Modern Deterministic Scenarios for Interest Rates Presented to the - - PowerPoint PPT Presentation
Modern Deterministic Scenarios for Interest Rates Presented to the Chicago Actuarial Association March 20, 2018 Mark E. Alberts, FSA, MAAA Agenda I. Background on Modern Deterministic Scenarios (MDS) research project II. Overview of MDS
Presented to the Chicago Actuarial Association March 20, 2018 Mark E. Alberts, FSA, MAAA
I. Background on Modern Deterministic Scenarios (MDS) research project II. Overview of MDS interest rate scenario development & results III. Overview of MDS analysis of common stocks, bond spreads, inflation
V. Questions
Society of Actuaries Research report: Sponsored by Financial Reporting Section, Smaller Insurance Company Section, Committee on Life Insurance Research. Posted September 2017. Primary Research Objective: Develop a set of deterministic cash flow testing scenarios that may be considered moderately adverse in varying interest rate environments, particularly the current low rate environment Secondary Research Objectives: Provide considerations in modeling inflation, investment spreads and equity returns
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Research Methodology: Identify or construct historical data series to use as basis of analysis Perform Conditional Tail Expectation (CTE) and other empirical analysis of historical data Construct scenario algorithms based on the historical data analysis Research Output: Report describing the research methods, assumptions and data sources Appendices detailing the analysis Excel workbooks to generate the MDS scenarios (Appendices J and K)
https://www.soa.org/research-reports/2017/2017-modern-deterministic-scenarios/
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New York 7 – Most common cash flow testing scenario set Previously required; no longer so in most states Concerns with applicability in low interest rate environment Other limitations – parallel shift convention; symmetry of increasing/decreasing scenarios; level of stress is untested Stochastic Scenarios – used by many, but not all, appointed actuaries May be impractical for smaller companies Results more difficult to interpret than deterministic scenarios Best-estimate or best-case?
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New York 7 – Historical prevalence of a 3% pop-up/pop-down (NY4, NY7) and +/- 5% over 10 years
Higher interest rates larger pops
For long rates, the maximum pop in either direction was 1.36% when the initial rate was 6% or less, but 3.04% when the initial rate was greater than 6%. (U.S Treasury data since 1953) For short rates, the maximum pop in either direction was 2.33% when the initial rate was 4% or less, but 6.46% when the initial rate was greater than 4%. (U.S Treasury data since 1953)
10 year changes vary with starting rate, demonstrating mean reversion pattern
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Short Rates Long Rates Pop-up 3% CTE98 >CTE99 Pop-down 3% CTE98 >CTE99 +5% over 10 yrs CTE96 CTE98
CTE93 CTE99
MDS Phase I: MDS Interest Rate Series Development MDS Phase II: Interest Rate Data Analysis MDS Phase III: MDS Scenario Construction MDS Phase IV: Common Stocks, Corporate Bond Spreads, Inflation
Challenges: Need a data series long enough to capture range of historical variation, but recent enough to be applicable Robust yield data on US Treasuries only available back to early 1950s. Is this adequate to provide long-term expectation? Earlier U.S. Government bond yield data generally only available aggregated by term Earlier U.S. Government bond yields represent poor measure of market interest rates, for various reasons The U.S. did not replace the UK as the world’s dominant economic power until after World War I , and was essentially a developing nation through the latter part of the 19th century
