LDIOpt: Liability Driven Investment Optimizations under uncertainty

Transcription

1 LDIOpt: Liability Driven Investment Optimizations under uncertainty OptiRisk Systems: White Paper Series Domain: Finance Reference Number: OPT 001 Last Update August 2011 contact:- All rights Phone: reserved +44 by (0)1895 OptiRisk Systems. For a demo info@optirisk-systems.co.uk or more information please

2 LDIOpt: Liability Driven Investment Optimizations under uncertainty By Arun LILA Arun LILA is an Employee of Optirisk Systems and He was a student of IIT Bombay. He closely works with Professor Gautam Mitra in the field of financial models and risk management. A banker is a fellow who lends you his umbrella when the sun is shining and wants it back the minute it begins to rain.. (Mark Twain) Scope This white paper sets out to explain an important financial planning model called the asset liability management (ALM); in particular it discusses why in practice, optimum planning models are used. The ability to build an integrated approach which combines liability models with that of asset allocation decisions have proved desirable and more efficient in that it can lead to better ALM decisions. The role of uncertainty and quantification of risk in these planning models is considered. This white paper will be of interest to corporate treasurers, financial planners, to fund managers in the pension & insurance industry, and to analysts who support ALM models in different financial institutions.

3 CONTENTS ALM: An Introduction An Optimisation Approach ALM models: Optimum Hedged Decisions under Uncertainty Risks faced by Financial Institutions & Risk Quantification Overlay strategies using interest rate swaps Past, Present & Future: A decision-making Computational and Modelling Framework Model Based-applications of ALM What is available on the market Broad perspective to compare ALM software s Concluding Remarks

4 ALM: An Introduction Many financial systems in the corporate as well as individual context are underpinned by a cash flow balancing (also called matching) activity. At an individual level typically a young professional may set up savings after child birth as he or she goes through the schools systems. The savings are assets suitably invested in bonds and shares and future payment for school fees are liabilities. At a corporate level many institutions take contributions from working employees of a corporation and invest these contributions by acquiring assets. These assets are, however, pledged to meet the pension payments of the individuals at future dates of their retirement. These pension payments are again the liabilities for the financial institution. A basic aspect of financial planning encompasses such matching activities of cash flows and is given the generic label: Asset and Liability Management or in short ALM. From a mathematical perspective these models can be set up in an equation form involving non-negative variables which represent inflow and outflow of funds and carry-over of retained assets and funds from one planning period to the next. The development of asset allocation strategies through time can be seen from Figure 1. In the asset management sector the first asset allocation strategy involved the basic concepts of diversification using fixed mix strategies, where pre-specified fixed proportions were invested in asset classes, for example 40/60 meaning 40% of the total mandate invested in equities and 60% in fixed income, and the investments were rebalanced to these fixed proportions at frequent intervals. Then fund managers moved to dynamic asset allocation strategies where excess return was gained via a quantitative model. Only at a later stage the liabilities of a company were taken into consideration before this a naive thought of "asset returns" would increase quicker than the liability returns was common. Academic research introduced asset and liability management under uncertainty within a fully edged model in the 1980's (for example Kusy and Ziemba, earlier models with one liability and one asset were introduced by Merton); but industry has been and is still reluctant to make use of these. Some companies that do use them include the pension plan of Austria Siemens Osterreich and Towers Perrin Tillinghast (now Towers Watson). Figure 1: Allocation Strategies Returning to the fundamental aspect that any company has both assets and liabilities, it is clear that in the course of business the company will benefit from cash inflows and also have to meet liabilities. From Figure 2, a typical cash flow cycle of an ALM problem is shown: At each time period the company receives cash inflows, but at the same time it needs to pay out cash flows; the difference between these two is carried forward to the next time period. When asset streams are greater than liability streams there is a surplus and vice-versa when liability streams are greater than asset streams, there is a deficit. A company will always try to make sure that there is always a surplus but, in situations where there is a deficit, corrective measures can be taken to protect the company financially in the

