1. Chapter 11
Bond Valuation

2. Measuring Return
Required Return: the rate of return an investor must earn on an investment to be fully compensated for its risk
For bonds, the risk premium depends upon:
the default, or credit, risk of the issuer
the term-to-maturity
any call risk, if applicable

3. Major Bond Sectors
Bond market is comprised of a series of different market sectors:
U.S. Treasury issues
Municipal bond issues
Corporate bond issues
Differences in interest rates between the various market sectors are called yield spreads

4. Factors Affecting Yield Spreads
Municipal bond rates are usually 20-30% lower than corporate bonds due to tax-exempt feature
Treasury bonds have lower rates than corporate bonds due to no default risk
The lower the credit rating (and higher the risk), the higher the interest rate
Discount (low-coupon) bonds yield less than premium (high-coupon) bonds

5. Factors Affecting Yield Spreads (cont’d)
Revenue municiple bonds yield more than general obligation municiple bonds due to higher risk
Freely callable bonds yield higher than noncallable bonds
Bonds with longer maturities generally yield more than shorter maturities

6. What is the single biggest factor that influences the price of bonds?
Interest Rates
Interest rates go G, bond prices go H
Interest rates go H, bond prices go G

7. What is the single biggest factor that influences the direction of interest rates?
Inflation
Inflation goes G, interest rates go G
Inflation goes H, interest rates go H

8. Figure 11.1 The Impact of Inflation on the Behavior of Interest Rates

9. Term Structure of Interest Rates and Yield Curves
Term Structure of Interest Rates: relationship between the interest rate or rate of return (yield) on a bond and its time to maturity
Yield Curve: a graph that represents the relationship between a bond’s term to maturity and its yield at a given point in time

10. Figure 11.2 Two Types of Yield Curves

11. Theories on Shape of Yield Curve
Slope of yield curve affect by:
Investors’ expectations regarding the future behavior of interest rates
Liquidity preferences of investors
Market segmentation (supply and demand for bonds of different maturities)
Risk premium and convexity

12. Theories on Shape of Yield Curve (cont’d)
Expectations Hypothesis
Shape of yield curve is based upon investor expectations of future behavior of interest rates
When investors expect interest rates to go up, they will only purchase long-term bonds if those bonds offer higher yields than short-term bonds; hence the yield curve will be upward sloping
When investors expect interest rates to go down, they will only purchase short-term bonds if those bonds offer higher yields than long-term bonds; hence the yield curve will be downward sloping

13. Theories on Shape of Yield Curve (cont’d)
Liquidity Preference Theory
Shape of yield curve is based upon the difference in risk between short-term and long-term bonds
If investors’ view long-term bonds as being riskier than short-term bonds, then rates on long-term bonds must be higher than rates on short-term bonds
Investors may view long-term bonds as being riskier because long-term bonds are less liquid and are subject to greater interest rate risk

14. Theories on Shape of Yield Curve (cont’d)
Market Segmentation Theory
Suggests that the bond market consists of distinct segments (based on maturity) due to the preferences of investors and borrowers
Supply and demand for funds in these distinct segments determine the level of short- and long-term interest rates
Therefore, an upward sloping yield curve is not a sign that investors expect rates to rise or a sign that investors see long-term bonds as being riskier than short-term bonds
Instead, an upward sloping curve means that the supply of short-term funds is high relative to borrowers’ needs, so rates on short-term bonds are lower than rates on long-term bonds

15. Interpreting Shape of Yield Curve
Upward-sloping yield curves result from:
Expectation of rising interest rates
Lender preference for shorter-maturity loans
Greater supply of shorter-term loans
Flat or downward-sloping yield curves result from:
Expectation of falling interest rates
Lender preference for longer-maturity loans
Greater supply of longer-term loans

16. Basic Bond Investing Strategy
If you expect interest rates to increase, buy short-term bonds
If you expect interest rates to decrease, buy long-term non-callable bonds

17. The Pricing of Bonds
Bonds are priced according to the present value of their future cash flow streams

18. The Pricing of Bonds (cont’d)
Bond prices are driven by market yields
Appropriate yield at which the bond should sell is determined before price of the bond
Required rate of return is determined by market, economic and issuer characteristics
Required rate of return becomes the bond’s market yield
Market yield becomes the discount rate that is used to value the bond

19. The Pricing of Bonds (cont’d)
Bond prices are comprised of two components:
Present value of the annuity of coupon payments, plus
Present value of the single cash flow from repayment of the principal at maturity
Compounding refers to frequency coupons are paid
Annual compounding: coupons paid once per year
Semi-annual compounding: coupons paid every six months

20. The Pricing of Bonds (cont’d)
Bond Pricing Example:
What is the market price of a $1,000 par value 20 year bond that pays 9.5 % compounded annually when the market rate is 10%?

