-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathDedication.lst
1137 lines (890 loc) · 40.1 KB
/
Dedication.lst
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
GAMS 24.8.5 r61358 Released May 10, 2017 WEX-WEI x86 64bit/MS Windows 10/29/17 22:16:05 Page 1
Dedication models
C o m p i l a t i o n
2
3 * Dedication.gms: Dedication models.
4
5 SET Time Time periods /2016 * 2039/;
6
7 ALIAS (Time, t, t1, t2);
8
9 SCALARS
10 Now 'Current year'
11 Horizon 'End of the Horizon';
12
13 Now = 2016;
14 Horizon = CARD(t)-1;
15
16 PARAMETER
17 tau(t) 'Time in years';
18
19 * Note: time starts from 0
20
21 tau(t) = ORD(t)-1;
22
23 SET
24 Bonds Bonds universe
25 /DK0009923641, DK0009923484, DK0009921942,
26 DK0009922403, DK0009922676, DK0009922916,
27 DK0009918138, DK0009923567, DK0009923054,
28 DK0009923138, DK0009922320/;
29
30
31 ALIAS(Bonds, i);
32
33 SCALAR
34 spread 'Borrowing spread over the reinvestment rate';
35
36 PARAMETERS
37 Price(i) 'Bond prices'
38 Coupon(i) 'Coupons'
39 Maturity(i) 'Maturities'
40 Liability(t) 'Stream of liabilities'
41 rf(t) 'Reinvestment rates'
42 F(t, i) 'Cashflows';
43
44 * Bond data. Prices, coupons and maturities from the Danish market
45
INCLUDE C:\Users\Leonard Lee\OneDrive\Documents\University Files\Core Modules
\Math & Stats Modules\Year 3\Sem 1(SEP)\Optimization in Finance\Proje
ct\BondData.inc
47 TABLE BondData(i,*)
48 Price Maturity Coupon
49 DK0009923641 102.35 2020 0.25
50 DK0009923484 101.02 2018 0.25
51 DK0009921942 100.61 2017 4
52 DK0009922403 109.89 2019 4
53 DK0009922676 113.95 2021 3
54 DK0009922916 107.63 2023 0.1
55 DK0009918138 149.49 2024 7
56 DK0009923567 99.71 2027 0.5
57 DK0009923054 109.46 2023 1.5
58 DK0009923138 112.39 2025 1.75
59 DK0009922320 168.26 2039 4.5;
60
61 * Copy/transform data. Note division by 100 to get unit data, and
62 * subtraction of "Now" from Maturity date (so consistent with tau):
63
64 Price(i) = BondData(i,"Price")/100;
65 Coupon(i) = BondData(i,"Coupon")/100;
66 Maturity(i) = BondData(i,"Maturity") - Now;
67
68 * Calculate the ex-coupon cashflow of Bond i in year t:
69
70 F(t,i) = 1$(tau(t) = Maturity(i))
71 + coupon(i) $ (tau(t) <= Maturity(i) AND tau(t) > 0);
72
73 * For simplicity, we set the short term rate to be 0.03 in each period
74
75 rf(t) = -0.015;
76 spread = 0.05;
77
78 DISPLAY F;
79
80 PARAMETER
81 Liability(t) Liabilities
82 /2016 = 1000000000, 2017 = 1000000000, 2018 = 1000000000,
83 2019 = 1000000000, 2020 = 1000000000, 2021 = 1000000000,
84 2022 = 1000000000, 2023 = 1000000000, 2024 = 1000000000,
85 2025 = 1000000000, 2026 = 1000000000, 2027 = 1000000000,
86 2028 = 1000000000, 2029 = 1000000000, 2030 = 1000000000,
87 2031 = 1000000000, 2032 = 1000000000, 2033 = 1000000000,
88 2034 = 1000000000, 2035 = 1000000000, 2036 = 1000000000,
89 2037 = 1000000000, 2038 = 1000000000, 2039 = 1000000000/;
90
91 POSITIVE VARIABLES
92 x(i) 'Face value purchased'
93 surplus(t) 'Amount of money reinvested'
94 borrow(t) 'Amount of money borrowed'
95 ;
96
97
98 VARIABLE
99 v0 'Upfront investment'
100 VplusFinal 'Final value of vplus to be maximized in model 2'
101 ;
102
103 SCALAR b0 'fixed budget';
104
105 EQUATION
106 Initial(t) 'Initialization of the investment'
