24 February 2010
Published in: Capital - models, ALM, Market risks
Portfolio replication is not only about capital
It's not just group risk that can benefit from the use of replicating portfolios. Other areas of an insurance company such as liability product design, market risk monitoring and performance measurement in investment management will also find the approach valuable, as Rudi Damhuis, Nidal Shamroukh and Andrew Waters of Algorithmics explain.
In recent years there has been greater emphasis placed on the ability of insurance companies to manage both sides of the balance sheet. Pressure from regulatory and supervisory bodies, ratings agencies and competitors, taken together with the ongoing market turmoil, has created an incentive for insurance companies to measure, manage and allocate their scarce capital more effectively.
Replicating portfolios can help to join the asset and liability sides of an insurance balance sheet together. Further, a closely related series of replicating portfolios can be employed to decompose asset-liability risks into components that can be priced, managed and owned by the different functional groups of the organization.
Portfolio replication offers insurance companies an efficient method of capturing the behavior of a liability portfolio under present and future market conditions by way of a portfolio of standard financial instruments. Time-sensitive applications (e.g., revaluation in volatile markets, stress testing) become a reality since the valuation of these financial instruments is a trivial exercise when compared to the simulation of the original liability portfolio. Furthermore, simulation-based techniques can be applied in a wide range of applications, such as market-risk management, calculation of capital requirements, investment benchmarking and sophisticated what-if analysis.
A series improvement
Initially, the core reason for implementing a replicating portfolio approach to liability approximation was to calculate economic capital in a more efficient manner. The applications of portfolio replication have since evolved beyond capital calculations, and can be further embedded into the decision-making process to enhance communication across the organization.
Though insurers still commonly use one replicating portfolio per liability to fulfill a host of applications, we submit that one size does not necessarily fit all, and that a series of replicating portfolios with a set of evolving assumptions could better help attribute, allocate and ultimately manage risk in an organization. What follows is a description of how a hypothetical insurance company might implement a multiple replication approach.
| User group |
Potential applications |
Replicating universe |
Constraints |
Replicating portfolio (RP) |
|---|---|---|---|---|
| Business Unit |
Liability product design and strategy |
Theoretical and real |
Minimal |
Synthetic RP |
| Group Risk |
|
Real |
As needed |
Minimum Risk RP |
| Asset Liability Management (ALM) |
|
Market |
|
|
| Investment Management |
|
Market |
Trade size |
Actual Asset Portfolios |
In the table, the stakeholders have been separated into groups, each with their own motives and goals: business unit, group risk, asset-liability management (ALM) and investment management. However, these groups are inextricably linked. For instance, the business unit is responsible for creating the liability, while the group risk department measures the risk incurred by the business units and allocates capital as optimally as possible. The ALM team works with the business unit to determine the risk appetite, asset allocation strategy and a liability benchmark. Investment management is tasked with executing an investment strategy that falls within the guidelines set out by the ALM team.
The unique business drivers for each group dictate the composition of the replicating universe and potential constraints imposed during the construction of the replicating portfolio. See panel ("Narrowing down the universe of replicating assets") for more details about selection of candidate instruments.
Enhancing communication
Replicating portfolios can act as a lingua franca that helps integrate the various departments of an insurance company by employing a consistent approach to emulate the richness and complexity of the underlying liabilities. By virtue of this common language (i e, liabilities represented as a portfolio of financial instruments), different stakeholder groups are able to understand the liability from a market-risk perspective.
This common understanding permits a meaningful discourse about the asset-liability mismatch, asset allocation strategies, hedging strategies or exposure to changes in the underlying yield curves, volatilities or equity markets. Consequently, functional groups are less likely to work in isolation from one another.
Replicating portfolios also serve as a method for communicating externally for market-consistent financial reporting to shareholders, regulators (e g, IFRS, Solvency II, Swiss Solvency Test, RBC C-3), and other important stakeholders (e g, ratings agencies, CFO Forum).
Main article continues after box.
Honing down the replicating assets
One of the biggest challenges in performing any portfolio replication is to ensure a "good" result by selecting the right items from an endless number of replicating instruments.
Bear in mind that a liability portfolio that extends 50 years with quarterly cash flows will yield 200 possible maturity dates. If 10 instrument types with 10 strike prices were selected for each maturity date, this would result in 20,000 replicating instruments. This could grow exponentially by varying the swaption terms or by including multiple underlying indices.
Using such a large replicating universe often leads to replicating portfolios with large numbers of instruments making it difficult to interpret the replicating portfolio economically. These replicating portfolios often suffer from other problems including large offsetting positions and port out-of-sample performance. Using a trading constraint and/or penalty is an effective way to deal with all these issues. In effect, the trading constraint causes the optimizer to pick only instruments that have the biggest impact on the replicating portfolio. This reduces the number of instruments chosen, improves economic interpretability, eliminates offsetting trades and improves out-of-sample performance.
Two specific techniques to assist in the filtering of a replicating universe are trade penalties and genetic algorithms.
Trading penalties
Using a trading constraint and/or penalty effectively prevents the inclusion of instruments in the replication that don't meaningfully contribute to the cash flow matching objective. This approach applies a penalty on a unit or monetary basis so that the inclusion of extraneous instruments is actively discouraged.
For instance, without trade penalties the optimization engine may attempt to synthesize a complex embedded option of the liability by going long and short on two very similar instruments. The inclusion of trading penalties allows a large number of instruments to be included in the initial universe and the optimization engine is engaged to distil them into a replicating portfolio containing only the most effective instruments.
