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CHAPTER 10.1 BOND CHARACTERISTICS AND TYPESBonds as IOU’s with coupon and principal payments.Treasuries ($ 5T), Municipals ($2T), Agency ($2T), Corporates ($4T), Mortgages ($4T), Asset Backed ($1.5T). Larger than the equity market, muni market alone has over 50,000 issuers, securitization has made structures extremely complicated particularly in the mortgage and credit markets. Issuers (esp. municipals may purchase insurance). Munis have Federal tax-exempt status if the issue is to benefit society at large. Some munis such as for sports facilities may be taxable. Good sites are and . ACCRUED INTEREST Some bond prices are in 32nds. A price of 142-30 implies 142 30/32 = 142.9375 per $100 face value. Bond prices are quoted with a mark-up, including commissions which vary by company. Done this way because of low liquidity. Bond prices are quoted net of accrued interest (flat prices)? When bonds are purchased in between coupon payments, the buyer has to pay the bond seller her part of the coupon which the buyer will receive after purchase. Accrued interest is this interest payable on the bond from the date of the prior coupon. T-bonds pay coupons semi-annually. The Treasury provides a half-year calendar. For Feb/Aug cycles, the half-year is 181 days (regular) and 182 days for a leap year. For March/September cycles, half-year is 184 days.16+30+31+30+31+31+15). So, if you have a March cycle bond paying an 8.875% coupon which is purchased 109 days after the last payment, the accrued interest per $100 bond is: = (109/184) * (0.50) * (0.08875) * 100 = 2.63OPTION FEATURES AND BONDSCALLABLE: Issuer can call & reissue if coupon > market yield (like a refi). These bonds may be priced based upon call date not maturity date if the chance of issuer exercise is high.AND PUTTABLE (option with bondholder. If coupon < market yield, put the bond, get the principal and reinvest at prevailing market yields (i.e shorten bond’s life). CONVERTIBLE (say $1000 bond converts to 40 shares of stock). Conversion ratio is 1:40, If stock at $30, there is value to conversion, price is $1,200, Conversion premium is $200. FLOATING RATE BONDSHere the coupon increases with interest rates. The floating rate may be indexed to the Fed funds rate/T-bill rate/prime rate/LIBOR or other. At times the rate is capped at some maximum. Frequency of reset could be daily/weekly/monthly/semi-annual/annual. At any payment date, the price of a floating rate bond is its par value. Auction-rate securities are often muni bonds which are long-term securities but the interest rate is set via a dutch auction, typically 7, 28 or 35 days. Many failed recently as there were few buyers and the banks refused to take up the excess supply! Port Authority ended up with a 20% effective rate !! INVERSE FLOATERS: A plain vanilla bond may be repackaged as a floater and an inverse floater. A 4% coupon bond is broken into a floater at LIBOR + 1% and an inverse floater at (3% – LIBOR). So, if rates rise, prices fall and coupon income falls too! Such bonds are hyper-sensitive to rate changes. Indexed Bonds: TIPSIssued with 3, 5 and 10 year maturities. Suppose a 10-year TIP pays 6% coupon and inflation is 2% for the past year. Then the face value is adjusted by 2% to 1020 and a 6% coupon is paid on it. Can think of the interest rate on these bonds as a risk-free real rate.When do you buy them ? When inflation expectations are low.P-I-K (Payment in Kind) BondsCan pay interest in cash or in other bonds. In some versions, interest is added on to the principal for later payment. MORTGAGES (not much in your book, but we’ve talked enough).STRIPSCoupon bearing Treasury bonds are stripped into a series of “stripped” bonds of various maturities. I-O and P-O STRIPSHere a mortgage bond is separated into an interest component and a principal component. The interest component is high in the early years and the principal component is high in the later years. Structured finance and securitizations refer to more complicated re-distributions of the payoffs rather than just principal and interest. These are leveraged and largely responsible for the credit crunch we are STILL in! 10.2 AND 10.3 BOND BASICS (ALSO RECAP FROM FIN 323?) 