Portfolio Risk Analysis
Wednesday, August 13, 2008Concept Details
Definitions
| VaR | Value at Risk shows how much of a portfolio's current value (NPV) is expected to change over a given time interval (here: 10 days) at a defined confidence level (here: 99%); |
|---|---|
| CFaR | Cash Flow at Risk shows how much of a portfolio's interest cash flows are expected to change over a given time interval (here: 10 days) at a defined confidence level (here: 99%); |
| current value (NPV) | portfolio or single instrument values at the date in question (representing discounted nominal values and interest cash flows); |
| simulated worst case scenario | portfolio value/ portfolio interest cash flows representing the 1% percentile by Monte Carlo simulation i.e. the 100-th worst of 10 000 scenarios; |
| 100 bps up/down scenario | scenario in which interest curve moves up/ down 1%; |
| single instrument VaR | each instrument's stand-alone value/ interest cash flows, i.e. not taking into account correlations between instruments; |
| marginal VaR | VaR without selected instrument(s); risk measure that shows how much risk increases (+) / decreases (-), if the instrument is eliminated from the portfolio; |
| key rate sensitivity | sensitivity to a change of any interest rate level on the yield curve, assuming all other rates are constant; |
| IRS | Interest Rate Swap |
The single instrument VaR/CFaR is calculated based on an isolated view of each individual loan and derivative instrument, while portfolio VaR/CFaR also considers correlations between instruments. The former represents risk based on consideration of a single instrument alone; the latter gives an aggregated risk measure. Single instrument VaR/CFaR uses different worst case scenario curves for each instrument. At the same time portfolio VaR/CFaR applies only one worst case curve for the whole portfolio. Note that total single instrument VaR/CFaR is a substantially larger value than total portfolio VaR/CFaR.
Table 1. Portfolio 10-day Value at Risk (at 99% confidence level)
| Instrument | Current value (NPV) | Single instrument 's worst case scenario value | Single instrument VaR | Portfolio VaR |
|---|---|---|---|---|
| loan 13y quarterly 3m Euribor (amortising) | -78 592 527 | -78 893 136 | -300 609 | |
| loan 15y semi-annually 6m Euribor (amortising) | -103 664 793 | -103 832 848 | -168 055 | |
| loan 11y quarterly 3m Euribor (amortising) | -66 240 777 | -66 739 434 | -498 656 | |
| loan 9y semi-annually 6m Euribor (amortising) | -44 282 797 | -44 615 146 | -332 349 | |
| loan 6y quarterly 3m Euribor (amortising) | -233 413 362 | -233 680 875 | -267 512 | |
| loan 13y semi-annually 6m Euribor (amortising) | -13 222 440 | -13 242 724 | -20 284 | |
| total loans | -539 416 697 | -541 004 163 | -1 587 466 | -1 058 310 |
| EUR IRS 6y @3.8% semi-annually | 2 732 564 | 1 974 755 | -757 809 | |
| EUR IRS 8y @4.5% semi-annually | 2 476 700 | 1 711 614 | -765 085 | |
| total derivatives | 5 209 264 | 3 686 369 | -1 522 894 | -1 015 263 |
| total | -534 207 433 | -537 317 793 | -3 110 360 | -2 073 573 |
Table 2. Portfolio 10-day Cash Flow at Risk (at 99% confidence level)
| Instrument | Sum of interest cash flows | Single instrument 's worst case scenario value | Single instrument CFaR | Portfolio CFaR |
|---|---|---|---|---|
| loan 13y quarterly 3m Euribor (amortizing) | -25 827 045 | -27 412 639 | -792 797 | |
| loan 15y semiannually 6m Euribor (amortizing) | -49 812 260 | -51 774 739 | -490 620 | |
| loan 11y quarterly 3m Euribor (amortizing) | -21 066 642 | -22 466 053 | -233 235 | |
| loan 9y semi-annually 6m Euribor (amortizing) | -14 191 807 | -15 124 748 | -116 618 | |
| loan 6y quarterly 3m Euribor (amortizing) | -36 725 221 | -39 428 704 | -270 348 | |
| loan 13y seminannually 6m Euribor (amortizing) | -673 920 | -755 118 | -6 766 | |
| total loans | -148 296 896 | -156 961 999 | -8 665 103 | -5 776 735 |
| EUR IRS 6y @3.8% semiannually | 2 863 782 | 2 033 820 | -76 157 | |
| EUR IRS 8y @4.5% seminannually | 2 594 449 | 1 758 880 | -57 819 | |
| total derivatives | 5 458 231 | 3 792 700 | -1 665 531 | -1 110 354 |
| total | -142 838 665 | -153 169 299 | -10 330 634 | -6 887 089 |
The charts below show the results of a Monte Carlo simulation that models interest rate yield curves over a period of 10 days using 10 000 simulations. The histograms are a good way of describing VaR or CFaR measures. The sums of interest cash flows (Chart 1) and portfolio values (Chart 2) are calculated according to the modelled interest yield curves.