5 short-term. In the long term however, a company continuing to accumulate shortfalls is likely to be in a serious financial position and may be on the verge of insolvency. To avoid this financial quagmire, requires advanced and meticulous financial planning, and for large organisations ALM is invaluable. Indeed at time of going to press, Bethlehem Steel, the third-largest US steel maker has filed for Chapter 11 bankruptcy protection, its burgeoning pension liabilities being cited as one of the major reasons for the decision. Figure 2: Illustration of ALM Cash Flows Surplus Wealth= Assets - PV (liabilities) - PV (goals) Asset allocation decision making is a crucial part of a company s risk management system. Currently, the idea of asset-class investing is becoming more complex than the usual preconceived notion of just investing in equities, fixed income products or cash products (Figure 3). This is mainly due to the fact that hundreds of separate and distinct asset classes can be identified, and still more are flooding the markets. In addition these asset classes have different risk and return combinations and their correlations to the other products vary. A landmark study Determinants of Portfolio Performance published in the Financial Analysts Journal (July-August 1986) by Brinson, Hood and Beebower demonstrates how powerful asset allocation is. The investment results of 91 very large pension funds were examined to determine how and why their results differed. They reasoned on the premise that only four elements could contribute to investment results: investment policy, individual security selection, market timing and costs. By using a regression analysis, they attributed the contribution (or lack of it) to each of the four elements. Their conclusions were quite astonishing. They found out that the biggest single factor explaining performance was simply the investment policy (asset allocation) decision that determined how much a fund should hold in stocks, bonds or cash. Even the newspapers have run headlines on the debate of asset allocation. The LA Times (4/9/97) quoted the following Academic studies have demonstrated that asset allocation among stocks, bonds and cash is the key to your portfolio s performance over time- much more important than the individual securities you select. Given this statement and the illustration of the study of the determinants of portfolio performance above, the idea of asset allocation and its importance starts to strike home. It is in this light that ALM has to

6 come into play to make sure that the asset allocation decisions are optimal and try to smooth the cash flows of financial institutions. Figure 3: A representation of Asset Allocations ALM: An Optimisation Approach An integrated asset and liability management (ALM) model sets out to find the optimal investment strategy by considering assets and liabilities simultaneously. The purpose of such an approach is to reduce risk and increase returns; it has been successfully used for banks, pension and insurance companies, university endowments, hedge funds, mutual funds and wealthy individuals. The decision maker under the ALM approach needs to have a good understanding of the financial markets in which the institution operates. ALM as described above represent the requirements and the constraints of the cash flow matching which can be achieved in (infinitely) many different ways. Through use of objectives and goals therefore we formulate optimisation models which lead to best ALM matching decisions. The objective of ALM is to maintain a match in the terms of rate sensitive assets (those assets that will move in search of the most competitive interest rates) with their funding sources (savings, deposits, equity, and external credit) in order to reduce interest rate risk while maximizing profitability. Interest rate risk is defined as the risk that changes in the current market interest rates will adversely impact the institution s financial performance. ALM models: Optimum Hedged Decisions under Uncertainty The Asset-Liability Management (ALM) problem has crucial importance to pension funds, insurance companies and banks where business involves large amount of liquidity. Indeed,

7 the financial institutions apply ALM to guarantee their liabilities while pursuing profit. The liabilities may take different forms: pensions paid to the members of the scheme in a pension fund, savers deposits paid back in a bank, or benefits paid to insure in the insurance company. A common feature of these problems is the uncertainty of liabilities and the resulting risk of underfunding. The other major uncertainty originates from asset returns. Together they constitute a nontrivial difficulty in how to manage risk in the model applied by the financial institution. The need for multi-period planning additionally complicates the problem. Thus optimum plans cannot be made in a deterministic way since the asset prices and the liabilities are not known with certainty in the future. Under these circumstances the concept of optimum plans is extended to optimum hedged plans. In order to achieve this, optimum allocation models are brought together with models of randomness which compute the possible future prices and liabilities (Figure 4). This combined paradigm of models is often known as the stochastic optimisation models. Using such SP models (Figure 5), it is possible to compute hedged decisions which may not be the best for any one realisation of the future but is robust in respect of different realisation of the future. It is easily seen that a good description of uncertainty may significantly improve on ALM decisions. Figure 4: ALM & Stochastic Prog. Integration, Figure 5: Two Stage Stochastic Prog. Risks faced by Financial Institutions & Risk Quantification In the finance world, future unpredictability is termed volatility: volatility of asset prices and uncertain liabilities clearly affects financial plans. In general such uncertainties lead to possible financial loss or in other words financial risk. But that does not mean uncertainty equates to or is synonymous with risk. Depending upon the decision-maker or the fund manager s utility, there are many alternative measures of risk. The choice of an appropriate risk measure that captures an individual s investment preferences has been, and continues to be, the subject of a long debate between academics and practitioners. This is not surprising, since without prior assumptions on the risk preferences of the individuals or the forms of the alternative distributions, it is likely that two individuals will consider risk from alternative perspectives. In general, risk measures can be divided in two groups depending on their perception of risk. The first group contains the so-called dispersion risk measures that quantify risk in