107 Initial2(t) 'Initialization of the investment in model 2'
108 CashFlowCon(t) 'Equations defining the cashflow balance'
109 Final(t) 'Horison constraint'
110 FinalSurplus 'Final surplus to be maximized in model 2'
111 ;
112
113 Initial(t)$(tau(t)=0).. v0 =E= SUM(i, Price(i) * x(i)) + surplus(t) -
borrow(t);
114
115 Initial2(t)$(tau(t)=0).. b0 =E= SUM(i, Price(i) * x(i)) + surplus(t)
- borrow(t);
116
117
118 CashFlowCon(t)$(tau(t)>0).. SUM(i, F(t,i) * x(i) ) + borrow(t) + ( ( 1 +
rf(t-1) ) * surplus(t-1) ) =E=
119 surplus(t) + Liability(t) + ( 1 + rf(t-1) +
spread ) * borrow(t-1);
120
121 Final(t)$(tau(t)=Horizon).. borrow(t) =E= 0;
122
123 FinalSurplus.. VplusFinal =E= sum(t$(ord(t)=card(t)), surplu
s(t) );
124
125
126 MODEL Dedication 'PFO Model 4.2.3' /Initial, CashFlowCon, Final/;
127
128 MODEL Dedication2 /Initial2, CashFlowCon, Final, FinalSurplus/
129
130 SOLVE Dedication MINIMIZING v0 USING LP;
131 DISPLAY v0.l, borrow.l, surplus.l, x.l;
132
133
134
135
136 * Simulation for different values of the reinvestment rate rf
137
138 SCALAR
139 ReinvRate reinvestment rate
140 SPR Spread;
141
142 *FILE DedicationHandle /"DedicationPortfolios.csv"/;
143
144 *DedicationHandle.pc = 5;
145
146 *PUT DedicationHandle;
147
148 *FOR ( ReinvRate = -0.04 to 0.02 by 0.005,
149
150 * rf(t) = ReinvRate;
151 * SPR = ReinvRate + 0.065;
152 * spread = SPR;
153
154 * SOLVE Dedication MINIMIZING v0 using LP;
155
156 * PUT "Reinvestment Rate","Inital Investments","Bond Names", "Bond Maturi
ties", "Coupons", "Present Value", "Spread"/;
157
158 * LOOP ( i,
159
160 * PUT ReinvRate:10:4,v0.l:10:4,i.tl,BondData(i,"Maturity"),Coupon(i),
(x.l(i)*Price(i)):10:4, SPR:10:4/;
161
162 * );
163
164 * PUT "Year", "Borrowed", "Surplus"/;
165
166 * LOOP ( t,
167
168 * PUT t.tl,(-borrow.l(t)):10:3,surplus.l(t):10:3/;
169
170 * );
171
172 *);
173
174
175
176
177 * Q6 Mismatch Generation(Dedication)
178
179 **Scenario 1
180 *PARAMETER r1(t)
181 */
182 *$ONDELIM
183 *$INCLUDE "SpotRates1.inc"
184 *$OFFDELIM
185 */;
186
187 *PARAMETERS
188 * PV(i) Present value of assets
189 * PV_Liab Present value of liability
190 * Mismatch Mismatch
191 * PVA(i) Present Value of Assets
192 *;
193
194 *PV(i) = SUM(t, F(t,i) / {1 + r1(t)}**(tau(t)) );
195 *PV_Liab = SUM(t, Liability(t) / {1 + r1(t)}**(tau(t)) );
196 *Mismatch = SUM(i, PV(i)*x.l(i)) - PV_Liab;
197 *PVA(i) = PV(i) * x.l(i);
198
199 *DISPLAY PV, PV_Liab, x.l, Mismatch;
200
201 *FILE Mismat /"Mismatch_Generation.csv"/;
202
203 *Mismat.pc = 5;
204
205 *PUT Mismat;
206
207 *PUT "Bonds","x(i)","PV(i)", "Present Value(assets)", "PV_Liab", "Mismatch
", "Mismatch Percent"/;
208
209 *LOOP (i,
210
211 * PUT i.tl,x(i):7:5,PV(i):7:5,PVA(i):7:5,0,0,0/;
212 *);
213
214 *PUTCLOSE Mismat;
215
216
217
218 * Extension of Dedication model
219
220 rf(t) = -0.015;
221 spread = 0.05;
222
223 PARAMETER r(t)
224 /
INCLUDE C:\Users\Leonard Lee\OneDrive\Documents\University Files\Core Modules
\Math & Stats Modules\Year 3\Sem 1(SEP)\Optimization in Finance\Proje
ct\SpotRates.inc
227 2017,0.0045
228 2018,0.0023
229 2019,0.0015
230 2020,0.0011
231 2021,0.0009
232 2022,0.0008
233 2023,0.0007
234 2024,0.0032
235 2025,0.0043
236 2026,0.0049
237 2027,0.0055
238 2028,0.0062
239 2029,0.0068
