UN-new chapter 17, AEXPECTED RETURN ON A ONE-YEARBONDWITH AN ADJUSTMENT FOR DEFAULTPROBABILITYFace value, F 100 Data table: expected return as function of Recovery % and PricePrice, P 100Annual coupon rate, Q 15% Recovery percentageNon-default probability, p 65% -2.50% 40% 50% 60% 70% 80% 90% 100%Recovery percentage, l 65% 80 10.94% 15.31% 19.69% 24.06% 28.44% 32.81% 37.19%Price of bond 85 4.41% 8.53% 12.65% 16.76% 20.88% 25.00% 29.12%Expected cash flow 97.5 #NAME? 90 -1.39% 2.50% 6.39% 10.28% 14.17% 18.06% 21.94%Expected return -2.50% #NAME? 100 -11.25% -7.75% -4.25% -0.75% 2.75% 6.25% 9.75%105 -15.48% -12.14% -8.81% -5.48% -2.14% 1.19% 4.52%A B C D E F G H I J K L M12345678910UN-new chapter 17, A按照违约概率调整的1年期债券的期望回报率面值, F 100 数据表: 期望收益作为回收率 % 和价格的函数价格, P 100年息票利率, Q 15% 回收率百分比不违约概率, p 65% -2.50% 40% 50% 60% 70% 80% 90% 100%回收率, l 65% 80 10.94% 15.31% 19.69% 24.06% 28.44% 32.81% 37.19%债券价格 85 4.41% 8.53% 12.65% 16.76% 20.88% 25.00% 29.12%期望现金流 97.5 #NAME? 90 -1.39% 2.50% 6.39% 10.28% 14.17% 18.06% 21.94%期望回报率 -2.50% #NAME? 100 -11.25% -7.75% -4.25% -0.75% 2.75% 6.25% 9.75%105 -15.48% -12.14% -8.81% -5.48% -2.14% 1.19% 4.52%A B C D E F G H I J K L M12345678910UN - new chapter 17, DPage 3CALCULATING THE EXPECTED BOND RETURNBond price 100.00% Payoff(tN) Payoff(N)Coupon rate, Q 9.3637% Cells F3:F7are calledpayoff1 inrow 209.36% Cells I3:I7are calledpayoff2 inrow 20109.36%Recovery rate, l 50% 9.36% 109.36%Bond term, N 10 9.36% 109.36%Initial rating C 50.00% 50.00%0.00% 0.00%A B C D ETransition matrix A 1.0000 0.0000 0.0000 0.0000 0.0000B 0.0600 0.9000 0.0300 0.0100 0.0000C 0.0200 0.0500 0.8800 0.0500 0.0000D 0.0000 0.0000 0.0000 0.0000 1.0000E 0.0000 0.0000 0.0000 0.0000 1.0000Initial vector 0 0 1 0 0Year 0 1 2 3 4 5 6 7 8 9Expected payoffs -1.0000 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?Expected yield #VALUE! #NAME?#NAME?Answer: A ten-year A bond will be riskless (look at the transition matrix) and will have expected return of 7%.A ten-year B bond will have to have a coupon rate of 7.6273% in order to have an expected return of 7%.A ten-year C bond will have to have a coupon rate of 9.3637% in order to have an expected return of 7%.You can do this by trial and error or by using the Excel Solver.A B C D E F G H I J K123456789101112131415161718192021222324252627282930313233UN - new chapter 17, DPage 410 11 12 13 14 15 16 17 18 19 20 21 22#NAME? 0.0000 0.0000 0.0000 0.0000 0 0 0 0 0 0 0 0L M N O P Q R S T U V W X123456789101112131415161718192021222324252627282930313233UN - new chapter 17, DPage 523 24 25 26 27 28 29 30 31 32 33 34 350 0 0 0 0 0 0 0 0 0 0 0 0Y Z AA AB AC AD AE AF AG AH AI AJ AK123456789101112131415161718192021222324252627282930313233UN - new chapter 17, DPage 636 37 38 39 400 0 0 0 0AL AM AN AO AP123456789101112131415161718192021222324252627282930313233UN - new chapter 17, DPage 7计算债券的期望回报率债券价格 100.00% Payoff(tN) Payoff(N)息票率, Q 9.3637%单元格F3:F7称为 清偿1在第20行9.36%单元格I3:I7 称为 清偿2 在第20行109.36%回收率, l 50% 9.36% 109.36%债券成熟期, N 10 9.36% 109.36%初始信誉等级 C 50.00% 50.00%0.00% 0.00%A B C D E转换矩阵 A 1.0000 0.0000 0.0000 0.0000 0.0000B 0.0600 0.9000 0.0300 0.0100 0.0000C 0.0200 0.0500 0.8800 0.0500 0.0000D 0.0000 0.0000 0.0000 0.0000 1.0000E 0.0000 0.0000 0.0000 0.0000 1.0000初始向量 0 0 1 0 0年 0 1 2 3 4 5 6 7 8 9期望清偿 -1.0000 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?