Introduction

This document is intended to provide consultants and other interested parties1 with a high-level overview of Hymans Robertson’s Economic Scenario Service (ESS), our proprietary economic scenario generator (ESG). The document is refreshed on a regular basis by the ESS Team and includes movements of the economic and financial variables, along with a summary of the ESS framework and governance.

We have avoided delving into the details of the models in order to control the document’s length; please speak to the ESS team if a more in-depth description of any aspect of the ESS is needed.

What is the ESS?

An Economic Scenario Generator (ESG) is a collection of models that enable us to generate thousands of random, but plausible, scenarios of what might happen to the economic (e.g. interest rates and inflation) and financial variables (e.g. stock market returns) at future time horizons. The ESS is a particular example of an ESG and is proprietary to Hymans Robertson.

The models within the ESS are intended to mimic the statistical properties of the returns, interest rates, and other variables of the real world, rather than explain or predict any particular future. Projecting lots of future possibilities means distributions of outcomes can be built up and analysed leading to richer / more complete advice on risks.

In order to do this, the models project financial / economic variables over multiple time steps (e.g. over 50+ years at monthly intervals) beginning from current market conditions. Picking up current market conditions at the outset makes the projections market consistent over the short term. Over the long term, the fundamental uncertainty about the future means we cannot know all the information that would be needed to inform predictability; however, historical evidence suggests that the statistical impacts of the unknown economic and financial drivers are reasonably stable even if the drivers themselves change dramatically over time.

There does of course remain the chance that the political, economic or market constructs break down or change completely (e.g. a move from a broadly capitalist to a communist system); the ESS does not allow for those very rare, potentially very extreme, but feasible scenarios.

Thus, the models within the ESS are chosen by finding a balance between:

ESS framework

At its core the ESS is a collection of stochastic models, each of which represent a particular variable of interest. For example, one model generates simulated nominal interest rate scenarios, while another model is responsible for generating simulated UK equity returns. These models are inter-related in several ways:

The standard simulation consists of 5,000 projections of up to 100 years at monthly time steps and are available across a range of financial instruments including various forms of equity, property, bonds and credit instruments. Bespoke funds, portfolios, and further individual instruments can be modelled within the same environment, if required.

The granular nature of the projections enables detailed risk metrics to be calculated for any strategic asset allocations and rebalancing mechanisms. In particular, the use of scenarios rather than just summary statistics (such as volatility, average returns or single correlation assumptions) means that risks of adverse outcomes can be measured directly.

Changes in risks and returns over the period

These charts highlight movements in median annualised returns and dispersions over a period of time. Changes are mainly driven by market conditions, which get captured in our monthly data refresh.

1 year dispersions

10 year dispersions

5 year returns

10 year returns

20 year returns

Interpreting movements in summary statistics over the period

The main driver of changes in returns over a given period is movements in nominal yield curves and credit spreads. The reason for this is that asset returns in the ESS are primarily defined in terms of the risk-free (cash) interest rate plus risk premiums. The assumptions underpinning the size of the risk premiums are subjective and updated less regularly, and so it is changes in yield curves2 that mainly affect return levels as we move from one data refresh to the next.

For growth assets such as equities, volatility is another source of risk. Equity return volatilities change from month to month, in line with changes in the level of historical 30-days volatility, which is used to set the initial level of return volatility in our equity models. Therefore, movements in historical volatility influence short term return volatility, whereas the long term volatility is dominated by the speed and level of mean reversion.

Risk & return

These charts present the risk and return characteristics of the ESS asset classes. Median annualised returns are shown over a 20 year period. The risk measures are shown over a selection of time periods to give an indication of the level of short and long term risk.

1 year risk

10 year risk

Nominal yield evolution

The plot below illustrates the evolution of the percentiles of spot rates across a range of maturities, at different projection horizons. Observe that the spot rates begin at the current yield curve (represented by the black dotted line) at the outset and as the projection horizon increases, the spot rate percentiles drift away from the current yield curve; this phenomenon is referred to as yield normalisation. The level of yield normalisation depends on subjective assumptions about the future market conditions to arrive at an average level of rates.

Please note that the percentiles that appear in each chart are not yield curves and should not be interpreted as such.

Credit - spreads over time

In this section we present some key summary statistics associated with a selection of credit portfolios modelled within the ESS.

This chart illustrates how yield spreads evolve over time in the credit model for portfolios with different maturities3 and credit ratings. Portfolios are regularly rebalanced to maintain their initial maturity throughout the projection. Yield spreads are calculated relative to the yield on a portfolio of fixed-interest government bonds of the same maturity as the credit-risky portfolio.

Credit - illiquidity premia

The chart below displays the illiquidity related excess returns associated with holding a portfolio of illiquid credit-risky bonds. The excess returns are calculated by comparing simulated returns against returns from a liquid portfolio of equivalent maturity and credit rating. Note that the excess returns shown here are associated with a regularly rebalanced portfolio of illiquid assets.

Correlations

Below we present the correlations between annualised returns at different projection horizons4.

1 year annualised returns

10 year annualised returns

20 year annualised returns

Probability of ruin

In this section we look at an example which demonstrates the risk of running out of money (i.e. ruin) when drawing down a regular, fixed level of income over a number of years. Assuming a fixed rate of the initial fund is withdrawn each year, each chart below plots the probability of fund ruin over different drawdown terms, and for each portfolio / asset class in which the fund is assumed to be invested.