240 2030,0.0075
241 2031,0.0082
242 2032,0.0089
243 2033,0.0096
244 2034,0.0102
245 2035,0.0108
246 2036,0.0114
247 2037,0.0119
248 2038,0.0124
249 2039,0.0129
251 /;
252
253 PARAMETERS
254 PV(i) Present value of assets
255 PV_Liab Present value of liability
256 B_Mismatch Biggest Mismatch
257 PVA(i) Present Value of Assets
258 NPVA Net Present Value of Assets
259 ;
260
261 PV(i) = SUM(t, F(t,i) / {1 + r(t)}**(tau(t)) );
262 PV_Liab = SUM(t, Liability(t) / {1 + r(t)}**(tau(t)) );
263 B_Mismatch = PV_Liab - SUM(i, PV(i)*x.l(i));
264
265 VARIABLE
266 mm 'Mismatch'
267 z 'objvalue'
268 ;
269
270 EQUATION
271 MismatchU 'Asset Liabilities Mismatch upper bound'
272 MismatchL 'Asset Liabilities Mismtach lower bound'
273 Mismatchdef 'Mismatch Definition'
274 objfunc 'Objective Func'
275 ;
276
277 Mismatchdef.. mm =E= PV_Liab - SUM(i, PV(i)*x(i));
278 MismatchU.. mm =L= B_Mismatch;
279 MismatchL.. mm =G= 0;
280 objfunc.. z =E= mm + v0;
281
282 MODEL Dedicationext 'PFO Model 4.2.3' /Initial, CashFlowCon, Final, Mismat
chU, MismatchL, Mismatchdef,objfunc/;
283 SOLVE Dedicationext MINIMIZING z USING LP;
284
285 PVA(i) = PV(i) * x.l(i);
286 NPVA = SUM(i, PVA(i))
287
288 DISPLAY v0.l, borrow.l, surplus.l, x.l, mm.l, NPVA, PV_Liab;
289
290 *MismatchL 'Asset Liabitilies Mismatch lower bound'
291 *MismatchL.. mm =G= 0;
292
293 *FOR ( ReinvRate = -0.04 to 0.02 by 0.005,
294
295 * rf(t) = ReinvRate;
296 * SPR = ReinvRate + 0.07;
297 * spread = SPR;
298
299 * SOLVE Dedicationext MINIMIZING mm USING LP;
300
301 * DISPLAY v0.l, borrow.l, surplus.l, x.l, mm.l;
302
303 *);
GAMS 24.8.5 r61358 Released May 10, 2017 WEX-WEI x86 64bit/MS Windows 10/29/17 22:16:05 Page 2
Dedication models
Include File Summary
SEQ GLOBAL TYPE PARENT LOCAL FILENAME
1 1 INPUT 0 0 C:\Users\Leonard Lee\OneDrive\Document
s\University Files\Core Modules\Math &
Stats Modules\Year 3\Sem 1(SEP)\Optimi
zation in Finance\Project\Dedication.g
ms
2 46 INCLUDE 1 46 .C:\Users\Leonard Lee\OneDrive\Documen
ts\University Files\Core Modules\Math
& Stats Modules\Year 3\Sem 1(SEP)\Opt
imization in Finance\Project\BondData
.inc
3 226 INCLUDE 1 213 .C:\Users\Leonard Lee\OneDrive\Documen
ts\University Files\Core Modules\Math
& Stats Modules\Year 3\Sem 1(SEP)\Opt
imization in Finance\Project\SpotRate
s.inc
COMPILATION TIME = 0.000 SECONDS 3 MB 24.8.5 r61358 WEX-WEI
GAMS 24.8.5 r61358 Released May 10, 2017 WEX-WEI x86 64bit/MS Windows 10/29/17 22:16:05 Page 3
Dedication models
E x e c u t i o n
---- 78 PARAMETER F Cashflows
DK0009923~ DK0009923~ DK0009921~ DK0009922~ DK0009922~ DK0009922~
2017 0.002 0.002 1.040 0.040 0.030 0.001
2018 0.002 1.002 0.040 0.030 0.001
2019 0.002 1.040 0.030 0.001
2020 1.002 0.030 0.001
2021 1.030 0.001
2022 0.001
2023 1.001
+ DK0009918~ DK0009923~ DK0009923~ DK0009923~ DK0009922~
2017 0.070 0.005 0.015 0.018 0.045
2018 0.070 0.005 0.015 0.018 0.045
2019 0.070 0.005 0.015 0.018 0.045
2020 0.070 0.005 0.015 0.018 0.045
2021 0.070 0.005 0.015 0.018 0.045
2022 0.070 0.005 0.015 0.018 0.045
2023 0.070 0.005 1.015 0.018 0.045
2024 1.070 0.005 0.018 0.045
2025 0.005 1.018 0.045
2026 0.005 0.045
2027 1.005 0.045
2028 0.045
2029 0.045
2030 0.045
2031 0.045
2032 0.045
2033 0.045
2034 0.045
2035 0.045
2036 0.045