8 terms of probability-weighted dispersion of results around a specific reference point, usually the expected value. Measures in this category penalize negative as well as positive deviations from a pre-specified target. Two of the most well-known and widely applied risk measures, in this group, are Markowitz s (1952, 1959) variance or standard deviation and the expected or mean absolute deviation of Adikson (1970) and Konno and Yamasaki (1991). The second group comprises measures which quantify risk according to results and probabilities below reference points, selected either subjectively or objectively. Such risk measures include the Expected Value of Loss from Domar and Musgrave (1944), Roy s (1952) Safety First, the Semi-Variance proposed by Markowitz (1959), and Fishburn s α t criterion (1977) that not only constitutes the generalized case for the above.below-target, risk measures. In 1993, this concept of loss beyond a target has taken considerable way, found by JP Morgan s analyst who introduced Value at Risk (JP Morgan, 1993) as a measure of loss to level beyond a given percentile of distribution. Regulation of risk is naturally important in the context of banks and financial institutions, planning and operations. The Bank of International Settlements (BIS) started their work in Basle in 1988 (Basle Accord) and since then introduced regulatory requirements which are frequently updated (2000, new accord 2002). These regulations are globally followed by financial institutions. The risks faced by financial institutions come from different sources of uncertainty. These are then classified accordingly. Today the following are the accepted areas of risk- operational, credit, liquidity, operational, systemic, political and legal risks. It is a widely accepted notion that financial institutions and more generally banks are in the business of managing risks. The better they manage these risks, the better placed they are in dealing with very rare but possibly commercially destructive events. Moreover, as it is known in the financial markets- a company s reputation is only as good as its last transaction; hence any let-up in controlling the different aspects of a business could severely dent its future expansion. The following are some of the financial risks that an organisation may encounter. By financial risks, broadly means that part of uncertainty that relates to the returns of assets arising from unanticipated and unpredictable events. These events may initiate runs on banks or create a banking panic. In this part, some of the more common risks are discussed. First of all, credit risk means the risk that arises in the event that counterparty defaults on its obligations. The losses can be very substantial for any firm- for example, defaults on mortgage payments or companies not honouring their bond repayments. Moreover, liquidity risks are defined as an event when it is difficult or expensive to make changes in the composition of one s portfolio. This usually takes place when there are crises in the global markets or following some unexpected political events. Furthermore, political risks are usually country-specific and relate to the political uncertainties and policies of a particular government- a current example of the existence of political risks could be Zimbabwe where recent events have created some instability and reduced investment in the economy. Finally, we could define a situation where the financial sector has collapsed and where runs on banks are present and problems of liquidity and defaults surface- an apocalyptic situation in a sense as systemic risk

9 Overlay strategies using interest rate swaps A swap is an agreement between two parties to exchange cash flows in the future; typically the cash flow exchanges can take place on several future dates (Figure 6). Plain vanilla interest rate swaps are the most common type of swaps in the financial market and the preferred type for pension funds and insurance companies. In an interest rate swap agreement, one party agrees to pay cash flows equal to interest at a predetermined fixed rate on a notional principal for a number of years. In return, it receives interest at a floating rate on the same notional principal for the same period of time. Engaging in a swap agreement is particularly liked by pension funds since it can be used to transform assets and liabilities from floating-rate to fixed-rate and vice versa. By the introduction of Liability Driven Investment strategies interest rate swaps were used by pension funds and insurance companies to lever a fixed income portfolio duration in order to match a larger share of the duration risk while limiting the allocation to fixed income. It is in principle possible to construct a portfolio of bonds or swaps which will match the cash flows: this portfolio would provide the pattern of cash flows with a very high degree of certainty. With no swap in place, schemes have net short position in long dated bonds (the liabilities): with a swap in place the scheme would still have a net short position but instead of a short position in long bonds, the swap converts this to a short position in cash. By buying an interest rate cap (floating cash flows) and selling an interest rate floor (fixed cash flows) to offset the cap premium, financial institutions can also limit the cost of liabilities to a band of interest rate constraints. This strategy, known as an interest rate collar, has the effect of capping liability costs in rising rate scenarios. In order to introduce the swaps into the models we can think of it as two additional cash flows: one outflow coming from the fixed leg of the swap and one inflow coming from the floating leg of the swap. We therefore need to add a set, new parameters and a new decision variable, which will then be added to the present value matching constraint and the matching constraint: Model Based-applications of ALM Figure 6: Plain vanilla Interest rate Swaps The basic concepts of ALM models under uncertainty were developed by Kallberg, White & Ziemba (1982) and Kusy & Ziemba (1986). Afterwards, large scale applications were