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Solution: Constructed two interest rate series – MDS Long Rate series (1729-2015) and MDS Short Rate series (1825-2015) Treasury yields used for as long as reliably available – 90 day for the Short series, beginning 1931; average of 20 and 30 year for the Long series, beginning 1953 Short rates 1918-1930 – prime bankers acceptances, 90 day Long rates 1923-1942 – Moody’s AAA less spread; 1943-1952 – US Government taxable bond yields, 15 years+ to call or maturity UK government rates used through WWI
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4.00 6.00 8.00 10.00 12.00 14.00 16.00
Interest Rates since 1953
20/30CMT Avg
12 Average 1990- 1953-
Source:
20/30CMT 5.39 6.21 FRB, H.15 Selected Interest Rates
2 4 6 8 10 12 14 16 1798 1803 1808 1813 1818 1823 1828 1833 1838 1843 1848 1853 1858 1863 1868 1873 1878 1883 1888 1893 1898 1903 1908 1913 1918 1923 1928 1933 1938 1943 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008 2013
Interest Rates since 1798
20/30CMT Avg US Long - Contemp
13 Average 1990- 1953- 1920- 1798+
Sources:
20/30CMT 5.39 6.21 NA NA FRB, H.15 Selected Interest Rates US Long 6.25 6.87 5.81 5.23 Measuringworth.com
2 4 6 8 10 12 14 16 1798 1803 1808 1813 1818 1823 1828 1833 1838 1843 1848 1853 1858 1863 1868 1873 1878 1883 1888 1893 1898 1903 1908 1913 1918 1923 1928 1933 1938 1943 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008 2013
Interest Rates since 1798
20/30CMT Avg US Long - Contemp UK Long Contemporary
14 Average 1990- 1953- 1920- 1798+
Sources:
20/30CMT 5.39 6.21 NA NA FRB, H.15 Selected Interest Rates US Long 6.25 6.87 5.81 5.23 Measuringworth.com UK Long 5.49 6.64 5.58 4.66 Measuringworth.com
2 4 6 8 10 12 14 16 1729 1735 1741 1747 1753 1759 1765 1771 1777 1783 1789 1795 1801 1807 1813 1819 1825 1831 1837 1843 1849 1855 1861 1867 1873 1879 1885 1891 1897 1903 1909 1915 1921 1927 1933 1939 1945 1951 1957 1963 1969 1975 1981 1987 1993 1999 2005 2011
Interest Rates since 1729
20/30CMT Avg US Long - Contemp UK Long Contemporary
15 Average 1990- 1953- 1920- 1798+ 1729+
Sources:
20/30CMT 5.39 6.21 NA NA NA FRB, H.15 Selected Interest Rates US Long 6.25 6.87 5.81 5.23 5.23 Measuringworth.com UK Long 5.49 6.64 5.58 4.66 4.42 Measuringworth.com
2 4 6 8 10 12 14 16 1729 1735 1741 1747 1753 1759 1765 1771 1777 1783 1789 1795 1801 1807 1813 1819 1825 1831 1837 1843 1849 1855 1861 1867 1873 1879 1885 1891 1897 1903 1909 1915 1921 1927 1933 1939 1945 1951 1957 1963 1969 1975 1981 1987 1993 1999 2005 2011
MDS Interest Rate Series since 1729
MDS Short Rate MDS Long Rate
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Key Observations:
inversions were normal; after that, rare
Challenges/Questions: How to define “moderately adverse” and analyze historical data for moderate adversity? Are New York 7 moderately adverse now? Were they ever? Is a moderately adverse rate change the same at the short and long end of the yield curve? Does “moderately adverse” vary with the initial interest rate environment? What scenario shapes are suggested by appropriate analytic frameworks?
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Solutions/Answers: Use generally accepted CTE70 definition of moderately adverse. Considering both tails, this translates to CTEL85 for the left tail and CTEH85 for the right tail Analysis of both short and long rates – no assumption of parallel shifts Four analytic frameworks/scenario types: Reversion scenarios Rate change scenarios Cyclical scenarios AIRG scenarios
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Traditional CTE analysis Expected value of a variable across a tail of the distribution Used in risk management to summarize stochastic loss results as value at risk Under principles-based reserves, stochastic reserves use a CTE70 standard CTE70 example: 100 scenarios with ranked losses of: $1, $2, $3,…, $99, $100.