2037 0.045
2038 0.045
2039 1.045
GAMS 24.8.5 r61358 Released May 10, 2017 WEX-WEI x86 64bit/MS Windows 10/29/17 22:16:05 Page 4
Dedication models
Equation Listing SOLVE Dedication Using LP From line 130
---- Initial =E= Initialization of the investment
Initial(2016).. - 1.0235*x(DK0009923641) - 1.0102*x(DK0009923484)
- 1.0061*x(DK0009921942) - 1.0989*x(DK0009922403) - 1.1395*x(DK0009922676)
- 1.0763*x(DK0009922916) - 1.4949*x(DK0009918138) - 0.9971*x(DK0009923567)
- 1.0946*x(DK0009923054) - 1.1239*x(DK0009923138) - 1.6826*x(DK0009922320)
- surplus(2016) + borrow(2016) + v0 =E= 0 ; (LHS = 0)
---- CashFlowCon =E= Equations defining the cashflow balance
CashFlowCon(2017).. 0.0025*x(DK0009923641) + 0.0025*x(DK0009923484)
+ 1.04*x(DK0009921942) + 0.04*x(DK0009922403) + 0.03*x(DK0009922676)
+ 0.001*x(DK0009922916) + 0.07*x(DK0009918138) + 0.005*x(DK0009923567)
+ 0.015*x(DK0009923054) + 0.0175*x(DK0009923138) + 0.045*x(DK0009922320)
+ 0.985*surplus(2016) - surplus(2017) - 1.035*borrow(2016) + borrow(2017)
=E= 1000000000 ; (LHS = 0, INFES = 1000000000 ****)
CashFlowCon(2018).. 0.0025*x(DK0009923641) + 1.0025*x(DK0009923484)
+ 0.04*x(DK0009922403) + 0.03*x(DK0009922676) + 0.001*x(DK0009922916)
+ 0.07*x(DK0009918138) + 0.005*x(DK0009923567) + 0.015*x(DK0009923054)
+ 0.0175*x(DK0009923138) + 0.045*x(DK0009922320) + 0.985*surplus(2017)
- surplus(2018) - 1.035*borrow(2017) + borrow(2018) =E= 1000000000 ;
(LHS = 0, INFES = 1000000000 ****)
CashFlowCon(2019).. 0.0025*x(DK0009923641) + 1.04*x(DK0009922403)
+ 0.03*x(DK0009922676) + 0.001*x(DK0009922916) + 0.07*x(DK0009918138)
+ 0.005*x(DK0009923567) + 0.015*x(DK0009923054) + 0.0175*x(DK0009923138)
+ 0.045*x(DK0009922320) + 0.985*surplus(2018) - surplus(2019)
- 1.035*borrow(2018) + borrow(2019) =E= 1000000000 ;
(LHS = 0, INFES = 1000000000 ****)
REMAINING 20 ENTRIES SKIPPED
---- Final =E= Horison constraint
Final(2039).. borrow(2039) =E= 0 ; (LHS = 0)
GAMS 24.8.5 r61358 Released May 10, 2017 WEX-WEI x86 64bit/MS Windows 10/29/17 22:16:05 Page 5
Dedication models
Column Listing SOLVE Dedication Using LP From line 130
---- x Face value purchased
x(DK0009923641)
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
-1.0235 Initial(2016)
0.0025 CashFlowCon(2017)
0.0025 CashFlowCon(2018)
0.0025 CashFlowCon(2019)
1.0025 CashFlowCon(2020)
x(DK0009923484)
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
-1.0102 Initial(2016)
0.0025 CashFlowCon(2017)
1.0025 CashFlowCon(2018)
x(DK0009921942)
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
-1.0061 Initial(2016)
1.04 CashFlowCon(2017)
REMAINING 8 ENTRIES SKIPPED
---- surplus Amount of money reinvested
surplus(2016)
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
-1 Initial(2016)
0.985 CashFlowCon(2017)
surplus(2017)
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
-1 CashFlowCon(2017)
0.985 CashFlowCon(2018)
surplus(2018)
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
-1 CashFlowCon(2018)
0.985 CashFlowCon(2019)
REMAINING 21 ENTRIES SKIPPED
---- borrow Amount of money borrowed
borrow(2016)
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
1 Initial(2016)
-1.035 CashFlowCon(2017)
borrow(2017)
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