1 2 3 …….. 20 100 100 100…….. 100 1000PRICE = ?YIELD = ?COUPONS Usually semi-annual. We assume annual. FACE VALUE - we’ll assume $1000PRICE = PV OF ALL CASH FLOWS DISCOUNTED AT YIELDCURRENT YIELD = Coupon/Price (approx) vs. Yield to Mat. SUPPOSE ABOVE BOND HAS A MARKET PRICE OF $1091.285.Q: WHAT IS ITS YIELD TO MATURITY (YTM) ?YTM = The rate at which the PV of cash flows equals bond price. Treat as PV/FV Problem: FV = 1000, PMT = 100, PV = 1091.285, N = 20 YRS, SOLVE FOR INTEREST RATE AS 9%.IDENTICAL TO THE IRR ON A 20 YEAR PROJECT WITH:INITIAL OUTLAY = $1091.285ANNUAL CF = 100 for YRS 1-20TERMINAL VALUE = $1000 AS with IRR, this yield YTM is earned only if intermediate coupons are reinvested. The YTM is calculated under the assumption that coupon reinvestment occurs at the YTM (or that coupons are “put back” into the bond).REVERSE EXAMPLE: TO PRICE A BOND, GIVEN ITS YIELD1 2 3 PRICE=?80 80 801000 GIVEN YTM = YIELD = 12% PRICE = 80 * PVIFA (3, 12%) + 1000 * PVIF (3, 12%) = 192.15 + 711.78 = 903.93(DISCOUNT BOND)SO,YIELD > COUPON PRICE < PAR (discount bond)YIELD < COUPON PRICE > PAR (premium bond)YIELD = COUPON PRICE = PAR (par bond)IF, COUPONS ARE SEMI-ANNUAL, THEN DOUBLE THE MATURITYHALVE THE YTM AND COUPON RATES Price premium Mat. (par)1000 time discountWith time, prices of all bonds move towards par. Path may be jagged because as interest rates change. FOR “PLAIN VANILLA” BONDS, maturity and coupon are fixed. At the time of issue, bonds are priced at par with coupons near the prevailing yield on similar bonds. The one exception is OID (original issue discount) bonds. After the issue, as rates change, yields on individual bonds change (not exactly) and the bond becomes a discount or a premium bond. Rate changes don’t really matter if your objective is to buy the bond and hold till maturity, but there is still concern about default risk. REALIZED COMPOUND YIELDS Recall that YTM implies coupons re-invested in the bond at its yield. Reality is that coupons may be re-invested (if at all) at a different rate than the YTM. So, the rate of return REALIZED is different and is called REALIZED COMPOUND YIELD (RCY).Calculate it for the 3-year bond assuming a 5% reinvestment rate.YTM = 12%1 2 3 PRICE=903.9380 80 80 100080 * FVIF (2,5%)= 88.2 80 (1.05) = 84.0 903.93 * FVIF (3, X%) = 1252.2X = 11.47% IS RCYTAXES AND OID BONDS.Suppose a 30 year zero is issued when rates were 10% per year. The price of the bond is 1000/(1.1)30 = $57.31 and it is issued at a $942.69 discount from par. After 1 year, the IRS imputes an interest rate of 10% and correspondingly imputes the price of the bond as 1000/(1.1)29 = 63.04. The difference 63.04 – 57.31 or 5.73 is taxed as ordinary income. However, over the year as rates change, the actual market price of the bond may be different from 63.04. IF the bond is sold, the difference between the market price and the IRS imputed bond price is treated as a capital gain or loss. 10.4 BOND PRICING: BOND PRICE CHANGES WITH TIME-1 REVISIT THE 3-YEAR 12% DISCOUNT BOND ABOVE. FIRST ASSUME THAT TIME PASSES AND RATES STAY THE SAME. YTM STAYS AT 12%1 2 3PRICE=903.93 80 80 80 1000 P=? = 80 PVIFA(2,12%)+1000 PVIF(2,12%) = 932.39 PRICE EVEN THOUGH YTM STAYS THE SAME.Q:RATE OF RETURN IF YOU BUY BOND AT 903.93 AND SELL AFTER ONE YEAR AT 932.90 ?(932.90 + 80 – 903.93)/903.93 = 12% (IS THE YIELD)Q: IS ABOVE TRUE FOR A PREMIUM BOND TOO? (I.E DOES ITS PRICE INCREASE ? NOIS ITS RETURN STILL 12% ?YESWHAT HAPPENS TO BOND’S PRICE AS RATES CHANGE ?SAY, YTM FALLS TO 8% IN 1 YEAR) YTM DROPS TO 8%1 2 3 PRICE=903.9380 80 80 1000 12% 8% P=? = 80 PVIFA(2,8%)+1000 PVIF(2,8%)= 1000.BOND BECOMES A PAR BOND, AFTER ONE YEAR. Q:RATE OF RETURN IF SELL AT THIS TIME?