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| Mensuel : | Edition de février 2010 |
| Rubrique : | Finance/Economie |
| Titre : | Recherche en Finance
Towards an integrated risk management process for funds |
| Article : | The standard portfolio theory doesn’t distinguish investors and asset managers and gives guidance on how a rational investor should choose his portfolio. Due to the duality of the optimization problem, there is no distinction between risk management and portfolio optimization. In reality, however, most of the investments are delegated to asset managers and this creates an agency problem which is at the root of the risk management topic. As far as the fund industry is concerned, under EU regulation, notably UCITS III, the Board is responsible for the risk management process and sub-contracting with the service providers, whereas the Asset Manager determines the portfolio strategy.
Proper Risk Governance implies the setting-up of checks and balances through the organizational structure. This implies the segregation of front- and back- as well as eventual middle-office functions. Also, the risk manager should directly report to the Board. The Board being responsible for the risk management process, it should have an adequate understanding of the risks, define the risk tolerances and supervise the risk management process. Risk management roles and responsibilities should be clearly defined and should be provided in written policies. Even though the risk manager’s primary role is to monitor and enforce risk limits, a more pro-active role may be warranted. The pro-active role of the risk manager might take place through the risk budgeting process. It might be worthwhile to segregate pro-active functions from control and monitoring functions. Nevertheless, an advanced process of strategic risk analysis is beneficial. The organizational distinction between the middle/back-office and the front-office is the direct consequence of the agency problem that is created by the asymmetry of information between the Board and the managers. There actually exists a double layer of agency relationships as there also exists an asymmetry of information between the shareholders (the investors) and the Board. It has been pointed out (Gil-Bazu and Verdu (2009)), this often matters, as in most cases, the Board has been nominated by the Management Company (ManCo, henceforth) at the inception of the fund, when the ManCo was major shareholder. After substantive in-flows, however, the Board nominated by the ManCo may still be in place, even though the ManCo has no shareholder majority anymore. There is thus a risk, that due to its relationship with the ManCo, the Board doesn’t cancel inefficient contracts. In this article, we will not focus on this second agency layer, as it doesn’t directly impact the risk management process. We focus on how a responsible board should implement the risk management. There has been an interest, quite recently, in the delegation issues in portfolio management. For a good overview consult (Stracca (2005)). Typically, the delegation problem is modeled through a Principal-Agent relationship. The investor is the Principal and the Agent is the Asset Manager or the ManCo. The portfolio delegation literature focuses on contractual issues. In a first step, the investors face a set of Managers and have to select the good ones that have the skills to generate outperformance. In a second step, the contract and the compensation rules have to incentivize the Manager to spend maximal effort to generate outperformance. The investors are thus supposed to structure the contract in such a way that 3 conditions are respected. First, the managers with superior skills are selected. Second, the contract incentivizes the Asset Manager to generate risk-adjusted outperformance once the contract is signed. Finally, the risk-sharing between the investor and the Asset Manager should also be optimal. Different compensation rules have been suggested, but they all face the drawback that, due to the fact that there is no direct relationship between effort spent by the manager and portfolio return it is extremely difficult to make sure the manager spends effort and to isolate performance stemming from sheer luck or hidden risks. The optimal compensation contract typically has two components. There is a fixed compensation part and a variable compensation part that depends on the deviations with respect to a benchmark. The benchmark is known in advance and it can be either stochastic or fixed. Mutual Funds, typically, are benchmarked with stochastic market based benchmark, generally given by an index that reflects the strategy of the fund. Hedge Funds, however, are mostly benchmarked with an absolute target which is given by the Hurdle rate. Hedge Funds often also have so-called High-water mark clauses which specify that past losses with respectd to the benchmark have to be made up before the variable fees are paid. As shown by Brown and Goetzmann (2003) this creates path dependent option like features. In the standard agency setting, there is a trade-off between risk sharing and effort inducement. However, in a portfolio delegation framework there doesn’t exist an optimal compensation rules that induces the manager to work harder. This