1. © Brammertz Consulting, 20111Date: 09.10.2015 Unified Financial Analysis Risk & Finance Lab Chapter 10: Sensitivity Willi Brammertz / Ioannis Akkizidis

2. © Brammertz Consulting, 20112Date: 09.10.2015 Sensitivity

3. © Brammertz Consulting, 20113Date: 09.10.2015 Sensitivity > General defintiony > Applies (in our defintion) also to higher order derivations > β generally market value

4. © Brammertz Consulting, 20114Date: 09.10.2015 Where analytical sensitivities work else

5. © Brammertz Consulting, 20115Date: 09.10.2015 Why bother with analytical solutions? > Calculation efficiency > Wide application (there are sufficient relevant cases) > Basis for many limits

6. © Brammertz Consulting, 20116Date: 09.10.2015 Interest rate sensitivity In the simplest case it is the $Duration measure: (-t*CF(t)*e^(-rt))

7. © Brammertz Consulting, 20117Date: 09.10.2015 Duration: Intuitive interpretation > Average time to repricing > Average gap > Immunization horizon

8. © Brammertz Consulting, 20118Date: 09.10.2015 Hedge Investment Horizon: point in time in which the value of a portfolio can be (almost) 100% achieved. Value Δ Gain/loss on reinvestments of CFL Time Duration Duration: Immunization horizon

9. © Brammertz Consulting, 20119Date: 09.10.2015 Key Rate Duration

10. © Brammertz Consulting, 201110Date: 09.10.2015 A simple example > A principal at maturity contract > Date of analysis: 31.12.00 > ValueDate: 1.1.01 > MaturityDate: 1.1.03 > Interest payment frequency: 1Q, regular > Notional: 1000 (asset) > Interest rate: 10%, 30/360 > Rate reset cycle: 1Y, regular > Rate spread: 0% > Events and results > Liquidity? > Sensitivity?

11. © Brammertz Consulting, 201111Date: 09.10.2015 Intuitive explanation Fixed cash flows Simple discounting applies Variable cash flows No spread What is its value? 1 1+r Interest calc 1+r Discounting

12. © Brammertz Consulting, 201112Date: 09.10.2015 Complex example

13. © Brammertz Consulting, 201113Date: 09.10.2015 Derivation of Table 10.4 Graphical representation t 0 1.1.00 t 1 1.4.00 t 2 1.7.00 t 3 1.10.00 YC(t 0 ) Rate reset ƒ(t 0, t 1, t 3 ) Discounting r(t 0, t 1 ) Discounting r(t 0, t 2 ) Point of analysis

14. © Brammertz Consulting, 201114Date: 09.10.2015 Sensitivity vector Effect of repricing mismatch

15. © Brammertz Consulting, 201115Date: 09.10.2015 Sensitivity vs. liquidity gap: Same example as chapter 8

16. © Brammertz Consulting, 201116Date: 09.10.2015 Sensitivity vs. liquidity > Liquidity: Sum the liquidity line per time bucket > Sensitivity: Sum the ZES line per time bucket

17. © Brammertz Consulting, 201117Date: 09.10.2015 Intuitive interpretation of ZES > We decompose everything into single expected cash flows > A single cash flow is equivalent to a zero bond > Sensitivity of a single zero bond is -t*CF(t)*e^(-rt) > Therefore we need to know from the contract > t > CF(t) > ZES shows this information > r comes from the market information > ZES is additive through all financial instruments!

18. © Brammertz Consulting, 201118Date: 09.10.2015 Other market sensitivity > FX > Stocks > Both derivable from ZES plus discounting information

19. © Brammertz Consulting, 201119Date: 09.10.2015 Credit exposure

20. © Brammertz Consulting, 201120Date: 09.10.2015 Current exposure: Example

21. © Brammertz Consulting, 201121Date: 09.10.2015 Current and potential exposure (taking future potential changes into account)

22. © Brammertz Consulting, 201122Date: 09.10.2015 Calculation of potential exposure

23. © Brammertz Consulting, 201123Date: 09.10.2015 Potential exposure via add-ons > Add-ons are pre-established (canned) volatility adjustments > Based on standard sensitivity buckets

24. © Brammertz Consulting, 201124Date: 09.10.2015 Basel II Haircuts > Haircuts: Deductions from collateral value > Similar function as Add-ons > Language is imprecise

25. © Brammertz Consulting, 201125Date: 09.10.2015 Mortality sensitivity Simple example 1 year life insurance

26. © Brammertz Consulting, 201126Date: 09.10.2015 Limits > Risk Limits (Chapter 11) > Sensitivity limits > Gap limits > First derivation limits (Interest rate, FX, Stock etc.) > Other limit types > Volume (book value, nominal value, market value) > Loss limits

27. © Brammertz Consulting, 201127Date: 09.10.2015 Gap limits

28. © Brammertz Consulting, 201128Date: 09.10.2015 Limit setting