OCTOBER 26–29, 2020

Session 6B: Economic Scenario Generation for Life, Pension and P&C Applications

Hal Pedersen

October 28, 2020

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Overview

The focus for this first part of our session is on interest rates. We are interested in three main questions.

1. What are some of the important features (i.e. stylized facts) of interest rates?2. What challenges does recent interest rate behavior present for real-world interest

rate models?3. What are the implications for next generation interest rate models and regulatory

tools such as the AAA/SOA (AIRG) interest rate generator?

Interest Rates - Persistent and Recurring Zero Interest Rates (3 Regimes in 100 Years)

Source: FRED, NBER and Ibbotson SBBI

Interest Rates - Changing Shapes Over Time (Is 9/30/2020 Yield Curve Problematic?)

Source: Federal Reserve Board of Governors H15 Data

Interest Rates (Changes Over the Last 9 Months)

Source: Federal Reserve Board of Governors H15 Data

Interest Rates – At What Level Should the Yield Curve Invert?

Source: FRED

Very High Levels of Federal Debt (from CBO - The 2020 Long-Term Budget Outlook, September 2020)

Interest Payments as % of Federal Revenue (https://data.worldbank.org/indicator/GC.XPN.INTP.RV.ZS?locations=US)

Interest Rates – Short Rate Trapped at Lower Bound While Long Rate is Fluctuating

Source: FRED

Interest Rates – How Does Volatility Behave Across Yield Tenors

Source: FRED

Interest Rates – Getting the Right Dynamics

• We can apply nonparametric estimation techniques to uncover what the data says about the volatility of changes in interest rates over short time periods.

• This informs our choice of model dynamics needed to capture persistent low interest rates.

• Interest rate volatility is linear at low and high rate levels and constant at intermediate levels.

• In practical terms, interest rate volatility has lognormal characteristics at low and high rate levels and Gaussian characteristics at intermediate levels.

• Such a hybrid volatility structure is not used in traditional interest rate models.• Some research suggests that this is a universal relationship across many financial

variables.• The following chart is for the local volatility of the US one-year treasury rate based

on daily data from 1962.

Interest Rate Dynamics

Source: Federal Reserve Board of Governors H15 Data

Interest Rates – Important Features (Stylized Facts)

• Interest rate levels fluctuate significantly over long periods.• Short term interest rates are usually lower than long term rates.• Yield curves change shape over time.• Inversions of the yield curve are an important recurring feature.• Levels at which yield curve inversions occur have trended lower over last 40 years.• Two fundamental characteristics of recent experience are:

1. Persistent and recurring low interest rates2. Long rate volatility exceeds short rate volatility for an extended period

• These two characteristics must be present in an interest rate generator that is used to manage risk over long term horizons. Life insurance, annuity and pension applications will need to include these characteristics.

• A robust interest rate model must also allow for an eventual normalization of interest rates.

Interest Rate - Challenges

• The most important challenge in practical real-world interest rate model development is the incorporation of simulation paths with:

1. Persistent and recurring low interest rates2. Short term rates pinned near zero accompanied by significant fluctuations in

long term rates• How do some of the traditional models stack up here?

o Affine modelso AAA/SoA model

• What other models could be used to address this challenge?

Classical Single-Factor Affine Interest Rate Models

Vasicek Model

• The Vasicek interest rate model has constant volatility. • It cannot produce realistic interest rate paths that remain near zero for extended

periods.

CIR Model

• The CIR model has volatility that goes to zero as the factor process approaches zero.• The model can capture persistent low rates. • The long rate cannot move if the short rate does not move. • The model cannot capture fluctuations in the long rate if the short rate is stuck at zero.

CIR Single-Factor Interest Rate Model [100 year simulated path]

Classical Multi-Factor Affine Interest Rate Models

• The main reason one moves from a single-factor to a multi-factor model is to better capture yield curve shapes, yield curve movements and the correlation of rates across the yield curve.

• If a single-factor model does not have the dynamics necessary to capture persistent low interest rates and to permit long rate volatility to exceed short rate volatility for an extended period then adding more of the same type of factors will not correct the problem.

• One may show using financial mathematics:a) it is harder for multi-factor models to generate persistent zero short rates

than it is for their single-factor model counterpartb) traditional multi-factor affine models such as Gaussian/Vasicek and CIR imply

that long rate volatility must be lower than short rate volatility at all times• Consequently, traditional multi-factor affine models are not well-suited to

persistent and recurring low interest rate modeling.

AAA/SOA Interest Rate Model [Academy's Interest Rate Generator (AIRG)]

Interest Rate Dynamics• Mean reverting long rate with stochastic volatility. • Mean reverting yield curve slope is used to determine short rate.• Yield curve is interpolated from short and long rates.• Hard yield floor is effective at short end of yield curve.

Model Performance• Model captures persistent low rates.• Model produces fluctuations in the long rate when the short rate is pinned near zero.• Hard floor on the short end of the yield curve induces direct arbitrage in the model.• Other more technical issues disqualify the model as arbitrage-free.