Chart 3 represents the interest yield curves used to calculate portfolio VaR and CFaR. Note that 100 bps up or down movements are quite extreme shifts in interest yield curves in 10 days.
100 bps up/ down scenarios provide a simple comparison with VaR and CFaR. Interest yield curve dynamics are often relatively complex and entail more than just yield curve shifts up and down.
Table 3. Portfolio value at different scenarios
| Loans | Derivatives | Total | |
|---|---|---|---|
| Current value (NPV) | -539 416 697 | 5 209 264 | -534 207 433 |
| 100 bps up scenario | -541 116 222 | 10 227 204 | -530 889 018 |
| 100 bps down scenario | -538 898 499 | 866 151 | -538 032 349 |
| simulated worst case scenario | -540 475 007 | 4 194 001 | -536 281 006 |
Table 4. Portfolio 10-day Value at Risk (at 99% confidence level) vs stress test results
| Loans | Derivatives | Total | |
|---|---|---|---|
| Stress test: 100 bps up | -1 699 525 | 5 017 940 | 3 318 415 |
| Stress test: 100 bps down | 518 197 | -4 343 113 | -3 824 916 |
| VaR* | -1 058 310 | -1 015 263 | -2 073 573 |
Table 5. Portfolio interest cash flows at different scenarios
| Loans | Derivatives | Total | |
|---|---|---|---|
| Sum of interest cash flows | -148 296 896 | 5 458 231 | -142 838 665 |
| 100 bps up scenario | -176 982 260 | 10 797 145 | -166 185 115 |
| 100 bps down scenario | -140 303 393 | 1 684 425 | -138 618 968 |
| simulated worst case scenario | -154 073 632 | 4 347 877 | -149 725 754 |
Table 6. Portfolio 10-day Cash Flow at Risk (at 99% confidence level) vs stress test results
| Loans | Derivatives | Total | |
|---|---|---|---|
| Stress test: 100 bps up | -28 685 364 | 5 338 914 | -23 346 450 |
| Stress test: 100 bps down | 7 993 504 | -3 773 806 | 4 219 697 |
| CFaR* | -5 776 735 | -1 110 354 | -6 887 089 |
Table 7. Portfolio 10-day timebased Cash Flow at Risk (at 99% confidence level)
| Fiscal year | Interest cash flows | Simulated worst case scenario | CFaR | %CFaR |
|---|---|---|---|---|
| 2009 | -11 614 572 | -12 199 690 | -585 118 | 5,0% |
| 2010 | -11 878 479 | -13 147 987 | -1 269 508 | 10,7% |
| 2011 | -12 739 093 | -14 509 754 | -1 770 661 | 13,9% |
| 2012 | -13 925 347 | -15 959 452 | -2 034 105 | 14,6% |
| 2013 | -11 935 742 | -12 853 720 | -917 979 | 7,7% |
| 2014 | -11 891 111 | -12 512 955 | -621 844 | 5,2% |
| 2015 | -9 601 158 | -10 104 292 | -503 135 | 5,2% |
| 2016 | -7 611 097 | -8 003 722 | -392 625 | 5,2% |
