1. Chapter 10 Bond Prices and Yields
Describes the financial instruments traded in primary and secondary markets.
Discusses Market indexes. Discusses options and futures.
McGraw-Hill/Irwin
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. 1

2. 10.1 Bond Characteristics
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3. 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%)
Potential for crowding out or overreliance on foreign financing
U.S. Credit Market Debt # excludes equities. Mortgage number includes pools, government debt numbers do not include pool backing obligations. Source Federal Reserve Flow Of funds Level Table L.4
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4. U.S. Credit Market Instruments O/S 2008 Q3
By Selected Major Borrowers (Not Exhaustive List)
Corporate & Foreign Bonds
Municipal Bonds G.O., Revenue, Notes
Mortgages
$11,262 Billion
(22%)
$2,669 Billion
(5%)
$14,720 Billion (28%)
Mortgage number includes pools, government debt numbers do not include pool backing obligations.
Source: Flow of funds tables, a PDF download from FRB. Foreign bonds in U.S. are about 2%.
Omitted categories: Open Market Paper, Bank Loans and Consumer Credit
A G.O. bond is a general obligation bond and is collateralized by the full taxing power of the municipality. A revenue bond is collateralized only by the revenues of a specific project such as a toll road. Hence, revenue bonds are riskier.
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5. Bond Characteristics Face or par value Coupon rate
Zero coupon bond
Compounding and payments
Accrued Interest
Indenture
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6. 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
Individual investors can buy $100 par T-notes and T-bonds but the standard is $1,000, although many times the bonds are bundled and sold as a group in multiples of $1,000.
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7. Figure 10.1 Prices and Yields of U.S. Treasuries
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8. 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
U.S. bonds are registered, most bonds in the rest of the world are bearer bonds. With bearer bonds you must clip off the coupon and mail it in to get your interest as you are not a registered owner, although a broker can do this for you. With registered bonds the issuer and the issuer’s trustee knows you are the owner and you will receive your interest and principal payments automatically. Registration helps the IRS ensure that interest income is declared.
The call provision is in the favor of the bond issuer, the issuer is likely to call in the bond when interest rates have fallen. The bond will be redeemed at a price over par, but the investor will be left with reinvesting in a lower interest rate environment. The firm is not going to call the bond unless its market value would have been above the call price. Most bonds are callable after an initial call protection period of 3 to 5 years. The quid pro quo is that bond issuers will have to pay a slightly higher yield rate if the bond is callable.
Convertible bonds may be converted to common stock at the option of the bondholder. This one is in the favor of the bondholder and the conversion ‘sweetener’ may reduce the required return.
In a putable bond the bondholder has the right to put the bond back, sell it back, to the bond issuer, usually on a coupon payment date.
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9. Figure 10.2 Listing of Corporate Bonds
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10. Other Domestic Issuers
Federal Home Loan Bank Board
Farm Credit Agencies
Ginnie Mae
Fannie Mae
Freddie Mac
Municipalities
Bonds issued by these entities may not have $1,000 par. Many will have substantially larger par amounts because of the institutional nature of these markets.
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11. 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
Yankee bonds are bonds issued in the U.S. by foreign borrowers; they are denominated in U.S. dollars. Likewise, Samurai bonds are issued in Japan by non-Japanese borrowers and are denominated in yen. Bulldog bonds are issued in Great Britain by non-British borrowers and are denominated in British pounds.
Eurodollar bonds are dollar denominated bonds issued outside the U.S. They are thus not regulated under U.S. securities laws the way Yankee bonds are. Yankee bonds must be registered with the SEC for example. Similarly Euroyen bonds are yen denominated bonds that are issued outside of Japan. These offerings allow banks and corporate treasurers to borrow money in different currencies and at different interest rates.
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12. 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
Inverse floaters were one of the securities held by Orange County Municipality when they went bankrupt. While they were holding the floaters interest rates rose about 200 basis points, creating large losses on the bonds. The losses, coupled with a high degree of leverage caused the fund to go bankrupt.
