Economic Scenario Generator Model July 2018 With risk management being front of mind in the world of Solvency II and SAM – through topics ranging from risk opmisaon to risk capital – consideraon should be given to the use of Economic Scenario Generator (ESG) models and their usefulness in providing risk management informaon. When discussing ESG models one generally refers to Real-World or Risk-Neutral approaches. Risk-neutral ESG models are normally used for pricing or valuing the cost of embedded opons and are not considered in this arcle. In this arcle I am discussing the use of ESGs using the Real-World approach without going into the detail of the underlying complex mathemacal algorithms – but rather by answering a few simple quesons and concluding by looking at abridged case studies. Kirchual Sauls Senior Consultant QED Actuaries & Consultants An ESG is a stochastic model that jointly simulates future economic and financial variables. Joint simulation means the model allows for interaction between variables in its projections e.g. local currencies tend to appreciate when local interest rates rise. ESG models tend to employ Monte Carlo simulations (a statistical technique) to perform thousands of simulations to provide a distribution for the metrics that the user is interested in. The different realisations for the variables modelled constitute “economic scenarios”. By jointly simulating the different economic variables, joint return distributions for multiple assets and liabilities can be obtained. The respective distributions feed into the financial institution's asset-liability models, permitting an assessment of a potentially large number of different sources of risk to the company. • The model show a realistic view of the economic and financial variables i.e. reflect key features captured in historic data. • Model output should include some extreme but plausible outcomes. • Interaction between variables should reflect generally accepted economic principles. Some typical applications include: • Investment Optimisations; • Economic Capital Assessments; and • Asset-Liability Modelling. Beyond the horizon. Together What is an ESG Model? What Makes for a Good Real - World ESG Model? What is a Real - World ESG Model Used for?
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Economic Scenario Generator Model July 2018
With risk management being front of mind in the world of
Solvency II and SAM – through topics ranging from risk
optimisation to risk capital – consideration should be given to the
use of Economic Scenario Generator (ESG) models and their
usefulness in providing risk management information.
When discussing ESG models one generally refers to Real-World
or Risk-Neutral approaches. Risk-neutral ESG models are
normally used for pricing or valuing the cost of embedded options
and are not considered in this article.
In this article I am discussing the use of ESGs using the Real-World
approach without going into the detail of the underlying complex
mathematical algorithms – but rather by answering a few simple
questions and concluding by looking at abridged case studies.
Kirchual Sauls
Senior Consultant
QED Actuaries & Consultants
An ESG is a stochastic model that jointly simulates future economic and financial variables.
Joint simulation means the model allows for interaction between variables in its projections e.g. local currencies tend to appreciate when local interest rates rise.
ESG models tend to employ Monte Carlo simulations
(a statistical technique) to perform thousands of
simulations to provide a distribution for the metrics that
the user is interested in.
The different realisations for the variables modelled
constitute “economic scenarios”. By jointly simulating
the different economic variables, joint return
distributions for multiple assets and liabilities can be
obtained. The respective distributions feed into the
financial institution's asset-liability models, permitting an
assessment of a potentially large number of different
sources of risk to the company.
• The model show a realistic view of the economic and financial variables i.e. reflect key features captured in historic data.
• Model output should include some extreme but
plausible outcomes.
• Interaction between variables should reflect generally
accepted economic principles.
Some typical applications include:
• Investment Optimisations;
• Economic Capital Assessments; and
• Asset-Liability Modelling.
Beyond the horizon. Together
What is an ESG Model? What Makes for a Good Real-World ESG
Model?
What is a Real-World ESG Model Used
for?
A Real-World ESG model can also be used to objectively identify economic stresses under a company’s Own Risk and Solvency Assessment (ORSA) at the company’s desired risk tolerance.
Let’s now consider case studies that detail how QED’s ESG model could be used in two of the typical applications noted above.
Background
A company with short-term liabilities is concerned that it is not leveraging enough on its significant excess assets due to a restrictive, low risk investment strategy that focuses only on cash and bonds.