(1000 + 80 – 903.93)/903.93 = 19.48%OLD BUYER EARNED 19.48%, NEW BUYERS GET 8%AVERAGE OVER 3 YEARS IS 12% (GEOMETRIC)Q:WHAT ABOUT AFTER ONE MORE YEAR? a) Say yields stay the same ? price is the same too.b) say yields increase ?price declines.10.5 CORPORATES AND DEFAULT RISKBond indenture is a contract between issuer and holder, essentially a set of restrictions on the issuer, such as:Sinking funds—since eventual principal payments can create cash crisis, bonds may be repurchased periodically instead. Subordination clauses—to restrict additional borrowingCovenants on dividend—cannot payoff to stockholdersCollateral—mortgages, securities, equipment, none. Default risk: Primary source is bond ratings agencies (Moodys. S&P or Fitch). Ratings are typically derived from examination of financial ratios: interest coverage, leverage, liquidity, profitability. Typically, lowest investment grade bonds are those deemed to have adequate capacity to pay interest and repay principal.Are ratings changes anticipated by the bond market? Generally, prices tend to move in advance of agency action. Bond Credit Quality RatingsRating agenciesCredit RiskMoody’s*Standard & Poor’s**Fitch Ratings**Investment gradeHighest qualityAaaAAAAAAHigh quality (very strong)AaAAAAUpper medium grade (strong)AAAMedium gradeBaaBBBBBBNot investment gradeLower medium grade (somewhat speculative)BaBBBBLow grade (speculative)BBBPoor quality (may default)CaaCCCCCCMost speculativeCaCCCCNo interest being paid or bankruptcy petition filedCDCIn defaultCDD* The ratings from Aa to Ca by Moody’s may be modified by the addition of a 1, 2 or 3 to show relative standing within the category.** The ratings from AA to CC by Standard & Poor’s and Fitch Ratings may be modified by the addition of a plus or minus sign to show relative standing within the category.HIGH YIELD BONDSOrigin with Drexel and Milken. About 25% are fallen angels, another 25% were issued below investment grade, about 50% from LBO restructuring. Credit quality appears higher these days. But a lot of the credit issues have moved to the credit derivatives market (CDO’s). BOND SPREADSFixed income market participants often make comparisons using spreads. The treasury yield spread (compares short vs long maturities)the NOB spread compares the spread between T-notes and bondsthe TED spread compares T-bills with Eurodollars.The High-yield spread compares junk bond yields with AAA corporates OPTION ADJUSTED SPREADS (OAS). Because of the various option features embedded in bonds, it has become common to think in terms of an option adjusted spread. For instance suppose a callable corporate bond trades at a spread of 100 basis points over Treasuries. If 60 of those are attributable to the risk differences of the bond over the Treasury and the 40 is attributable to the option feature. The OAS is 60 basis points. 108013561595CHAPTER 10.6 YIELD CURVES ()(Play with the dynamic YC in charts/)a) Yield curves represent the interest rates available for investments of different maturities, but with similar risks. Strictly speaking, the term structure of rates refers to the relationship between default-free zero coupon securities and their maturities. But can draw yield curves for other risk classes as well. b) Yield curves are rarely flat for all maturities as the YTM implies.c) Yields are not known but are inferred from prices.d) Sometimes prices are known only for bonds of some maturities and have to be inferred.IN THE REAL WORLD start with a set of zero-coupon Treasuries, for which the following prices are quotedTime to Mat PriceInferred Spot Rate Discount factor1-year909.0910%0.909092-year811.6211%0.811623-year711.7812%0.71178Discount factors are just the PV of a $1 face value bond. In