Chapter 10

Bond Prices and Yields

Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

10.1 Bond Characteristics

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U.S. Credit Market Instruments O/S 2008 Q3

U.S. Equity Market (Common)

U.S. Credit Market Debt

Debt by Selected Major Borrowers (Not Exhaustive List):

U.S. Government Securities (Includes Agency & GSE)

%s are percent of Total U.S. Credit Market Debt, source is Federal Reserve Flow of Funds

$19,648 Billion

$51,796

$13,850 (27%)

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U.S. Credit Market Instruments O/S 2008 Q3

By Selected Major Borrowers (Not Exhaustive List)

Corporate & Foreign Bonds

Municipal BondsG.O., Revenue, Notes

Mortgages

$11,262 Billion

(22%)

$2,669 Billion

(5%)

$14,720 Billion(28%)

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Bond Characteristics• Face or par value

• Coupon rate– Zero coupon bond

• Compounding and payments– Accrued Interest

• Indenture

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Treasury Notes and Bonds

• T Note maturities range up to 10 years• T bond maturities range from 10 to 30 years• Bid and ask price

– Quoted in dollars and 32nds as a percent of par– Typical par = $1,000

• Accrued interest – Quoted price does not include interest accrued

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Figure 10.1 Prices and Yields of U.S. Treasuries

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Corporate Bonds & Debt

• Most bonds are traded over the counter• Par = $1,000• Registered versus Bearer bonds• Call provisions• Convertible provision• Put provision (putable bonds)• Floating rate bonds• Preferred Stock

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Figure 10.2 Listing of Corporate Bonds

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Other Domestic Issuers• Federal Home Loan Bank Board

• Farm Credit Agencies

• Ginnie Mae

• Fannie Mae

• Freddie Mac

• Municipalities

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International Bonds

• Foreign bonds– Issued by a borrower from a country other than the

one in which the bond is sold.– Bonds are denominated in the currency of the country

in which it is sold. • Yankee bonds, Samurai bonds, Bulldog bonds

• Eurobonds– Bonds issued in the currency of one country but sold

in other national markets. • Eurodollar bonds, Euroyen bonds

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Innovations in the Bond Market

• Inverse floaters– Coupon rate falls when interest rates rise & vice versa

• Asset-backed bonds– Income from specified assets is used to service the

bond• Pay-in-kind bonds

– Bond issuer may choose to pay interest by giving the investor a bond rather than cash

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Innovations in the Bond Market

• Catastrophe bonds– In the event of a specified ‘disaster’ the bond

issuer’s required payments are reduced or eliminated.

• Indexed bonds – Payments are tied to a price index or the price of a

commodity.• TIPS (Treasury Inflation Protected Securities) With TIPS

the par value of the bond increases with the Consumer Price Index.

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Hypothetical Principal and Interest Payments on a TIPS

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10.2 BOND PRICING

10-15

Bond Prices & Yieldsa) Bond Price for a corporate bond:

C = Coupon = 10%, interest rate = ytm = r = 12%, Maturity = N or T = 10 years, P = price, Par = $1,000

What is the bond’s price using semiannual compounding?

2N

2N

1TT ½r)(1

Par

½r)(1

½$CP

$885.30 $311.80 $573.50P

64.8% 35.2%

20

20

1TT )06.(1

$1,000

)06.(1

$50P

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Bond Pricing Between Coupon Dates

• The flat price or quoted price assumes the bond is purchased on a coupon payment date.

• If the bond buyer purchases a bond between payment dates the buyer’s invoice price = flat price + accrued interest.

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Bond Pricing Between Coupon Dates

• A bond has a flat price of $925.30 and an annual coupon of $42.50. 160 days have passed since the last coupon payment and there are 182 days separating the coupon payments. What is the bond’s invoice price?

payments coupon between Days

payment coupon last since Days

2

Coupon$ AnnualInterest Accrued

$18.68182

160

2

$42.50Interest Accrued

Interest AccruedPrice Flatprice Invoice

$943.98$18.68$925.30price Invoice

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10.3 BOND YIELDS

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Bond Prices and Yields• Prices and Yields (required rates of return)

have an inverse relationship

• When yields get very high the value of the bond will be very low

• When yields approach zero, the value of the bond approaches the sum of the cash flows

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• YTM is the discount rate that makes the present value of a bond’s payments equal to its price

• Find the YTM for a 8% coupon, 30-year bond selling at $1,276.76

• Assumption of this calculation?