A key consideration, given the short-term nature of the underlying liabilities, is that the company keeps sufficient levels of liquid funds.
Proposal
With assistance of an ESG model, we will identify where the current asset mix is relative to the optimal investment portfolios at various levels of risk.
An optimal asset mix is defined as one that maximises return at a given level of risk or minimises risk at a given level of return. Risk here is defined as the volatility of investment returns.
The only restriction imposed is that no less than 10% of total assets should be invested in cash at any time due to the client’s liquidity requirement.
Methodology
• Generate 10,000 return simulations from each of the desired asset classes over a 3-year horizon based on historical data;
• Construct 500 possible asset mixes of the chosen asset classes (subject to the liquidity requirement);
• Calculate the mean and volatility of returns over a 3-year period for each asset mix based on the
10,000 simulations; and,
• Identify the optimal asset mix at each level of risk/
return based on the 5 million (i.e. 10,000 x 500) data points produced.
The next graph illustrates the mean return and volatility of each of the 500 asset mixes considered.
Each blue dot on the next graph represents a different asset mix and shows the expected return of the asset mix over the next 3 years on the vertical axis and the relative riskiness (volatility) on the horizontal axis.
For each level of riskiness, one can identify several asset mixes, all producing a different level of expected return. The optimal asset mix for any level of riskiness will therefore be the asset mix that provides the highest expected return.
Asset mixes on the dotted green line represents optimal investment portfolios at each level of risk. This green line therefore represents the efficient frontier which indicates all the optimal asset mixes.
As expected, the expected return of asset mixes on the efficient frontier increases as the riskiness of the asset mixes increases.
A company can therefore decide on a level of risk that they are willing to accept and choose an asset mix that falls on the efficient frontier at that level of riskiness to optimise their investments.
Background
A life insurer that considers poor investment returns, expense inflation and the impact of yield curve movements on its liabilities as its key financial risks wants to identify the minimum amount of capital it needs to hold to withstand ruin subject to its risk tolerance.
Ruin happens when the value of an insurer’s liabilities exceeds the value of its assets.
The insurer is willing to accept a 1-in-200 chance of ruin over the next 5-years.
Proposed Methodology
• Use the ESG model to jointly simulate 10,000 scenarios of investment market returns, inflation and the 30-year risk-free yield curve over the next 5-years;
• Use the yield curves to calculate the actuarial liability
and the investment market returns to grow company investments for each simulation;
Case Study 1: Investment Optimisation
Case Studies
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Mean Return
Return volatility
Mean Return vs Volatility
Case Study 2:
Economic Capital Assessment
• Use this information combined with the insurer’s business plans over the next 5-years to project the insurer’s balance sheet for each of the 10,000
scenarios;
• Sum the amounts by which liabilities exceed assets
at every instance of ruin over the 5-year projection, for each of the 10,000 scenarios. This value represents the capital the insurer needs to hold to withstand ruin for the scenario (ignoring discounting); and,
• Identify the 5-year balance sheet projection with the 1-in-200 worst outcome from the 10,000 scenarios i.e. the scenario with the 50
th highest capital
requirement as defined above. The amount of capital required under this scenario is the minimum amount of capital the insurer should hold.
The exact approach to determining the appropriate amount of capital the company should hold can be tailored to each company.
For example, capital can be assessed at a different risk tolerance level and/or allowance can be made for dividend payments in the balance sheet projection consistent with the company’s dividend policy.
The application illustrated by the case studies are examples of the use of Real-World ESG models by direct insurers, reinsurers and benefit funds to develop the optimal investment strategy or determine economic capital and thereby increase expected return, measure risk and/or reduce risk.
QED’s in-house ESG model can be used to project investment indices, yield curves, inflation and foreign
exchange rates, all of which can be calibrated to specific companies’ needs.
Feel free to contact us for more information on our ESG model and how it can be used in your business.
