Intensive Actuarial Training for Bulgaria January 2007 Lecture 4 – Life Insurance Reserve & Minimum Capital By Michael Sze, PhD, FSA, CFA

Concept of Reserve Required asset built-up to cover expected future shortfall in contributions to cover all benefits This should be regarded as liability for the insurance program There are several different measures of the reserve –Statutory reserves are legal minimum –GAAP reserves are realistic –Gross premium reserves are based on gross premiums

Statutory Reserves Purpose: to ensure that the insurance company can pay benefits when due Required to use conservative assumptions –Low interest rate –High mortality rates –Immediate recognition of all expenses Based on net premium reserve Because of the conservative assumptions –Net income after expenses < required reserve increase –Surplus strain

Net Premium Reserves Omit lapses, expenses, dividends, taxes Assumes death at end of year t V x =A x+t – t P x x ä x+t Fackler formula t V x =[( t-1 V x + t P x )(1+i t )- t DB x q x+t ]/p x+t

GAAP Reserves Purpose: To decide the value of the insurance company Use realistic assumptions –Realistic interest rate –Lower mortality rate –Partial deferral of acquisition cost Results in lower initial expenses and higher profits

Components of GAAP Rreserves Two major components: benefit reserves, and expense reserves Benefit reserves –Exclude all expenses not related to benefit payouts –Grades into t V x in n years Deferred acquisition expense reserves –Exclude all benefits –If amortized over n years, then 0 profit means n AS x = 0 Assumptions are more conservative than pricing

Gross Premium Reserves Equal to PV(future benefits and expenses) – PV(future premium) Reserve formula uses 100% of gross premium Much deferral of acquisition cost May produce low first year reserve Front-end loading the earnings This is minimum reserve to meet future obligations

Uses of the Gross Premium Reserves Used to set gross premium Represents the minimum reserve to meet future obligations Test adequacy of reserve Test whether deferred acquisition cost can be recovered Determine PV(future profit): good if < t V x

Minimum Required Capital Capital =equity=surplus = assets – liabilities Need positive required capital to withstand possible risks on –Asset default –Insurance –Interest rate –Interest spread –Other Typical insurance company targets –250% of minimum legal required surplus –Be 99% sure of staying solvent according to model

Asset Default Risk Permanent loss in value, e.g. hold bond issued by company which goes bankrupt Adjustment for asset default probabilities –Estimate default probability: say 0.3% for A bonds –Estimate value loss on default bond: say 50% –Subtract 0.15% (=.5 x 0.3%) from investment return Asset default factors –May be 2 x default probability for each asset –For total portfolio, use weighted average of factors –Asset default risk = asset default factor x ( solvency reserve – policy loan)

Insurance Risk Risk that actual claims worse than pricing assumptions for: –Mortality –Morbidity –Persistency –Expenses –Investment income Size of random fluctuations are lower for larger companies

Mortality, Morbidity, Persistency Risks Mortality risk = mortality error x (death benefit – solvency reserve) Morbidity risk = morbidity error x (disability benefit – solvency reserve) Persistency risk = lapse rate error x (cash surrender value – solvency reserve)

Interest Rate Risk Policies lapse when interest rate increases –Policy holders cash policies to invest elsewhere –Insurance company sells bond to pay cash value –Big loss if invested long for good credited rates –Match durations of investments and liabilities –Interest rate risk factors depends withdrawal penalties charged Trouble raising cash to pay claims Interest rate risk = interest risk factor x (solvency reserve – policy loan)

Interest Spread Risk Insurance company fails to achieve pricing interest spread ( earned interest – credited) –Poor coordination: pricing, investment, administration –Guarantee interest higher than actual return –No good investment opportunities –Market changes –Minimum interest guarantee set too high: competitive Interest spread risk = interest spread factor x (solvency reserve – policy loan)

Other Risks Other risks include: –Mispricing –Lawsuits –Tax changes –Adverse publicity followed by lapses –Accounting standard changes –Inflation or expense increase due to regulations –Poor management –Fraud Other risks = other risk factor x premium

Impact of Required Capital Required capital = [asset default risk + mortality risk + morbidity risk + interest rate risk + interest spread risk + other risk] / (1 – asset default factor) Required capital cannot be distributed as dividend May invest the assets backing the required capital more aggressively