1 CashFlowCon(2017)
-1.035 CashFlowCon(2018)
borrow(2018)
(.LO, .L, .UP, .M = 0, 0, +INF, 0)
1 CashFlowCon(2018)
-1.035 CashFlowCon(2019)
REMAINING 21 ENTRIES SKIPPED
---- v0 Upfront investment
v0
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
1 Initial(2016)
GAMS 24.8.5 r61358 Released May 10, 2017 WEX-WEI x86 64bit/MS Windows 10/29/17 22:16:05 Page 6
Dedication models
Model Statistics SOLVE Dedication Using LP From line 130
MODEL STATISTICS
BLOCKS OF EQUATIONS 3 SINGLE EQUATIONS 25
BLOCKS OF VARIABLES 4 SINGLE VARIABLES 60
NON ZERO ELEMENTS 187
GENERATION TIME = 0.078 SECONDS 4 MB 24.8.5 r61358 WEX-WEI
EXECUTION TIME = 0.078 SECONDS 4 MB 24.8.5 r61358 WEX-WEI
GAMS 24.8.5 r61358 Released May 10, 2017 WEX-WEI x86 64bit/MS Windows 10/29/17 22:16:05 Page 7
Dedication models
Solution Report SOLVE Dedication Using LP From line 130
S O L V E S U M M A R Y
MODEL Dedication OBJECTIVE v0
TYPE LP DIRECTION MINIMIZE
SOLVER CPLEX FROM LINE 130
**** SOLVER STATUS 1 Normal Completion
**** MODEL STATUS 1 Optimal
**** OBJECTIVE VALUE 21200048181.1546
RESOURCE USAGE, LIMIT 0.063 1000.000
ITERATION COUNT, LIMIT 32 2000000000
IBM ILOG CPLEX 24.8.5 r61358 Released May 10, 2017 WEI x86 64bit/MS Windows
Cplex 12.7.1.0
Space for names approximately 0.00 Mb
Use option 'names no' to turn use of names off
LP status(1): optimal
Cplex Time: 0.02sec (det. 0.14 ticks)
Optimal solution found.
Objective : 21200048181.154640
---- EQU Initial Initialization of the investment
LOWER LEVEL UPPER MARGINAL
2016 . . . 1.000
---- EQU CashFlowCon Equations defining the cashflow balance
LOWER LEVEL UPPER MARGINAL
2017 1.0000E+9 1.0000E+9 1.0000E+9 0.967
2018 1.0000E+9 1.0000E+9 1.0000E+9 0.982
2019 1.0000E+9 1.0000E+9 1.0000E+9 0.982
2020 1.0000E+9 1.0000E+9 1.0000E+9 0.997
2021 1.0000E+9 1.0000E+9 1.0000E+9 0.992
2022 1.0000E+9 1.0000E+9 1.0000E+9 1.007
2023 1.0000E+9 1.0000E+9 1.0000E+9 0.978
2024 1.0000E+9 1.0000E+9 1.0000E+9 0.945
2025 1.0000E+9 1.0000E+9 1.0000E+9 0.960
2026 1.0000E+9 1.0000E+9 1.0000E+9 0.974
2027 1.0000E+9 1.0000E+9 1.0000E+9 0.943
2028 1.0000E+9 1.0000E+9 1.0000E+9 0.958
2029 1.0000E+9 1.0000E+9 1.0000E+9 0.972
2030 1.0000E+9 1.0000E+9 1.0000E+9 0.987
2031 1.0000E+9 1.0000E+9 1.0000E+9 0.959
2032 1.0000E+9 1.0000E+9 1.0000E+9 0.927
2033 1.0000E+9 1.0000E+9 1.0000E+9 0.896
2034 1.0000E+9 1.0000E+9 1.0000E+9 0.865
2035 1.0000E+9 1.0000E+9 1.0000E+9 0.836
2036 1.0000E+9 1.0000E+9 1.0000E+9 0.808
2037 1.0000E+9 1.0000E+9 1.0000E+9 0.780
2038 1.0000E+9 1.0000E+9 1.0000E+9 0.754
2039 1.0000E+9 1.0000E+9 1.0000E+9 0.729
---- EQU Final Horison constraint
LOWER LEVEL UPPER MARGINAL
2039 . . . -0.729
---- VAR x Face value purchased
LOWER LEVEL UPPER MARGINAL
DK0009923641 . . +INF 0.017
DK0009923484 . . +INF 0.023
DK0009921942 . 8.4290E+8 +INF .
DK0009922403 . 9.1373E+8 +INF .
DK0009922676 . 9.8013E+8 +INF .
DK0009922916 . . +INF 0.091
DK0009918138 . 2.3861E+9 +INF .
DK0009923567 . 2.7765E+9 +INF .
DK0009923054 . . +INF 0.013
DK0009923138 . . +INF 0.010
DK0009922320 . 7.0698E+9 +INF .
---- VAR surplus Amount of money reinvested
LOWER LEVEL UPPER MARGINAL
2016 . . +INF 0.047
2017 . 4.4162E+8 +INF .
2018 . . +INF 0.015
2019 . 4.7873E+8 +INF .
2020 . . +INF 0.020
2021 . 5.0858E+8 +INF .
