2. ALM and pricing of life insurance products Vladimír Krejčí Prague, 1 April 2004

3. Main tasks of ALM  Investment strategy  Product design and pricing  Capital and risk management

4. Product design and pricing  Design  Passing the investment risk to clients  Possibility to hedge the risk borne by shareholders  Pricing (profit testing)  Reasonable assumptions about  Future yields  Discount rate

5. Let‘s start – question 1  Does profitability of a life insurance product depend on investment strategy?

6. Example 1  Single premium endowment without profit sharing  Policy term 10 years  Zero mortality and lapse rates  Let‘s assume 2 scenarios of investments  a) 10Y government zero coupon bond  b) 10Y corporate zero coupon bond

7. Traditional DCF approach  Let‘s measure profitability in the form of Value Added by New Business  Different investment return assumptions  a) VANB = EUR 10  b) VANB = EUR 15  RDR increased by 2% in b)  a) VANB = EUR 10  b) VANB = EUR 12  Possibility to increase allocated capital

8. Alternative approach  The same cashflows in the first day  Premium paid, expenses  After the first day:  Liabilities: the same in both a) and b) (technical reserves of EUR 100)  Assets:  a) EUR 100 in government bond  b) EUR 100 in corporate bond

9. Alternative approach In other words:

10. „We do not invest risk free and therefore our yields will be higher than risk free.“  Risky investment strategy increases the profit potential  You can make more profits if you are good (succesful, lucky)  But it increases the loss potential as well  „…our yields will be probably higher…“  => it does not increase market value

11. Does profitability of this life insurance product depend on investment strategy?  Traditional DCF  YES  Alternative approach  NO  What approach is more appropriate?

12. Question 2  Is market value the appropriate measure?  Why do we have different PV?  Information, investment horizon, risk attitude  What decisions are we willing to base on our PV?

13. Credit risk  Corporate bond from the example 1 valued via DCF  Expected future cashflow  Notional amount * (1 - probability of default*(1-recovery rate))  We could also allow for cost of capital  PV = EUR 102,5  Isn‘t this PV the right one from our shareholders‘ point of view?

14. Why is the market price different?  What factors we did not allow for?  Market can expect different probability of default  Potential downgrades  Volatility of credit spreads  Market can have different cost of capital  Investors are risk averse

15. How did the market arrive at the price?  Supply / Demand  consensus of market participants  Who are market participants?  Banks, insurance companies, investment funds, …  Komercni banka, CSOB, Ceska sporitelna, Ceska pojistovna, ING, Deutsche bank, Morgan Stanley, Meril Lynch, Bank of America, Credit Lyonais, …  Very well educated, trained and experienced teams  Very well informed teams – equally informed  Efficient market

16. Stock markets  Forward on stocks – what is the forward price?  Expected yield (arbitrage)  Risk free yield  Stock returns over a long horizon  Sentiment, trends, bull/bear markets

17. Interest rates risk, duration mismatch  What do we estimate?  Macroeconomic development  Decisions of billions of people all around the world  Estimate of these decisions by thousands of analysts and market players  Sentiment, media, psychology, hedging  Time horizon

18. Why is our PV different than market value?  Do we have better know how?  Are we better informed?  Are the markets efficient?  Do we really have arguments for the PV we have calculated?

19. Why is our PV different than market value?  We do not have better information, so …  …our shareholders have to be differently risk averse than the market…  do we know their utility function that well?  …or not interested in short term results  what about if the investment strategy reports high losses and we say these are only temporary?

20. Is market value the appropriate measure for us?  What decision are we willing to base on our PV?

21. What decisions are we willing to base on our PV?  Purchase of particular security  Investment strategy  Liability product design and pricing

22. Summary  Is market value the appropriate measure for valuation of life insurance liabilities?  Does profitability of this life insurance product depend on investment strategy?

23. A practical problem

24. Profit in life insurance is a small sum of  Large positive numbers  Premium income, investment income  Large negative numbers  Claims, expenses  It is very difficult to adjust the discount rate to particular investment assumptions

25. The problem – cont. The smaller the profit, the bigger the problem  Low interest rate environment  Lower margins are relatively more sensitive to changes in investment income  Products with profit sharing  Change in profit sharing  Change in company‘s margin  Do we have market evidence for use of the traditional EV in M&A?

26. Suggested solution  EV with risk free investment returns and risk free discount  Do we know to evaluate the mortality, lapse, expense, … risks?  Risk free EV can be some comparative basis – the traditional EV should not be higher (negative value of mortality, lapse, expense, … risks)

27. Suggestion 2  EV with cashflow specific discount rates

28. Products with profit sharing  Short introduction

29. What about products with profit sharing?  Risky investment strategy increases the profitability (compared to risk free strategy) if you pass to clients more risks and less profits  If you pass to clients more profits than risks then:  The riskier investments, the lower profitability

30. What about products with profit sharing?  How to compare the passed profits and risks?  Contingent claims valuation methods  Low interest rate environment  Very low expected profit sharing rates  Limited space for passing the risk (= losses)  Simple estimate on passing more profits/risk may be possible