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MDS Empirical CTE Analysis CTE measure applied to historical values rather than projected values CTE measure applied to: Interest rates Changes in interest rates from time X to time X+t Must consider both tails: Because losses may result from either high or low interest rates To achieve CTE70, BOTH tails must sum to 30% Our analysis used an equal split: CTEL85 (left or low rate tail); CTEH85 (right
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Challenges/Questions: How to turn a set of historical statistics into projection scenarios? What is the right number of scenarios? Is there a right number of scenarios? What dynamics should be captured in the scenarios? With parameters that vary by interest rate grouping, how to avoid discontinuities at the boundaries of the rate groupings? What is the right balance between simplicity and reasonable reproduction of historical patterns?
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Reversion framework
Hypothesis: Beyond t years, there is little correlation between ix and ix+t Empirical analysis summary: The correlation between ix and ix+t does become minimal for t of 15-20 years CTE values are as follows:
CTEL85 CTEH85 Short Rates 0.52% 6.35% Long Rates 2.59% 7.56%
Scenario description: Scenarios revert to moderately low (CTEL85) and moderately high (CTEH85) reversion targets over 15 years Reversion targets are independent of starting level of interest rates Four different reversion patterns
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CTEL95 CTEL90 CTEL85 CTEL80 CTEL70 Mean CTEH70 CTEH80 CTEH85 CTEH90 CTEH95 MDS Short 0.13 0.26 0.52 0.80 1.26 3.34 5.43 5.89 6.35 7.22 8.68 MDS Long 2.35 2.48 2.59 2.67 2.80 4.11 6.15 6.89 7.56 8.52 9.94
4.00 6.00 8.00 10.00 12.00
MDS Interest Rate Series - CTE Analysis of Average Rates
MDS Short MDS Long
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Moderately adverse long-term reversion targets:
minimum values
Additional Scenario Development Considerations
Interest rate pop-ups/downs Delayed reversion
Scenario Smoothing Considerations
None
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Reversion Scenario Construction Notes:
Short Rate Long Rate Low CTE target 0.50% 2.60% High CTE target 6.25% 7.50%
Scenario Number Scenario Name Scenario Description MDS1 Reversion - High Grade linearly to an 85HCTE (right tail) reversion target over a 15 year period MDS2 Reversion - Low Grade linearly to a 85LCTE (left tail) reversion target over a 15 year period MDS3 Delayed Reversion - High Long and Short Rates level for 5 years, then grade linearly to 85HCTE reversion target over a 10 year period MDS4 Delayed Reversion - Low Long and Short Rates level for 5 years, then grade linearly to 85LCTE reversion target over a 10 year period MDS5 Pop-up with Reversion - High Initial pop-up, then Grade linearly to 85HCTE reversion target by year 15 MDS6 Pop-down with Reversion - Low Initial pop-down, then Grade linearly to 85LCTE reversion target by year 15 MDS7 Delayed Pop-up with Reversion - High Long and short rates level for 5 years followed by pop-up, then Grade linearly to 85HCTE reversion target by year 15 MDS8 Delayed Pop-down with Reversion - High Long and short rates level for 5 years followed by pop-down, then Grade linearly to 85LCTE reversion target by year 15 CTE Reversion Target Scenarios
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12/31/16 Reversion Scenario Notes:
1.00 1.50 2.00 2.50 3.00 0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930
MDS Long Rate - Reversion Target Scenarios - Low vs. NY5 and NY7
MDS2 MDS4 MDS6 MDS8 NY5 NY7
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12/31/16 Reversion Scenario Notes:
2.00 3.00 4.00 5.00 6.00 7.00 8.00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
MDS Long Rate - Reversion Target Scenarios - High vs. NY2 and NY4
MDS1 MDS3 MDS5 MDS7 NY2 NY4