10 developed. They include the Russell-Yasuda Kasai model by Carino, Kent, Myers, Stacy, Sylvanus, Turner, Watanabe & Ziemba. One of the areas in which ALM is widely applied is the banking sector. In particular, ALM models for banks are created in line with the Basel II accord. Pioneering work includes Kusy and Ziemba (1986), where they introduce a multiperiod stochastic linear programming ALM model for the Vancouver City and Savings Credit Union. The goal is to maximize expected income minus expected costs. The drawback is that the model is not truly dynamic and the way of describing uncertainties is kept simple. Finally, there is a dynamic model for ALM for defined benefit pension funds, by Cees Dert (1995). This paper presents a scenario-based optimisation model for analysing the investment policy and funding policy of pension funds, taking into account the development of the liabilities in conjunction with the economic environment. The ALM model presented can be used to compute ALM strategies which specify investment decisions and contribution levels to be set under a wide range of future circumstances. Dert found that decisions reached were different when using dynamic ALM strategies compared to static policies. Also, the use of the ALM model resulted in strategies with lower funding costs, the probabilities of underfunding were substantially smaller and the magnitude of deficits, reflected by the costs of remedial contributions, has been reduced dramatically. Boender et al. (1998) developed and described the ORTEC model, which again uses multistage stochastic programming. The ALM system for Towers Perrin-Tillinghast by Mulvey (2000) has three components: a scenario generator (CAP:Link), an optimization simulation model (OPT:Link), and a liability- and financial-reporting module (FIN:Link). It is a system used by a financial firm that makes use of multi- stage stochastic programming. A third application field of ALM is for Insurance Companies: one of the most famous implemented models for insurance companies is the Russell-Yasuda Kasai model (Carino et al. (1998)); it is a large-scale multiperiod stochastic programming model. The objective is to maximize discounted expected wealth minus discounted expected penalty costs, while meeting regulatory requirements, keeping enough cash reserves and offering competitive insurance policies. According to the authors, the model has enabled Yasuda to make use of a state-of-the-art decision-making and risk-management tool that provides valuable insights into the complex choices and restrictions to which the business is exposed. Then there is the computer-aided asset/ liability management (CALM) stochastic programming model for dynamic ALM by Consigli & Dempster (1998). They present the CALM model which has been designed to deal with uncertainty affecting both assets (in either the portfolio or the market) and liabilities (in the form of scenario dependent payments or borrowing costs). The discussion continues with the presentation of Stavros Zenios. paper on; ALM under uncertainty for Fixed Income Securities, (1995). His model made it possible to capture the increasing complexities of the fixed-income markets. He also found that the use of stochastic models is well justified given their superior performance over traditional immunization techniques. The CALM model has also been used for Pioneer (Dempster (2002)). Hoyland et al. (2001) analyze the implications of regulations in the Norwegian life insurance companies using a multistage stochastic ALM model. Their results show that some regulations (the annual guaranteed rate of return for example) do not coincide with the insurance holders' best