2022 . . +INF 0.043
2023 . . +INF 0.047
2024 . 1.3666E+9 +INF .
2025 . 6.7815E+8 +INF .
2026 . . +INF 0.045
2027 . 2.1085E+9 +INF .
2028 . 1.3950E+9 +INF .
2029 . 6.9224E+8 +INF .
2030 . . +INF 0.042
2031 . . +INF 0.046
2032 . . +INF 0.045
2033 . . +INF 0.043
2034 . . +INF 0.042
2035 . . +INF 0.040
2036 . . +INF 0.039
2037 . . +INF 0.038
2038 . . +INF 0.036
2039 . . +INF 0.729
---- VAR borrow Amount of money borrowed
LOWER LEVEL UPPER MARGINAL
2016 . . +INF 0.001
2017 . . +INF 0.049
2018 . . +INF 0.034
2019 . . +INF 0.050
2020 . . +INF 0.030
2021 . . +INF 0.050
2022 . . +INF 0.006
2023 . 5.0095E+8 +INF .
2024 . . +INF 0.048
2025 . . +INF 0.049
2026 . . +INF 0.002
2027 . . +INF 0.048
2028 . . +INF 0.049
2029 . . +INF 0.049
2030 . . +INF 0.006
2031 . 6.8186E+8 +INF .
2032 . 1.3876E+9 +INF .
2033 . 2.1180E+9 +INF .
2034 . 2.8740E+9 +INF .
2035 . 3.6564E+9 +INF .
2036 . 4.4663E+9 +INF .
2037 . 5.3044E+9 +INF .
2038 . 6.1720E+9 +INF .
2039 . . +INF .
LOWER LEVEL UPPER MARGINAL
---- VAR v0 -INF 2.120E+10 +INF .
v0 Upfront investment
**** REPORT SUMMARY : 0 NONOPT
0 INFEASIBLE
0 UNBOUNDED
GAMS 24.8.5 r61358 Released May 10, 2017 WEX-WEI x86 64bit/MS Windows 10/29/17 22:16:05 Page 8
Dedication models
E x e c u t i o n
---- 131 VARIABLE v0.L = 2.12000E+10 Upfront investment
---- 131 VARIABLE borrow.L Amount of money borrowed
2023 5.009510E+8, 2031 6.818574E+8, 2032 1.387580E+9, 2033 2.118002E+9
2034 2.873990E+9, 2035 3.656437E+9, 2036 4.466270E+9, 2037 5.304447E+9
2038 6.171960E+9
---- 131 VARIABLE surplus.L Amount of money reinvested
2017 4.416225E+8, 2019 4.787281E+8, 2021 5.085797E+8, 2024 1.366621E+9
2025 6.781472E+8, 2027 2.108509E+9, 2028 1.395024E+9, 2029 6.922410E+8
---- 131 VARIABLE x.L Face value purchased
DK0009921942 8.429045E+8, DK0009922403 9.137263E+8
DK0009922676 9.801269E+8, DK0009918138 2.386057E+9
DK0009923567 2.776484E+9, DK0009922320 7.069836E+9
GAMS 24.8.5 r61358 Released May 10, 2017 WEX-WEI x86 64bit/MS Windows 10/29/17 22:16:05 Page 9
Dedication models
Equation Listing SOLVE Dedicationext Using LP From line 283
---- Initial =E= Initialization of the investment
Initial(2016).. - 1.0235*x(DK0009923641) - 1.0102*x(DK0009923484)
- 1.0061*x(DK0009921942) - 1.0989*x(DK0009922403) - 1.1395*x(DK0009922676)
- 1.0763*x(DK0009922916) - 1.4949*x(DK0009918138) - 0.9971*x(DK0009923567)
- 1.0946*x(DK0009923054) - 1.1239*x(DK0009923138) - 1.6826*x(DK0009922320)
- surplus(2016) + borrow(2016) + v0 =E= 0 ; (LHS = 0)
---- CashFlowCon =E= Equations defining the cashflow balance
CashFlowCon(2017).. 0.0025*x(DK0009923641) + 0.0025*x(DK0009923484)
+ 1.04*x(DK0009921942) + 0.04*x(DK0009922403) + 0.03*x(DK0009922676)
+ 0.001*x(DK0009922916) + 0.07*x(DK0009918138) + 0.005*x(DK0009923567)
+ 0.015*x(DK0009923054) + 0.0175*x(DK0009923138) + 0.045*x(DK0009922320)
+ 0.985*surplus(2016) - surplus(2017) - 1.035*borrow(2016) + borrow(2017)
=E= 1000000000 ; (LHS = 1000000000)
CashFlowCon(2018).. 0.0025*x(DK0009923641) + 1.0025*x(DK0009923484)
+ 0.04*x(DK0009922403) + 0.03*x(DK0009922676) + 0.001*x(DK0009922916)