期望收益率 #VALUE! #NAME?#NAME?答案: 一个10年期等级为 A 的债券是无风险的(参看转换矩阵)，其期望回报率为7%。一个10年期等级为 B 的债券，为了获得7%的期望回报率，必须具有的息票利率为7.6865%。一个10年期等级为 C 的债券，为了获得7%的期望回报率，必须具有的息票利率为15.1271%。你可以通过Excel Solver采用试错法来得到答案。A B C D E F G H I J K123456789101112131415161718192021222324252627282930313233UN - new chapter 17, DPage 810 11 12 13 14 15 16 17 18 19 20 21 22#NAME? 0.0000 0.0000 0.0000 0.0000 0 0 0 0 0 0 0 0L M N O P Q R S T U V W X123456789101112131415161718192021222324252627282930313233UN - new chapter 17, DPage 923 24 25 26 27 28 29 30 31 32 33 34 350 0 0 0 0 0 0 0 0 0 0 0 0Y Z AA AB AC AD AE AF AG AH AI AJ AK123456789101112131415161718192021222324252627282930313233UN - new chapter 17, DPage 1036 37 38 39 400 0 0 0 0AL AM AN AO AP123456789101112131415161718192021222324252627282930313233UN - new chapter 17, DPage 11CALCULATING THE EXPECTED BOND RETURNBond price 100.00% Payoff(tN) Payoff(N)Coupon rate, Q 11.000% Cells F3:F7are calledpayoff1 inrow 2011.00% Cells I3:I7are calledpayoff2 inrow 20111.00%Recovery rate, l 67% 11.00% 111.00%Current date 17-七月-07 11.00% 111.00%Bond maturity 17-七月-17 67.00% 67.00%Initial rating C 0.00% 0.00%A B C D ETransition matrix A 1.0000 0.0000 0.0000 0.0000 0.0000B 0.0600 0.9000 0.0300 0.0100 0.0000C 0.0200 0.0500 0.8800 0.0500 0.0000D 0.0000 0.0000 0.0000 0.0000 1.0000E 0.0000 0.0000 0.0000 0.0000 1.0000Initial vector 0 0 1 0 00 1 2 3 4 5 6 7 8 9Year 17-七月-0717-七月-0817-七月-0917-七月-1017-七月-117-七月-1217-七月-1317-七月-1417-七月-1517-七月-16Expected payoffs -1.0000 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?Expected yield #NAME? #NAME?#NAME?A B C D E F G H I J K12345678910111213141516171819202122232425262728UN - new chapter 17, DPage 121017-七月-17#NAME?L12345678910111213141516171819202122232425262728UN - new chapter 17, DPage 13计算期望债券收益债券价格 100.00% Payoff(tN) Payoff(N)票面利率, Q 11.000%单元格F3:F7称为 清偿1在第20行11.00% 单元格I3:I7 称为 清偿2 在第20行111.00%回收率, l 67% 11.00% 111.00%当前日期 17-七月-07 11.00% 111.00%到期日 17-七月-17 67.00% 67.00%初始等级 C 0.00% 0.00%A B C D E转换矩阵 A 1.0000 0.0000 0.0000 0.0000 0.0000B 0.0600 0.9000 0.0300 0.0100 0.0000C 0.0200 0.0500 0.8800 0.0500 0.0000D 0.0000 0.0000 0.0000 0.0000 1.0000E 0.0000 0.0000 0.0000 0.0000 1.0000初始向量 0 0 1 0 00 1 2 3 4 5 6 7 8 9年 17-七月-0717-七月-0817-七月-0917-七月-1017-七月-117-七月-1217-七月-1317-七月-1417-七月-1517-七月-16期望清偿 -1.0000 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?期望收益率 #NAME? #NAME?#NAME?A B C D E F G H I J K12345678910111213141516171819202122232425262728UN - new chapter 17, DPage 141017-七月-17#NAME?L12345678910111213141516171819202122232425262728UN - new chapter 17, DPage 15CALCULATING THE EXPECTED BOND RETURNBond price 95.00% Payoff(tN) Payoff(N)Coupon rate, Q 5.000% Cells F3:F7are calledpayoff1 inrow 215.00% Cells I3:I7are calledpayoff2 inrow 21105.00%Recovery rate, l 70% 5.00% 105.00%Current date 19-十二月-07 5.00% 105.00%Bond maturity 17-七月-17 70.00% 70.00%Initial rating B 0.00% 0.00%Bond invoice price 0.9712 #NAME?A B C D ETransition matrix A 1.0000 0.0000 0.0000 0.0000 0.0000B 0.0600 0.9000 0.0300 0.0100 0.0000C 0.0200 0.0500 0.8800 0.0500 0.0000D 0.0000 0.0000 0.0000 0.0000 1.0000E 0.0000 0.0000 0.0000 0.0000 1.0000Initial vector 0 1 0 0 00 1 2 3 4 5 6 7 8 9Year 19-十二月-0717-七月-0817-七月-0917-七月-1017-七月-117-七月-1217-七月-1317-七月-1417-七月-1517-七月-16Expected payoffs -0.9712 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?Expected yield #NAME? #NAME?