result is known as the ‘irrelevance result’. This result holds irrespective of whether the contract contains a benchmark. A benchmark, unless it is the optimal conditional portfolio, is a distorting factor. Hence, restrictions have to be imposed on the manager’s trading set. This is an interesting result in terms of industry regulation. The irrelevance result and the fact that restrictions on the trading set have to be imposed rationalizes the recourse to risk management and risk limits. The Board’s responsibility in terms of risk management is thus to select a benchmark that is in line with the risk profile of the fund and determine the risk limit or limits of the fund or positions. Of course, the Board is also responsible for the HR and IT elements relevant to risk management, but this is not the topic here. The foregoing developments imply that the Board has to develop a top-down approach to the risk management and measurement and this is the issue that we aim to address. As discussed in the foregoing section, the function of the benchmark is to distinguish performance related to systematic risk factors from performance due to superior selection skills. From an operational viewpoint, the role of the benchmark is also to control the deviation of the portfolio with respect to the benchmark. As pointed out in the “Risk Principles for AM”, a kind of Best Practices Guide, the main risk is that the performance will fall short of the benchmark. Finally, benchmarks are also often used to compare fund performance to the benchmark. Benchmarking is an issue and (Sensoy (2009)) suggests that approximately 35% of benchmarks are not in line with the risk profile of the fund. Deviations from the benchmark are typically controlled through the trading error variance (TEV). Even though this approach is much used in practice, the TEV evaluates positive and negative deviations from the benchmark in the same way. We argue that the benchmark selection should be integrated with the risk management process. As the benchmark measures risk-adjusted performance, the benchmark should be in line with the risk measure that is used in the process and be used to determine the global risk exposure of the fund. For instance, if the global exposure of the fund is measured with the Value at Risk (VaR, henceforth), then the benchmarks expected return should be in line with the risk implied by the VaR. If returns are normally distributed, the VaR being the product of volatility with a multiplying factor, the benchmark could be selected by construction of an efficient frontier in the mean-variance space and by determining the equilibrium expected return for the respective volatility of the funds risk profile. The multivariate normality of returns, however, has been questioned by Embrechts et al. (2002). This has led to the application of new risk measures, notably VaR and Expected Shortfall (ES). The benchmark should thus be deduced from equilibrium relationship between return and one of the chosen risk measures. The choice of the risk measure, however, depends on the aggregation properties and here the notion of coherency of the risk measure plays a major role. Coherent capital allocation has been a research topic since the seminal work of Artzner et al. (1999). The first major contribution to the issue of coherent economic capital allocation was provided by Denault (2001). More exactly, the problem addressed is the following. Adding different business units or sub-portfolios leads to diversification effects, thus the sum of the risks of the subcomponents is larger than the risk of the sum of the subcomponents. However, the benefits of risk reduction due to the portfolio composition have to be divided among the different subcomponents. More recently, a new approach based on the notion of coherent risk measure has evolved. Kalkbrener (2005) develops an axiomatic approach based on subadditive and positively homogeneous risk measures (see appendix). The suggested axiomatization presumes that the risk capital allocated to a subportfolio depends exclusively on the distribution of that subportfolio and the distribution of the whole portfolio, not on the decomposition of the other subportfolios. Kalkbrener suggests three axioms for capital allocations. First, linear aggregation makes sure that the sum of the risk capital of the sub-portfolios equals the risk capital of the aggregate portfolio. Second, there are some diversification effects. Third, continuity ensures that small portfolio adjustments have a limited impact of the risk capital of the sub-portfolios. Kalkbrener shows that: - If there exists a linear, diversifying capital allocation with respect to a given risk measure, then the latter is positively homogeneous and sub-additive. - If the given risk measure is positively homogeneous and sub-additive then the capital allocation rule based on that measure is a linear, diversifying capital allocation. We are interested in deviations with respect to the benchmark and those can be measured with the shortfall measure presented in the appendix. Although these types of measures have been known for some time, they have not been used in practice till recently. Bertsimas et al. (2004) were the first to analyze the use of shortfall measures in an optimizing framework. An expected