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13. 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.
For the catastrophe bonds the disaster is typically a natural disaster that would adversely affect the bond issuer, perhaps a property and casualty insurer who would have to make large payouts if a major earthquake or flood occurred. Oriental Land Co., the manager of Tokyo Disneyland issued this type bond in 1999 with a provision to reduce the final payment if an earthquake occurred near the park.
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14. Hypothetical Principal and Interest Payments on a TIPS
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15. 10.2 BOND PRICING
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16. Bond Prices & Yields a) 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?
The 64.8% and 35.2% affect the riskiness of the bond, to wit, the extent to which the bond's price will be affected by an interest rate change.
Textbooks often use T for a time counter but many of the students’ calculators will use N.
64.8%
35.2%
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17. 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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18. Bond Pricing Between Coupon Dates
A bond has a flat price of $ and an annual coupon of $ days have passed since the last coupon payment and there are 182 days separating the coupon payments. What is the bond’s invoice price?
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19. 10.3 BOND YIELDS
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20. 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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21. Promised Yield to Maturity (YTM)
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?
This is a trial and error solution unless you have a financial calculator.
The assumption of this calculation is that each $40 coupon is reinvested at 3% (the promised ytm).
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22. Figure 10.3 The Inverse Relationship Between Bond Prices and Yields
First note that bond prices move inversely to interest rates. This is easy to explain. Ask students how they would respond if they are holding a bond paying them 6% interest, and similar new bonds coming out now pay 7%. They would sell the 6% bond and buy the 7%. The selling action on the 6% will reduce the bond’s price until it gives a 7% yield rate. The mathematics is easy to explain as well.
Note the curvilinear relationship between bond prices and yields. This is called convexity. Different bonds have different curvatures or convexities.
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23. 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
The current yield is the annual dollar coupon divided by the price. It is a measure of the annual return if you do not sell the bond (it excludes any capital gain or loss). It may be used to compare to dividend yields on stocks.
Important note: Anytime you calculate the yield on a bond using the bond price formula you are assuming that the investor will reinvest each coupon as it is received for the remaining time to maturity and will earn the promised ytm on the reinvested coupon. A heroic assumption indeed! This is why the HPY above should use the actual reinvestment rate on the coupon. You would then calculate the HPY using the modified internal rate of return methodology taught in corporate finance and presented in the text.
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24. Yield to Call Illustrated
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25. Figure 10.4 Bond Prices: Callable and Straight Debt
Note the ceiling on the callable bond’s price at lower interest rates. This is because the bond will be called at low enough rates.
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26. Figure 10.5 Growth of $1000 invested in a 2 year bond
This graph makes an important point. The future value of the coupons depends on the reinvestment rate. An investor will not earn the promised yield unless they reinvest the coupons at the promised ytm.
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27. Example 10.5 Growth of $1000 invested in a 2 year bond
This example illustrate the importance of the reinvestment rate on the coupons on the investor’s HPY. The future value of the coupons depends on the reinvestment rate. An investor will not earn the promised yield unless they reinvest the coupons at the promised ytm.
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28. 10.4 BOND PRICES OVER TIME
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29. 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?
A premium bond is priced above par because the coupon rate is too high relative to what the bond is supposed to be yielding. The only way to get the expected yield down to the ytm is to have the bond priced above par. In this case, the current yield on the bond will be above the promised yield. Hence there must be a capital loss on the premium bond over the year to get the overall yield down to the promised ytm.
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30. Figure 10.6 Premium and Discount Bonds over Time
This illustrates the “Pull to Par” discussed on the prior slide.
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31. Figure 10.7 The Price of a Zero Coupon Bond over Time
How does one earn a rate of return on a zero coupon bond?
What are STRIPS?
How is the price appreciation taxed?
STRIPS are Treasury securities where the coupon payments and the final principal payment are ‘stripped’ out and sold separately. These can be useful for cash matching when a payment is due in a set time period in the future.
