【正文】 ations of the nominal spread. The nominal spread is the simplest to use and to understand. It is simply an issue’s yield to maturity minus the YTM of a Treasury security of similar maturity. Therefore, the use of the nominal spread suffers from the same limitations as the YTM. l: Describe the zerovolatility spread and explain why it is superior to the nominal spread. The static spread (or Zspread) is the spread not over the Treasury’s YTM, but over each of the spot rates in a given Treasury term strucure. In other words, the same spread is added to all riskfree spot rates. The Zspread is inherently more accurate (and will usually differ from) the nominal spread since it is based upon the arbitragefree spot rates, rather than a given YTM. m: Explain how to pute the zerovolatility spread, given a spot rate curve. Suppose that the above calculated spot rates are based upon . government bonds, and that we observe a 3year, 9% annual coupon Westby Machine Tool bond trading at . The YTM = % and the YTM of the three year Treasury is 12%. Nominal Spread = YTMWestby – YTMTreasury = – = % To pute the Zspread, set the present value of the bond’s cash flows equal to today’s market price. Discount each cash flow at the appropriate zero coupon bond spot rate plus a spread SS which equals 167 basis points (see below). Note that this spread is found by trialanderror. In other words, pick a number ―SS‖, plug it into the righthand side of the equation and see if the result equals . If the righthand side equals the left, then you have found the Zspread. If not, pick another ―SS‖ and start over. = [9 / ( + SS)1] + [9 / ( + SS)2] + [109 / ( + SS)3] = % n: Explain why the zerovolatility spread will diverge from the nominal spread. This LOS is essentially the same as LOS . The static spread (or Zspread) is the spread not over the Treasury’s YTM, but over each of the spot rates in a given Treasury term structure. In other words, the same spread is added to all riskfree spot rates. The Zspread is inherently more accurate (and will usually differ from) the nominal spread since it is based upon the arbitragefree spot rates, rather than a given YTM. o: Explain the optionadjusted spread for a bond with an embedded option and explain the option cost. The option adjusted spread (OAS) is used when a bond has embedded options. The OAS can be though of as the difference between the static or Zspread and the option cost. For the exam, remember the following relationship between the static spread (Zspread), the OAS, and the embedded option cost: ZSpread – OAS = Option Cost in % Terms. Also remember that you use the Zspread for risky bonds that do not contain call options in an attempt to improve on the shortings of the na?ve or nominal spread. If the bond has an embedded option and the cash flows of the bond are dependent on the future path of interest rates, then remove the option from the spread by using the OAS. p: Illustrate why the nominal spread hides the option risk for bonds with embedded options. It is worth noting that a large Zspread value can result from either ponent. Therefore, a large Zspread could be the result of a large option cost implying that the investor may not be receiving as much pensation for default and other risks as may be initially perceived. q: Explain a forward rate. Spot interest rates as derived above are the result of market participant’s tolerance for risk and their collective view regarding the future path of interest rates. If we assume that these results are purely a function of expectations (called the expectations theory of the term structure of interest rates), we can use spot rates to estimate the market39。ll arrive at the same conclusion. AEY = {1 + (nominal yield / payments per year)} payments per year 1 AEY = {1 + (.0625 / 2)2 1 = % Therefore, the semiannualpay bond still has a greater true yield. h: Calculate the discount margin measure for a floater and explain the limitation of this measure. Example: Suppose that given a semiannual coupon bond with a 5year maturity pays 180 basis points over LIBOR. LIBOR is currently %, and the bond is currently trading at . Expected CPN = $1,000 * ( + )/2 = $. On the calculator, N = 10, FV = 1,000, PMT = , PV = 。 for example, the bond39。s YTM! ? This is the reinvestment assumption that39。s well below a bond39。 CPT I/Y = * 2 = 12%. Yield to call (YTC): Some bonds may be called (repurchased prior to maturity) at the option of the issuer. Investors are typically interested in knowing what the yield will be if the bond is called by the issuer at the first possible date. This is called yield to first call or yield to call (YTC). There are two modifications to our YTM formula necessary to determine yield to first call, 1) maturity date is shortened to the first call date, and 2) maturity value is changed to call price. Continuing from the previous example, assume the cash value of each coupon is $30, and the first call price is $1,060 in 2 years, N = 4, FV = 1,060, PMT = 30, PV = 。 CPT PV = ? N = , I/Y = 6, FV = 1030, PMT = 0。 CPT PV = ? N = , I/Y = 6, FV = 30, PMT = 0。d do the following: Bond value = 1000 / (1 + .08/2)10*2 = On your financing calculator, N = 10*2 = 20, FV = 1000, I/Y = 8/24。 FV = 1000。 FV = 1000。 FV = 1000。s difficult to know how long it will be before the bond is converted into stock. e: Compute the value of a bond, given the expected cash flows and the appropriate discount rates. Example: Annual coupons. Suppose that we have a 10year, $1,000 par value, 6% annual coupon bond. The cash value of each coupon is: CPN= ($1,000 * )/1 = $60. The value of the bond with a yield to maturity (interest rate) of 8% appears below. On your financial calculator, N = 10, PMT = 60, FV = 1000, I/Y = 8。re dealing with an annuity of coupon payments, plus a la