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Fixed Income Section Topic and Lecture Map. Bond Basics (C 14) Definitions, basic pricing, yield measures, default risk Measuring Interest Rate Risk (C 16) Duration and Convexity Bonds with embedded options Managing Interest Rate Risk (C 16) Immunization (duration matching), swaps
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Fixed Income SectionTopic and Lecture Map • Bond Basics (C 14) • Definitions, basic pricing, yield measures, default risk • Measuring Interest Rate Risk (C 16) • Duration and Convexity • Bonds with embedded options • Managing Interest Rate Risk (C 16) • Immunization (duration matching), swaps • Term Structure (C 15) • Interpreting the term structure, pricing off the yield curve
Bond BasicsLecture Map • Definitions • Basic bond pricing • Straight-up YTM pricing • Yield measures • Credit Risk • Credit ratings • YTM v. expected yield • Bond Indenture agreements • The risk shifting game
Bond Description • Bond is a borrowing arrangement • Bondholders are lenders – just like banks • Bond obligates the issuer to make specified payments to the bondholder on specified dates – very contractual • This is why bonds are called “fixed income”; the amount (almost always) and timing (almost always) is fixed • Bond makes periodic coupon payments and at maturity pays par or face value, which is usually $1,000
Treasury Notes and Bonds • Treasury Notes: maturity 1 – 10 years • Treasury Bonds: maturity > 10 years • Longest maturity issued by the government is now 20 years – government stopped issuing the 30 yr maturity last year • Notes and Bonds make semiannual coupon payments • Price quotes are % of par (par = $1,000) • May 2004 notes, ask price 107:21 = 10721/32 = 107.656% X $1,000 = $1,076.56 PLUS accrued interest • Ask yield quoted is a bond equivalent yield (semi X 2) • Premium bonds (price > par) have yields quoted to call date – assumes they will be called at par at the first opportunity
Corporate Bonds • Pay semiannual interest • Every six months, in maturity month and 6 months from maturity month • Bond maturing in April pays ½ X Coupon rate X $1,000 in April and October • Unsecured bonds are called debentures • There is a payment hierarchy of bonds issued by a single firm; lower seniority bonds (paid after senior bonds) are called subordinated debentures, or more commonly, junior debt • Pricing: price quotes are percentage of par ($1,000) • To get the price you pay, take close price percentage X $1,000 PLUS accrued interest (interest earned since last coupon pmt)
Example of Pricing with Accrued Interest • Par = $1,000 • 5.5% bond making semi-annual payments (i.e., every 182 days) • Last payment occurred 32 days ago • Price quoted is 103:26 • = 10326/32 = 103.8125% X $1,000 = $1,038.125 • Semiannual interest payment • = $1,000 X 5.5% X ½ = $27.50 per 182 days • Daily interest earned = $27.50 / 182 days = $0.1511/day • Accrued interest on bond = $0.1511 X 32 days ≈ $4.84 • Transaction price of the bond is • $1,038.125 + $4.84 = $1,042.97
Bond Markets • Treasury bond markets are very liquid, very deep • Corporate bond markets can be thin • Thin market is a market in which there are only a few investors trading a particular bond at a particular time • Many bonds are listed on the NYSE, but most bonds are traded over the counter in a network of bond dealers • The combination of a thin market and trading that occurs through a private network makes it difficult to get bond prices – this is one of the things that Bloomberg sells
Bond Features – Call Provision • Call provision • Allows firm to purchase the bond for a specified call price (typically par, or at least between par and 105) • The call provision usually kicks in after some years have passed • If you’re a bondholder, is a call provision a good thing or a bad thing? Effect on coupon rate and/or yield? • A call provision is mainly a feature of corporates. The Treasury no longer issues callable bonds, but it used to so some are still out there. Maturity date of callable Ts is given as a range specifying the call period.
Bond Features and Types – Convertibles and Puttables • Convertible Bonds • Conversion ratio gives the number of shares of common stock for which each bond may be exchanged • e.g., each bond convertible into 20 shares of stock • If you’re a bondholder, is this convertibility a good thing or a bad thing? Effect on coupon rate and/or yield? • Puttable Bonds or Put Bonds • Gives the bondholder the right to sell or “put” the bond back to the firm, usually for par. • When is this option exercised?
