tailieunhanh - Lecture Financial modeling - Topic 11A: Default-adjusted bond return

Topic 11A - Default-adjusted bond return. After completing this topic, you should be able to: Use transition matrices to compute multi-period default probabilities, understand the difference between a bond’s YTM and default-adjusted expected return, compute default-adjusted expected bond return given a transition matrix and recovery rate. | Financial Modeling Topic #11A: Default-Adjusted Bond Return L. Gattis 1 Learning Objectives Use transition matrices to compute multi-period default probabilities Understand the difference between a bond’s YTM and default-adjusted expected return Compute default-adjusted expected bond return given a transition matrix and recovery rate 2 3 YTM vs. Expected Return The Yield-to-maturity is sometimes referred to as the “promised yield” because it is the discount that equates the market price to the present value of promised coupon and principal payments. The bonds expected return is the discount rate that equates market price to the present value of expected cash flows. To compute expected cash flows we need to know the probability of default and the payment in the event of default (Recovery). To complicate things further, default can happen immediately or through a gradual degradation of the issuer’s creditworthiness 4 Bond Rating Terminology Bond credit ratings are attempts to assess the probability that a company will default. Credit Event occurrence that suggests a default is likely Includes: rating change (also called a rating transition), failure to make bond payment, and declaration of bankruptcy Recovery rate fraction of par recovered in default 5 6 Historical Credit Rating Transition Matrix Rating at beginning of period Rating at End of period The main diagonal shows probability of no transition Sum of rows is 100% (accounts for all possible changes) 7 Calculating 2-yr Default Probability of “B” bond using 1-yr Transition Matrix 8 2- Period Transition Matrix MMult(tmatrix,tmatrix) Cumulative Prob. of default at t=2 9 2- Period Transition Matrix (With Prior Default Rating: E) MMult(tmatrix,tmatrix) Prob. of default at t=2 (Conditional on survival in t=1) Prob. of default prior to t=2 10 Expected Bond Returns with coupons and recovery Compute the expected cash flow at each coupon payment (t) Expected bond returns = IRR of expected cash flows Expected Cashflow at | Financial Modeling Topic #11A: Default-Adjusted Bond Return L. Gattis 1 Learning Objectives Use transition matrices to compute multi-period default probabilities Understand the difference between a bond’s YTM and default-adjusted expected return Compute default-adjusted expected bond return given a transition matrix and recovery rate 2 3 YTM vs. Expected Return The Yield-to-maturity is sometimes referred to as the “promised yield” because it is the discount that equates the market price to the present value of promised coupon and principal payments. The bonds expected return is the discount rate that equates market price to the present value of expected cash flows. To compute expected cash flows we need to know the probability of default and the payment in the event of default (Recovery). To complicate things further, default can happen immediately or through a gradual degradation of the issuer’s creditworthiness 4 Bond Rating Terminology Bond credit ratings are attempts to assess the

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