Rate change framework Hypothesis: The t-year change in interest rates, ix+t - ix , is asymmetric and varies in direction and magnitude based on the value of ix Empirical analysis summary: When ix is high, rates tend to decrease and vice versa When ix is high, rate changes tend to be larger and vice versa Short rates tend to change more rapidly than long rates Unsuccessful at regressing rate changes against starting rate Scenario description: Scenarios are based on moderately low (CTEL85) and moderately high (CTEH85) t-year changes in interest rates, where t=1 to 30 Interest rates stratified in four groups to determine the moderately low and moderately high interest rate changes vary by the starting level of rates
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0.00 2.00 4.00 6.00 8.00 1yr Chg 5yr Chg 10yr Chg 15yr Chg 20yr Chg 25yr Chg 30yr Chg
Rate Change CTE Statistics - Total
Long Rate - CTEL85 Long Rate - CTEH85 Short Rate - CTEL85 Short Rate - CTEH85
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Notes on Yearly Average Rate Change Targets:
from starting date, and build scenarios from these statistics
years, but continue much longer
0.00 2.00 1yr Chg 5yr Chg 10yr Chg 15yr Chg 20yr Chg 25yr Chg 30yr Chg
Long Rate Changes - CTEL85 by Initial Interest Rate Group
Total 2.00-2.75 2.75-3.75 3.75-6.00 6.00-10.00 10.00+
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Notes on Yearly Average Rate Change Targets:
by the data.
Additional Scenario Development Considerations
Interest rate pop-ups/downs
Scenario Smoothing Considerations
For each interest rate group, we ended up with CTEL85 and CTEH85 vectors with 30 values (rate change periods of 1 to 30 years). These vectors were very noisy and required smoothing before we could use them as scenario parameters. Because the CTEL85 and CTEH85 vectors were computed independently for each interest rate group, discontinuities at the boundaries of the interest rate groups had to be smoothed through a blending technique.
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Rate Change CTE Scenario Construction Notes:
Scenario Number Scenario Name Scenario Description MDS9 85HCTE Rate Changes Change from initial rate based on 85HCTE (right tail) historical change statistics for the applicable interest rate group MDS10 85LCTE Rate Changes Change from initial rate based on 85LCTE (left tail) historical change statistics for the applicable interest rate group MDS11 85HCTE Change w Transitional Pop-up Change from initial rate based on 85HCTE (right tail) historical change statistics for the applicable interest rate group, with initial pop-up based on 85HCTE transitional change MDS12 85LCTE Change w Transitional Pop-down Change from initial rate based on 85LCTE (left tail) historical change statistics for the applicable interest rate group, with initial pop-down based on 85LCTE transitional change Rate Change CTE Scenarios
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12/31/16 Rate Change Scenario Notes:
at 16-18 years and ending 60-80bps above initial rate
1.00 1.50 2.00 2.50 3.00 3.50 4.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
MDS Long Rate - Rt Chg CTE Scenarios - Low vs. NY5 and NY7
MDS10 MDS12 NY5 NY7
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12/31/16 Rate Change Scenario Notes:
ultimate levels for 25 years, and pops much smaller
2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
MDS Long Rate - Rt Chg CTE Scenarios - High vs. NY2 and NY4
MDS9 MDS11 NY2 NY4
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Cyclical Scenario Construction Notes:
are more judgmental. Scenarios reflect two key observations:
AIRG Scenario Construction Notes:
generated using the Academy Interest Rate Generator
Scenario Number Scenario Name Scenario Description MDS13 Cyclical, 20 year cycle 20 year cycles of interest rates - 5 years declining, 10 years flat, 5 years increasing. MDS14 Cyclical, 40 year cycle 40 year cycles of interest rates - 10 years declining, 20 years flat, 10 years increasing. MDS15 AIRG CTEH85 Rates based on 1000 scenarios from Academy interest rate generator, CTEH85 of cumulative average rates, annualized. MDS16 AIRG CTEL85 Rates based on 1000 scenarios from Academy interest rate generator, CTEL85 of cumulative average rates, annualized. Interest Rate Cycle Scenarios: AIRG-based Scenarios:
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Cyclical and AIRG Scenario Notes:
are the most like a cyclical scenario.
compared with NY and high rate MDS scenarios. MDS16 relationship to NY5 similar to other low MDS scenarios.
