1. Fall-01 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html FIBI Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html DAC

2. Zvi WienerDAC slide 2 Life Insurance yearly contribution 10,000 NIS yearly risk premium 2,000 NIS first year agent’s commission 3,000 NIS promised accumulation rate 8,000 NIS/yr After the first payment there is a problem of insufficient funds. 8,000 NIS are promised (with all profits) and only 5,000 NIS arrived.

3. Zvi WienerDAC slide 3 10,000 NIS Risk 2,000 NIS Client’s 8,000 NIS Agent 3,000 NIS insufficient funds if the client leaves insufficient profits

4. Zvi WienerDAC slide 4 Risk measurement The reason to enter this transaction is because of the expected future profits. Assume that the program is for 15 years and the probability of leaving such a program is . Fees are – 0.6% of the portfolio value each year – 15% real profit participation

5. Zvi WienerDAC slide 5 Obligations The most important question is what are the obligations? The Ministry of Finance should decide Transparent to a client Accounted as a loan

6. Zvi WienerDAC slide 6 One year example Assume that the program is for one year only and there is no possibility to stop payments before the end. Initial payment P 0, fees lost L 0, fixed fee a% of the final value P 1, participation fee b% of real profits (we ignore real). Investment policy TA-25 (MAOF).

7. Zvi WienerDAC slide 7 Liabilities (no actual loan) Assets (no actual loan)

8. Zvi WienerDAC slide 8 Total=Assets-Liabilities Fair value

9. Zvi WienerDAC slide 9 Liabilities (actual loan) Assets (actual loan)

10. Zvi WienerDAC slide 10 Total=Assets-Liabilities (loan)

11. Zvi WienerDAC slide 11 2 years liabilities (no actual loan) 2 years assets (no actual loan) In reality the situation is even better for the insurer, since profit participation fees once taken are never returned (path dependence).

12. Zvi WienerDAC slide 12 2 years fair value, no loan

13. Zvi WienerDAC slide 13 2 years liabilities (with a loan) 2 years assets (with a loan)

14. Zvi WienerDAC slide 14 Stock index Profit No loan With a loan 10 years, L 0 =7%

15. Zvi WienerDAC slide 15 Partial loan - portion q Theoretically q can be negative.

16. Zvi WienerDAC slide 16 Mixed portfolio When the investment portfolio is a mix one should analyze it in a similar manner. Important: an option on a portfolio is less valuable than a portfolio of options. Another risk factor - leaving rate should be accounted for by taking actuarial tables as leaving rate.

17. Zvi WienerDAC slide 17 Conclusions It is a reasonable risk management policy not to take a loan against DAC. Up to some optimal point it creates a useful hedge to other assets (call options and shares) of the firm. Intuitively DAC is good when the stock market performs badly and profit participation is valueless. DAC performs bad when the market performs well.