AAA/SOA Interest Rate Model [100 year simulated path]

Shadow Rate Models [Fischer Black’s 1995 idea of “Interest Rates as Options”]

Interest Rate Dynamics• Arbitrage-free model with risk-neutral and real-world versions.• Gaussian shadow rates are simplest, other shadow rate dynamics possible.

Risk-Neutral:

Real- World:

Short-Rate:

• Short-rate is used to compute term structure as an expectation.• Can be implemented as a multi-factor model.• Captures persistent low rates.• Produces fluctuations in the long rate when the short rate is pinned near zero.• Drawback is increased computational complexity from nonlinear aspect of model.

Single-Factor Shadow Rate Model [100 year simulated path]

Implications for Interest Rate Models• Very high federal debt burden tends to be disinflationary.• Strong pressure on the Fed to keep interest rates low.• The Fed is monetizing extraordinary amounts of government debt.• As an actuary applying stochastic interest rate models, one must form a coherent

view on what the simulation output should be like.• In the short to medium term, a case can be made that we are in a period of

persistent low interest rates. Longer term, the model should allow for rates to rise in line with the historical record.

• In our current environment, setting long-term calibration targets and validation metrics is difficult.

• Traditional models are not well-suited to modeling the type of interest rate environment we are currently in.

• Changes in model capabilities and dynamics are needed.

Conclusions• Recent experience poses significant challenges for traditional interest rate models.• Emerging consensus is that robust models must produce simulated paths with:

✓ persistent and recurring low interest rates✓ extended periods for which the short rate is near zero and longer tenor rates

fluctuate significantly• This is a significant challenge for life, annuity and pension applications since we

need good models over long horizons.• Actuaries have a distinguished history as pioneers in interest risk management,

theory and modeling.• Milton Friedman began his career as an actuary.

[https://www.youtube.com/watch?v=61YLb2V4M6Y]

• Paul Milgrom FSA is the joint recipient of the 2020 Nobel Prize in Economics for his work in auction theory. 35 years ago he published “Measuring the Interest Rate Risk”, Transactions of the Society of Actuaries, Volume 37, 1985

• Our profession will rise to these challenge but significant work remains.

2020 SOA Annual MeetingSession 6B: Economic Scenario Generator (ESG)Extending the Model

Presenter: Daniel Finn

October 28, 2020

Extending the Model

• Once we have the Treasury model set we need to extend it

• Corporate Bonds• Structured Securities• Equities

• Inflation• GDP

2

Extending the Model

• Once we have the Treasury model set we need to extend it

• Corporate Bonds• Structured Securities• Equities

• Inflation• GDP

3

Corporate Bonds

• The first thing we need to decide is what we’re modeling

• E.g. the Academy model only simulates total return

• Most companies need more information• Yields

• Transitions• Defaults and recoveries

4

Equities

• Needs can depend heavily on intended usage

• P&C company• Dividends• Total returns

• Life company might need to add volatility measure

• Pension fund might need multiple equity indices

5

Key Characteristics

• We’ve decided what to model

• Now, need to decide HOW to model them• What are the key characteristics?

6

Key Characteristics - Equities

• Expect High Returns

• Average has been about 10% per year for the S&P 500• Over 4% higher than Treasuries

• Can be VERY volatile

• Around 20% annual standard deviation• Occasional rapid drops: 1Q 2020 saw nearly 20% drop

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Source: ©2020 Bloomberg, L.P.

Key Characteristics - Equities

• Drops can also be VERY long lasting

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Source: ©2020 Bloomberg, L.P.Historical S&P 500

Key Characteristics - Equities

• VERY different picture for Corporate Spreads

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Source: ©2020 Bloomberg, L.P.

Know Your Audience

• Ideally, we would like one model to meet all needs

• Reality is more complicated• Different Time Horizons• Different Types of Analysis

10

Know Your Audience

• P&C Companies

• Short horizons: 1 – 5 years• Often tail focused (e.g. 3 in 10,000 for Economic Capital)

• Life Companies• Long horizons: 10+ years• More central focused (e.g. Risk vs Reward)

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Know Your Audience

• This will Impact the Calibration Criteria

12

Life Focus - Historical Correlation

S&P 500 1.00

AA 0.01

A 0.14

BBB 0.33

High Yield 0.64

Prepared by Conning, Inc. Sources: GEMS® Economic Scenario Generator scenario and ©2020 Bloomberg, L.P.

Pension Focus – Full Relationship

FTSE 100 (United Kingdom)

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Know Your Audience - Pitfalls

• Be careful not to over specify the model

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SPX & Int TSY - Rolling Monthly Correlations

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Bringing It All Together - Equities

• Stochastic Volatility• Helps create fatter tails• May want to add a jump process

• Stochastic Dividends

• Related to Other Variables• Treasuries• Corporates

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Bringing It All Together - Equities

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Prepared by Conning, Inc. Sources: GEMS® Economic Scenario Generator scenario and ©2020 Bloomberg, L.P.

