z1------1Y spot rate
z2-----2Y spot rate
r------2Y T-Note YTM
C------coupon rate(案例中假设为6%)
P------par value(案例中假设为100)
| YTM |
|
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
z2 |
|
2.7915% |
2.6000% |
2.7000% |
2.8000% |
2.9000% |
3.0000% |
3.1000% |
3.2000% |
3.3000% |
3.4000% |
3.5000% |
3.6000% |
3.7000% |
3.8000% |
3.9000% |
4.0000% |
4.1000% |
4.2000% |
4.3000% |
4.4000% |
4.5000% |
4.6000% |
4.7000% |
4.8000% |
4.9000% |
5.0000% |
| z1 |
2.5000% |
2.5028% |
2.5056% |
2.5084% |
2.5112% |
2.5140% |
2.5168% |
2.5196% |
2.5224% |
2.5252% |
2.5279% |
2.5307% |
2.5335% |
2.5362% |
2.5390% |
2.5417% |
2.5444% |
2.5472% |
2.5499% |
2.5526% |
2.5553% |
2.5581% |
2.5608% |
2.5635% |
2.5662% |
2.5689% |
| z1 |
2.6000% |
2.6000% |
2.6028% |
2.6056% |
2.6084% |
2.6112% |
2.6140% |
2.6168% |
2.6196% |
2.6224% |
2.6252% |
2.6280% |
2.6307% |
2.6335% |
2.6362% |
2.6390% |
2.6417% |
2.6445% |
2.6472% |
2.6500% |
2.6527% |
2.6554% |
2.6581% |
2.6608% |
2.6635% |
2.6662% |
| z1 |
2.7000% |
2.6972% |
2.7000% |
2.7028% |
2.7056% |
2.7084% |
2.7113% |
2.7141% |
2.7169% |
2.7196% |
2.7224% |
2.7252% |
2.7280% |
2.7308% |
2.7335% |
2.7363% |
2.7390% |
2.7418% |
2.7445% |
2.7473% |
2.7500% |
2.7527% |
2.7555% |
2.7582% |
2.7609% |
2.7636% |
| z1 |
2.8000% |
2.7943% |
2.7972% |
2.8000% |
2.8028% |
2.8056% |
2.8085% |
2.8113% |
2.8141% |
2.8169% |
2.8197% |
2.8225% |
2.8252% |
2.8280% |
2.8308% |
2.8336% |
2.8363% |
2.8391% |
2.8418% |
2.8446% |
2.8473% |
2.8500% |
2.8528% |
2.8555% |
2.8582% |
2.8609% |
| z1 |
2.9000% |
2.8915% |
2.8943% |
2.8972% |
2.9000% |
2.9028% |
2.9056% |
2.9085% |
2.9113% |
2.9141% |
2.9169% |
2.9197% |
2.9225% |
2.9253% |
2.9280% |
2.9308% |
2.9336% |
2.9363% |
2.9391% |
2.9419% |
2.9446% |
2.9474% |
2.9501% |
2.9528% |
2.9556% |
2.9583% |
| z1 |
3.0000% |
2.9886% |
2.9915% |
2.9943% |
2.9972% |
3.0000% |
3.0028% |
3.0057% |
3.0085% |
3.0113% |
3.0141% |
3.0169% |
3.0197% |
3.0225% |
3.0253% |
3.0281% |
3.0308% |
3.0336% |
3.0364% |
3.0391% |
3.0419% |
3.0447% |
3.0474% |
3.0501% |
3.0529% |
3.0556% |
| z1 |
3.1000% |
3.0858% |
3.0886% |
3.0915% |
3.0943% |
3.0972% |
3.1000% |
3.1028% |
3.1057% |
3.1085% |
3.1113% |
3.1141% |
3.1169% |
3.1197% |
3.1225% |
3.1253% |
3.1281% |
3.1309% |
3.1336% |
3.1364% |
3.1392% |
3.1419% |
3.1447% |
3.1474% |
3.1502% |
3.1529% |
| z1 |
3.2000% |
3.1829% |
3.1857% |
3.1886% |
3.1915% |
3.1943% |
3.1972% |
3.2000% |
3.2028% |
3.2057% |
3.2085% |
3.2113% |
3.2141% |
3.2169% |
3.2197% |
3.2225% |
3.2253% |
3.2281% |
3.2309% |