11 interest. Frangos et al. (2004) propose a discrete time model of an insurance company incorporating transaction costs, nonlinear financial constraints and feasible portfolio control strategies. Within the rebalancing constraints, the monetary value of assets sold is equal to the monetary value of assets bought plus transaction costs. To calculate a time-dependent portfolio strategy feasible control is applied. The Prometeia model by Consiglio (2005) is an example of a multi period stochastic programming ALM for an Italian insurance company: the model has multi period guarantees with bonuses paid at each sub period; the bonus is a fraction of the portfolios excess return above the guaranteed rate during each sub period. A rather new application of ALM is models for hedge and mutual funds. A detailed introduction is given in Ziemba (2003), where stochastic programming is used for risk control and optimal betting strategies. When added to a portfolio, hedge funds significantly improve the trade-off between risk and return. Further ALM models have been created for University Endowment Funds: in Merton (1991) the author sets out that universities offer education, training, research and storage of knowledge and that all of these activities incur a specific cost. University inflows consist of business income, property and grants. The corresponding ALM problem has been formulated and solved as a stochastic dynamic programming model. ALM for wealthy individuals and families has been extensively explained by Ziemba(2003). Especially if high taxes apply and the income depends only on assets, a stochastic programming model might reallocate the assets while reducing the risk of unfavourable outcomes. Given that there are various complex financial products being traded in the markets and over-the-counter, not only has it become much harder to assess the potential risks of some of these stand-alone products but also the problem of integrating these risks in the risk management system has arisen. Some research has been done on this topic by Martin Holmer on Integrated Asset-Liability Management: An Implementation Case Study. His article looks at integrated ALM which he views as a new management perspective that is creeping its way into the more inventive financial intermediaries in reaction to problems inherited from the older functional management perspective. For the latter, an organization has to be structured into different functional units (e.g., marketing, asset management, etc.), the decisions of which are synchronized by a corporate plan based on macroeconomic forecast. However, the lack of precision in predicting macroeconomic variables has forced the hands of some banks in looking for alternative management perspectives. Hence the new concept of integrated ALM, as its name implies, is more focused on integrating the various units of the organisation in order to include all the functional activity related to a line of business. Decisions are taken with the help of computer models, also trying to ascertain the uncertainty of the future business environment, and to generate profitable strategies by structuring the assets and liabilities of the business line across a series of alternative future scenarios. By comparing these alternative ways, a crucial difference can be spotted which is that, decisions are made using profitability calculations based on a single-scenario planning forecast, while, for the integrated ALM, decisions are made using risk-adjusted or hedged profitability calculations based on multiple-scenario

12 possibilities. This is just a brief synopsis of how ALM can be used in the decision-making process. Past, Present & Future: A decision-making Computational and Modelling Framework There are well-known models such as the Markowitz mean-variance model which has been used to capture uncertainty and make hedged decisions. Unfortunately, it relies entirely on history and makes a single period static decision. The real question that should be asked is: whether history should be taken into account to make future decisions? History doesn t always repeat. So the answer is that historical data should not be ignored. However, our models should be forward-looking with event trees of future scenarios. The flow of data and processing this into an analytic database (datamarts) and finally use of ALM model which support hedged optimum decisions are shown in Figure 7. The complete decision making framework can be seen as three separate sections combined with each other to achieve the optimum decision under uncertainty (Figure 7): A set of mathematical programming models make up the decision models, they can be deterministic linear programming, stochastic programming, dynamic programming, robust programming or any other preferred mathematical program. The data input comes from scenario generators either as a set of discrete realisations (scenarios) or as a forecast; the user should use a variety of scenario generators to represent different random parameters and/or simulated scenarios. The next important building block is simulation and decision evaluation which answers the question of "how" the decision models behave. This could be during backtesting, stress testing, what-if analysis or even in-sample testing. The final step is to look at performance measures where this can range from statistical measures (standard deviation, kurtosis etc), risk measures (VaR, CVaR, etc) or risk adjusted performance measures (Sharpe ratio, Sortino ratio, Information ratio, etc). Figure 7: From Historical data to Optimum ALM decisions