+ 0.07*x(DK0009918138) + 0.005*x(DK0009923567) + 0.015*x(DK0009923054)
+ 0.0175*x(DK0009923138) + 0.045*x(DK0009922320) + 0.985*surplus(2017)
- surplus(2018) - 1.035*borrow(2017) + borrow(2018) =E= 1000000000 ;
(LHS = 1000000000)
CashFlowCon(2019).. 0.0025*x(DK0009923641) + 1.04*x(DK0009922403)
+ 0.03*x(DK0009922676) + 0.001*x(DK0009922916) + 0.07*x(DK0009918138)
+ 0.005*x(DK0009923567) + 0.015*x(DK0009923054) + 0.0175*x(DK0009923138)
+ 0.045*x(DK0009922320) + 0.985*surplus(2018) - surplus(2019)
- 1.035*borrow(2018) + borrow(2019) =E= 1000000000 ; (LHS = 1000000000)
REMAINING 20 ENTRIES SKIPPED
---- Final =E= Horison constraint
Final(2039).. borrow(2039) =E= 0 ; (LHS = 0)
---- MismatchU =L= Asset Liabilities Mismatch upper bound
MismatchU.. mm =L= 541763521.725853 ; (LHS = 0)
---- MismatchL =G= Asset Liabilities Mismtach lower bound
MismatchL.. mm =G= 0 ; (LHS = 0)
---- Mismatchdef =E= Mismatch Definition
Mismatchdef.. 1.00556722723243*x(DK0009923641)
+ 1.00039316142342*x(DK0009923484) + 1.03534096565455*x(DK0009921942)
+ 1.114971444209*x(DK0009922403) + 1.14483933388213*x(DK0009922676)
+ 1.002081591986*x(DK0009922916) + 1.53075132646785*x(DK0009918138)
+ 0.99544246523363*x(DK0009923567) + 1.09963220245325*x(DK0009923054)
+ 1.11795282900195*x(DK0009923138) + 1.6842248400558*x(DK0009922320) + mm
=E= 21878805702.9704 ;
(LHS = 21337042181.2445, INFES = 541763521.725853 ****)
---- objfunc =E= Objective Func
objfunc.. - v0 - mm + z =E= 0 ;
(LHS = -21200048181.1546, INFES = 21200048181.1546 ****)
GAMS 24.8.5 r61358 Released May 10, 2017 WEX-WEI x86 64bit/MS Windows 10/29/17 22:16:05 Page 10
Dedication models
Column Listing SOLVE Dedicationext Using LP From line 283
---- x Face value purchased
x(DK0009923641)
(.LO, .L, .UP, .M = 0, 0, +INF, 0.0170791784063637)
-1.0235 Initial(2016)
0.0025 CashFlowCon(2017)
0.0025 CashFlowCon(2018)
0.0025 CashFlowCon(2019)
1.0025 CashFlowCon(2020)
1.0056 Mismatchdef
x(DK0009923484)
(.LO, .L, .UP, .M = 0, 0, +INF, 0.0231902662534168)
-1.0102 Initial(2016)
0.0025 CashFlowCon(2017)
1.0025 CashFlowCon(2018)
1.0004 Mismatchdef
x(DK0009921942)
(.LO, .L, .UP, .M = 0, 842904453.798081, +INF, 0)
-1.0061 Initial(2016)
1.04 CashFlowCon(2017)
1.0353 Mismatchdef
REMAINING 8 ENTRIES SKIPPED
---- surplus Amount of money reinvested
surplus(2016)
(.LO, .L, .UP, .M = 0, 0, +INF, 0.0471072115384615)
-1 Initial(2016)
0.985 CashFlowCon(2017)
surplus(2017)
(.LO, .L, .UP, .M = 0, 441622484.609574, +INF, 0)
-1 CashFlowCon(2017)
0.985 CashFlowCon(2018)
surplus(2018)
(.LO, .L, .UP, .M = 0, 0, +INF, 0.0152083511361248)
-1 CashFlowCon(2018)
0.985 CashFlowCon(2019)
REMAINING 21 ENTRIES SKIPPED
---- borrow Amount of money borrowed
borrow(2016)
(.LO, .L, .UP, .M = 0, 0, +INF, 0.00126298076923059)
1 Initial(2016)
-1.035 CashFlowCon(2017)
borrow(2017)
(.LO, .L, .UP, .M = 0, 0, +INF, 0.0491067942210073)
1 CashFlowCon(2017)
-1.035 CashFlowCon(2018)
borrow(2018)
(.LO, .L, .UP, .M = 0, 0, +INF, 0.0338742647666174)
1 CashFlowCon(2018)
-1.035 CashFlowCon(2019)
