1. Chapter 9
Debt Instruments
Quantitative Issues

2. Pricing a Bond where P0 = price of bond today T = maturity of the bond
Y = appropriate discount rate
PAR = par or face value of the bond

3. Bond Prices with Semiannual Payments
Divide coupon payment by two
Multiply maturity of bond by two.
Divide discount rate by two

4. Bond Yields & Rates Coupon rate (nominal yield)
Current yield (coupon / price)
Yield to maturity (YTM = IRR)
Realized compound yield to maturity (RCYTM)
Yield to First (earliest) Call
Realized return

5. ABC Example Coupon: $40 per year Par Value: $1,000 Maturity: 6 years
Callable: in 3 $1040
Price: $950

6. Coupon Rate Stated dollar return of fixed-income investment
Equals annual interest payments divided by par value

7. Current Yield
Bond’s coupon rate divided by current market price OR
Stock’s indicated dividend rate divided by per-share price

8. Yield to Maturity
Measure of bond yield that takes into account capital gain or loss, as well as coupon payments
Discount rate that would make present value of bond’s cash flows (payments plus face value at maturity) equal purchase price of bond
where C = the coupon payment

9. Yield Relationships

10. Yield to Call where Tc = time to earliest call
Yc = yield to first call
Almost identical to YTM, except
Call price replaces par value
Time to call replaces term to maturity

11. Realized Rate (Yield)
Ex post rate of return or yield from investment (internal rate of return)
where TH = holding period
YH = realized rate of return

12. Bond Price Volatility Bond prices and interest rates inversely related
Maturity effect: longer a bond’s term to maturity, greater percentage change in price for given change in interest rates
Coupon effect: lower a bond’s coupon rate, greater percentage change in price for given change in interest rates
Yield-to-maturity effect: For given change in interest rates, bonds with lower YTMs have greater percentage price changes than bonds with higher YTMs – all other things equal

13. Which Bond’s Price Is Most Volatile?
Bond X: 25 years to maturity, 10% coupon rate, and a 6% YTM
Bond Y: 10 years to maturity, 2% coupon rate, and a 6% YTM
Bond Z: 17.5 years to maturity, 6% coupon rate, and a 4% YTM

14. Answer Based on maturity effect, it would be X
Based on coupon effect, it would be Y
Based on yield-to-maturity effect, it would be Z

15. Duration
Weighted average amount of time until present value of bond’s purchase price repaid to the investor
Based on time-weighted present value of bond’s principal and interest payments divided by the bond’s price
Used as measure of bond’s sensitivity to interest rate changes

16. Formula for Duration Where P0 = price of the bond today
Y = yield to maturity
Ct = cash flow in period t (coupon, principal or both)
T = term to maturity

17. Equation 9-6 Insert Equation Where Y = yield to maturity
C = coupon rate
T = term to maturity

18. Uses of Duration Price volatility index Immunization
Larger duration statistic, more volatile price of bond
Immunization
Interest rate risk minimized on bond portfolio by maintaining portfolio with duration equal to investor’s planning horizon

19. Major Characteristics of Duration
Duration of zero-coupon bond equal to term to maturity
Duration of coupon bond always less than term to maturity
Inverse relationship between coupon rate and duration
(continued)

20. Major Characteristics of Duration (continued)
Inverse relationship between yield to maturity and duration
Direct relationship between maturity and duration

21. Modified Duration
Adjusted measure of duration used to estimate a bond’s interest rate sensitivity D* = D  (1 + YTM) % Chg in price of bond = –D x % Chg in YTM % Chg in price of bond = – D* x [Chg in YTM]

22. Convexity

23. Portfolio Duration
Market value weighted average of durations of individual securities in the portfolio

24. Components of Interest Rate Risk
Price Risk
Reinvestment Rate Risk

25. Price Risk
Risk of existing bond’s price changing in response to unknown future interest rate changes
If rates increase, bond’s price decreases
If rates decrease, bond’s price increases

26. Reinvestment Rate Risk
Risk associated with reinvesting coupon payments at unknown future interest rates
If rates increase, coupons are reinvested at higher rates than previously expected
If rates decrease, coupons are reinvested at lower rates than previously expected

27. Immunizing a Portfolio
If a single time horizon goal, purchasing zero-coupon bond whose maturity corresponds with planning horizon
If multiple goals, purchasing series of zero-coupon bonds whose maturities correspond with multiple planning horizons
(continued)

28. Immunizing a Portfolio (continued)
Assembling and managing bond portfolio whose duration is kept equal to planning horizon
Note: this strategy involves regular adjustment of portfolio because duration of portfolio will change at SLOWER rate than will time itself

29. Bond Swaps
Technique for managing bond portfolio by selling some bonds and buying others
Possible benefits achieved:
tax treatment
yields
maturity structure
trading profits

30. Types of Swaps Substitution swap Intermarket spread swap
Tax swap
Intermarket spread swap
Pure-yield pick-up swap
Rate anticipation swap

31. Strategies for Managing a Bond Portfolio
Bullet Portfolio
– Entire portfolio is placed in one maturity
Bond ladders
Equally distributed dollar allocations over time
Barbells
Majority of dollar allocations in shortest-term and longest-term holdings

32. Yield Curve or Term Structure
Vertical axis: yield to maturity
Horizontal axis: term to maturity
Bonds of like quality
Always based on Treasuries

33. Shapes of Yield Curve
Rising: Most common (used to be only one observed)
Falling: Next most common
Humped
Flat: Rare

34. Types of Yield Curves

35. Theories of the Yield Curve
Unbiased expectations
Long-term rates reflect market’s expectation of current and future short-term rates.
Preferred habitat
Significantly more attractive rates can induce investors and borrowers out of their preferred maturity structures
(continued)

36. Theories of Yield Curve (continued)
Market Segmentation:
Yields reflect supply and demand for each maturity class.
Liquidity Preference:
Borrowers are risk averse and demand premium for buying long-term securities
Yield curves tend to be upward sloping.
(continued)

37. Theories of the Yield Curve (continued)
Preferred habitat
Significantly more attractive rates can induce investors and borrowers out of their preferred maturity structures
Unbiased expectations
Long-term rates reflect market’s expectation of current and future short-term rates.

38. Factors Affecting Bond Yields
General credit conditions: Credit conditions affect all yields to one degree or another.
Default risk: Riskier issues require higher promised yields.
Term structure: Yields vary with maturity
Duration: Weighted average amount of time until present value of purchase price is recouped.
Coupon effect: Low-coupon issues offer yields that are partially taxed as capital gains.
(continued)

39. Factors Affecting Bond Yields (continued)
Seasonings: Newly issued bonds may sell at slight discount to otherwise-equivalent established issues.
Marketability: Actively traded issues tend to be worth more than similar issues less actively traded.
Call protection: Protection from early call tends to enhance bond’s value.
Sinking fund provisions: Sinking funds reduce probability of default, thereby tending to enhance bond’s value.
Me-first rules: Bonds protected from diluting effect of additional borrowings are generally worth more than otherwise-equivalent unprotected issues.