#NAME?A B C D E F G H I J K1234567891011121314151617181920212223242526272829UN - new chapter 17, DPage 161017-七月-17#NAME?L1234567891011121314151617181920212223242526272829UN - new chapter 17, DPage 17计算期望债券收益债券价格 95.00% Payoff(tN) Payoff(N)票面利率, Q 5.000%单元格F3:F7称为 清偿1在第21行5.00% 单元格I3:I7 称为 清偿2 在第21行105.00%回收率, l 70% 5.00% 105.00%当前日期 19-十二月-07 5.00% 105.00%到期日 17-七月-17 70.00% 70.00%初始等级 B 0.00% 0.00%债券报价 0.9712 #NAME?A B C D E转换矩阵 A 1.0000 0.0000 0.0000 0.0000 0.0000B 0.0600 0.9000 0.0300 0.0100 0.0000C 0.0200 0.0500 0.8800 0.0500 0.0000D 0.0000 0.0000 0.0000 0.0000 1.0000E 0.0000 0.0000 0.0000 0.0000 1.0000初始向量 0 1 0 0 00 1 2 3 4 5 6 7 8 9年 19-十二月-0717-七月-0817-七月-0917-七月-1017-七月-117-七月-1217-七月-1317-七月-1417-七月-1517-七月-16期望清偿 -0.9712 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?期望收益率 #NAME? #NAME?#NAME?A B C D E F G H I J K1234567891011121314151617181920212223242526272829UN - new chapter 17, DPage 181017-七月-17#NAME?L1234567891011121314151617181920212223242526272829UN - new chapter 17, DPage 19CALCULATING THE EXPECTED BOND RETURNBond price 100.00% Payoff(tN) Payoff(N)Coupon rate, Q 11.417% Cells F3:F7are calledpayoff1 inrow 2111.42% Cells I3:I7are calledpayoff2 inrow 21111.42%Recovery rate, l 55% 11.42% 111.42%Current date 17-七月-07 11.42% 111.42%Bond maturity 17-七月-14 55.00% 55.00%Initial rating C 0.00% 0.00%Bond invoice price 1.0000 #NAME?A B C D ETransition matrix A 1.0000 0.0000 0.0000 0.0000 0.0000B 0.0600 0.9000 0.0300 0.0100 0.0000C 0.0200 0.0500 0.8800 0.0500 0.0000D 0.0000 0.0000 0.0000 0.0000 1.0000E 0.0000 0.0000 0.0000 0.0000 1.0000Initial vector 0 0 1 0 00 1 2 3 4 5 6 7 8 9Year 17-七月-0717-七月-0817-七月-0917-七月-1017-七月-117-七月-1217-七月-1317-七月-1417-七月-1517-七月-16Expected payoffs -1.0000 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? 0.0000 0.0000Expected yield #NAME? #NAME?#NAME?A B C D E F G H I J K1234567891011121314151617181920212223242526272829UN - new chapter 17, DPage 201017-七月-170.0000L1234567891011121314151617181920212223242526272829UN - new chapter 17, DPage 21计算期望债券收益债券价格 100.00% Payoff(tN) Payoff(N)票面利率, Q 11.417%单元格F3:F7称为 清偿1在第21行11.42% 单元格I3:I7 称为 清偿2 在第21行111.42%回收率, l 55% 11.42% 111.42%当前日期 17-七月-07 11.42% 111.42%到期日 17-七月-14 55.00% 55.00%初始等级 C 0.00% 0.00%债券报价 1.0000 #NAME?A B C D E转换矩阵 A 1.0000 0.0000 0.0000 0.0000 0.0000B 0.0600 0.9000 0.0300 0.0100 0.0000C 0.0200 0.0500 0.8800 0.0500 0.0000D 0.0000 0.0000 0.0000 0.0000 1.0000E 0.0000 0.0000 0.0000 0.0000 1.0000初始向量 0 0 1 0 00 1 2 3 4 5 6 7 8 9年 17-七月-0717-七月-0817-七月-0917-七月-1017-七月-117-七月-1217-七月-1317-七月-1417-七月-1517-七月-16期望清偿 -1.0000 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? 0.0000 0.0000期望收益率 #NAME? #NAME?#NAME?A B C D E F G H I J K1234567891011121314151617181920212223242526272829UN - new chapter 17, DPage 221017-七月-170.0000L1234567891011121314151617181920212223242526272829