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Chapter 9

Chapter 9. Debt Instruments Quantitative Issues. Learning Objectives. Bond Valuation Yield Measures Duration Managing Bond Portfolios Term Structure Factors affecting Prices/Yields. Five Bond Pricing Theorems. Bond prices move inversely to changes in interest rates

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Chapter 9

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  1. Chapter 9 Debt Instruments Quantitative Issues

  2. Learning Objectives • Bond Valuation • Yield Measures • Duration • Managing Bond Portfolios • Term Structure • Factors affecting Prices/Yields

  3. Five Bond Pricing Theorems • Bond prices move inversely to changes in interest rates • The longer the maturity of a bond, the more price sensitive the bond • The price sensitivity of bonds to changes in interest rates increases as maturity increases, but at a decreasing rate • Bonds with lower coupons are more price sensitive • Yield decreases have a greater impact on bond prices than similar yield increases

  4. TI BA II Plus (Pro) - BOND PRICES • The price of a bond (PB) is a combination of a present value of an annuity (the present value of the coupons to be received) and the present value of the face (par) value of the bond. • PB = $Coupon * PVIFA + $Face * PVIF

  5. COMPUTING BOND PRICES using the BA II Plus • Example: Suppose we have a bond paying a 12% coupon rate ($120), paid semi-annually. The bond matures in 20 years and has a face value of $1,000. If the current market rate (YTM) is 9%, how much should this bond sell for (price)? • In this type of problem we will use all five TVM keys; [ N ] [ I/Y ] [ PV ] [ PMT ] [ FV ]

  6. COMPUTING BOND PRICES using the BA II Plus • The bond pays coupons (interest) twice a year (semi-annual): We set the periods per year (P/Y) and (C/Y) to 2. • The 12% coupon rate ( $120 per year) is paid in two [PMT=] $60 installments. • The bond will have a maturity (face, par) value [FV] of $1000.00. • The current market rate is [I/Y] 9% (the required YTM for bonds in this risk class).

  7. COMPUTING BOND PRICES using the BA II Plus • BA II PLUS Solution 1. ENTER 20 [2nd] [N], [N] N = 40.00 2. ENTER 9 [I/Y] I/Y = 9.00 3. ENTER 60 [PMT] PMT = 60.00 4. ENTER 1000 [FV] FV = 1,000.00 5. PRESS [CPT] [PV] PV = -1,276.02 We would have to pay $1,276.02 to buy this bond today.

  8. COMPUTING BOND PRICES using the BA II Plus • What if the current YTM is 8.5%? • Enter 8.5, press [I/Y] • Press [CPT] [PV]: PV = - 1,333.85 • Clearly, a lower YTM results in a higher price. • What if the current YTM is 9.5%? • Enter 9.5, press [I/Y] • Press [CPT] [PV]: PV = - 1,222.04 • Clearly, a lower YTM results in a higher price. Bond prices move inversely to changes in interest rates

  9. Yield Measures • Coupon Rate = Annual Coupon ÷ $1000 • Current Yield = Annual Coupon ÷ Price • Yield To Maturity = actual rate earned on bond if held to maturity (same concept as IRR) • To compute YTM: CLR TVM, then • Set P/Y value (2 or 4 are typical) • Enter N, [-]Price (PV), interest PMT, FV ($1000 typical) • Compute I/Y • Text Example (p9.9): P/Y = 2, N = 12, PV = -950, PMT = 20, FV = 1000. CPT I/Y = 4.9741

  10. Yield to Maturity • Yield to maturity is the rate at which a bond’s cash flows are discounted • Changes as market interest rates change • Yield to maturity and coupon rate (CR) • If P(b) < F, then YTM > CR (discount bond) • If P(b) = F, then YTM = CR • If P(b) > F, then YTM < CR (premium bond)

  11. Actual Return & Yield to Maturity • If you buy a bond and hold it until maturity, will your actual return equal the bond’s yield to maturity? • No, unless you can reinvest the coupons at the yield to maturity rate • If reinvestment rate is less than YTM, actual return will be less than YTM • If reinvestment rate is greater than YTM, actual return will be greater than YTM

  12. Yield Relationships (Fig 9-2)

  13. Computing Yield to [First] Call • Bonds may be issued “Callable” during periods of high interest rates. The “callable” feature allows the issuer to recall the bonds and reissue the debt at lower rates. • Recalls typically require a premium to be paid. • Example: Suppose you are considering buying a 10% coupon bond (paid quarterly) recallable in 3 years at 107.5 (a premium of $75 in addition to any accrued interest). The FV = 1075 and the N value would be 3 * P/Y. • The bond currently sells for $1464.07. What is the YTFC (yield to first call)? YTM = 6%

  14. Computing Yield to [First] Call • N = 3 * 4 = 12 • PV = - 1464.07 • PMT = 25 • FV = 1075 • [CPT] [I/Y] = 2.3133 • This is obviously not a good deal. • Right off the bat – you’re taking a $389.07 capital loss. • The $75 early call premium is insufficient to cover the expected capital loss. • The YTFC (2.3133%) is less than the current YTM (6%). • You’re better off buying a new issue bond.

  15. Assessing Interest Rate Risk • Bond Price Volatility • 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 YTM have greater percentage price changes than bonds with higher YTM – all other things equal.

  16. Assessing Interest Rate Risk • A bond’s interest rate risk is defined as the sensitivityofprice to a change in YTM. • Which bond is more price sensitive? • Bond A: 10% coupon, 10 year maturity • Bond B: 5% coupon, 5 year maturity • We can’t say without some sort of summary measure of interest rate risk • Such a measure is called duration

  17. Duration • Duration measures the amount of time before the investor receives the “average” dollar from a bond • Duration is a function of a bond’s coupon rate, time to maturity and yield to maturity • Duration: • Increases as the coupon rate decreases • Increases as the time to maturity increases • Increases as yield to maturity decreases • The longer the duration of a bond, the more sensitive its price to a given change in interest rates.

  18. Duration • Formulas for Duration Note: Exponents in Eq. 9-5 should be t not T Denominator above is also equal to the current price (DCF)

  19. Duration • 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 • Principal Characteristics • 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 • Direct relationship between maturity and duration

  20. Duration • 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]

  21. Interest Rate Risk • 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 • 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

  22. Bond Portfolio Immunization • Strategies a Function of Needs • 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 • 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.

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

  24. Managing Bond Portfolios • Types of Swaps • Substitution swap (tax loss issues) • Inter-market spread swap (transports vs. utilities) • Pure-yield pick-up swap • Rate anticipation swap: Yield expectations • Portfolio Structure • Bullet Portfolio (one maturity date) • Bond ladders (equally distributed dollar allocations over time) • Barbells (varying maturities) • Allocations to shortest-term and longest-term holdings

  25. Term Structure of Interest Rates • Typical: rising to right (see Fig 9-5, pp 9.35) • Normal • Inverted • Flat • Theories of Term Structure • Expectations (spot vs. forward rates – see pp 9.38ff) • Liquidity Preference (premiums for longer terms) • Market Segmentation (effects of supply & demand) • Preferred Habitat (maturity preference)

  26. 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. • Coupon effect: Low-coupon issues offer yields that are partially taxed as capital gains. • 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 Requirements: reduce probability of default

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