Bond Features and Types – Asset Backed Bond • Payments on asset backed bonds are tied to the income from a specific asset or set of assets • Mortgage Backed Securities • Car Loan Backed Securities • Credit Card Loan backed securities • “David Bowie bonds” pay income from royalties on David Bowie catalog • IP backed securities?
Bond Features and Types – TIPS (Indexed Bonds) • TIPS are “Treasury Inflation Protected Securities” • These are treasury bonds with interest rates (payments) tied indexed to the CPI • Indexing works such that the par value of the TIPS increases each year by the CPI percentage in the year, and because the coupon rate is applied to par in each year, the coupon amount keeps up with inflation • Also note that at maturity the par payment is not $1,000 but rather $1,000(1+CPI1)(1+CPI2)…(1+CPIT) • The effect is that a TIPS is both default-risk free (like regular Treasury) and inflation-risk free
Bond Pricing – Using your calculator • $1,000 par, 8% coupon, 7 years to maturity, semi-annual coupon payments (this goes without saying from now on). What’s the price of the bond if market YTM is 6%? • n : 7 x 2 = 14 • PMT : 8% x 1000 x ½ = $40 • FV : par = $1,000 • i : YTM/2 = 6/2 = 3 • hit the PV button, and get -1,112.96 (negative by calculator convention) • Why is the price greater than $1,000?
Where does the discount rate, or yield, on a bond come from? • Discount rates reflect time value and risk (THIS IS ALWAYS TRUE, for ALL ASSETS) • Risks of a bond are: • Interest rate risk, or inflation • This can be thought of as time value or “loss risk” • Credit risk, also called Default Risk • Bond Yield = Real Rate of Interest + Expected Inflation + Default Risk Premium
The Price of a Bond over Time • All bonds sell for par just prior to maturity • Premium bond prices fall as they approach maturity • Discount bond prices rise as they approach maturity • An extreme version of this is seen with zero coupon bonds • Zeros sell at deep discount and the “interest” is earned through price appreciation over time to par payment at maturity • Zeros are typically created, not born. Created by bond dealers who take Treasuries and “strip off” the interest payments and create an interest only strip and a principal only zero
Yields, yields, yields • Yield to Maturity (YTM) • Current Yield • Yield to Call • Realized Compound Yield • Holding Period Return
Yield to Maturity • The Yield to Maturity is defined as the discount rate that makes the present value of the future bond payments (coupons and par) equal to the price of the bond • Ever hear of something like that? What do we call discount rates like that? • YTM is a bond equivalent yield, or annual percentage rate (APR), which comes from applying simple interest rules (annualize by multiplying, not raising to a power) • YTM is just 2 x semi-annual YTM, not (1+ semiYTM)2 – 1 • When people talk about “yield”, they’re almost always talking about yield to maturity
Calculating YTMwith Invoice prices • $1,000 par, 8% coupon, 7 years to maturity, price of the bond is $1,112.96. What’s the YTM? • n : 7 x 2 = 14 • PMT : 8% x 1000 x ½ = $40 • FV : par = $1,000 • PV : price = -1,112.96 • hit i on your calculator, and get 3.00 • Now, that’s a semi-annual rate. To get the YTM you multiply by 2, so YTM = 2 x 3.00 = 6.00% • The effective annual yield is (1.03)2 – 1 = 6.09%
Calculating YTMwith par percentage price • $1,000 par, 8% coupon, 7 years to maturity, price of the bond is $1,112.96 => invoice price as % of par is quoted as 111.296. What’s the YTM? • n : 7 x 2 = 14 • PMT : 8% x 100 x ½ = 4 • FV : par = 100 • PV : price = -111.296 • hit i on your calculator, and get 3.00 • Now, that’s a semi-annual rate. To get the YTM you multiply by 2, so YTM = 2 x 3.00 = 6.00% • The effective annual yield is (1.03)2 – 1 = 6.09%
Current Yield • Current Yield = Annual Coupon Payment Bond Price • For the previous example, the current yield is 80 / 1,112.96 = 7.19% (or 8/111.296) • Coupon yield > current yield because premium bond, and coupon yield calculated off of par while current yield calculated off of price • Current yield > YTM because YTM accounts for price dropping to par at maturity
Yield to Call • For callable bonds that look likely to be called prior to maturity, it makes more sense to calculate a yield to call than a YTM • The yield to call is just like the YTM, just replace maturity date with expected call date and replace par amount with call price • What type of bonds get called? Premium or discount bonds?