13 What is available on the market? With new breakthroughs in technology, it was no surprise researchers tried to apply their findings in ways that are useful to institutional and private investors. In fact, some interesting software s were created to cater the need of this niche market. In this section, we name some of them and in the next section we describe the different feature to compare these software s. First of all, there is LDIOpt, which is an asset-liability management tool, developed by OptiRisk systems for liability driven investment simulation application that can help in decision-making for institutions. Like OptiRisk there is PROFITstar, which provide services for asset-liability management, budgeting and simulation application. There are number of players in the market who provide tools and consultancy in the field of ALM, Portfolio optimization and risk analysis like Algorithmics offer AlgoALM, Axioma offer Axioma Portfolio Optimizer, D-Fine offer consultancy services for bank ALM, FINARCH, FISERV,Ortec finance and Calypso ALM/LDI portfolio construction etc. The software provider Surya is one that has developed products such as MitiGet (a market risk control system) and Balm (a bank asset liability management system). Broad perspective to compare ALM software s There are number of software available in the financial market which has application in area of Asset-liability management (ALM). These software s have different focus area in the financial market, also they uses different methodology to solve the problems. Here we are making an attempt to locate some major characteristic to compare these software s. Following are some broadly defined feature by them we can compare the ALM software s available in financial Market. 1. The focus of the tool: - The ALM area of finance has been widely studied for its use in pension funds, insurance companies, individual ALM and other institutional investment portfolios. The focus can be defined as the application area of the tool like Banks ALM, insurance ALM and Pension ALM etc. 2. Predictive analytical Models: - The core of predictive analytical models relies on capturing relationships between explanatory variables and the predicted variables from past occurrences, and exploiting it to predict future outcomes. For the ALM based portfolio we can further define the predictive analytical models as follows:- 2.1 Method of predicting Asset Price:- Which method is used to predict the asset prices like Factor models, CAPM etc. 2.2 Method of predicting Asset return and Volatility:- Which method is used to predict the asset return and Volatility s like GARCH model, ARCH model 2.3 Liability Predictive Models:- Liability Predictive modelling is the application of statistical techniques and algorithms to understand the behaviours of liability stream and predict future values. These models are

14 for HR compensation, Insurance, Bank, General Insurance, Pension, Life Insurance etc. 3. Asset Allocation decision Models:- In ALM the asset allocation models are the centre of the ALM tools. Asset Allocation models are used to find the optimal allocation to reduce the mismatch between asset and liabilities and proportion of wealth invested in risky and risk free asset as per the utility function of the pension fund and insurance companies. Followings are the few ways to compare these models. 3.1 Optimization Model: - Here we define the type and methodology behind the Optimization model used into the software. 3.2 Risk Constraint Model:- In these kind of model we check whether any special constraint has been introduced in the optimization model to manage the risk and to follow the regulatory systems. Such models are Fix- Mix model, VaR and CVaR based models. 3.3 Stochastic Optimization models:- the accountability of uncertainty comes under the stochastic models, they capture the uncertainty by different continuous or discrete scenarios and yield a hedged solution. Two stage stochastic models, multistage stochastic model, chance constraints models are example of stochastic optimization models 3.4 Robust Optimization Model:- Robust optimization is a field of optimization theory that deals with optimization problems where robustness is sought against uncertainty and/or variability in the value of a parameter of the problem. In particular, robust optimization models come under the stochastic optimization paradigms. We can distinguish between problems dealing with local and global models of robustness; and between probabilistic and non-probabilistic models of robustness. Modern robust optimization deals primarily with non-probabilistic models of robustness that are worst case oriented and as such usually deploy Wald's maximin models. In the last decade advanced optimization techniques had gathered intensive attentions of the academicians and industries. We also keep these non-traditional models such as ANN, GA, GP and ACO under robust optimization techniques. 4. Simulation, decision evaluation and Performance measures:- For every Models in operations research, engineering and finance we need to simulate, evaluate the decision and measure the performance of the inhabited models. 4.1 Simulation Methods:- Simulation can be done by number of ways as example by fixing the initial portfolio and rebalancing it in future time, rolling over a particular time interval and fixing the company specific assets or liabilities etc. 4.2 Decision Evaluation:- There are different types of decision evaluation techniques, by them the decision taken can be evaluated. Some of them