Genetic algorithms
A genetic algorithm uses a Darwinian evolutionary approach to instrument selection, filtering through a large financial instrument universe one subset at a time, allowing instruments in well-fitting subsets to survive in successive generations. This process of natural selection evaluates each subset on the basis of its potential strength as a replicating portfolio, and if deemed fit enough the subset will survive to seed the next generation. In each generation, successful subsets are randomly combined or mutated to produce an additional generation of subsets for evaluation. Paired algorithms (e.g., fittest-with-fittest, fittest-with-random or random-with-random) and cross-over algorithms are used to construct the subsets for future generations.
Unless perfect portfolio replication is achieved over a number of successive generations, the algorithm will terminate based upon existing criteria (e g, number of generations, increase in accuracy is marginal).
Multiple purposes, multiple replications
The synthetic RP is meant to be the best likeness of the replicated liability portfolio; it defines the practical limit on the ability to replicate the liability cash flows. Any residual deviations stem from the fact that the underlying liability model behaves in such a fashion that no financial instrument is able to replicate it. The business unit can use the synthetic RP in the design and pricing of new products by evaluating the behavior of the products and potential hedges under an unlimited number of market scenarios.
As there is no requirement to purchase or trade the instruments of the replicating portfolio in the marketplace, the synthetic RP is derived from a universe of theoretical and real financial instruments. We define theoretical instruments as financial instruments with custom pay-offs that are designed to capture specific aspects of the cash flows or that mirror the model employed by the actuarial projection system. Real instruments include both vanilla (e g, bonds, swaps, swaptions, forwards) and standard exotic instruments (e g, Asian, barrier, composite index options).We are not constrained by the availability of these instruments in the marketplace; 40-year European options are not typically traded, for example, but their market characteristics are readily understood and are therefore easily valued.
The minimum risk RP can be employed by group risk in the valuation of liabilities to satisfy regulatory or external reporting, intra-period valuation (i e, daily), market-risk hedging and economic capital computations for market risk. Given these applications it is important for this replication to closely match the sensitivities and profit and loss profile of the liability.
The minimum risk RP departs from the synthetic RP by restricting the replicating universe to include only real instruments. It is worth noting that theoretical instruments may not always be necessary to replicate a liability, in which case the minimum risk RP and synthetic RPs would be equivalent.
The minimum risk RP establishes a cut-off point where the business hands over the risks to the ALM team. The market risk associated with the minimum risk RP becomes the responsibility of the ALM function while the residual minimum risk, relative to the actual liabilities, remains with the group risk department.
The best hedge RP is used by the ALM team to ascertain the degree to which the liability portfolio can be hedged if no ALM constraints were imposed and acts as the starting point for portfolio construction.
The best hedge RP replicating universe is limited to market instruments, i e, those instruments that actually exist in the marketplace, regardless of availability. This portfolio can be seen as a constrained set of the minimum risk RP, as fictitious instruments (e g, 50-year zero coupon bond) would no longer be included. Additional constraints could include transaction costs to reflect new business, changes to existing business and minimum position size.
This approach could be extended to inform liability-driven investing strategies. The ALM team could perform a risk-return optimization in which expected shortfall of the surplus is minimized at the 99.5% confidence interval. The minimum risk RP is the starting point for such an exercise; constraints could be applied, and the resulting efficient frontier would help guide strategic asset allocation decisions.
The ALM benchmark RP involves overlaying the expert judgment of the ALM team on top of the best hedge RP. The replicating universe adheres to guidelines mandated by the ALM team. For example, the team can specify statutory or management limits, minimum liquidity ratios, strategic or tactical asset allocation policies and duration targets.
These constraints introduce additional relative risk by deviating further away from the minimum risk and best hedge RPs. The resulting ALM benchmark RP can be used to manage strategic or tactical asset allocation decisions and can serve as a benchmark for investment managers.
Although actual asset portfolios can be modelled directly, they embody actual investment decisions and are the essential bookend to the analysis. The relative risk arising from the deviation against the ALM benchmark RP is owned and managed by investment management and a portion of their compensation could be based upon the investment manager's ability to generate returns against the liability benchmark set out by the ALM team.
Although the mechanics of portfolio replication are consistent in each of the cases outlined above, the replicating universe, constraints and resulting portfolio can vary greatly.
Once a series of replicating portfolios has been established, a wealth of information and relevant reporting can be gleaned by performing relative risk analysis across the various portfolios. This allows for a clear delineation of responsibility and highlights any issues needing attention. For instance, by comparing the ALM benchmark RP with the minimum risk RP, the asset allocation decisions taken by the ALM team can be evaluated and refined. Using this chain of replicating portfolios, an insurance firm can link the two ends of their balance sheets and attribute ALM risks, and profits, to different functions within the firm. (See group risk management illustration above).
Greater insight into risk
The major advantage of replicating portfolios is their ability to bring asset and liability portfolios together from a wide range of different business units into a single coherent capital and risk framework. Though it is common practice to employ one replication to service a wide variety of applications, it is our proposition that a multiple replication approach can provide even greater insights into the organization's risks. The risk of the original liability can be decomposed into actionable pieces that can then be allocated to the responsible management function.
One benefit of the multiple replication approach is that various user groups within the company become more closely integrated since the same language is being spoken by actuaries, risk managers and finance and investment managers. This common foundation enhances the comprehension and communication of the organizational goals and the insurer is able to operate more effectively as a united entity.
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