Promised Yield to Maturity (YTM)

2N

2N

1TT ½r)(1

Par

½r)(1

½$CP

60

60

1TT ½r)(1

$1,000

½r)(1

$4076.276,1$

%3r

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Figure 10.3 The Inverse Relationship Between Bond Prices and Yields

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Alternative Measures of Yield• Current Yield

– Annual dollar coupon divided by the price

• Yield to Call

– Call price replaces par

– Call date replaces maturity

• Holding Period Yield

– Considers actual reinvestment rate on coupons

– Considers any change in price if the bond is sold prior to maturity

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Yield to Call Illustrated

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Figure 10.4 Bond Prices: Callable and Straight Debt

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Figure 10.5 Growth of $1000 invested in a 2 year bond

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Example 10.5 Growth of $1000 invested in a 2 year bond

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10.4 BOND PRICES OVER TIME

10-28

Premium and Discount Bonds

• Premium Bond– Coupon rate exceeds yield to maturity– Bond price will decline to par over its maturity

• Discount Bond– Yield to maturity exceeds coupon rate– Bond price will increase to par over its maturity

• Can you explain why these price change will occur?

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Figure 10.6 Premium and Discount Bonds over Time

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Figure 10.7 The Price of a Zero Coupon Bond over TimeHow does one earn a rate of return on a zero coupon bond?

Nr)(1

ParP

What are STRIPS?

How is the price appreciation taxed?

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10.5 DEFAULT RISK AND BOND PRICING

10-32

Default Risk and Ratings• Main Ratings Companies

– Moody’s Investor Service– Standard & Poor’s– Fitch

• Main Rating Categories– Investment grade– Speculative grade (junk bonds)

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Figure 10.8 Definitions of Bond Rating Classes

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Factors Used by Rating Companies

• Coverage ratios– TIE and Fixed Charges Coverage ratio

• Leverag e ratios– Debt to equity or Debt to assets

• Liquidity ratios– Current and quick ratio

• Profitability ratios– Return on assets and return on equity

• Cash flow to debt– Cash flow to debt

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Financial Ratios and Default Risk

10-36

Protection Against Default• Sinking funds

– Issuer may repurchase a given fraction of the outstanding bonds each year, or

– Issuer may either repurchase at the lower of open market price or at a pre-specified price, usually par; bonds are chosen randomly

• Serial bonds– Staggered maturity dates

• Subordination of future debt– Senior debt holders must be paid in full before junior

debt holders.

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Protection Against Default• Dividend restrictions

– Limit on liquidating dividends

• Collateral– A specific asset pledged against possible default on a

bond.

– What is a bond called that has no specific collateral?

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Figure 10.9 Callable Bond Issued by Mobil

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Example 10.10 YTM and Default

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Figure 10.10 Yields Spreads on 10 year bonds

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Credit Default Swaps

A credit default swap (CDS) is an insurance policy on the default risk of a bond or loan.•The seller of the swap collects an annual premium (and sometimes an upfront fee) from the swap buyer.

•The buyer of the swap collects nothing unless the bond issuer or loan borrower defaults, in which case the seller of the swap essentially pays the drop in value from par to the swap buyer.

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Credit Default Swaps

• CDSs can be used to speculate on financial health of firms.– Swap buyer need not hold the underlying bond or

loan.– At their peak there were reportedly $63 trillion worth

of CDS; US GDP is about $14 trillion. – What is the implication of the size of this market if the

economy experiences greater than expected defaults?

– Did this contribute to the Financial Crisis of 2008?

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Credit Default Swaps

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Credit Default Swaps

• New regulations on CDS will be implemented– CDS contracts will be required to be traded on

an exchange with collateral requirements to limit risk.

– Exchange trading will also increase transparency of positions of institutions.

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10.6 THE YIELD CURVE

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Term Structure of Interest Rates

• Relationship between yields to maturity and maturity

• Yield curve: a graph of the yields on bonds relative to the number of years to maturity– Have to be similar risk or other factors would

be influencing yields

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Figure 10.12 Treasury Yield Curves

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Theories of the Term Structure• Expectations

– Long term rates are a function of expected future short term rates

– Upward slope means that the market is expecting higher future short term rates

– Downward slope means that the market is expecting lower future short term rates

• Liquidity Preference– Upward bias over expectations– The observed long-term rate includes a risk premium

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Figure 10.13 Returns to Two 2-year Investment Strategies

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Forward Rates Implied in the Yield Curve

)1301.1()11.1()12.1(

)1()1()1(12

1

1

fyy nnn

nn

For example, using 1-yr and 2-yr rates

Longer term rate, yn = 12%

Shorter term rate, yn-1 = 11%

Forward rate, a one-year rate in one year = 13.01%

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Figure 10.14 Illustrative Yield Curves

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Figure 10.15 Term Spread

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