1. Bond Prices and Yields Part 2

2. Yield Curve A curve can be developed that shows various annualized yields-to-maturity, y, against times-to-maturity, T, for bonds from the same issuing entity or from issuing entities with the same risk y 0 T 2

3. Current US Treasury Yield Curve 3 www.treasury.gov

4. Bond Credit Rating From Investopedia 4

5. Yield Curve A corporate bond, say a AA rated bond, might have the following yield curve y 0 T AA Corporate Bond Yield Curve U.S. Treasury Debt Yield Curve risk premium or credit spread 5

6. Zero Coupon Yield Curve An especially useful version of the yield curve plots zero coupon bond yields against times-to-maturity A zero coupon yield curve depicts pure interest rates with no ambiguity due to coupon reinvestment risk These curves are not observable since no bonds with time to maturity greater than one year are issued, but can be constructed from coupon bond yield curves 6

7. Liquidity Risk Liquidity risk results from a bond issue having few buyers and sellers o The issue is ‘illiquid’ or not ‘liquid’ Older U.S. Treasuries (referred to as ‘off the run’) can trade with a liquidity rate premium compared with newer issued U.S. Treasuries (referred to as ‘on the run’) y = f(risk free time value of money, credit risk, liquidity risk) 7

8. Price – Yield Curve F=$1000 c=7% semiannual T=4.5 yrs Illustrates how price changes as yield-to-maturity changes for a particular bond ( c, m, N, and F are constant) Each (p,y) point results from a DCF 8

9. Homework 13 Plot the price – yield curve for the following bond o Par value: $100 o c = 3% o m = 2 o N = 5, T = 5.0 o Plot P for yields, y, varying from.5% to 6.0% Chose a y increment that results in a smooth curve Submit a knitr pdf with echoed code, plot, and markdown descriptions 9

10. Determine the Fair Price of a Bond In this case c, N, m and the zero coupon yield curve, z i, are known Compute the fair value, P zizi 0 T i for zero coupon bonds t i for bond cash flows CF i Cash flow diagram Zero coupon bond yield curve 10 P

11. Determine the Fair Price of a Bond F=$1000 c=7% semiannual T=4.5 yrs With the following zero coupon yield curve 11

12. Homework 14 Calculate the fair price of the bond from the previous slide Print a table with cash flows, discount factors, and discounted cash flows Submit a knitr pdf with echoed code, discount factor plot, and markdown descriptions 12

13. Amortizing Bond or Loan Bond principal is repaid periodically, not all at maturity Examples are home and automobile loans - amortizing loan Given the nominal annual interest rate, r, m, P, and N, what is the monthly payment, C? C : monthly payment o Includes principal repayment and interest N : number of years m : number of compounding periods per year (12 for home and auto loans) r : nominal fixed interest rate for the loannominal fixed interest rate for the loan P : loan principal (the mortgage amount) Solve for C using Excel Goal Seek, R uniroot, … o Find the value of C that equates the left and right hand sides 13

14. Amortizing Bond 14 F F C

15. Homework 15 You wish to borrow $300,000 at 6.5% annual fixed with monthly payments for 30 years What is your monthly payment? What is your total payout over 30 years? How much total interest will you pay? Submit a knitr pdf with echoed code and detailed markdown descriptions 15

16. Formulas Annuity o An annuity is a finite sequence of fixed payments, C. If the nominal yield is y, then the present value, P, is o The formula can be rearranged to compute the fixed payment, C, if the present value, P, is known 16

17. Formulas Annuity Example o Home mortgage example $300,000 loan at 6.5% fixed rate compounded monthly for 30 years 17

18. Formulas Bonds o Annuity for coupon payment plus the discounted par value o Example: F=$1000, c=7% semi-annual, T=4.5 yrs, y (annual nominal yield) = 8% 18

19. Formulas Bonds o Bond with fractional initial period 19 d-e=139 e=227 previous coupon next coupon 6/30/15 6/30/16 6/30/17 6/30/18 6/30/19 6/30/20 6/30/21 F = $1000 c = 5% C= $50 y = 6% e = 227 days d = 366 days N, M = 6 m =1 Now 11/16/201 5 C F+C

20. Formulas Bond with fractional initial period 20 d-e=139 e=227 previous coupon next coupon 6/30/15 6/30/16 6/30/17 6/30/18 6/30/19 6/30/20 6/30/21 F = $1000 c = 5% C= $50 y = 6% e = 227 days d = 366 days N, M = 6 m =1 Now 11/16/201 5 C F+C

21. Formulas Bond with fractional initial period 21 d-e=139 e=227 previous coupon next coupon 6/30/15 6/30/16 6/30/17 6/30/18 6/30/19 6/30/20 6/30/21 F = $1000 c = 5% C= $50 y = 6% e = 227 days d = 366 days N, M = 6 m =1 Now 11/16/201 5 C F+C