Moderator: Nathan W. Hardiman, FSA, MAAA

Transcription

1 Session 50 IF, Economic Scenario Generator in a Low Interest Rate Environment Moderator: Nathan W. Hardiman, FSA, MAAA Presenters: Jean-Philippe Larochelle, FSA, CERA Marshall Lin, FSA, MAAA Francisco Javier Orduna, FSA, MAAA Hal Warren Pedersen, ASA

2 Economic Scenario Generator in a Low Interest Rate Environment Society of Actuaries 2015 Annual Meeting Session 050 IF October 12, 2015, 15:30 16:45 CONNING One Financial Plaza Hartford, CT Conning, Inc.

3 Low Interest Rates What Does the Data Say? Extensive interest rate data is available for major economies for the recent past decades. Long time series of interest rate data is available for some economies. It is natural to look to history for some guidance on what the very low interest rates of today may portend. Unfortunately, even when long histories are available, very little of that history that is similar to the interest rate levels that we are experiencing today. Furthermore, there are many challenges in making comparisons across widely different periods of time. For example, the period of very low interest rates we are experiencing now in the United States is numerically similar to the data for parts of the 1930s and 1940s; but the overall economic conditions in the US are not comparable between these two time epochs. Changes in tax law, government policies, and socio-political circumstances can make comparisons across epochs difficult. 2

4 US Interest Rates 1 Year Yield History The all-time lows were primarily due to tax effects. Source: Ibbotson SBBI Yearbook, Bloomberg Bloomberg, L.P. 3

5 US Interest Rates 10 Year Yield History Source: Ibbotson SBBI Yearbook, Bloomberg, Global Financial Data Bloomberg, L.P. 4

6 US Interest Rates Monthly Changes in 1Yr and 10Yr Yields It is not surprising that when the 1 year rate is pinned at zero it hardly moves. It is notable the 10 year rate is changing a lot in recent years and comparable to the 1990s. Source: Ibbotson SBBI Yearbook, Bloomberg, Global Financial Data Bloomberg, L.P. 5

7 Canadian Interest Rates Long Bond Yield History Source: Bank of Canada 6

8 Canadian Long Bond Yield History with Inflation Source: Bank of Canada and CANSIM 7

9 UK Interest Rates Long Run History (2.5% Consol Yield) Low for the series is 2.25% in Source: UK Debt Management Office 8

10 German Interest Rates 1 Year Yield Collapse Source: German Bundesbank Data 9

11 German Interest Rates 10 Year Yield Short of a Lifetime Lows of 7bp occurred on 17Apr2015, 20Apr2015 and 21Apr2015. Source: German Bundesbank Data 10

12 Japanese Interest Rates Recent History Source: Bloomberg, L.P. 11

13 Recent Swiss Yield Curves Source: Swiss National Bank 12

14 Recent US Yield Curves Source: Bloomberg Bloomberg, L.P. 13

15 US Corporate Bond Yields Source: FRED Database (St. Louis Federal Reserve Bank) 14

16 US Corporate Bond Spreads Source: FRED Database (St. Louis Federal Reserve Bank) 15

17 Summary of Yield Data Long term interest rates for developed economies are at or near alltime historical lows. Short term interest rates for developed economies are zero or even negative. Corporate bond yields and spreads, are typical by historical standards, and are not at all-time historical lows. The Japanese experience shows that ultra-low interest rate environments can persist for extended periods of time. It is remarkable that German 10-year government bond yields recently got down to 7bp. It is incredible that the Swiss National Bank reports that the Yields of the Confederation bonds Yields on pure discount papers for 10 year tenor for the month of January 2015 was -7bp. All this is happening while it seems that the world is sitting on large amounts of debt. 16

18 Dynamics Are Different in Recent Years (PCA Jan1998 Dec2008) Principal components analysis on monthly changes in US Yields. Normalized eigenvectors corresponding to largest eigenvalues. Source: Bloomberg & Conning Statistical Analysis Bloomberg, L.P. 17

19 Dynamics Are Different in Recent Years (PCA Jan2009 Jul2015) Principal components analysis on monthly changes in US Yields. Normalized eigenvectors corresponding to largest eigenvalues. Source: Bloomberg & Conning Statistical Analysis Bloomberg, L.P. 18

