CHAPTER 7 Bonds and Their Valuation

1. CHAPTER 7Bonds and Their Valuation Key features of bonds Bond valuation(price) Measuring yield(return) Assessing risk

2. What is a bond? • A long-term standard debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond.

3. Key Features of a Bond • Par value – face amount of the bond, which is paid at maturity (assume $1,000). • Coupon rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest. • Maturity date – years until the bond must be repaid. • Issue date – when the bond was issued.

4. 0 1 2 n r ... Value CF1 CF2 CFn The value of financial assets

5. Bond valuation model • Rd is the required return of the bond. It is also the market rate of interest of the bond, and yield to maturity (YTM) of the bond. • Rd is NOT coupon rate

6. 0 1 2 n r ... 100 + 1,000 Vb = ? 100 100 What is the value of a 10-year, 10% annual coupon bond, if rd = 10%?

7. Using a financial calculator to value a bond • This bond has a $1,000 lump sum due at t = 10, and annual $100 coupon payments beginning at t = 1 and continuing through t = 10, the price of the bond can be found by solving for the PV of these cash flows. 10 10 100 1000 INPUTS N I/YR PV PMT FV OUTPUT -1000

8. An example:Increasing inflation and rd • Suppose inflation rises by 3%, causing rd = 13%. When rd rises above the coupon rate, the bond’s value falls below par, and sells at a discount. 10 13 100 1000 INPUTS N I/YR PV PMT FV OUTPUT -837.21

9. An example:Decreasing inflation and rd • Suppose inflation falls by 3%, causing rd = 7%. When kd falls below the coupon rate, the bond’s value rises above par, and sells at a premium. 10 7 100 1000 INPUTS N I/YR PV PMT FV OUTPUT -1210.71

10. Semi-annual coupon bond • Majority of bonds pay interest semiannually. • Coupon rate=10%/Y • Going (nominal) interest=5% • 15 year bond • Solution: P semi annual=$1523.26 • How: N=15*2 i=5/2 PMT=$100/2 • Compared with annual coupon bond, which should have a higher price? • P annual=$1518.98

11. What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887? • Must find the rd that solves this model.

12. Using a financial calculator to find YTM • Solving for I/YR, the YTM of this bond is 10.91%. This bond sells at a discount, because YTM > coupon rate. 10 - 887 90 1000 INPUTS N I/YR PV PMT FV OUTPUT 10.91

13. Find YTM, if the bond price was $1,134.20. • Solving for I/YR, the YTM of this bond is 7.08%. This bond sells at a premium, because YTM < coupon rate. 10 -1134.2 90 1000 INPUTS N I/YR PV PMT FV OUTPUT 7.08

14. Relationship between interest and bond price (inversely realted) Interest Rate Bond Value 12% 10% 8% 874.50 1,000 1,152.47

15. Interest sensitivity and maturity • Annual Coupon rate=10% % change 1 yr rd 10yr % change +4.8% $1,0485%$1,386 +38.6% $1,000 10% $1,000 -4.3% $95715%$749 -25.1% The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk.

16. Interest sensitivity and coupon rate 10 year annual bond % change 5%crd 10%c % change +44% $1,0005%$1,386 +38.6% $693 10% $1,000 -28% $49815%$749 -25.1% • Low coupon bond has CF concentrated at the end of maturity from repayment of principal. • The bond with lower coupon rate is more sensitive to interest rate changes

17. Calculation details

18. Summary of Factors that Affect bond Prices and Price sensitivity when Interest Rates Change • Interest Rate • negative relation between interest rate changes and bond price • increasing interest rates correspond to bond price decrease (at a decreasing rate) • Time Remaining to Maturity • longer time to maturity corresponds to larger price change for a given interest rate change • Coupon Rate • the lower the coupon rate, the bigger the price change for a given change in interest rates

19. Reinvestment risk • The risk that bondholders have to reinvest future cash flows (coupon and principal when expires)at lower interest rates if general interest level declines • EXAMPLE: Suppose you just won $500,000 playing the lottery. You intend to invest the money and live off the interest.

20. Reinvestment Rate Risk Example • You may invest in either a 10-year bond or a series of ten 1-year bonds. Both 10-year and 1-year bonds currently yield 10%. • If you choose the 1-year bond strategy: • After Year 1, you receive $50,000 in income and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000. • If you choose the 10-year bond strategy: • You can lock in a 10% interest rate, and $50,000 annual income for 10 years.

21. CONCLUSION: Nothing is riskless! Interest risk is a big concern in low interest environment, and reinvestment risk is a big concern in high interest environment Conclusions about Interest Rate and Reinvestment Rate Risk

22. Default Risk If an issuer defaults, investors receive less than the promised return. Influenced by the issuer’s financial strength and the terms of the bond contract.

23. Bond ratings are designed to reflect the probability of a bond issue going into default. High risk demands high yield. (PIGS 4 are paying high yield on their bonds) Evaluating Default Risk:Bond Ratings

24. Optional: Bond investing in real world • Find bond information • Where to buy? • Don’t buy individual bond (unless risk-free T bond) • Risk-free could be illusion, price does change • Bond ETF (HYG,JNK, BSV, SCPB)

25. Factors to consider when investing in bonds • Yield • For single bond: current yield( annual interest payment/current price) and yield to maturity(consider principal payment). • For bond ETF or mutual fund: Yield (current yield) and SEC yield (consider ytm and expense) • Default risk and rating • Interest risk and duration • Duration: the effective maturity of a bond (average maturity for a bond ETF)

26. Optional: practical questions • Is Treasury bond really risk-free? • Risk free bond price changes • Is it good time to buy bonds now? • Interest changes • LT vs. ST bond • Should I buy individual high-yield corporate bond?

27. Example of treasure bond • Yahoo-Finance-Market data-Bond • Comparing LT bond yield with ST yield • Expectation of interest rate • Default risk? • Interest risk and time to maturity

28. Examples of bond portfolio • HYG (bond ETF) • 12-month Yield: the sum of a fund’s total trailing 12-month interest and dividend payments divided by the last month’s ending share price (NAV) plus any capital gains distributed over the same period. • SEC yield: based on 30-day period ending on the last day of previous month, reflects the deduction of the fund’s expenses.

29. Examples of bond portfolio • Rating(default risk): • Duration(interest risk) • Duration: Average years to maturity • Longer duration is more sensitive to interest changes • When interest rate increases from 3% to 4%, a bond with duration of 4 years will see price decline of approximate 4*(4%-3%)=4%

30. Examples of bond portfolio • Portfolio holdings • Weight, maturity and coupon rate • Risk of each individual issue and the benefit of diversification • Compared with other bond ETF • BSV (ST T bond+ corporate,yield,grade, duration) • SCPB (corporate A bond) • JNK-high yield (similar to HYG)