Discount Rates in General Insurance Pricing

Transcription

1 Discount Rates in General Insurance Pricing Peter Mulquiney, Brett Riley, Hugh Miller and Tim Jeffrey Peter Mulquiney, Brett Riley, Hugh Miller and Tim Jeffrey This presentation has been prepared for the Actuaries Institute 2014 General Insurance Seminar. The Institute Council wishes it to be understood that opinions put forward herein are not necessarily those of the Institute and the Council is not responsible for those opinions.

2 Why this paper? Discount rates often overlooked Challenge yield curve projection Response to research request Discount rates important Low interest rate environment

3 Key findings Two models & their rates Risk free rate & ERP: negative correlation Understand relationship b/w ROE & TSR Be careful using ground up ROE estimate M-C is contentious: can allow for frictions

4 Key findings Yield projection Across cycles, spot & forward rates close Spot better for normal yield curve Alternative formula: further improvement Using single rates vs spot may distort ROE Shifting investments to replicating portfolio

5 Background No recent major advances in discount rates Academic literature Regulated vs unregulated classes Discount rates affect idea of fair price in regulated classes

6 Pricing Models IRR Investment income T=0 T=1 Net shareholder - Assets cash flow Premium Claims + expenses Tax T=2 Net shareholder cash flows discounted with single discount rate (ROE) The single discount rate ROE reflects time value of money and riskiness of cash flows Premium chosen to set NPV to zero Model well understood: Expected values for cash flows Franchise value & intangibles? How to choose ROE?

7 Pricing Models Myers-Cohn Investment income T=0 T=1 Net Shareholder - Assets Cash flow Premium Claims + expenses Tax T=2 Considers same cash flows as IRR Premium chosen to set NPV of shareholder cash flows to zero Key difference: each cash flow discounted using separate rate reflecting riskiness of cash flow Claims + expenses: R L (return on liabilities) Investment returns: R A (asset return) Taxes: R L and R F (risk free rate)

8 Pricing Models Comparison In practice IRR is preferred for a number of reasons Underlying assumptions Practicality Interpretation Ability to account for individual risks IRR MC Following slides on discount rate assumption setting will focus on IRR

9 Assumption Setting Risk Free Rates Role in IRR is indirect discount rate for claims liabilities which impacts capital projections Most accept CGBs as best proxy for risk free Required by APRA for general insurance liability valuations. Some argue for a loading for illiquidity risk Allowed for some life insurance annuities

10 Assumption Setting Return on Equity 12 month change in credit spread on 3year BBB bonds 6.0% 4.0% 2.0% -4.0% y = x R² = % -5.0% -4.0% -3.0% -2.0% -1.0% 0.0% 1.0% 2.0% 3.0% -2.0% -6.0% 12 month change in 3 year yield on Commonwealth Government Bonds Unregulated classes: ROE only limited by market realities. Tends to be stable Regulated classes: ROE should be set based on an appropriate asset pricing model. CAPM one common model

11 Assumption Setting Return on Equity ROE vs TSR Ground-up estimates of ROE possible Approach similar to Myers-Cohn Produces premiums consistent with free competition Needs adjustment to allow for market imperfections (frictions).

12 Example Single Discount Rate Class of Business Result Context CTP Motor ROE (IRR) Cohort 9.4% 30.1% Result Context Base - single rate CTP sensitivity Using spot rates Upward curve Inverted curve Profit Margin Cohort 12.6% 7.3% Net loss ratio (inflated & discounted) Cohort 75% 69% Gross expense ratio Cohort 12% 19% Capital Base to GWP Net Accounting Loss Ratio ROE (NPAT / Net Assets) Steady state portfolio Steady state portfolio Steady state portfolio Insurance Margin Steady state (Insurance Profit / NEP) portfolio 134% 29% 92% 73% 9.4% 30.1% 12.7% 9.8% ROE (IRR) Cohort 9.4% 9.9% 8.5% Profit Margin Cohort 12.6% 12.6% 12.6% Net loss ratio (inflated & discounted) Cohort 75% 75% 75% Gross expense ratio Cohort 12% 12% 12% Capital Base to GWP Net Accounting Loss Ratio ROE (NPAT / Net Assets) Steady state portfolio Steady state portfolio Steady state portfolio Insurance Margin Steady state (Insurance Profit / NEP) portfolio 134% 132% 135% 92% 92% 93% 9.4% 10.1% 8.4% 12.7% 13.5% 11.3%