utility maximizer would choose, from a set of portfolios with the same expected return, the one with the lowest VaR. A natural approach of portfolio optimization would thus consist in maximizing VaR as a function of portfolio weights. As VaR is not a convex function of portfolio weights this leads to computational difficulties (see Lemus et al. (1999)). For investors with concave utility, maximization is equivalent to minimizing the shortfall at the risk level a (see appendix). Shortfall also bears relationships with coherent risk measures (Artzner (1999), Delbaen (2000)). As shortfall is to be used in portfolio optimization it integrates the expected return and shortfall can be expressed as the sum of the target return and the tail conditional expectation. Due to this mean-adjustment shortfall violates translation invariance and positivity. The properties described in the appendix will actually turn out to be very useful for portfolio optimization. Bertsimas et al. (2004) explain how shortfall betas can be constructed from shortfall measures. The shortfall beta can be interpreted as the relative change in shortfall when varying the weight of a certain asset. Note that as with the standard beta, the weighted sum of betas equals unity. This is a very useful property as it gives a decomposition of the portfolio shortfall into individual assets’ contributions. Note that the betas depend on the respective confidence intervals and can be calibrated for different levels of risk tolerance. IFB’s Fund Due Diligence Expert Team is actively working on those topics and this article is an overview of a Working Paper that is going to be published in February and has been presented at a Conference in Frankfurt (http://www.hedgework.de/). Readers interested in the details should contact the author. Dr. Michel Verlaine Associate Professor of Finance ICN Business School Expert for IFB Advisory Services Michel.verlaine@icn-groupe.fr ICN Business School jointly with IFB Advisory offer Executive Education programs on the subjects treated in this page. IFB Fund Due Diligence Expert team also provides consulting activities on these topics. For further details the author can be contacted via the contact details above. www.icn-groupe.fr www.ifb-group.com Appendix GRAPHIQUE VOIR JOURNAL References Acerbi, C. and Tasche, D. (2002) “On the coherence of expected shortfall”, Journal of Banking and Finance, Vol. 26, p. 1487-1503. Agarwal, V., Daniel, N. and Naik, N. (2009) “Role of Managerial Incentives and Discretion in Hedge Fund Performance”, The Journal of Finance, Vol. LXVI, Oct. 2009 Artzner, P., Delbaen, F., Eber, J.-M. and Heath D. (1999) “Coherent Measures of Risk”, Mathematical Finance, Vol. 9, p. 203-228. Bank Committee on Banking Supervision (2008) Range of practices and issues in economic capital modelling, Consultative Document. Bertsemas, D., Lauprete, G. and Samarov, A. (2004) “Shortfall as a Risk Measure: properties, optimizations and applications”, Journal of Economic Dynamics and Control, Vol. 28, 1353-1381 Brown, S. and Goetzmann, W. (2003) “Hedge Funds with style”, Journal of Portfolio Management 29, 101-112. Chan, N. Getmansky, M. Haas, S. (2007) “Systemic Risk and Hedge Funds” in M. Carey and R. Stulz, eds., The Risks of Financial Institutions and the Financial Sector,. Chicago, IL: University of Chicago Press Denault, M. (2001) “Coherent allocation of Risk Capital”, Journal of Risk, 4(1), p. 1-34. Dorfleitner, G. and Buch, A. (2008) “Coherent risk measures, coherent capital allocations and the gradient allocation principle”, Insurance:Mathematics and Economics, Vol. 42, p. 235-242. Embrechts, P., McNeil, A., Straumann, D.:(2002) “Correlation and dependence in risk management: properties and pitfalls” In: Risk Management: Value at Risk and Beyond, ed. M.A.H. Dempster, Cambridge University Press, Cambridge, pp. 176-223 Fischer, T. (2003) “Risk Capital allocation by coherent risk measures based on one-sided moments”, Insurance: Mathematics and Economics, Vol. 32, P. 135-146. Garcia, R., Renault, E. and Tsafack, G. (2007) “Proper Conditioning for Coherent VaR in Portfolio Management”, Management Science, Vol. 53. Getmansky, M., Lo, A. and Makarov, I. "An Econometric Model of Serial Correlation and Illiquidity in Hedge-Fund Returns", Journal of Financial Economics 74(2004), 529-609. Gil-Bazu, J. and Ruiz-Verdu, P. (2009) “The Relation between Prize and Performance in the Mutual Fund Industry”, Journal of Finance, October issue Kalkbrener, M. (2005) “An Axiomatic Approach to Capital Allocation”, Mathematical Finance, Vol. 15, p. 425-437. Lemus,G., Samarov, A. and Welsch, R. (1999) “Portfolio analysis based on Value-at-Risk” Proceedings of the 52 session of ISI, Vol. 3 Lo, A., Petrov, C. and Wierzbicki, M. (2003) “It’s 11 PM-Do You Know Where Your Liquidity Is? The Mean-Variance-Liquidity Frontier”, Journal of Investment Management, 1, 55-93. Lo, A. and Wang, J. (2000) “Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory”, Review of Financial Studies 13, 257-300. Sensoy, B. (2009) “Performance evaluation and self-designated benchmark indexes in the mutual fund industry”, Journal of Financial Economics, Vol. 92, p. 25-39. Stracca, L. (2005) “Delegated Portfolio Management: A Survey of the Theoretical Literature”, ECB Working Paper Series. |