Historical S&P 500 Simulated S&P 500

Bringing It All Together - Corporates

• Yield Curves by Rating

• Linked to Treasuries• Calibrated to each other

• Linkages Between Key Variables• High spreads indicate larger future defaults• Spread movements tied to Equity returns

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Bringing It All Together - Corporates

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Prepared by Conning, Inc. Sources: GEMS® Economic Scenario Generator

2020 SOA Annual MeetingSession 6B: Economic Scenario Generator (ESG) Applications by Pension ALM Practitioners

Presenter: Pawel Piesowicz

October 28, 2020

Agenda• How is ESG used by pension ALM practitioners

• What properties of ESG are most important• What are its necessary qualities

• How do ALM practitioners evaluate ESG from the perspective of suitability and applicability to their work

• What were evaluation criteria• Which characteristics are most valuable

• What customizations (adjustments and calibrations) may be necessary when using an external vendor's ESG

• Interest rates• Alternative asset classes• Local issues (e.g. provincial bonds in Canada)

• Questions

4

How is ESG used by pension ALM practitioners

• Project important metrics:• funded status• contribution requirements• pension expense

• Assess risk, benefit security, probability of achieving objectives

• Compare alternate asset mixes, various investment options

• Compare alternate benefit designs

• Optimize risk/reward trade-offs

• Manage cash flow & liquidity risk

• Better understanding of risk – ability to avoid unrewarded risk and take highly rewarded risks

• Better understanding of true plan costs

5

Examples of analysis performed using ESG

AttributeProjectOptimize

6

Retiree Portfolio Actives' Portfolio

Asset Mix Study IllustrationDemographics: 50% retired, 50% active members (Closed Plan)

Traditional "60/40" Investing Demographic Focused Investing

Market Cap Weighted Equities

Universe Bonds

Equities

Infrastructure

Real Estate

Bond OverlayProvincial Bonds

Corporate Bonds

Private Debt

Mortgages

50% Retiree Cash Flow Coverage (3-yr) 100%

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What properties of ESG are most important

• Internal consistency• Fixed income returns

• Ranking of expected returns and volatilities

• Relation to historical data

• Reflecting initial capital markets conditions

• Plausible future states• Realistic distributions (e.g. fat tails, skew)

• Dynamic volatility and correlation effects

• Alternatives' modeling

• Ease of explanation to clients

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Distribution of Returns

• Volatilities and Correlations• Typically based on historical data

• Length of historical period to be considered

• Implied volatility from options

• Simpler models assuming lognormal distribution

• More complex models for stochastic projections• Autoregressive

• Regime-switching

• Truncated Levy-stable

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Alternatives' Modeling

• Illiquidity premium

• Unsmoothing

• Survival bias

• J-curve effect

• Non-homogenous classes

• Interpolations and linear combinations (regression)

• Risk factors approach

• CAPM approach

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Polling question

• What ESG are you using in your work?• ESG built by my employer internally• ESG purchased externally with substantial customization

internally• ESG purchased externally with minimal customization

internally• Don't know / Not using ESG

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How do ALM practitioners evaluate ESG

• Satisfies the most important properties

• Reliable support

• Good documentation and training materials

• Transparent• Able to see how all aspects of model are specified, parameter values, etc.

• Relatively easy to use• Integrate easily in internal technology environment

• Reasonable storage, compute requirements

• Flexible API (application programming interface)

• Easy to automate workflows

• Reasonable cost

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How do ALM practitioners evaluate ESG

• Robust and flexible• Able to address specific needs

• Complete market risk and asset class coverage• Including alternative assets and derivatives

• Facility to estimate future pension valuations

• Discounting using different curves

• Ability to perform meaningful calculations of risk measures such as conditional tail expectation (CTE)

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What customizations may be necessaryInvestment Environment: Not even thinking about, thinking about raising rates

10 Year Government of Canada Bond Yields

0.0%

2.5%

5.0%

7.5%

10.0%

12.5%

15.0%

1985 1990 1995 2000 2005 2010 2015 2020Source: Bloomberg Finance L.P. As of August 31, 2020. For illustrative purposes only.

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Polling question

• What is a reasonable forecast for ALM purposes for the 10-year Treasury yield in 10 years?

• 3%• Between 1.5% and 5%• Between -0.5% and 5.5%• Between -1.5% and 8%• None of the above

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What customizations may be necessary• Ensuring wide range of interest rates

• Adjusting to increase probability of rates staying low or declining

Back to Normal Low Rates for Longer

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What customizations may be necessary• Adding an asset class

• Creating a new class by adjusting parameters of an existing class

• Using regression analysis to map an asset class to a combination of existing classes

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Final remarks

• ESG is indispensable for pension ALM practitioners

• ESG must• Be internally consistent

• Reflect initial capital markets conditions

• Forecast plausible future states

• ESG software should be• Robust and flexible

• Customizable

• Not a "black box"

• Questions?

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Questions?