raw trans data
Column1 Column2 Column3 Column4 Column5 Column6 Column7 Column8 Column9 Column10
AAA 87.37 8.63 0.58 0.04 0.17 0.04 0.04 0.00 3.14
AA 0.51 87.24 7.39 0.57 0.08 0.10 0.03 0.03 4.06
A 0.04 1.69 88.23 5.26 0.36 0.14 0.03 0.07 4.18
BBB 0.01 0.11 3.48 86.48 3.62 0.56 0.10 0.21 5.43
BB 0.02 0.04 0.17 4.74 77.59 7.45 0.56 0.73 8.70
B 0.00 0.03 0.10 0.18 4.42 75.65 4.64 3.52 11.45
CCC/C 0.00 0.00 0.16 0.23 0.66 11.72 44.06 29.14 14.02
Derivation
Options for handling the NRs that we discussed Average One-Year Letter Rating Migration Rates, 1981-2018
A) spread NR evenly From/to AAA AA A BBB BB B CCC D NR
B) divide each percentage by the column M number AAA 87.37% 8.63% 0.58% 0.04% 0.17% 0.04% 0.04% 0.00% 3.14% 96.87%
i.e. remove them from the cohort AA 0.51% 87.24% 7.39% 0.57% 0.08% 0.10% 0.03% 0.03% 4.06% 95.95%
i.e. spread it out proportionately A 0.04% 1.69% 88.23% 5.26% 0.36% 0.14% 0.03% 0.07% 4.18% 95.82%
C) increase proportionately, but only for downgrade BBB 0.01% 0.11% 3.48% 86.48% 3.62% 0.56% 0.10% 0.21% 5.43% 94.57%
or only for speculative grade or lower BB 0.02% 0.04% 0.17% 4.74% 77.59% 7.45% 0.56% 0.73% 8.70% 91.30%
D) put them all in default B 0.00% 0.03% 0.10% 0.18% 4.42% 75.65% 4.64% 3.52% 11.45% 88.54%
E) half of (B) and half of (C) or (D) CCC 0.00% 0.00% 0.16% 0.23% 0.66% 11.72% 44.06% 29.14% 14.02% 85.97%
Matrix that we left off with in class 0.00%
Options for making adjustments From/to AAA AA A BBB BB B CCC D Check
A) increase entry by geometric average along row AAA 90.18% 8.91% 0.60% 0.04% 0.18% 0.04% 0.04% 0.01% 100.00%
B) extrapolate from main diagonal and continue pattern AA 0.53% 90.92% 7.70% 0.59% 0.08% 0.10% 0.03% 0.03% 100.00%
– linear regression A 0.04% 1.76% 92.08% 5.49% 0.38% 0.15% 0.03% 0.07% 100.00%
– log linear/geometric/proportional BBB 0.01% 0.12% 3.68% 91.45% 3.83% 0.59% 0.11% 0.22% 100.00%
C) interpolate/extrapolate along a diagonal BB 0.02% 0.04% 0.19% 5.19% 84.98% 8.16% 0.61% 0.80% 100.00%
D) do nothing B 0.00% 0.03% 0.11% 0.20% 4.99% 85.44% 5.24% 3.98% 100.00%
CCC 0.00% 0.00% 0.19% 0.27% 0.77% 13.63% 51.25% 33.90% 100.00%
Then to rebalance each row Your proposed matrix – Don’t change the blue main diagonal entries. Those automatically adjust to ensure rows add to 100% (option (B) from at left)
A) distribute the change by taking away from the neighbours From/to AAA AA A BBB BB B CCC D Check
B) take it from the diagonal AAA 90.18% 8.91% 0.60% 0.04% 0.18% 0.04% 0.04% 0.01% 100.00%
AA 0.53% 90.92% 7.70% 0.59% 0.08% 0.10% 0.03% 0.03% 100.00%
A 0.04% 1.76% 92.08% 5.49% 0.38% 0.15% 0.03% 0.07% 100.00%
BBB 0.01% 0.12% 3.68% 91.45% 3.83% 0.59% 0.11% 0.22% 100.00%
BB 0.02% 0.04% 0.19% 5.19% 84.98% 8.16% 0.61% 0.80% 100.00%
B 0.00% 0.03% 0.11% 0.20% 4.99% 85.44% 5.24% 3.98% 100.00%
CCC 0.00% 0.00% 0.19% 0.27% 0.77% 13.63% 51.25% 33.90% 100.00%
Graph of downgrades
Downgrades but not default
Log of percentage From rating Space them for the graph and interpolate
Number of notches down 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11
1 – 2.42 – 2.56 – 2.90 – 3.26 – 2.51 – 2.95 1 -2.4181253683 -2.4909124279 -2.5636994875 -2.7330199461 -2.9023404047 -3.0826033399 -3.2628662752 -2.8844015152 -2.5059367552 -2.7273384081 -2.9487400611