15 Conclusions are like: stress testing, backtesting, in-sample testing, out-of-sample testing, scenario analysis and what-if analysis etc. 4.3 Performance Measures:- The performance of any fund can be measured using different measurements. Some can use the most common ones: from academia: (1) the standard deviation of returns, (2) the Sharpe ratio, (3) Value at Risk, (4) the Jensen Index and from industry practice: (5) the Sortino ratio, (6) the Treynor ratio, (7) the Modigliani or M-Square Measure Recent financial convulsions has placed greater emphasis on liquidity management with tighter regulations and reporting requirements. The central decision problem in Asset and Liability Management (ALM) is to construct a portfolio for a pension fund and an insurance company that takes into account the future outflows (liabilities). In this white paper, important recent developments and the pragmatic approaches to the ALM models and systems have been presented. An explanation to show how ALM is becoming the linchpin of firms financial management has been given, especially under conditions of uncertainty which requires risk management. An illustration of how ALM and SP is integrated using an optimisation and risk control paradigm have also been discussed. So where does ALM take us in the future? Well, modelling the true uncertainty may still be an area under investigation. Moreover, the ability to devise software that can add more features would be most welcome. For example, presently it is not possible to incorporate TAA in ALM. SP has proved to be a powerful modelling approach to optimum decision-making under uncertainty. It has been shown to be more appropriate in many applications. Improvements in the new technologies and solution methods have made SP a viable optimisation tool, especially in the domain of asset and liability management. References 1. Brinson, G.P., L.R. Hood, and G.L. Beebower (1986): Determinants of portfolio performance, Financial Analysts Journal. 2. Carino D.R., T. Kent, D.H. Myers, C. Stacy, M. Sylvanus, A.L. Turner, K. Watanabe, and W.T. Ziemba (First published in 1994): The Russell-Yasuda Kasai Model: An asset/ liability model for a Japanese insurance company using multistage stochastic programming, Worldwide Asset and Liability Modelling. 3. Consigli G., M.A.H. Dempster (Printed in Annals of OR): The CALM stochastic programming model for dynamic asset/ liability management. 4. Dert, C. (1995): A dynamic model for asset/ liability management for defined benefit pension funds, Worldwide Asset and Liability Modelling.

16 5. Klassen, P. (1997): Solving stochastic programming models for asset/ liability management using iterative disaggregation, Research Memorandum. 6. Kyriakis, T., G. Mitra, and C.Lucas (2001): An ALM model with downside risk and cvar constraints, Presented to Asset Liability Management Conference, Cyprus 7. Zenios, S. (1995): Asset and liability management under uncertainty for fixed income securities, Annals of Operations Research. 8. Pirbhai M. (2008): Asset Liability Management Using Stochastic Programming, OptiRisk Systems: 9. Mitra S. (2008): Scenario Generation for Stochastic Programming, OptiRisk Systems: White Paper Series, Schwaiger K., Mitra G., and Lucas C. (2007): Models and Solution Methods for Liability Determined Investment, OptiRisk Systems: White Paper Series, Schwaiger K., Mitra G., and Lucas C. (2007): Models and Solution Methods for Liability Determined Investment, Report, CARISMA, Brunel University. 12. Schwaiger K., Mitra G., and Lucas C. (2008): Evaluation and Simulation of Liability Determined Investment Models, Report, CARISMA, Brunel University 13. Pirabhai M. and Mitra G. (2008): Asset Liability Management using Stochastic Programming, Asset and Liability Management Tools: A Handbook for Best Practice, pp Schwaiger K., Mitra G., and Lucas C. (2010): Alternative Decision Models for Liability-Driven Investment, Asset Liability Management: Handbook, pp Hussin S., Mitra G., Roman D., and Ahmad W. (2010): Employees Provident Funds of Singapore, Malaysia, India and Sri Lanka: A Comparative Study, Asset Liability Management: Handbook, pp Schwaiger K. (2009): Asset and Liability Management under uncertainty: Models for decision making and evaluation, Phd thesis. CARISMA, Brunel University. 17. Ziemba W., and Mulvey J. (1998): Worldwide Asset and Liability Modelling, Cambridge University Press. 18. Ziemba W. (2003): The Stochastic Programming Approach to Asset, Liability, and Wealth Management. CFA Institute. 19. Dempster M., Germano M., Medova E., and Villaverde M. (2003): Global Asset Liability Management," British Actuarial Journal, vol. 9, pp Zenios S. and Ziemba W. (2007): Handbook of asset and liability management: Applications and Case Studies. North Holland. 21. OptiRisk Systems, AMPL Studio User Manual, OptiRisk Systems, AMPLNet Internal User Manual, OptiRisk Systems, SAMPL/SPInE User Manual. 24. OptiRisk Systems, FortMP Manual, Optirisk Systems, FortSP: A Stochastic Programming Solver, LA Times: 04/09/ Financial Times: 16/10/2001.