【正文】 CPT PV = N = 3, PMT = 0, I/Y = , FV = 108。s embedded in any present valuebased yield measure implies that all coupon (or principal) payments must be reinvested at a specific rate of return。s YTM. ? Failure to reinvest coupons will result in a realized yield that39。 CPT PV = ? N = , I/Y = 6, FV = 30, PMT = 0。s par value. Bond value = M / (1 + i/m)n*m Example: A zero coupon bond. Suppose we have a 10year, $1,000 par value, zero coupon bond. To find the value of this bond given its being price to yield 8% (pounded semiannually), you39。 n = 3*2。re dealing with a convertible (or exchangeable) bond, rather than a straight bond in which case, it39。re dealing with an annuity of coupon payments, plus a large single cash flow, as represented by the recovery of principal at maturity, or when the bond is retired. These cash flows, along with the required rate of return on the investment, are then used in a present value based bond model to find the dollar price of a bond. b: Explain the three steps in the valuation process. The value of any financial asset can be determined as the sum of the asset’s discounted cash flows. There are three steps: ? Estimate the cash flows. ? Determine the appropriate discount rate. ? Calculate the sum of present values of the estimated cash flows. c: Explain what is meant by a bond39。 FV = 1000。 FV = 1000。 CPT PV = ? N = , I/Y = 6, FV = 30, PMT = 0。 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 = 。s YTM! ? This is the reinvestment assumption that39。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 = 。s relatively easy to pute just about any spot rate. To do so, we consider Z1 to be equivalent to 1f0 (the 1year forward rate 0 periods from today). For example, given our set of 1year forward rates of 4 percent for the first year, percent for the second year, and percent for the third year, we can calculate Z3, the 3year spot rate: (1+Z3)3 = (1 + 1f0) * (1 + 1f1) * (1 + 1f2) Z3 = [() * () * ()]1/3 1 = % : Introduction to the Measurement of Interest Rate Risk a: Distinguish between the full valuation approach and the duration/convexity approach for measuring interest rate risk, and explain the advantage of using the full valuation approach. The most straightforward method to measure interest rate risk is the full valuation approach. Essentially this boils down to the following steps: ? Begin with the current market yield. ? Estimate hypothetical changes in required yields. ? Revalue the bonds using the new required yields. ? Compare the resulting price changes. b: Compute the interest rate risk exposure of a bond position or of a bond portfolio given a change in the interest rates. This approach is illustrated below, first for Bond X, second for Bond Y, and third for a twobond portfolio prising positions in X and Y. Consider two optionfree bonds: X is an 8。ll actually earn 8% on the investment is to reinvest all the coupons (and any other intermediate cash flows) at an 8% rate of return. Anything more or less, and the actualy yield will be more or less. Thus, YTM is only an estimate of what you might earn given you fulfill the reinvestment assumption! All three sources of return (coupons, principal, and reinvestment ine) have to be considered in what Fabozzi calls total dollar return. f: Discuss the factors that affect reinvestment risks. The key point to take away from this is that you need to reinvest coupon cash flows at the YTM or your realized return will not be equal to the YTM. This is called reinvestment risk. YTM (and other traditional yield measures) contain a good deal of reinvestment risk. Other things being equal, the amount of reinvestment risk embedded in a bond will increase with: ? Higher coupons because there39。s equal to the bond39。s why the use of a series of spot rates to discount bond cash flows is considered to be an arbitragefree valuation procedure. To pute the value of a bond using spot rates, all you do is calculate the present value of each cash flow (coupon payment or par value) using a spot rate, and then add up the present values. l: Explain how the process of stripping reconstitution forces the price of a bond toward its arbitragefree value so that no arbitrage profit is possible. It is possible to strip coupons from . Treasuries and resell them, as well as to aggregate stripped coupons and reconstitute them into . Treasury coupon bonds. Therefore, such arbitrage arguments ensure that . Treasury securities trade at or very near their arbitragefree prices. The determination of spot rates and the resulting term structure is usually done using riskfree (., sovereign or Treasury) securities. These spot rates then form the basis for valuing