Financial Risk Management of Insurance EnterprisesReview...TodayAsset/Liability ManagementThe ALM ProcessALM of InsurersThe Goal of ALMThe Goal of ALM (p.2)Price/Yield RelationshipSimplificationsExamining Interest Rate SensitivityPrice Changes on Two Zero Coupon Bonds Initial Interest Rate = 8%Price Volatility Characteristics of Option-Free BondsMacaulay DurationMacaulay Duration (p.2)Applying Macaulay DurationModified DurationModified Duration and Macaulay DurationAn ExampleSolution to ExampleExample ContinuedSlide 22Other Interest Rate Sensitivity MeasuresA Different MethodologyA Different Methodology (p.2)Error in Price PredictionsSlide 27ConvexityComputing ConvexityExamplePredicting Price with ConvexityAn Example of PredictionsNotes about ConvexityConvexity is GoodNext TimeFinancial Risk Management of Insurance EnterprisesIntroduction to Asset/Liability Management, Duration & ConvexityReview...•For the first part of the course, we have discussed:–The need for financial risk management–How to value fixed cash flows–Basic derivative securities–Credit derivatives•We will now discuss techniques used to evaluate asset and liability riskToday•An introduction to the asset/liability management (ALM) process–What is the goal of ALM?•The concepts of duration and convexity–Extremely important for insurance enterprisesAsset/Liability Management•As its name suggests, ALM involves the process of analyzing the interaction of assets and liabilities•In its broadest meaning, ALM refers to the process of maximizing risk-adjuste d return•Risk refers to the variance (or standard deviation) of earnings•More risk in the surplus position (assets minus liabilities) requires extra capital for protection of policyholdersThe ALM Process•Firms forecast earnings and surplus based on “best estimate” or “most probable” assumptions with respect to:–Sales or market share–The future level of interest rates or the business activity–Lapse rates–Loss development•ALM tests the sensitivity of results for changes in these variablesALM of Insurers•For insurance enterprises, ALM has come to mean equating the interest rate sensitivity of assets and liabilities–As interest rates change, the surplus of the insurer is unaffected•ALM can incorporate more risk types than interest rate risk (e.g., business, liquidity, credit, catastrophes, etc.)•We will start with the insurers’ view of ALMThe Goal of ALM•If the liabilities of the insurer are fixed, investing in zero coupon bonds with payoffs identical to the liabilities will have no risk•This is called cash flow matching•Liabilities of insurance enterprises are not fixed–Policyholders can withdraw cash–Hurricane frequency and severity cannot be predicted–Payments to pension beneficiaries are affected by death, retirement rates, withdrawal–Loss development patterns changeThe Goal of ALM (p.2)•If assets can be purchased to replicate the liabilities in every potential future state of nature, there would be no risk•The goal of ALM is to analyze how assets and liabilities move to changes in interest rates and other variables•We will need tools to quantify the risk in the assets AND liabilitiesPrice/Yield Relationship•Recall that bond prices move inversely with interest rates–As interest rates increase, present value of fixed cash flows decrease•For option-free bonds, this curve is not linear but c onvexPrice/yield curveYieldPriceSimplifications•Fixed income, non-callable bonds•Flat yield curve •Parallel shifts in the yield curveExamining Interest Rate Sensitivity•Start with two $1000 face value zero coupon bonds•One 5 year bond and one 10 year bond•Assume current interest rates are 8%Price Changes on Two Zero Coupon BondsInitial Interest Rate = 8%Principal R 5 year Change 10 year Change1000 0.06 747.2582 9.7967% 558.3948 20.5532%1000 0.07 712.9862 4.7611% 508.3493 9.7488%1000 0.0799 680.8984 0.0463% 463.6226 0.0926%1000 0.08 680.5832 0.0000% 463.1935 0.0000%1000 0.0801 680.2682 -0.0463% 462.7648 -0.0925%1000 0.09 649.9314 -4.5038% 422.4108 -8.8047%1000 0.1 620.9213 -8.7663% 385.5433 -16.7641%Price Volatility Characteristics of Option-Free BondsProperties1 All prices move in opposite direction of change in yield, but the change differs by bond2+3 The percentage price change is not the same for increases and decreases in yields4 Percentage price increases are greater than decreases for a given change in basis pointsCharacteristics1 For a given term to maturity and initial yield, the lower the coupon rate the greater the price volatility2 For a given coupon rate and intitial yield, the longer the term to maturity, the greater the price volatilityMacaulay Duration•Developed in 1938 to measure price sensitivity of bonds to interest rate changes•Macaulay used the weighted average term-to-maturity as a measure of interest sensitivity•As we will see, this is related to interest rate sensitivityMacaulay Duration (p.2)Macaulay Duration = index for period= total number of period= number of coupon payments per yearPresent value of cash flow in period t= Total present value of cash flows (price)t PVCFk PVTCFtnkPVCFPVTCFtttntt1Applying Macaulay Duration•For a zero coupon bond, the Macaulay duration is equal to maturity•For coupon bonds, the duration is less than its maturity•For two bonds with the same maturity, the bond with the lower coupon has higher durationPercentage change in priceMacaulay duration Yield change 100  11yieldkModified Duration•Another measure of price sensitivity is determined by the slope of the price/yield curve•When we divide the slope by the current price, we get a duration measure called modified duration•The formula for the predicted price change of a bond using Macaulay duration is based on the first derivative of price with respect to yield (or interest rate)Modified Duration and Macaulay DurationdurationMacaulay )1(11)1(1i duration Modified)1(1iPiCFtPPiCFPtttti = yield CF = Cash flowP = priceAn ExampleCalculate:What is the modified duration of a 3-year, 3% bond if interest rates are 5%?Solution to ExamplePeriod Cash Flow PV t x PV1 3 2.86 2.86 2 3 2.72 5.44 3 103 88.98 266.93 Total 94.55 275.23 Macaulay duration =Modified duration =275 2394 552 912 911052 77......Example Continued•What is the predicted price