Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 11 Bond Valuation.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Chapter 11

Bond Valuation

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 11-2

Bond Valuation and Analysis

• Learning Goals

1. Explain the behavior of market interest rates, and identify the forces that cause interest rates to change.

2. Describe the term structure of interest rates, and note how yield curves can be used by investors.

3. Understand how bonds are valued in the marketplace.


Bond Valuation and Analysis

• Learning Goals (cont’d)

4.Describe the various measures of yield and return, and explain how these standards of performance are used in bond valuation.

5.Understand the basic concept of duration, how it can be measured, and its use in the management of bond portfolios.

6.Discuss the various bond investment strategies and the different ways these securities can be used by investors.


For bonds, the risk premium depends upon:• the default, or credit, risk of the issuer• the term-to-maturity• any call risk, if applicable

Measuring Return

• Required Return: the rate of return an investor must earn on an investment to be fully compensated for its risk

Required ReturnOn Investment

=Real Rateof Return +

Expected InflationPremium

+Risk Premiumfor Investment


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


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


Factors Affecting Yield Spreads(cont’d)

• Revenue muni bonds yield more than general obligation muni bonds due to higher risk

• Freely callable bonds yield higher than noncallable bonds

• Bonds with longer maturities generally yield more than shorter maturities


Interest rates go , bond prices go

Interest rates go , bond prices go

What is the single biggest factor that influences the price of bonds?

• Interest Rates


What is the single biggest factor that influences the direction of interest rates?

• Inflation

Inflation goes , interest rates go

Inflation goes , interest rates go


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


Economic Variables that Affect Interest Rates

Economic Interest RateVariable Change Effect

Change in money supply Slow increase DSlow decrease C

Change in money supply Fast increase CFast decrease D

Federal Budget Deficit CSurplus D

U.S. Economic Activity Recession DExpansion C


Economic Variables that Affect Interest Rates (cont’d)

Economic Interest RateVariable Change Effect

Federal Reserve Policies Slower growth DFaster growth C

Foreign Interest Rates Higher CLower D


Term Structure of Interest Ratesand 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


Figure 11.2 Two Types of Yield Curves


Theories on Shape of Yield Curve

• Slope of yield curve affect by:

– Inflation expectations

– Liquidity preferences of investors

– Supply and demand


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

– If expecting higher inflation, investors demand higher interest rates on longer maturities to compensate for risk

– Increasing inflation expectations will result in upward-sloping yield curve

– Decreasing inflation expectations will result in downward-sloping yield curve



• Liquidity Preference Theory

– Shape of yield curve is based upon the length of term, or maturity, of bonds

– If investors’ money is tied up for longer periods of time, they have less liquidity and demand higher interest rates to compensate for real or perceived risks

– Investors won’t tie their money up for longer periods unless paid more to do so



• Market Segmentation Theory– Shape of yield curve is based upon the supply and demand

for funds

– The supply and demand changes based upon the maturity levels: short-term vs. long-term

– If more borrowers (demand) want to borrow long-term than investors want to invest (supply) long-term, then the interest rates (price) for long-term funds will go up

– If fewer borrowers (demand) want to borrow long-term than investors want to invest (supply) long-term, then the interest rates (price) for long-term funds will go down


Interpreting Shape of Yield Curve

• Upward-sloping yield curves result from:– Higher inflation expectations– Lender preference for shorter-maturity loans– Greater supply of shorter-term loans

• Flat or downward-sloping yield curves result from:– Lower inflation expectations– Lender preference for longer-maturity loans– Greater supply of longer-term loans


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


The Pricing of Bonds

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

Bond price =Present value of the annuityof annual interest income +

Present value of thebond's par value


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



• 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



• Bond Pricing Example:

– What is the market price of a $1,000 par value 20 year bond that pays 9 ½ % compounded annually when the market rate is 10%?


Ways to Measure Bond Yield

• Current yield

• Yield-to-Maturity

• Yield-to-Call

• Expected Return


Current Yield

• Simplest yield calculation

• Only looks at current income

Current yield =Annual interest

Current market price of the bond


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


Yield-to-Maturity (cont’d)

• Yield-to-Maturity Example:

– Find the yield-to-maturity on a 7 ½ % ($1,000 par value) bond that has 15 years remaining to maturity and is currently trading in the market at $809.50?


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


Yield-to-Call (cont’d)

• Yield-to-Call Example:

– Find the yield-to-call of a 20-year, 10 ½ % bond that is currently trading at $1,204, but can be called in 5 years at a call price of $1,085?


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


Expected Return (cont’d)

• Expected Return Example:

– Find the expected return on a 7 ½% bond that is currently priced in the market at $810 but is expected to rise to $960 within a 3-year holding period?


Bond Duration

• Bond Duration: A measure of bond price volatility, which captures both price and reinvestment risk and which is used to indicate how a bond will react in different interest rate environments


Bond Duration (cont’d)

• Improvement over yield-to-market because factors in reinvestment risk

• Compares the sensitivity to changes in interest rates

• Bond Duration is the average amount of time that it takes to receive the interest and the principal

• Calculates the weighted average of the cash flows (interest and principal payments) of the bond, discounted to the present time


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 Concept of Duration (cont’d)

• Bond duration is a better indicator than bond maturity of impact of interest rates on bond price (price volatility)– If interest rates are going up, hold bonds with

short durations

– If interest rates are going down, hold bonds with long durations


Measuring Duration

• Steps in calculating 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 relative value by the year in which the cash flow is to be received

– 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


Table 11.1 Duration Calculation for a 7.5%, 15-Year Bond Priced to Yield 8%


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.


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


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 years)

– 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



• 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)



• 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


Chapter 11 Review

• Learning Goals

1. Explain the behavior of market interest rates, and identify the forces that cause interest rates to change.

2. Describe the term structure of interest rates, and note how yield curves can be used by investors.

3. Understand how bonds are valued in the marketplace.


Chapter 11 Review (cont’d)

• Learning Goals (cont’d)4. Describe the various measures of yield and return, and

explain how these standards of performance are used in bond valuation.

5. Understand the basic concept of duration, how it can be measured, and its use in the management of bond portfolios.

6. Discuss the various bond investment strategies and the different ways these securities can be used by investors.


Figure 11.3A Yield Curves on U.S. Treasury Issues


Figure 11.3B Yield Curves on U.S. Treasury Issues


Table 11.2 Bond Immunization

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 11 Bond Valuation.

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Transcript of Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 11 Bond Valuation.