20 Models for Low Interest Rate Environments Dynamic Nelson-Siegel models (DNS). Macro finance models (DNS with VAR macro variables, other approaches) Quadratic interest rate models. Shadow rate models. Krippner zero lower bound (ZLB) models. There is a rich collection of models that are being actively researched for low interest rate environments. Ideally, the models should capture prolonged periods of low rates and be capable of returning to normal interest rate dynamics later in the simulation. Limited data (historical experience) means that there is a considerable amount of expert judgment involved. Risk management is part art! 19

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22 Real-world interest rate scenarios in a low-interest-rate environment a practitioner s view 2015 Annual Meeting Society of Actuaries Session 050 IF economic scenario generator in a low interest rate environment Marshall Lin, FSA, MAAA, CFA Francisco Orduña, FSA, MAAA 12 October 2015

23 Ernst & Young LLP disclaimer The views expressed by the presenters are not necessarily those of Ernst & Young LLP This material has been prepared for general informational purposes only and is not intended to be relied upon as accounting, tax or other professional advice Please refer to your advisors for specific advice Page 1 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

24 Key questions How does your Economic Scenario Generator (ESG) cope with the current low interest rate environment and what are its limitations? What alternatives can practitioners explore? Page 2 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

25 Discussion topics ESG in the low interest rate environment Case study impact on actuarial liabilities Page 3 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

26 ESG in the low interest rate environment Page 4 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

27 Economic scenario generation in the life insurance industry The use of economic scenario generators (ESG) continues to rise, from supporting deterministic analyses to the valuation of principles-based reserves. North American life insurance companies use real-world stochastic interest rates for a variety of applications, including but not limited to: Canadian Asset Liability Method U.S. statutory valuation, Actuarial Guideline (AG) 43 U.S. regulatory capital requirements (C-3 Phase 1) U.S. GAAP, SOP 03-1 Asset adequacy analysis cash flow testing Risk analysis, economic capital ESG used for real-world interest rates Third party 25% AIRG 47% Homegrown 28% *Based on a proprietary survey of U.S. life insurance companies Page 5 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

28 Key features in real-world stochastic interest rate models Mean reversion Most common real-world interest rate stochastic models assume that interest rates will revert toward a specified rate, commonly referred to as the mean reversion target. The mean reversion target is the primary driver of best estimate measures Progression of average projected yield curves Sources of uncertainty Instantaneous changes in interest rates are modeled through a volatility parameter and the level of interest rates in the projection. Long-term changes in interest rates are primarily impacted by the mean reversion strength and the assumed volatility level. Sources of uncertainty are the primary driver of tail-based measurements. t = 0 t = 1 t = 5 t = 10 t = 20 Mean-reversion Model Vasicek Cox-Ingersoll-Ross Black-Karasinski Stochastic differential equation dddd = aa bb rr dddd + σσσσσσ dddd = aa bb rr dddd + σσ rrdddd dddddd(rr) = aa bb ln(rr) dddd + σσσσσσ Page 6 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

29 Expectations of long-term interest rates A significant number of economists and actuaries expect that interest rates to stay low in the near future. While there is a general consensus that interest rates will eventually revert to historical levels, there are significant disagreements about when and how this will happen Path to mean reversion target 7% 6% Mean reversion point 5% 4% 3% 2% 1% 0% Current interest rate Projection Year Page 7 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

30 Current uses of real-world stochastic interest rates Economic scenario that poses the most significant economic stress to insurance companies* Prolonged Low Interest Rates 40% Adverse Equity Market Movements Rapid Increase in Interest Rates 24% 24% Widening Credit Spreads 12% * Based on a proprietary survey of US life insurance companies Our research was primarily focused on designing an alternative real world interest rate scenario generator that helps actuaries to: Address an unprecedented low interest rate environment and a transition to high interest rate environment in an unknown future period Explicitly reflect different views on the expected path of interest rates Page 8 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

31 Regime-switching model Overview Calibrated historical interest rates to two regimes: the current low interest rate environment and the preceding historical period Historical one-year Treasury rate 15% 10% High regime Low regime 5% 0% High regime Simulates an interest rate environment similar to the period Mean reversion point (MRP) closer to historical average Interest rates move toward MRP with high volatility and low mean reversion strength Low regime Simulates interest rates based on the postfinancial crisis environment ( ) Lower MPR and stronger mean reversion strength Interest rates move around the MRP with low volatility Page 9 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