2 – 5.12 – 5.13 – 5.58 – 5.13 – 5.09 2 -5.1180970489 -5.1220215947 -5.1259461406 -5.3550344098 -5.584122679 -5.3566407376 -5.1291587963 -5.1115640396 -5.0939692829
3 – 7.79 – 7.09 – 6.53 – 6.85 3 -7.7922456983 -7.4409007825 -7.0895558668 -6.8090700773 -6.5285842878 -6.6902548409 -6.851925394
4 – 6.35 – 6.87 – 8.07 4 -6.3453267154 -6.6058695154 -6.8664123154 -7.4677208221 -8.0690293288
5 – 7.79 – 8.07 5 -7.7922456983 -7.931315409 -8.0703851198
6 – 7.79 6 -7.7922456983
Log of percent for notches downgrade
1 1 2 3 4 5 6 7 8 9 10 11 -2.4181253683429569 -2.4909124279182775 -2.5636994874935986 -2.7330199460994784 -2.9023404047053578 -3.0826033399475494 -3.262866275189741 -2.8844015151995981 -2.5059367552094547 -2.7273384081376433 -2.9487400610658314 2 1 2 3 4 5 6 7 8 9 10 11 -5.1180970488799655 -5.1220215947436074 -5.1259461406072502 -5.3550344097971037 -5.5841226789869571 -5.3566407376336596 -5.1291587962803629 -5.1115640395671136 -5.0939692828538643 3 1 2 3 4 5 6 7 8 9 10 11 -7.7922456983064938 -7.4409007825342286 -7.0895558667619643 -6.8090700772948871 -6.5285842878278091 -6.6902548409246378 -6.8519253940214666 4 1 2 3 4 5 6 7 8 9 10 11 -6.3453267153701685 -6.6058695154089619 -6.8664123154477545 -7.4677208221113567 -8.0690293287749579 5 1 2 3 4 5 6 7 8 9 10 11 -7.7922456983064938 -7.9313154090400921 -8.0703851197736913 6 1 2 3 4 5 6 7 8 9 10 11 -7.7922456983064938
Graph of upgrades
Upgrades
Log of percentage From rating Space them for the graph and interpolate
Number of notches up 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11
1 -523.7% -403.8% -330.2% -295.8% -299.7% -199.3% 1 -5.2371717757 -4.6374573391 -4.0377429025 -3.6700254549 -3.3023080072 -3.1302108296 -2.9581136519 -2.9777141916 -2.9973147312 -2.4950081726 -1.992701614
2 -778.1% -675.7% -628.6% -619.8% -487.0% 2 -7.7813472563 -7.2689812353 -6.7566152142 -6.5213614219 -6.2861076295 -6.2421802425 -6.1982528554 -5.5338833488 -4.8695138421
3 -915.5% -773.3% -678.6% -592.4% 3 -9.154510487 -8.4437685497 -7.7330266125 -7.2595330664 -6.7860395203 -6.3548569443 -5.9236743682
4 -842.6% -799.0% -628.7% 4 -8.426173793 -8.2080930588 -7.9900123246 -7.1382960933 -6.2865798619
5 ERROR:#NUM! ERROR:#NUM! 5 ERROR:#NUM! ERROR:#NUM! ERROR:#NUM!
6 ERROR:#NUM! 6 ERROR:#NUM!
Log of percent for notches upgrade
1 1 2 3 4 5 6 7 8 9 10 11 -5.2371717757174743 -4.6374573391187344 -4.0377429025199945 -3.6700254548805162 -3.302308007241038 -3.1302108295674875 -2.9581136518939375 -2.9777141915541629 -2.9973147312143884 -2.495008172625937 -1.992701614037486 2 1 2 3 4 5 6 7 8 9 10 11 -7.7813472563231771 -7.268981235270159 -6.7566152142171418 -6.5213614218749694 -6.2861076295327978 -6.2421802424643591 -6.1982528553959213 -5.5338833487719699 -4.8695138421480184 3 1 2 3 4 5 6 7 8 9 10 11 -9.1545104870155125 -8.4437685497423178 -7.7330266124691232 -7.2595330663835824 -6.7860395202980408 -6.3548569442716678 -5.9236743682452948 4 1 2 3 4 5 6 7 8 9 10 11 -8.4261737930290685 -8.2080930588265222 -7.9900123246239767 -7.1382960932793198 -6.2865798619346629 5 1 2 3 4 5 6 7 8 9 10 11 0 0 0 6 1 2 3 4 5 6 7 8 9 10 11 0