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Economic Capital: “The Heart of Decision Making”- Asia Banker

Summit 2011Portfolio Optimization, Replication &

Response Surface Modeling into the Risk Process

Chicago | London | Singapore

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Efficient ERM calculations facilitated by powerful approximation techniques based on

Replicating Portfolios

Response Surface Modeling

Portfolio Optimizer provides clients with the ability to turn risk analysis into strategic decisions

Presentation Overview

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Definition of Replicating Portfolio: a portfolio that generates the same cash flows as the source (reference) portfolio under all possible scenarios

Ideally, matching period-specific cash flows is more accurate than cumulative cash flows

In general, the process of determining the appropriate replicating portfolio is a “best fit” process that requires the use of a suitable optimization routine

Replicating portfolio should contain the smallest number of instruments that replicate the source portfolio cash flowsAlways possible to add more instruments, but these add marginal information

Often Replication can be an iterative process, gradually increasing the universe of possible instruments until the fits are sufficiently accurate

Replicating Portfolios Generate Same Cash Flows but with Fewer/Simpler Instruments

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RP is an approach that can be used to include assets & liabilities that have not previously been covered

Often business units use distinct modeling platforms and models

Conversion to a single platform is difficult both logistically and “politically”

Replicate with same instruments as source portfolio to intelligently stratify portfolios

Useful when aggregating data based on risk metrics

A replication routine to mimic cash flows through a variety of forecasts allows for quicker processing and decision making

E.g., Economic capital simulations may be computed on RP more efficiently

Replicating Portfolios Can FacilitateEnterprise Risk Calculations

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Distilling a complex portfolio into hedgeable instruments facilitates communication with traders

Improves intuition and makes portfolio more transparent

RP is an approach that can be used to “synthesize” complex instruments

Useful when processing time is crucial

Also works for instruments or structures that the Framework cannot yet model

Synthesized instrument can be priced if each of the replicating instruments is itself priced

Replicating Portfolios Can FacilitateHedging Strategies

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RP Results for Universal Life: Along Any Particular Path, Cash Flow Mismatch is Small

RP fits cash flows from Universal Life policies

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Identify Outlier Path/Period Replicating Portfolio Values and Qualify Fit

Easy to see outliers, harder to identify how often outliers occur

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Cumulative Distribution of Replication Error Clearly Identifies Global Goodness of Fit

Cumulative distribution clearly indicates that

about 90% of path/periods are fit

exactly

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Market value sensitivity analysis is computationally expensive, especially when there are a large number of scenarios under consideration

Computation time is exacerbated by any of the following:Complexity of the instruments

Size of the portfolio

Number of scenarios

… or any combination!

Although fitting response surfaces require some “pre-run” scenarios (exact number depends on the problem), ultimately further scenarios are processed very quickly

Response Surface Models Fit Market Value “Surface” in Terms of Risk Factors

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VaR is the perfect candidate for RSMParticularly when the portfolio has structured transactions

Great way to leverage 400 scenarios into 10,000!

Regulatory capital standards rely on VaR as measure of required capital

Insurance Solvency II standard is predicated on VaR for each risk “module”

Basel II Advanced Market Risk Approach uses VaR for trading portfolios

Response Surface Modeling Can Improve VaR Calculation times & Accuracy Dramatically

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Example: Cumulative Distribution of Market Value Changes for a CMO

2000 full valuations for VaR scenarios Pricing Method No RSM RSM

Number of full valuations

2000 60

VaR95% - 85,967,315 - 87,225,207

60 full valuations for training

scenarios only

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Using RP, RSM or just running multiple scenarios (stochastically or deterministically), clients can leverage the Framework to study the space of possibilities

Along each path, the Framework enforces modeling consistency across all of the relevant risk factorsResults in the production of a tremendous amount of information

By focusing on a few risk measures, clients are able to summarize the vast amount of simulation data into risk metrics, for example:

Liquidity profiles, gap cash flows, earnings at riskMarket value sensitivities, Value at RiskLosses, economic capital, regulatory capital

Management relies on these risk metrics to make business decisions as well as to monitor past decisions

Scenario Analysis Allows Clients to Study Complex Model Spaces

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Risk metrics summarize a distribution into a single number that is easier for senior management to digest

However, Risk Metrics Typically Only Provide Part of the Picture

Difference betweenQuantile and Mean

Mean Quantile

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Construct the efficient frontier and assess compositional differences vis-à-vis current portfolio

Identify which portfolios to invest in and where to divestModify origination strategies to improve portfolio risk adjusted return

Quantify which assets are best for securitization depending on whether the objective is to minimize funding cost or reduce risk

Define optimal hedging strategies to:Keep bank’s exposures within policy limits

Find economic hedges without compromising too much income

Find optimal balance sheet structure to maximize return to shareholders while maintaining liquidity ratio constraints

QRM’s Portfolio Optimizer Was Designed to Provide Answers to Many Strategic Questions

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Efficient Frontier Analysis Highlights Effect of Capital Constraints on Optimal Portfolio

Basel May Reduce Attainable Returns

Some Optimal Portfolios are Not Affected by Basel

Current portfolio is sub-optimal

Ex

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Standard Deviation (Return)

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If you would like a copy of the full version of this presentation or any additional information please contact:

Charles.richard@qrm.com or

Srinivas.raju@qrm.com

Thank you for your attention

Please enjoy the Asian Bankers Summit!

Additional QRM information

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