32 Prolonged low-interest-rate environment Transition probabilities can be used to reflect different views of how long we will stay in the current low-interest-rate environment. Using a 15% transition probability translates to an average of 6.7 years before transitioning out of the low-interest-rate environment. User can increase/decrease the transition probability to reflect a particular view of how long the current low-interest-rate environment will persist. 5.5% Average of simulated 7-year rates 4.5% 3.5% 0.75% 0.76% Transition Pr Transition Pr Transition Pr. 2.5% 1.5% Page 10 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

33 Alternative ESG: Regime-switching Key-rate CIR Regime-switching: Uses a Markov Chain process to model the transition between regimes Annual Transition Probability To Low Regime To High Regime From Low Regime 85.0% 15.0% From High Regime 2.1% 97.9% Key-rate: Models each spot rate on the curve individually Advantage: Increased flexibility, precision and control over desired outcomes Disadvantage: Complexity and large number of parameters Alternatives: Function-based models (i.e. Nelson-Siegel). Uses the Cox-Ingersoll-Ross (CIR) stochastic differential equation in each regime Calibrated the model with Maximum Likelihood Estimates (MLE) based on historical treasury rates Complied with the AIRG calibration criteria Page 11 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

34 Case study Impact on actuarial liabilities Page 12 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

35 Projected interest rates - AIRG AIRG 7-year rate projection 18% 16% 14% 12% Rates in 2045 AIRG 5% percentile 2.030% 50% percentile 3.799% 95th percentile 75th percentile 25th percentile Historical Average 10% 95% percentile 6.305% 8% 6% 4% 2% 0% Page 13 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

36 Projected interest rates - RSCIR RSCIR 7-year rate projection 18% 16% 14% 12% Rates in 2045 AIRG 5% percentile 1.179% 50% percentile 4.679% 95th percentile 75th percentile 25th percentile Historical Average 10% 95% percentile 9.464% 8% 6% 4% 2% 0% Page 14 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

37 Sample RSCIR scenario 10% 8% 1 year 7 year 6% 20 year Low Regime High regime 4% 2% 0% Page 15 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

38 Cash flow testing deterministic scenarios We built a DA model and ran Cash Flow Testing projections Minimum guarantees ranging from 1% to 4%. We tested the deterministic NY7 scenarios in the DA model at 6/30/2015 CFT Results: 30-year projections, in $ millions NY7 Description Ending Surplus 1 Level Increasing 3,787 3 Up / Down 1,272 4 Pop Up 3,247 5 Decreasing (522) 6 Down / Up Pop Down (592) Page 16 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

39 Cash flow testing stochastic scenarios Ending Surplus: 30-year projections, in $ millions VaR AIRG RSCIR 7.5% Trans. Pr. RSCIR 15% Trans. Pr. RSCIR 30% Trans. Pr. 50.0% 1, ,024 1, % 1, % 575 (166) (62) % 226 (430) (470) (557) 99.5% 102 (489) (693) (721) Compared to the AIRG, RSCIR produced results with: Higher probability of asset deficiency Increased tail risk Page 17 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

40 Worst scenarios - AIRG Only 2 out of the 1,000 scenarios generated negative ending surplus The worst scenarios are the ones with extremely high rates (20%+ 7yr rate) Scenarios where rates stay low are the next group of worst scenarios 7-year rate (%) Worst AIRG Scenarios #1 worst scenario #2 worst scenario #3 worst scenario #4 worst scenario #5 worst scenario Projection year Page 18 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

41 Worst scenarios - RSCIR The worst scenarios under RSCIR captured the scenarios companies considered to be the most significant risks Prolonged low interest rates Rapid increase in interest rates at different projection periods 7-year rate (%) Worst RSCIR Scenarios #1 worst scenario #2 worst scenario #3 worst scenario #4 worst scenario #5 worst scenario Projection year Page 19 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

42 Closing remarks How does your Economic Scenario Generator (ESG) cope with the current low interest rate environment and what are its limitations? Commonly used ESGs may not fully address the unique challenges presented by the current low interest rate environment What alternatives can practitioners explore? Alternative tools such as regime switching features can help practitioners to better appraise the impact of a prolonged low interest rate environment We are interested in hearing your thoughts Marshall Lin marshall.lin@ey.com Office: (212) Francisco Orduña francisco.orduna@ey.com Office: (212) Page 20 Real-world interest rate ESG in a low-interest-rate environment A practitioner s view

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