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Chapter 11 Bond Valuation

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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

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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

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**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

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**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

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**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

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**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

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**Figure 11.1 The Impact of Inflation on the Behavior of Interest Rates**

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**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

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**Figure 11.2 Two Types of Yield Curves**

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**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

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**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

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**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

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**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

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**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

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**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

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

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**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

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**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

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**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%?

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**Ways to Measure Bond Yield**

Current yield Yield-to-Maturity Yield-to-Call Expected Return

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Current Yield Simplest yield calculation Only looks at current income

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**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

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**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?

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**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

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**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?

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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

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**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?

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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.

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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%.

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**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.

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**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

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**Table 11. 1 Duration Calculation for a 7**

Table Duration Calculation for a 7.5%, 15-Year Bond Priced to Yield 8%

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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.

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**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

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**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

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**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)

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**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

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