YTM and Reinvestment Risk • VERY IMPORTANT : YTM assumes that all coupon payments can be invested at the YTM • In other words, you will only earn the YTM – even if you hold the bond to maturity – if you can reinvest all the coupon payment at the YTM until maturity • How likely is that? • This is called reinvestment risk
Reinvestment Risk in Fixed Income • Fixed Income makes periodic payments • The calculated YTM on an FI instrument assumes the holder will reinvest all coupon payments at the YTM • How realistic is that? • The risk that an investor will not be able to reinvest coupon payments at the YTM is called reinvestment risk
Total Returnthe book calls this “Horizon Analysis” • There is nothing to prevent you from calculating an expected return on an FI instrument incorporating an explicit reinvestment rate based on expectations about the future • The total return is a measure of yield that incorporates an explicit assumption about the reinvestment rate • This is an ex-ante measure of expected yield • You can also incorporate an expectation of future YTM => future selling price at some date prior to maturity
Federal Tax Treatment of Fixed Income • Interest is taxable, so coupons received on FI investments are taxable, and interest earned through reinvestment is also taxable • Taxes reduce the amount of each coupon payment. This reduces the amount of money available for reinvestment • Taxes reduce the interest on interest, thus reducing the total future value of an FI investment • There are also capital gains taxes on FI, • That can be complicated and you’ll need to look it up for your particular situation
Realized Compound Yield • Can only be calculated ex-post • If the reinvestment rate is less than the YTM, then the realized compound yield is going to be less than the YTM • If the reinvestment rate is greater than the YTM, then the realized compound yield is going to be greater than the YTM • Examples in the book are straightforward (pages 464-466)
Default Risk (aka Credit Risk) • For corporate bonds, there is, of course, some probability that the bond may default prior to making all scheduled payments • They may never make payment, or they may make smaller payments, or they may make smaller payments later • Any of these scenarios will hurt the bondholder • Credit risk is measured by the bond rating agencies • Moody's (little letters, numbers) and S&P (all caps, + and -)
Bond Ratings • Moody's • Aaa, Aa, A, Baa, Ba, B, Caa, Ca, C, D • Also may add 1, 2, 3, e.g., Aa1 better than Aa2 • S&P • AAA, AA, A, BBB, BB, B, CCC, CC, C, D • Investment Grade bonds are bonds rates BBB, Baa or better • Important distinction because pension funds are precluded from holding anything but investment grade • Bonds that are rated below BBB, Baa are called junk bonds • Are the junk bonds of a firm safer or riskier than the stock of the firm?
Bond Ratings and Spreads(Spreads are essentially Default Premiums)
Information in Bond Rating Changes(not much) • Accusation recently (Enron et. al.) that the rating agencies only downgrade after the bad news is announced • Consistent with this accusation, early studies showed no price moves around rating changes, but did find price moves before rating changes • More recent studies have found stock price changes after rating downgrades (but nothing after upgrades)
YTM and Expected YTM • The bonds of firms in serious financial distress often sport very high yields, both YTM and current yields • e.g., last Spring the AMR 9s16 had a listed YTM of 45% • What’s going on with that? Did investors really expect to earn 45% on AMR bonds?
Bond Indenture Agreements • The bond indenture agreement is the contract that defines how the firm has to treat the bondholders • Generally the indenture agreement includes a lot of restrictions on the actions the firm can take • Remember, bondholders don’t get to vote on things like stockholders do. So once they give their money up, the only thing they’ve got for protection is the bond indenture agreement
Bond Indentures • Sinking fund • Put a little money aside every year so there’s enough money to pay the par when it comes due • Dividend restrictions • Shareholders like money just like everyone else. Imagine no indenture agreement. What would the shareholders vote for just after they got the bondholders’ money? • Subordination • If you buy a spot at the front of the line, you don’t want anyone to cut. In other words, you don’t want the stockholders selling that “front of the line spot” again after they’ve sold it to you.
The Risk Shifting game • Imagine a firm with assets slightly less (about 10% less) than debt (i.e., A < D) • What is E worth in this scenario? • Who decides the actions of the firm? • Imagine two projects, both cost A. • PROJECT 1 – safe 10% return • PROJECT 2 – 5% chance it makes 3A (triples the investment), 95% chance of losing all of A invested • Which project do shareholders choose, and why? • Which project do bondholders want, and why?