2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
MDS Long Rate - AIRG Scenarios vs. NY2 and NY5 12/31/2015
MDS15 MDS16 NY2 NY5
2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
MDS Long Rate - Int Rt Cycle Scenarios
MDS13 MDS14 NY3 NY6
Analytic approach and results:
Data: Monthly S&P500 price and dividends 1871-2015 (Robert Shiller) One-tailed CTE analysis of price shocks and holding period returns at various CTE levels, with results as follows: Holding period should correspond to the life of the business and the projection horizon. Also developed a method to incorporate equity price shocks into CFT results
38 CTE level 10 20 30 40 Annualized Holding Period Returns CTE60 4.4% 6.4% 7.0% 7.2% CTE70 3.5% 6.1% 6.6% 6.8% CTE80 2.5% 5.6% 6.3% 6.5% Holding Period Price Shock CTE60
CTE70
CTE80
Holding Period Standard & Poor's 500 CTE Statistics 1871-2015
Analytic approach and conclusions:
Data: Moody’s AAA and Baa bond averages 1919-2015 (Federal Reserve) vs. MDS Long interest rates Two-tailed CTE analysis of spreads, in total and by interest rate group, with results as follows: No correlation of spreads and interest rate levels. Reasonable to assume spreads to revert to long term averages or to a CTE level, depending on whether the business is more at risk of widening or tightening spreads.
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Interest Groups Mean Variance CTEL85 CTEH85 Mean Variance CTEL85 CTEH85 Total
0.55 0.33 0.23 1.17 1.74 0.74 0.81 2.97
Interest Group 1
0.40 0.26 0.25 0.84 1.39 0.58 0.85 2.26
Interest Group 2
0.39 0.27 0.15 0.95 1.65 0.78 0.65 2.77
Interest Group 3
0.54 0.33 0.24 1.15 1.87 0.90 0.81 3.44
Interest Group 4
0.73 0.33 0.30 1.30 1.69 0.46 1.13 2.43
Interest Group 5
0.62 0.23 0.28 0.95 2.33 0.54 1.76 3.27
Moody’s AAA Moody’s Baa
Historical Analysis of Corporate Bond Spreads, Moody's Seasoned Corporate Bond Spreads to MDS Long Rate
Analytic approach and conclusions: Data: U.S. Urban CPI 1919-2015 (measuringworth.com), compared with MDS Long and Short Interest Rate series Attempted to regress inflation rates to either Long or Short Interest rates, but observed little correlation One-tailed CTE analysis of spreads, with results as follows: Conclusions very judgmental due to limited data and little correlation. Reasonable best-estimate inflation assumption is 0.5% Short rate spread CTE70 Short rate spread of -4.0% driven by overweighting of WWII
40 Spread Statistic MDS Short MDS Long Mean Spread to CPI 0.57% 2.29% Standard Deviation 4.30% 4.39% 30th percentile
1.26% CTE70
Historical Spread Statistics, Interest Rates vs. CPI Inflation Rates, 1919-2015
The MDS project was successful in providing actuaries with:
1. A set of scenarios that can reasonably be considered moderately adverse. 2. An analytic framework that actuaries can apply to evaluate moderately adverse conditions with respect to interest rates. 3. A historical series of interest rates beginning in 1729 that actuaries can use for their own interest rate analysis. 4. Historical analysis and framework for considering inflation rates, corporate bond spreads and equity returns in a consistent way.
But is not without limitations:
It merely opens the book on the work that can be done to better assess moderately adverse economic conditions. Even with 287 years of data, the number of data points is sparse and required significant smoothing. Some may question the applicability of the data underlying the analysis.
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