Homework answers / question archive / Part 1) Implementation The goal of this part is to derive the term structure of interest rates from market quotes on US Treasury bills and Treasury notes

Part 1) Implementation The goal of this part is to derive the term structure of interest rates from market quotes on US Treasury bills and Treasury notes

Finance

Share With

Part 1) Implementation
The goal of this part is to derive the term structure of interest rates from market quotes on US Treasury bills and Treasury notes. Today is the evening of September 29°, 2021. Attached you find the Wall Street Journal (WSJ) quotes for Treasury bills and Treasury notes. All quotes in the WSJ are expressed in terms of bond equivalent yields (BEY). Please make sure that you count correctly, and report clearly, the number of days between each maturity. Multiply the price by 10 in order to get it consistent with a par value of 1,000. 
1. Let us start by constructing the first point of the yield curve, which we choose as the last available date in December. Let us focus on the related Treasury bill, which we denote by "bond 1". Focus on the column ASKED YIELD, which provides you with the BEY for the Treasury Bill of the corresponding maturity. 
Derive what we denote by r1. Please notice that r1 does not refer to the yield to maturity of a 1-year zero-coupon bond, but it represents the BEY of a Treasury Bill with time to maturity equal to the difference between December 31" 2021 and September 29° 2021. 
2. We now proceed to determine the second point of the yield curve through coupon stripping. We progress by increments of six months. As a general rule, always pick the bond with maturity at the last available day of the month. If there are several bonds on that same day, choose the one with the highest coupon rate. We denote this second bond by "bond 2". 
a. Compute the total number of days from today until this second maturity. 
b. Do you choose to select the "Asked" or the "Bid" column as the price of the bond that you use for this task? Why? Please remember that the bid price is the price at which investors are willing to buy that bond, and the ask price is the price at which investors are willing to sell that bond. 
c. Compute the accrued interest and the price of "bond 2". 
d. Our goal is to find the price of an "artificial" security that consists exclusively of the next coupon paid by "bond 2", hence isolating the last coupon and the par value. What is the interest rate that you would use to discount only the next coupon? Express this in semiannual terms. 
e. Convert the semiannual interest rate that you wrote at step d) above to its equivalent interest rate that covers the time period from today to the next coupon. 
f. Find the present value today of this "artificial" security that consists only of the next coupon. 
g. Now we are ready to focus on another "artificial" security, which pays only the lost coupon plus par value of "bond 2". Compute its present value today. 
h. Find the yield to maturity r2 of this second "artificial" security consisting of the stripped last coupon and par value of "bond 2". i. Convert the yield to maturity computed at step h) above in semiannual terms. j. Convert the semiannual value found in step i) above to its corresponding BEY. 
3. We continue with the third point of the term structure. Proceeding with the same logic outlined in step 2) above, we now focus on the Treasury bond the maturity of which comes six month after the maturity of "bond 2". We denote this security by "bond 3". 
a. Calculate the accrued interest of "bond 3". b. Find today's price of "bond 3". c. Compute the present value of the first stripped coupon. d. Compute the present value of the second stripped coupon. 
e. Given your findings in steps a) to d) above, find the present value today of the last coupon plus par value. 
f. Determine the yield to maturity of the "artificial zero-coupon bond" that consists of the last coupon plus par value of "bond 3". 
g. Convert the yield to maturity determined at step f) in semiannual terms. 
h. Transform the semiannual yield to maturity in its corresponding BEY. 
4. Proceed in the same fashion by six-month increments to construct pure discount bonds with maturities of up to 5 years from the first point of the term structure. Plot the entire yield curve writing time on the X axis in the format "Month year" (i.e., "December 2021"). 
5. Compute the term premia for all maturities.