Maturity Coupon Bid Asked Chg Asked
3/31/2019 1.250 99.4375 99.4531 -0.0156 2.414
9/30/2019 1.000 98.3828 98.3984 -0.0078 2.675
3/31/2020 1.375 97.8984 97.9141 -0.0078 2.829
9/30/2020 2.000 98.2734 98.2891 -0.0313 2.897
3/31/2021 1.250 95.9844 96.0000 0.0078 2.937
9/30/2021 1.125 94.7188 94.7344 -0.0469 2.988
a. Convert price quotes into the actual prices (multiply by 10).
b. Convert annual coupon rates into the actual semi-annual coupons, expressed in dollars.
c. Show the cash flow table (time line) for your bonds. This table should organize each payment of each bond according to the time when it will be paid.
d. Using the same bootstrapping method as in the example on pages 8--10 of your Review of Bond Concepts handout, calculate the first six rates of the term structure of interest rates.
-Show equations which you used to find each of the six rates with the data plugged into them (use Insert Equation in Word to type your equations).
-Present annualized rates.
So we discount risk free cash flows at the term structure. To discount at the term structure is to view a risk free cash flow as a coupon bond and to price it accordingly as a portfolio of discount bonds Remark 1: If we discount cash flows at a constant rate, rr, e.g., isk free we are assuming the term structure is flat Remark 2: Preview: we will, in general, adopt the following procedure for discounting risky cash flows. CF1 CF2 CF3 CFT ECF ECF ECFT i.e., we add risk premia, {}ri, to the risk free discount rates (the term structure) to reflect the cash flow risk. In the above abstraction ri+u, reflects the rate of return on securities, which pay off only in period t and with cash flow risk similar to CFt 4. Constructing the Term Structure in Practice. Although the term structure is defined by the prices of discount bonds of all maturities, the U.S. Treasury does not issue pure discount bonds of more than one year term. Rather, it issues coupon bonds of a variety of maturities But just as we priced coupon bonds as portfolios of discount bonds, we may go the other direction and uncover the embedded discount bond prices provided we have enough coupon bonds of differing maturities with which to work. That is, we want to construct the no arbitrage prices of discount bonds, were they to exist. We illustrate this procedure as follows 1.An example Suppose, we observe treasuries of one, two, three, and four-year maturity all selling at par with, respectively, yearly coupons of 6%, 6.5%, 7.2% and 9.5%. The associated cash flows are as folloWS: So we discount risk free cash flows at the term structure. To discount at the term structure is to view a risk free cash flow as a coupon bond and to price it accordingly as a portfolio of discount bonds Remark 1: If we discount cash flows at a constant rate, rr, e.g., isk free we are assuming the term structure is flat Remark 2: Preview: we will, in general, adopt the following procedure for discounting risky cash flows. CF1 CF2 CF3 CFT ECF ECF ECFT i.e., we add risk premia, {}ri, to the risk free discount rates (the term structure) to reflect the cash flow risk. In the above abstraction ri+u, reflects the rate of return on securities, which pay off only in period t and with cash flow risk similar to CFt 4. Constructing the Term Structure in Practice. Although the term structure is defined by the prices of discount bonds of all maturities, the U.S. Treasury does not issue pure discount bonds of more than one year term. Rather, it issues coupon bonds of a variety of maturities But just as we priced coupon bonds as portfolios of discount bonds, we may go the other direction and uncover the embedded discount bond prices provided we have enough coupon bonds of differing maturities with which to work. That is, we want to construct the no arbitrage prices of discount bonds, were they to exist. We illustrate this procedure as follows 1.An example Suppose, we observe treasuries of one, two, three, and four-year maturity all selling at par with, respectively, yearly coupons of 6%, 6.5%, 7.2% and 9.5%. The associated cash flows are as folloWS