The IRS rules that the built in price increase due to approaching maturity on all original issue discount (OID) bonds is taxable as interest income and is taxed at the investor’s ordinary income tax rate. Any other gains or losses on the OID bond are treated as capital gains or losses. This is true for all OIDs, not just zeros.
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32. 10.5 DEFAULT RISK AND BOND PRICING
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33. Default Risk and Ratings
Main Ratings Companies
Moody’s Investor Service
Standard & Poor’s
Fitch
Main Rating Categories
Investment grade
Speculative grade (junk bonds)
During the credit crisis of 2008 the spread between Treasury bonds and junk bond yields widened from 3% in 2007 to 15% at the start of 2009!
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34. Figure 10.8 Definitions of Bond Rating Classes
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35. 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
The Fixed Charges Coverage ratio adds lease and sinking fund and any other fixed payments to the interest expense to calculate an earnings to fixed cash obligations ratio.
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36. Financial Ratios and Default Risk
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37. 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.
Note that sinking funds and serial bonds are designed to help ensure the issue can pay off the principal as it comes due. However a bond investor could be hurt by the second type of sinking fund if interest rates fall. Serial bonds are not callable and this is a plus, but the staggered maturities can reduce the liquidity of the bonds and make them more expensive.
Liquidating dividends are usually prohibited
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38. 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?
Note that sinking funds and serial bonds are designed to help ensure the issue can pay off the principal as it comes due. However a bond investor could be hurt by the second type of sinking fund if interest rates fall. Serial bonds are not callable and this is a plus, but the staggered maturities can reduce the liquidity of the bonds and make them more expensive.
A bond without collateral is called a debenture.
Liquidating dividends are usually prohibited
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39. Figure 10.9 Callable Bond Issued by Mobil
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40. Example 10.10 YTM and Default
In October 2008, Ford Motor Co % bonds due in 2028 were rated CCC and were selling at 33% of par with a ytm of 20%. However, investors realized there was a significant possibility they would not receive the promised cash flows and the yield based on expected cash flows was much less than the 20% promised ytm.
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41. Figure 10.10 Yields Spreads on 10 year bonds
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42. 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.
Hedge funds (and AIG!) are the main sellers of CDSs. Have 60% of investment grade and 80% of low grade debt default swaps.
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43. 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?
More detail can help students to understand this problem: With the CDS there was no principal investment required, a low capital requirement (important if regulated) and if seller has strong credit rating, little collateral was required. The result was excessive risk taking on both sides. Buyers take on more risk because they are insured, even though insurer’s collateral was woefully inadequate. Seller does not plan on having to ever make the payment so does not have sufficient collateral or credit to get it. This is also a good example of extrapolation bias discussed in the behavioral chapter. Financial modelers had modeled only a 5% percent chance of any drop in home prices on a national basis. … So their models told them writing the swaps was not risky.
As the text points out the lack of transparency in this market helped cause the credit freeze up after the subprime mortgage crisis began. No one could tell the obligations and exposure of counterparties so it was too risky to make a loan. AIG had over $400 billion in CDS contracts on subprime mortgages and other loans and was obviously going bankrupt. If AIG went under, it might have trigged defaults at other institutions that were counting on payments from AIG to protect their own investments. Ultimately the government decided it was too risky to let AIG become insolvent.
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44. Credit Default Swaps
Hedge funds (and AIG!) are the main sellers of CDSs. Have 60% of investment grade and 80% of low grade debt default swaps.
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45. 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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46. 10.6 THE YIELD CURVE
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47. 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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48. Figure 10.12 Treasury Yield Curves
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49. 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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50. Figure 10.13 Returns to Two 2-year Investment Strategies
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51. Forward Rates Implied in the Yield Curve( 1 + y ) n ( 1 + - + y ) n 1 ( 1 f ) = n n - 1 n ( 1 . 12 ) 2 ( 1 . 11 ) 1 = ( 1 .
1301 )
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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52. Figure 10.14 Illustrative Yield Curves
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53. Figure Term Spread
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