13 Example IRR Sensitivity CTP ROE sensitivity 1 Motor ROE sensitivity 1 Red Amber Green Red Amber Green Assumption Variation >2% 1-2% <1% >4% 2-4% <2% Net claim cost per $100 gross premium + / - 10% (inflated & disc.) Gross expense rate + / - 2% Inflation + / - 1% Discount rate + / - 0.5% Outstanding claims risk margin (APRA) Premium liability risk margin (APRA) 1 Measures absolute value of change in ROE + / - 4% + / - 4%

14 Example Myers-Cohn Liability Beta Equity Risk Premium 3% 11% 10% 9% 8% 7% 6% 5% 4% 3% 2% 2% 4% 13% 11% 10% 9% 8% 6% 5% 4% 2% 1% 0% 5% 14% 13% 11% 10% 8% 6% 5% 3% 2% 0% -2% 6% 16% 14% 12% 10% 8% 6% 4% 2% 1% -1% -3% Risk Free Rate 2.1% 13% 12% 10% 9% 8% 6% 5% 4% 2% 1% 0% 3.1% 13% 11% 10% 9% 8% 6% 5% 4% 2% 1% 0% 4.1% 13% 11% 10% 9% 8% 6% 5% 4% 3% 1% 0% 5.1% 12% 11% 10% 9% 8% 6% 5% 4% 3% 1% 0%

15 Return on equity 30% 25% 20% 15% 10% 5% 0% Yield projection the issue Time gap between pricing and premium creates interest rate risk Can lock in yield curve by hedging, but not common A full powered projection is difficult and unjustified Two simpler approaches are expectations (shifted forward curve) and static (assume curve remains fixed. Neither necessarily optimal Target Actual

16 Performance of simple predictors Average bias (basis points) Yield curve Slope No. months Forward Expect. Static Spot Diff. Inverted < -0.25% Flat -0.25% to 0.25% Normal > 0.25% Normal - steep > 1% Total Root MSE (basis points) Yield curve Slope No. months Forward Expect. Static Spot Diff. Inverted < -0.25% Flat -0.25% to 0.25% Normal > 0.25% Normal - steep > 1% Total Overall performance is very similar, but static approach has slight advantage when yield curve has unusual shape

17 Estimated ββ (percentage) Our alternative approach ff tt (ss + δδ) ββff tt+δδ ss + 11 ββ ff tt With ff tt (ss) =Forward rate at time ss, term tt δδ = Projection period Colour key width of 90% confidence interval: 15% 30% 45% 60% 75% 90% 105% 120% 135% 145% A combination of expectations and mean reversion. Estimated by linear regression on data,

18 Improved prediction Average squared error in estimation, terms 0 through Jul-92 Jul-93 Jul-94 Jul-95 Jul-96 Jul-97 Jul-98 Jul-99 Jul-00 Jul-01 Jul-02 Jul-03 Jul-04 Jul-05 Jul-06 Jul-07 Jul-08 Jul-09 Jul-10 Jul-11 Jul-12 Our formula leads to 20-30% reduction in error, and a 65% win rate vs expectations method. Dampens extreme movements Our mean curve has slowly lowered over time Formula Expectations hyp Static

19 Implications Changes to premiums of around 1-2%, depending on method Currently the extra mean reversion leads to higher projected yields (lower premiums)

20 Key findings Two models & their rates Risk free rate & ERP: negative correlation Understand relationship b/w ROE & TSR Be careful using ground up ROE estimate M-C is contentious: can allow for frictions

21 Key findings Yield projection Across cycles, expectations & static rates close Expectations can show some bias Alternative formula: further improvement Using single rates vs spot may distort ROE Shifting investments to replicating portfolio