21. Ways to Measure Bond Yield
Current yield
Yield-to-Maturity
Yield-to-Call
Expected Return

22. Current Yield
Simplest yield calculation
Only looks at current income

23. Yield-to-Maturity Most important and widely used yield calculation
True yield received if the bond is held to maturity
Assumes all interest income is reinvested at rate equal to market rate at time of YTM calculation—no reinvestment risk
Calculates value based upon PV of interest received and the appreciation of the bond if held until maturity
Difficult to calculate without a financial calculator

24. Yield-to-Maturity (cont’d)
Yield-to-Maturity Example:
Find the yield-to-maturity on a 7.5 % ($1,000 par value) bond that has 15 years remaining to maturity and is currently trading in the market at $809.50?

25. Yield-to-Call Similar to yield-to-maturity
Assumes bond will be called on the first call date
Uses bonds call price (premium) instead of the par value
True yield received if the bond is held to call

26. Yield-to-Call (cont’d)
Yield-to-Call Example:
Find the yield-to-call of a 20-year, 10.5 % bond that is currently trading at $1,204, but can be called in 5 years at a call price of $1,085?

27. Expected Return
Used by investors who expect to actively trade in and out of bonds rather than hold until maturity date
Similar to yield-to-maturity
Uses estimated market price of bond at expected sale date instead of the par value

28. Expected Return (cont’d)
Expected Return Example:
Find the expected return on a 7.5% bond that is currently priced in the market at $ but is expected to rise to $960 within a 3-year holding period?

29. Bond Duration
Bond Duration: A measure of bond price sensitivity to interest rate changes.
Macauley duration: Weighted average maturity of all cash flows, with the weight given by the present value of the cash flow, divided by the current bond price.

30. Bond Duration
Modified duration: Macauley duration/(1+y), measures the percentage change in bond value per change in interest rate
Example: A bond as a Macauley duration of 7.00 and is priced to yield 5%. If the market interest rate goes up so that the yield goes up to 5.5%, the percentage change in the bond price is:
-7*(5.5%-5%)/(1+5%)=-3.33%
The bond price will go down by 3.33%.

31. The Concept of Duration
Generally speaking, bond duration possesses the following properties:
Bonds with higher coupon rates have shorter durations
Bonds with longer maturities have longer durations
Bonds with higher YTM lead to shorter durations
The bond duration as a sensitivity measure works better for small rate moves, but may not work well for large moves due to convexity effects.

32. Measuring Duration Steps in calculating Macauley duration
Step 1: Find present value of each coupon or principal payment
Step 2: Divide this present value by current market price of bond
Step 3: Multiple this ratio by the year in which the bond makes each cash payment
Step 4: Repeat steps 1 through 3 for each year in the life of the bond then add up the values computed in Step 3

33. Table 11. 1 Duration Calculation for a 7
Table Duration Calculation for a 7.5%, 15-Year Bond Priced to Yield 8%

34. Bond Immunization
Strategy to derive a specified rate of return regardless of what happens to market interest rates over holding period
Seeks to offset the opposite changes in bond valuation caused by price effect and reinvestment effect
Price effect: change in bond value caused by interest rate changes
Reinvestment effect: as coupon payments are received, they are reinvested at higher or lower rates than original coupon rate
Bond immunization occurs when the average duration of the bond portfolio just equals the investment time horizon.

35. Bond Investment Strategies
Conservative Approach
Main focus is high current income
High credit quality bonds are used
Usually longer holding periods
Aggressive Approach
Main focus is capital gains
Usually shorter holding periods with frequent bond trading
Use forecasted interest rate strategy to time bond trading

36. Bond Investment Strategies (cont’d)
Buy-and-hold strategy
Replace bonds as they mature or quality declines
Bond ladder strategy
Set up “ladder” by investing equal amounts into varying maturity dates (i.e. 3-, 5-, 7- and 10-year)
As bonds mature, purchase new bonds with 10-year maturity to keep ladder growing
Provides higher yields of longer-term bonds and dollar-cost averaging benefits

37. Bond Investment Strategies (cont’d)
Bond Swaps
Occur when investor sells one bond and simultaneously buys another bond in its place
Yield pickup swap strategy
Sell a lower yielding bond and replace it with a comparable credit quality bond with higher yield
Often done between different bond sectors (i.e. industrial bonds vs. utility bonds)

38. Bond Investment Strategies (cont’d)
Tax swap strategy
Sell a bond that has declined in value, use the capital loss to offset other capital gains, and repurchase another bond of comparable credit quality
Watch out for wash sales—new bond cannot be an identical issue to old bond