Question

Use the information on bond yields for September 2016 and September 2017 to answer the following questions. YOU MUST SHOW YOUR WORK

                                                        1-Year Bond Yields (%) Sept 2016 and 2017

                                                                             2016                                                         2017

US Treasury	0.68%	1.36%
Corporate AAA	0.73	1.49
Corporate AA	1.22	1.62
Corporate A	1.42	1.82
Corporate BBB	2.15	1.85
Municipal AAA	0.75	1.09
Municipal AA	0.88	1.23
Municipal A	0.99	1.28

                

                                                                     US Treasury Yield Curve

                 1 Mo      3 Mo      6 Mo      1 Yr         2 Yr         3 Yr         4 Yr         5 Yr         10 Yr      20 Yr      30 Yr

9/17                      0.96          1.06       1.20       1.31        1.47        1.62        1.92        2.16        2.33       2.63       2.86

9/16                      0.16          0.26       0.42       0.58        0.75        0.86        1.12        1.39       1.56       1.96       2.28

                                                                               5-year TIPS

                                                            9/17               0.16%

                                                           9/16               -0.17%

A. Using 5-year bond yields, calculate the expected rate of inflation in September 2016 and September 2017:

2017:

2016:

B. Calculate the probability of default on a corporate BBB bond in September 2016 and September 2017:

2017:

2016:

C. Assuming a 35% tax bracket, calculate the tax equivalent yield for a Municipal AAA bond in September 2017.

Answer 1

TIPS: Treasury inflation-protected securities

y : yield of g sec

t : yield of tips

r: expected inflation rate

1+t = (1+y)/(1+r)

1+r = (1+y)/(1+t)

r = (y-t)/(1+t)

Sept 2016

y = 0.86% & t = -0.17%

Therefore r = (0.86% -(-0.17)%)/(1+(-0.17%))

r = 1.03%/(1-0.0017) = 1.0317% (expected inflation in sep 2016)

Sep 2017

y = 1.62% & t = 0.16%

Therefore r = (1.62% -0.16%)/(1+0.16%)

r = 1.46%/(1+0.0016) = 1.458% (expected inflation in sep 2017)

(b) p: probability of default

z: credit spread b/w bond & US treasury

r: recovery rate (assumed = 40%)

p = z/(1-r)

BBB bond sep 2016:

z = 2.15% - 0.68% = 1.47%

p = 1.47%/(1-40%) = 1.47%/0.6 = 2.45% (probability of default within 1 year)

BBB bond sep 2017:

z = 1.85% - 1.36% = 0.49%

p = 0.49%/(1-40%) = 0.49%/0.6 = 0.817% (probability of default within 1 year)

(c) Tax equivalent yield = Tax free yield/(1-tax rate)

= 1.09%/(1-35%) = 1.09%/0.65 = 1.676%