Drawdown 4% of initial fund

Drawdown 8% of initial fund

Drawdown 12% of initial fund

Calibrating the ESS models

Model calibration is the process by which our models are parameterised to generate realistic dynamics. Our calibration approach involves combining three sources of information:

  1. Market data (current and historical) which is useful for understanding how returns and other variables have behaved in the past (and therefore provide information about how they might behave in future). Information from these sources is treated cautiously and suitably modified before using.
  2. Economic theory which helps frame the historical data, providing a guide to the range of plausible hypotheses we might want our models to demonstrate. For example, we would want to avoid generating nominal interest rates that are significantly below zero, on the basis that lenders would rather hold cash than lend at substantially negative rates.
  3. Expert judgement is overlaid because the future may not behave like that past, and in some cases there is very little objective information to rely on. One such example is the level to which we expect risk-free interest rates to trend to over very long time horizons; there is a lack of traded instruments at ultra-long maturities to guide this decision and so we incorporate market views from central banks, asset managers, etc. when forming these assumptions.

Types of calibration

There are two types of calibration that the ESS team undertakes:

Annual calibrations

Calibrations that take place roughly once per year and are used as an opportunity to assess the appropriateness of the choice of models in the ESS, and whether the longer term, subjective aspects of the calibration (i.e. source 3 above) are still appropriate. It is also used to validate data sources and revise calibration tools if needed.

In summary, under these calibrations we usually review one or more of the following:

  • The parameters that are subjectively chosen (e.g. the equity risk premium), through:
    • Checking on new empirical evidence or studies undertaken by academic researchers.
    • Consulting with our colleagues who set capital market assumptions for our investment practice.
    • Views taken based on other sources, e.g. investment manager publications.
  • The models themselves, i.e. the particular equations that are used. For example, several years ago we changed the equations for modelling interest rates to allow negative interest rates after these were observed.
  • Whether new models for new asset classes are needed or if some additional features should be built in.
  • The sources we use for the monthly data refresh. We check they are still appropriate, available and contain the correct information.
  • Introducing more efficient calibration tools, e.g. EMM for SVJD model calibrations.

A selection of subjective assumptions currently embedded within the ESS for the UK economy are presented in the table below.

ESS assumptions for UK Target value
Nominal short/long rate short-term expectation As implied by initial yield curve*
Nominal short rate long-term expectation 3.6% p.a.
Nominal long rate long-term expectation 3.6% p.a.
Real short/long rate short-term expectation As implied by initial yield curve*
Real short rate long-term expectation 1.8% p.a.
Real long rate long-term expectation 1.3% p.a.
Equity risk premium 3.5% p.a.
Default recovery rate for credit assets 35.0%

* As implied by initial yield curve means that the target is derived from market conditions; for real and nominal interest rates, this means the expected path of interest rates over the short term is determined by the shape of the market yield curve at the outset of the projection.

Monthly data refresh

Every month we refresh the model calibration to allow for updated market conditions like movements in yield curves and recent equity volatility. By doing this we ensure that the starting point for our simulations matches observed conditions in the markets. The more subjective elements of the calibration (e.g. long term interest rate normalisation levels) are typically not adjusted during monthly data refreshes. Short term equity volatility, initial credit spreads, and initial yield curves are the main variables that change from month to month.

Governance and compliance

The ESS is used across Hymans Robertson’s institutional investment and retail clients as well as underpins the risk models embedded in the APIs that we offer some asset managers.

The models are maintained and developed by a dedicated team of actuaries, financial modelling experts, and software developers, with additional support from the wider Insights & Analytics team. The models were originally developed in 2000 and have been maintained and used continuously since then. These were extensively redeveloped in a major overhaul lasting 2 years from 2014 in order to accommodate a wider set of asset classes and improved performance. Use of the models to support actuarial and regulated advice means the ESS and outputs from it are subject to scrutiny by many professionals, both internal to Hymans Robertson and third parties, as well as regulators.

The model and its calibration are governed and documented in accordance with our professional actuarial requirements from Institute and Faculty of Actuaries and the requirement to provide fair customer treatment. It is TAS100 compliant. Two separate groups help define the governance framework surrounding the ESS: the Change Group and the Technical Modelling and Assumptions Group.

Furthermore, it is overseen by Model Quality Group (auditing fitness of purpose and governance), Model Expert Group (checking the appropriateness of model usage), Risk Oversight Group (challenging the ESS assumptions and reasonableness of outputs), and Technical Professional Actuaries Group (overseeing the professionalism aspects).

Summary statistics

Summary statistics associated with a selection of ESS asset classes / funds are presented below.

For the risk metrics:

For the returns we look at various percentiles of annualised returns over specified time periods.

Risk after 1 years

Risk after 10 years

Returns after 5 years

Returns after 10 years

Returns after 20 years

  1. E.g. clients who take an interest in the technical details underlying our stochastic modelling.↩︎

  2. The shape and level of the nominal yield curve determines the expected path that cash rates take over the earlier projection years in the ESS.↩︎

  3. We model bond portfolios with the following maturities: ultra-short, short, medium, and long maturity portfolios have maturities of 2, 4, 14, and 24 years respectively.↩︎

  4. FIG and ILG are abbreviations for fixed-interest gilts and index-linked gilts respectively.↩︎