reality, the spot rates above are “inferred” by traders from the prices for pure discount bonds of various maturities that they observe. So, the following are equivalent statements:1-year zeros yield 10% The 1-year spot rate is 10%c) To discount cash flows in 1 year, use 10%d) The price of a 1-year zero = 1000/(1.10)1 = 909.09What happens when the Fed adjusts short-term rates? Do the rates on all maturity adjust equally (parallel shift)?. During the last few rate hikes, the long maturity yield did not move as much. SLOPE OF THE YIELD CURVEA steep yield curve often precedes an economic upturn. A flat YC curve often precedes an economic slowdown (transitory) An inverted yield curve often precedes a recession THEORIES ABOUT THE SHAPE OF THE YC ARE: a) THE PURE EXPECTATIONS HYPOTHESIS Forward rates = Expected Future Spot Rates b) Most investors are short-term, see risk in lending long-term. And require a premium for giving up liquidity Forward rates HIGHER than expected future short rates Upsloped yield curve (always) THIS IS THE LIQUIDITY PREFERENCE HYPOTHESISc) Financial institutions have a preference for different maturities because of the nature of their business (Life insurers want long maturities, property insurers want shorter..) THIS IS MARKET SEGMENTATION STRATEGIES AROUND THE YIELD CURVE ARE:a) bullet: concentrate on one maturityb) barbell: concentrate on 2 extremes (very short + very long)c) ladder: equal money across all maturitiesd) Riding the yield curve (very short-term)When YC’s are upward sloping, as a bond approaches maturity, it is valued at lower yields and higher prices, so hold and sell before maturity to pick up some return. E.G CURRENT Yield curve is 1-yr bonds earn 6%, 2-year bonds earn 7% per year. EXPECT YIELD CURVE TO STAY THE SAMEWITH TIME, MAT YIELDS INTUITION a)BUY 1-YR BOND => GET 6% b)BUY 2-YR BOND AND SELL AFTER ONE YEAR(YIELD CURVE SAME) 7%7% 873.44 1000 6% 943.40 1000RETURN = (943.40 – 873.44)/873.44 = 8%NOTE THAT “expecting the YC to stay the same” is one kind of forecast of future interest rates. YC same Next year’s spot rate will be 6% (like this year). (1-yr 6%, 2-yr 7%). Expected spot rate will drop. This expectation is different from what is implied in the forward rate. (forward rate is 8%). e) Can forecast expected yields on bonds of different maturities (see below). HORIZON ANALYSIS (page 355)Consider 3 bondsA:5-year maturity, 6% coupon, YTM = 9%B;10-year maturity, 8% coupon,YTM = 9%C;15-year maturity, 4% coupon, YTM = 9%You have a 5 year investment horizon, and if you buy longer bonds, they will be sold at the prevailing market price. All coupons will be reinvested.Forecasts of rates are 7% for years 1-5 AND 8% for yrs 6-15.WHICH BOND TO CHOOSE? YTM PriceFV Bonds price Terminal HPR(coupons) (in 5 yrs) valueA9%883.31345.04 a1000.001345.04 8.77%B9%935.82460.06 b1000.00 c1460.06 9.30%C9%596.97230.03 731.60 d 961.6310.00%PICK BOND Ca For A, FV (coupons) are 60 * FVIFA (5, 7%) = 345.04b For B, FV (coupons) are 80 * FVIFA (5, 7%) = 460.06c For B, Price = par as prevailing yield is 8% = coupond For C, Price = 40*PVIFA (10, 8%) + 1000*PVIF (10, 8%)=$ 731.60CHAPTER 11. 1 BOND PRICE DYNAMICSPrices atBOND% chgYTM=12 YTM=10 YTM=8 % chg___________________________________________________________ (1) (2) (3) (4) (5) (6)10-yr, 12% -11.18% 1000.00 1125.85 1268.41 12.66%15-yr, 12% -13.20% 1000.00 1152.13 1342.34 16.51%20-yr, 12% -14.55% 1000.00 1170.23 1392.67 19.01%20-yr, 4% -17.72% 402.48 489.14 607.22 24.14%20-yr, 0% -30.22% 103.70 148.60 214.50 44.35%___________________________________________________________FROM COL(2) FOR THE SAME COUPON, LONGER MATURITY BONDS HAVE GREATER PRICE SENSITIVITY TO YIELD CHANGES (1st 3 BONDS)DOWN COL(2), FOR THE SAME MATURITY, LOW COUPON BONDS GREATER PRICE SENSITIVITY TO YIELD CHANGES (LAST 3). SAME FOR COLUMN (6) ................
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