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# Chapter 9

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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 years @ \$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 • 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 sensitivityD* = 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 InterestRate 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 • 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.