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2009 Seminar for the Appointed Actuary Discounting in the Current

Explore discounting in the current economic environment, various methods like internal rate of return, duration-weighted yield. Understand advantages & disadvantages for accurate actuarial calculations.

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2009 Seminar for the Appointed Actuary Discounting in the Current

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  1. Canadian Institute of Actuaries L’Institutcanadien des actuaires 2009 Seminar for the Appointed Actuary Discounting in the Current Economic Environment (PD-3)September 17, 2009 Colloque pour l’actuaire désigné 2009

  2. Part 1 – Derivation of Discount Rate Part 2 – Derivation of Margin for Discount Rate Part 3 – Other Considerations 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Discounting in the Current Economic Environment

  3. Discounting in the Current Economic Environment Part 1 – Derivation of Discount Rate 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  4. Standard of Practice (SOP) 2240.01 “The expected investment return rate for calculation of the present value of cash flow is that to be earned on the assets which support the policy liabilities.” 2240.02 “The actuary need not verify the existence and ownership of the assets at the balance sheet date but would consider their quality.” 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  5. Considerations (SOP 2240.01) Method of valuing assets and reporting investment income Return on the assets at the balance sheet date Investment expenses, and losses from default risk (C-1 risk) Allocation of those assets and that income among lines of business Yield on assets acquired after the balance sheet date Capital gains and losses on assets sold after the balance sheet date 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  6. Balance Sheet Yield Since there are different methods for classifying assets, the term balance sheet yield has different meaning depending on the selected method. Asset ClassificationBalance Sheet Yield Available for Sale Market Value Yield Held for Trading Market Value Yield Held to Maturity Amortized Yield 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  7. Different Methodologies There are three methods commonly used to determine the discount rate. Internal rate of return model Duration weighted yield Balance Sheet value weighted yield 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  8. Internal Rate of Return Model This model is based on the notion that if assets and liabilities are perfectly matched, the discount rate should be the same as the balance sheet yield underlying the assets. When matching is not perfect, reinvestment risk exists. The discount rate produced by this model will vary from the balance sheet yield of the assets in relation to the amount of mismatch between the assets and liabilities. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  9. Internal Rate of Return Model ∞ M = (Wt + Lt) / (1 + d)t t=1 M = balance sheet value of assets that provide the cash in-flow Wt = excess cash in-flow withdrawn at the end of month t Lt = expected loss payment in month t d = discount rate 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  10. Advantages Explicit matching of cash inflows and outflows monthly/quarterly Automatic minimizing asset/liability mismatch Explicit recognition of maturity of bonds and reinvestment Intuitively superior Disadvantages Claims payment data (especially for unexpired portion of the policies) is rarely available monthly and probably can not be accurately projected with confidence Requires explicit assumption about reinvestment policy and rate (current yield curves) Does not recognize default risk explicitly; discount rate increases as quality deteriorates Difficult to use, requires detailed cashflow matching; not suitable for common stocks 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Internal Rate of Return Model

  11. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Duration Weighted Yield

  12. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Balance Sheet Value Weighted Yield

  13. The duration is a measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows. Since the entire cash flow of a zero-coupon bond occurs at maturity, the duration of such a bond is equal to the time between the valuation date and maturity date. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Duration

  14. Macaulay Duration is the weighted average maturity of a bond where the weights are the relative discounted flows in each period. Modified Duration is a modified version of the Macaulay Duration that reflects changes in interest rates. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Duration

  15. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Example

  16. Advantages Simple to use Can handle preferred stocks and common stocks with modification Disadvantages No explicit matching of cash inflows and outflows No explicit recognition of maturity of bonds and reinvestment 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Weighted Yield Models

  17. Investment expenses should be recognized explicitly. If portfolio yield is 4.0% and investment expenses are 0.25%, the discount rate before margins should be 3.75%. Investment expenses: 1. From Company’s Annual Return 2. From Company 3. Judgment 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Investment Expenses

  18. Discounting in the Current Economic Environment Part 2 – Derivation of Margin for Discount Rate 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  19. Standard of Practice (SOP) 2250.02 “The actuary should select a margin for adverse deviations for an assumption that is within the range defined by the low margin and the high margin for that assumption. The criteria for selection of that margin are the considerations for that assumption.” 2250.09 “The margin for investment return rate is a deduction from the expected investment return rate per year.” 2250.10 The levels of margin for investment return rates is between 50 and 200 basis points 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  20. Different Methodologies There are three commonly used methods to determine the margin for discount rate. Judgment Scoring Models Explicit Quantification 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  21. Scoring Models A scoring model evaluates several considerations and assigns low, medium or high margin situations to each consideration and produces an indicated margin. Examples of considerations: Quality of Investment Portfolio Matching of investments to claim payments Investment Climate 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  22. Explicit Quantification of Margins This approach estimates the margin for investment return as the sum of three risk margins: Credit risk margin Asset/Liability Mismatching risk margin Timing risk margin 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  23. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 How to Estimate Credit Risk?