3.2337% |
3.2365% |
3.2392% |
3.2420% |
3.2447% |
3.2475% |
3.2502% |
| z1 |
3.3000% |
3.2800% |
3.2829% |
3.2857% |
3.2886% |
3.2915% |
3.2943% |
3.2972% |
3.3000% |
3.3028% |
3.3057% |
3.3085% |
3.3113% |
3.3141% |
3.3169% |
3.3198% |
3.3226% |
3.3254% |
3.3281% |
3.3309% |
3.3337% |
3.3365% |
3.3393% |
3.3420% |
3.3448% |
3.3475% |
| z1 |
3.4000% |
3.3771% |
3.3800% |
3.3828% |
3.3857% |
3.3886% |
3.3914% |
3.3943% |
3.3972% |
3.4000% |
3.4028% |
3.4057% |
3.4085% |
3.4113% |
3.4142% |
3.4170% |
3.4198% |
3.4226% |
3.4254% |
3.4282% |
3.4310% |
3.4337% |
3.4365% |
3.4393% |
3.4421% |
3.4448% |
| z1 |
3.5000% |
3.4742% |
3.4771% |
3.4799% |
3.4828% |
3.4857% |
3.4886% |
3.4914% |
3.4943% |
3.4972% |
3.5000% |
3.5028% |
3.5057% |
3.5085% |
3.5113% |
3.5142% |
3.5170% |
3.5198% |
3.5226% |
3.5254% |
3.5282% |
3.5310% |
3.5338% |
3.5366% |
3.5393% |
3.5421% |
| z1 |
3.6000% |
3.5712% |
3.5741% |
3.5770% |
3.5799% |
3.5828% |
3.5857% |
3.5886% |
3.5914% |
3.5943% |
3.5971% |
3.6000% |
3.6028% |
3.6057% |
3.6085% |
3.6114% |
3.6142% |
3.6170% |
3.6198% |
3.6226% |
3.6254% |
3.6282% |
3.6310% |
3.6338% |
3.6366% |
3.6394% |
| z1 |
3.7000% |
3.6683% |
3.6712% |
3.6741% |
3.6770% |
3.6799% |
3.6828% |
3.6857% |
3.6886% |
3.6914% |
3.6943% |
3.6971% |
3.7000% |
3.7028% |
3.7057% |
3.7085% |
3.7114% |
3.7142% |
3.7170% |
3.7198% |
3.7226% |
3.7254% |
3.7283% |
3.7310% |
3.7338% |
3.7366% |
| z1 |
3.8000% |
3.7654% |
3.7683% |
3.7712% |
3.7741% |
3.7770% |
3.7799% |
3.7828% |
3.7857% |
3.7885% |
3.7914% |
3.7943% |
3.7971% |
3.8000% |
3.8029% |
3.8057% |
3.8085% |
3.8114% |
3.8142% |
3.8170% |
3.8198% |
3.8227% |
3.8255% |
3.8283% |
3.8311% |
3.8339% |
| z1 |
3.9000% |
3.8624% |
3.8653% |
3.8683% |
3.8712% |
3.8741% |
3.8770% |
3.8799% |
3.8828% |
3.8857% |
3.8885% |
3.8914% |
3.8943% |
3.8971% |
3.9000% |
3.9029% |
3.9057% |
3.9085% |
3.9114% |
3.9142% |
3.9170% |
3.9199% |
3.9227% |
3.9255% |
3.9283% |
3.9311% |
| z1 |
4.0000% |
3.9594% |
3.9624% |
3.9653% |
3.9682% |
3.9711% |
3.9741% |
3.9770% |
3.9799% |
3.9827% |
3.9856% |
3.9885% |
3.9914% |
3.9943% |
3.9971% |
4.0000% |
4.0029% |
4.0057% |
4.0086% |
4.0114% |
4.0142% |
4.0171% |
4.0199% |
4.0227% |
4.0255% |
4.0283% |
| z1 |
4.1000% |
4.0565% |
4.0594% |
4.0623% |
4.0653% |
4.0682% |
4.0711% |
4.0740% |
4.0769% |
4.0798% |
4.0827% |
4.0856% |
4.0885% |
4.0914% |
4.0943% |
4.0971% |
4.1000% |
4.1029% |
4.1057% |
4.1086% |
4.1114% |
4.1142% |
4.1171% |
4.1199% |
4.1227% |
4.1255% |
| z1 |
4.2000% |
4.1535% |
4.1564% |
4.1594% |
