Casualty Actuarial Society Experienced Practitioner Pathway Seminar Lecture 8 – Inflation Stephen P. D’Arcy, FCAS, MAAA, Ph.D. Robitaille Chair of Risk and Insurance California State University – Fullerton D’Arcy Risk Consulting, Inc.

Overview General discussion of inflation/deflation Why inflation/deflation matters to insurers Historical inflation/deflation rates Modeling future inflation/deflation Applications of inflation/deflation model 2EPP Lecture 8: Inflation

Why Study Inflation/Deflation Now? Recent inflation rates have been low Potential for dramatic change –Recession could lead to deflation Financial crisis of 2008 Euro crisis –Expansionary policies could lead to high inflation Quantitative easing in developed countries Rapid growth in some developing countries Increased uncertainty exists for inflation forecasts 3EPP Lecture 8: Inflation

What is Inflation? For consumers –Change in prices –Change in cost-of-living For investors –Impacts purchasing power of investments –Real vs. nominal interest rates For insurers –One of the most significant risks facing insurers –Affects cost of doing business, underwriting results and investment performance 4EPP Lecture 8: Inflation

Inflation Measures Consumer Price Index Potential biases –Substitution effects –Quality changes –New products Cost-of-living index 5EPP Lecture 8: Inflation

Inflation and Insurance Costs Expense component for all insurers –Wages –Cost of goods used in operations Property-liability insurance losses –Replacement cost coverage for property –Medical cost inflation for injuries –Social inflation for jury awards Life insurance and annuities benefits –Indexed policy benefits 6EPP Lecture 8: Inflation

Extreme Inflation Scenarios Deflation –During Depression –Japan 1980s-90s Hyperinflation –European countries 1920s –Mexico –Various Latin American countries 7EPP Lecture 8: Inflation

Managing Inflation/Deflation Risk: Investments Fixed income investments –Default rates rise during deflationary periods –Market values decline when inflation increases Inflation indexed bonds –Limited availability –Current low real returns Equities –Short term impact negative –Long term impact mixed 8EPP Lecture 8: Inflation

Managing Inflation/Deflation Risk: Underwriting Property-liability insurers –Loss reserves need to account for inflation –Policy terms Adjust length based on economic conditions Index deductibles and retentions –Adjust frequency of rate changes Life insurers –Lapse rates increase with inflation Index face value and premiums –Cap inflation indices for annuities 9EPP Lecture 8: Inflation

Historical Inflation Rates United States Canada Mexico Japan Other countries available at: 10EPP Lecture 8: Inflation

United States Annual Inflation Rate EPP Lecture 8: Inflation

Canadian Annual Inflation Rate EPP Lecture 8: Inflation

Japanese Annual Inflation Rate EPP Lecture 8: Inflation

Mexican Annual Inflation Rate EPP Lecture 8: Inflation

Proposed Regimes for Inflation Model Based on US and Canadian Experience Deflation –Inflation rate is negative Moderate inflation –Inflation rate from 0 to 6% High inflation –Inflation rate over 6% 15EPP Lecture 8: Inflation

Inflation/Deflation Discussion How likely do you think it is that the U. S. will be in a deflationary regime within five years? How likely do you think it is that the U. S. will be in a high inflation regime within five years? 16EPP Lecture 8: Inflation

US (97 years) Canada (95 years) FrequencyMeanFrequencyMean All Years 3.4% 3.3% Negative13.4%-4.0%9.5%-5.5% 0 to 6%66.0%2.6%70.5%2.3% >6%20.6%10.5%20.0%10.7% Historical Inflation/Deflation Experience 17EPP Lecture 8: Inflation

Inflation Generator Model Model documentation – effect-deflation.aspxhttp:// effect-deflation.aspx Provides details about using the model 18EPP Lecture 8: Inflation

Using the Model EPP Lecture 8: Inflation

Using the Model EPP Lecture 8: Inflation

Using the Model EPP Lecture 8: Inflation

Using the Model EPP Lecture 8: Inflation

Using the Model EPP Lecture 8: Inflation

Using the Model EPP Lecture 8: Inflation

Using the Model EPP Lecture 8: Inflation

Using the Model EPP Lecture 8: Inflation

A Model of Inflation 27EPP Lecture 8: Inflation

Discrete Process in Model Model projects inflation process in monthly time steps Future inflation process is weighted average of past inflation and mean reversion level 28EPP Lecture 8: Inflation

Month Initial1.00% 11.17% 21.32% 31.46% 41.59% 51.71% 61.81% 71.91% 82.00% 92.09% % % % Impact of Discrete Process 29EPP Lecture 8: Inflation

Annualized Inflation Projections Model projects a sample path for the monthly inflation process over next 50 years –User can enter number of sample paths However, the “inflation rate” is based on the cumulative (compounded) monthly process 30EPP Lecture 8: Inflation

From the Model… Inflation “process” needs to be compounded to measure annualized rate of inflation 31EPP Lecture 8: Inflation

Regime Switching At any point in time, parameters of process drive future inflation However, model can switch between three separate inflation regimes –“Normal” inflation –High inflation –Low inflation (deflation) Switching between regimes is based on a probability matrix 32EPP Lecture 8: Inflation

Initial Regime Parameters 33EPP Lecture 8: Inflation

Initial Transition Matrices 34EPP Lecture 8: Inflation

Transition Probabilities and Regime Duration Monthly Likelihood of Remaining Annual Equivalent Switching Mean (In years) Median (In years) 99.9%1.2% %2.4% %3.5% %4.7% %5.8% %7.0% %8.1% %9.2% %10.3% %11.4% %16.6% %21.5% EPP Lecture 8: Inflation

Running a Simulation User enters “ModelInput” parameters –Parameters of process for each regime –Transition probabilities across regimes –Initial inflation value “DefineOutput” –Choose the inflation rates of interest Start projections 36EPP Lecture 8: Inflation

Output Summary statistics for inflation output Inflation values for all sample paths –Can export for further analysis 37EPP Lecture 8: Inflation

Applications of the Inflation Generator Model can be used as engine for other applications –Inflation component of an economic capital model –Medical claim inflation may be modeled from general inflation rate –Salary increases for pension projections –Interest rates may be correlated with some target inflation 38EPP Lecture 8: Inflation

References Inflation/Deflation Report available at: User Guide available at: 39EPP Lecture 8: Inflation