming more commonplace under the title ‘risk budgeting’. One of the major benefits of this approach is that it explains why the UK pensions industry has gravitated to funds of a particular set of tracking errors in each asset class. The market is a great finder of solutions – the maths often follows later!
o How should we set appropriate bet sizes within a stock level portfolio? This is the true inverse problem. We make heavy use of an approximation to the covariance matrix that calculates a Euclidean distance measure as a suitable proxy. This can be shown to work well empirically within asset classes. (Moreover, the outlier rejection techniques we use to assess the asset allocation universe are directly related to this approximation.) After all, a fund with 10 +1% positions and 10 –1% positions is a less risky animal than a fund with 1 +10% position and 1 –10% position.
We also take this consequence of the covariance matrix approximation further to find expressions for the tracking errors of arbitrary portfolios (from the highly aggressive 10-stock portfolios through intermediate strength portfolios through to the index fund), in good agreement with system derived measurements. The tail of uninvested small stocks is of particular importance. The core results are used by us to suggest the numbers and extents of overweighted stocks for any particular portfolio, as part of the “flight envelope” for fund managers.
We can use similar techniques to estimate the effect on tracking error of inserting industry bets into portfolios, since globalisation of sectors is an emergent theme. We make use of the distance measure not only for the standard application in setting fund specifications – but for others too, such as for fund turnover constraint setting.
o How far should ideas be supported within a portfolio? When we re-derive core capital asset pricing model (CAPM) results in an active fund context, we find expressions for the optimal portfolio and information ratio. We make use of our new approximation to the covariance matrix, which allows simple expressions for portfolio weightings to be derived. The shapes of the formulae make intuitive sense: for example, the efficient frontier is a straight line through the origin. The formulae provide a useful starting point for setting stock weightings, when tradability of stocks is not a major issue. One (pretty obvious) outcome is that all CAPM results require predicted returns, reducing the theoretical information ratio dramatically. A topical application of the formulae we have derived is a hedge fund optimiser that is suitable for asset allocation.
A way of implementing buys, sells and holds in a portfolio has been investigated. The output of this investigation is a methodology – a smooth way to mutate a portfolio from on-index to progressively more aggressive stances, by taking a predefined level of risk producing results in close agreement with the computer system optimisers, when fed with the same preferences. The key is the algorithm used to treat the no-short-selling constraint.
We have put in place a robust framework for addressing non-standard mandates, all the way from working with the client on the relevant benchmark, through delegating the risk to the various teams, to setting sensible fund specifications. Along the way we have found answers to some of the more interesting problems in fund management, such as why UK pension funds have the shape they do.
This work shows that risk management has additional benefits, if harnessed on behalf of the organisation as a whole.
While other organisations will have their own way of addressing the problems we have outlined here, we feel that clients can be confident that their money is managed in a coherent and disciplined way, designed to ensure that just the right amount of risk is taken into client funds.
Julian Coutts is investment risk director at Standard Life Investments in Edinburgh

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