4.1623% |
4.1652% |
4.1682% |
4.1711% |
4.1740% |
4.1769% |
4.1798% |
4.1827% |
4.1856% |
4.1885% |
4.1914% |
4.1943% |
4.1971% |
4.2000% |
4.2029% |
4.2057% |
4.2086% |
4.2114% |
4.2143% |
4.2171% |
4.2199% |
4.2227% |
| z1 |
4.3000% |
4.2505% |
4.2534% |
4.2564% |
4.2593% |
4.2623% |
4.2652% |
4.2681% |
4.2711% |
4.2740% |
4.2769% |
4.2798% |
4.2827% |
4.2856% |
4.2885% |
4.2914% |
4.2943% |
4.2971% |
4.3000% |
4.3029% |
4.3057% |
4.3086% |
4.3114% |
4.3143% |
4.3171% |
4.3199% |
| z1 |
4.4000% |
4.3475% |
4.3504% |
4.3534% |
4.3564% |
4.3593% |
4.3622% |
4.3652% |
4.3681% |
4.3710% |
4.3740% |
4.3769% |
4.3798% |
4.3827% |
4.3856% |
4.3885% |
4.3914% |
4.3942% |
4.3971% |
4.4000% |
4.4029% |
4.4057% |
4.4086% |
4.4114% |
4.4143% |
4.4171% |
| z1 |
4.5000% |
4.4445% |
4.4474% |
4.4504% |
4.4534% |
4.4563% |
4.4593% |
4.4622% |
4.4651% |
4.4681% |
4.4710% |
4.4739% |
4.4768% |
4.4798% |
4.4827% |
4.4856% |
4.4885% |
4.4914% |
4.4942% |
4.4971% |
4.5000% |
4.5029% |
4.5057% |
4.5086% |
4.5114% |
4.5143% |
| z1 |
4.6000% |
4.5414% |
4.5444% |
4.5474% |
4.5503% |
4.5533% |
4.5563% |
4.5592% |
4.5622% |
4.5651% |
4.5681% |
4.5710% |
4.5739% |
4.5768% |
4.5797% |
4.5827% |
4.5856% |
4.5885% |
4.5914% |
4.5942% |
4.5971% |
4.6000% |
4.6029% |
4.6057% |
4.6086% |
4.6115% |
| z1 |
4.7000% |
4.6384% |
4.6414% |
4.6444% |
4.6473% |
4.6503% |
4.6533% |
4.6562% |
4.6592% |
4.6621% |
4.6651% |
4.6680% |
4.6710% |
4.6739% |
4.6768% |
4.6797% |
4.6826% |
4.6855% |
4.6884% |
4.6913% |
4.6942% |
4.6971% |
4.7000% |
4.7029% |
4.7057% |
4.7086% |
| z1 |
4.8000% |
4.7353% |
4.7383% |
4.7413% |
4.7443% |
4.7473% |
4.7503% |
4.7532% |
4.7562% |
4.7591% |
4.7621% |
4.7650% |
4.7680% |
4.7709% |
4.7739% |
4.7768% |
4.7797% |
4.7826% |
4.7855% |
4.7884% |
4.7913% |
4.7942% |
4.7971% |
4.8000% |
4.8029% |
4.8058% |
| z1 |
4.9000% |
4.8323% |
4.8353% |
4.8383% |
4.8413% |
4.8443% |
4.8472% |
4.8502% |
4.8532% |
4.8562% |
4.8591% |
4.8621% |
4.8650% |
4.8680% |
4.8709% |
4.8738% |
4.8768% |
4.8797% |
4.8826% |
4.8855% |
4.8884% |
4.8913% |
4.8942% |
4.8971% |
4.9000% |
4.9029% |
| z1 |
5.0000% |
4.9292% |
4.9322% |
4.9352% |
4.9382% |
4.9412% |
4.9442% |
4.9472% |
4.9502% |
4.9531% |
4.9561% |
4.9591% |
4.9620% |
4.9650% |
4.9679% |
4.9709% |
4.9738% |
4.9767% |
4.9797% |
4.9826% |
4.9855% |
4.9884% |
4.9913% |
4.9942% |
4.9971% |
5.0000% |
从以上数据表可以直接得出结论：
- z1 < z2，z1 < YTM < z2 (如图中绿色区域值，表示正常情况)\
- z1 = z2，z1 = YTM = z2
- z1 > z2，z1 > YTM > z2 (利率倒挂)
综上我们可以得出结论：N年期的T-Note的YTM不会超过N年期中N个spot rate的最大值。