REMAINING 21 ENTRIES SKIPPED
---- v0 Upfront investment
v0
(.LO, .L, .UP, .M = -INF, 21200048181.1546, +INF, 0)
1 Initial(2016)
-1 objfunc
---- mm Mismatch
mm
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
1 MismatchU
1 MismatchL
1 Mismatchdef
-1 objfunc
---- z objvalue
z
(.LO, .L, .UP, .M = -INF, 0, +INF, 0)
1 objfunc
GAMS 24.8.5 r61358 Released May 10, 2017 WEX-WEI x86 64bit/MS Windows 10/29/17 22:16:05 Page 11
Dedication models
Model Statistics SOLVE Dedicationext Using LP From line 283
MODEL STATISTICS
BLOCKS OF EQUATIONS 7 SINGLE EQUATIONS 29
BLOCKS OF VARIABLES 6 SINGLE VARIABLES 62
NON ZERO ELEMENTS 204
GENERATION TIME = 0.047 SECONDS 3 MB 24.8.5 r61358 WEX-WEI
EXECUTION TIME = 0.047 SECONDS 3 MB 24.8.5 r61358 WEX-WEI
GAMS 24.8.5 r61358 Released May 10, 2017 WEX-WEI x86 64bit/MS Windows 10/29/17 22:16:05 Page 12
Dedication models
Solution Report SOLVE Dedicationext Using LP From line 283
S O L V E S U M M A R Y
MODEL Dedicationext OBJECTIVE z
TYPE LP DIRECTION MINIMIZE
SOLVER CPLEX FROM LINE 283
**** SOLVER STATUS 1 Normal Completion
**** MODEL STATUS 1 Optimal
**** OBJECTIVE VALUE 21200712254.5609
RESOURCE USAGE, LIMIT 0.047 1000.000
ITERATION COUNT, LIMIT 2 2000000000
IBM ILOG CPLEX 24.8.5 r61358 Released May 10, 2017 WEI x86 64bit/MS Windows
Cplex 12.7.1.0
Space for names approximately 0.00 Mb
Use option 'names no' to turn use of names off
LP status(1): optimal
Cplex Time: 0.00sec (det. 0.13 ticks)
Optimal solution found.
Objective : 21200712254.560925
---- EQU Initial Initialization of the investment
LOWER LEVEL UPPER MARGINAL
2016 . . . 1.000
---- EQU CashFlowCon Equations defining the cashflow balance
LOWER LEVEL UPPER MARGINAL
2017 1.0000E+9 1.0000E+9 1.0000E+9 0.966
2018 1.0000E+9 1.0000E+9 1.0000E+9 0.981
2019 1.0000E+9 1.0000E+9 1.0000E+9 0.980
2020 1.0000E+9 1.0000E+9 1.0000E+9 0.995
2021 1.0000E+9 1.0000E+9 1.0000E+9 0.991
2022 1.0000E+9 1.0000E+9 1.0000E+9 1.006
2023 1.0000E+9 1.0000E+9 1.0000E+9 0.977
2024 1.0000E+9 1.0000E+9 1.0000E+9 0.944
2025 1.0000E+9 1.0000E+9 1.0000E+9 0.959
2026 1.0000E+9 1.0000E+9 1.0000E+9 0.973
2027 1.0000E+9 1.0000E+9 1.0000E+9 0.942
2028 1.0000E+9 1.0000E+9 1.0000E+9 0.957
2029 1.0000E+9 1.0000E+9 1.0000E+9 0.971
2030 1.0000E+9 1.0000E+9 1.0000E+9 0.986
2031 1.0000E+9 1.0000E+9 1.0000E+9 0.958
2032 1.0000E+9 1.0000E+9 1.0000E+9 0.926
2033 1.0000E+9 1.0000E+9 1.0000E+9 0.895
2034 1.0000E+9 1.0000E+9 1.0000E+9 0.864
2035 1.0000E+9 1.0000E+9 1.0000E+9 0.835
2036 1.0000E+9 1.0000E+9 1.0000E+9 0.807
2037 1.0000E+9 1.0000E+9 1.0000E+9 0.780
2038 1.0000E+9 1.0000E+9 1.0000E+9 0.753
2039 1.0000E+9 1.0000E+9 1.0000E+9 0.728
---- EQU Final Horison constraint
LOWER LEVEL UPPER MARGINAL
2039 . . . -0.728
LOWER LEVEL UPPER MARGINAL
---- EQU MismatchU -INF . 5.4176E+8 .
---- EQU MismatchL . . +INF 0.999
---- EQU Mismatchd~ 2.188E+10 2.188E+10 2.188E+10 0.001
---- EQU objfunc . . . 1.000
MismatchU Asset Liabilities Mismatch upper bound
MismatchL Asset Liabilities Mismtach lower bound
Mismatchdef Mismatch Definition
objfunc Objective Func