  24. Credit Risk (Spread in Basis Points) Selected Based on Issuer

  25. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Credit Risk Margin Example

  26. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 How to Estimate Asset/Liability Mismatching Risk?

  27. Potential Interest Rate Movement Examine the interest rate movement from 1951 – 2008 Estimate the liability duration, say 2 years. Calculate a two year change: Yi = base year yield Yi+2 = yield two years after i two year change = (Yi+2 –Yi) / Yi 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  28. Y1979 = 10.77% Y1981 = 15.97% Change1981-1979 = 48.28% Y2002 = 3.55% Y2004 = 2.92% Change2004-2002 = - 17.75% 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Potential Interest Rate Movement Examples 1 – 3 Year Canada Bond Series

  29. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Potential Interest Rate Movement in Run-off Period

  30. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Asset/Liability Mismatching Risk Margin Example

  31. ∞∞ PV =  Lt / (1+d)t,  Lt = L t t = L / (1+d)D, Lt = paid losses in year t D = duration of liabilities If D is shortened by 10%, the reduction in discount is equivalent to decreasing the discount rate by approximately 10%d. More precisely, ^ L / (1+d)D = L / (1+d).9D 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 How to Estimate Claims Payment Pattern (Timing) Risk?

  32. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Timing Risk Margin Example

  33. Calculation of Timing Risk Margin If D = 2.03 years d = 4.0% ^ then d = 3.59% Margin = 0.41% ≈ 41 bp Approximation would produce margin of 10% of 4.0% or 40 bp. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  34. Calculation of Total Margin The margin for investment return is the sum of three risk margins: Credit risk margin – 108 bp Asset/Liability Mismatching risk margin – 64 bp Timing risk margin – 41 bp Total risk margin – 213 bp. Margin would be capped at 200 bp. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  35. Advantages Compare duration of assets and liability only – no matching Explicit recognition of default risk Disadvantages Could understate reinvestment rate risk especially for a portfolio with a small number of bonds 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Explicit Quantification of Margins

  36. Discounting in the Current Economic Environment Part 3 – Other Considerations 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  37. How to Estimate Foreign Exchange Risk? If foreign liabilities > foreign assets, then a decline in the Canadian dollar relative to the foreign currency could increase the liability more than the corresponding gain in the asset value. In such a situation, may need to increase margin. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  38. Fixed Income Assets Held to Maturity In a declining interest rate environment: assets duration < liability duration may require an estimate to reduce the discount rate and / or increase the margin for investment return. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  39. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 Asset/Liability Mismatching Risk Margin Example

  40. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 How to Handle Stocks? • Preferred stock with retractable option by the holder: duration can be determined with the first retractable date as maturity date. Treat it like a bond with high credit risk. • Common stock: use expected total return (dividend + price appreciation) and exclude its value in the coverage ratio calculation. Yb=duration weighted yield of bonds Ys=expected total return of stocks Mb=balance sheet value of bonds Ms=market value of stocks

  41. Application of Discount Rates The Appointed Actuary estimates the unpaid claims liability on a gross, ceded, and net basis. Should the discount rate differ between the gross, ceded and net liabilities or should they be the same? Two Approaches 1. Same discount rate for gross and net unpaid claims. 2. Net discount rate different from ceded discount rate. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  42. Net discount rate different from ceded discount rate? The gross claims liabilities include a portion transferred to other insurance enterprises (ceded portion) The other insurance enterprises hold assets unknown to the Company. Therefore, it is reasonable to determine the present value of the ceded portion using a different discount rate. One option is to determine the discount rate for the ceded portion based on the interest rate equivalent to that of a portfolio of Canada bonds or strip coupons with matching amount to the expected payments plus a provision for adverse deviations. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  43. Ceded Discount Rate For Canadian dollar payments: use a hypothetical strip bond yield curve from Bank of Canada. For US dollar payments: use US Treasury strip bonds. Match the expected ceded claims payments with sufficient cash inflows in item 1. Margin is the minimum required amount. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

  44. 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009 2008 & 2007 Ceded Discount Rate

  45. Questions ? 2009 Seminar for the Appointed Actuary Colloque pour l’actuairedésigné 2009

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