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Chapter 11

Bond Valuation

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Bond Valuation and Analysis

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.

3. Understand how bonds are valued in the marketplace.

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Bond Valuation and Analysis

Goals

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.

6. Discuss the various bond investment strategies.

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For bonds, the risk premium depends upon:• the default, or credit, or 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 Inflation

Premium

Risk Premiumfor Investment

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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

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

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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

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

Inflation

Inflation goes , interest rates go

Inflation goes , interest rates go

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The Impact of Inflation on the Behavior of Interest Rates

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Economic Variables that Affect Interest Rates Economic Interest Rate

Variable 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

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Economic Variables that Affect Interest Rates Economic Interest Rate

Variable Change Effect

Federal Reserve Policies Slower growth DFaster growth C

Foreign Interest Rates Higher CLower D

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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

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Two Types of Yield Curves

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Theories on Shape of Yield Curve

Slope of yield curve affect by:

Inflation expectations

Liquidity preferences of investors

Supply and demand

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Theories on Shape of Yield Curve

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

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Theories on Shape of 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

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Theories on Shape of Yield Curve

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

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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

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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

Bond price Present value of the annuity

of annual interest income

Present value of thebond's par value

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The Pricing of Bonds

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

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

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%?

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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

Current yield Annual interest

Current market price of the bond

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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

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?

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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

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?

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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

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?

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Bond Duration

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

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Bond Duration

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

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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

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The Concept of Duration

Bond duration is a better indicator than bond maturity of the impact of interest rates on bond price (price fluctuation) (Remember Reinvestment…)

If interest rates are going up, hold bonds with short durations

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

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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

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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

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

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Bond Investment Strategies

Bond Swaps 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

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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Review

Goals

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

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

3. Understood how bonds are valued in the marketplace.

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Review

Goals

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

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

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

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The End!

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Chapter 11

Additional Chapter Art

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Yield Curves on U.S. Treasury Issues

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Yield Curves on U.S. Treasury Issues

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Bond Immunization