Consider the following information on a yield curve (where t = 0 is now) Time (in years) to Maturity (TTM) Effective Annual Rate 1 .01 2 .015 3 .02 4 .0225 5 .0235 Using this yield curve, calculate the present value of the following payment streams: a. $100 at t = 1, b. $100 at t = 2, c. $100 at t = 3, d. $100 at t = 4, e. $100 at t = 5, f. $100 at t = 1 and $100 at t = 4 g. $200 at t = 2 and $200 at t = 5 Also using the above yield curve, calculate the forward rate for the one-year yield next year at t = 1. If you take your answer to b above divided by your answer to a above and then subtract 1, do you get the same answer? Consider the following two strategies for getting a return over three years: Strategy 1: Invest for three years at the three year rate; Strategy 2: invest at the two-year rate for two years and then roll over into the one-year rate in two years. You can calculate a forward rate for the one-year rate in two years (at t = 2) by considering the one-year rate in two years that would make you indifferent between Strategy 1 and Strategy 2. What is that forward rate?
Consider the following information on a yield curve (where t = 0 is now) Time (in years) to Maturity (TTM) Effective Annual Rate 1 .01 2 .015 3 .02 4 .0225 5 .0235 Using this yield curve, calculate the present value of the following payment streams: a. $100 at t = 1, b. $100 at t = 2, c. $100 at t = 3, d. $100 at t = 4, e. $100 at t = 5, f. $100 at t = 1 and $100 at t = 4 g. $200 at t = 2 and $200 at t = 5 Also using the above yield curve, calculate the forward rate for the one-year yield next year at t = 1. If you take your answer to b above divided by your answer to a above and then subtract 1, do you get the same answer? Consider the following two strategies for getting a return over three years: Strategy 1: Invest for three years at the three year rate; Strategy 2: invest at the two-year rate for two years and then roll over into the one-year rate in two years. You can calculate a forward rate for the one-year rate in two years (at t = 2) by considering the one-year rate in two years that would make you indifferent between Strategy 1 and Strategy 2. What is that forward rate?
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Go to the http://www.federalreserve.gov/releases/h15/data.htm to examine historical daily interest rates on U.S. Treasuries.
Scroll down to "Treasury constant maturities" and in the row "1-month" under "Nominal" click "Business day."
As you can see, rates on the one-month U.S. Treasury bill are provided for each business day from July 31, 2001 to the present. For this assignment you are asked to pick a business date five years ago this month. (For example, in January 2012 I would pick a business date in January 2007.)
Then, using this row and the subsequent rows below it under âTreasury Constant Maturitiesâ determine the shape of the yield curve (See Figure 6.11in the textbook for examples of Treasury yield curves) on that date five years ago based on the rates published by the Fed by completing the table below for the listed Treasury maturities (see example below):
| Business Date Chosen Five Years Ago | 7/15/2010 |
| 1-month Nominal T-bill Rate on that Date | 0.16 |
| 3-month Nominal T-bill Rate on that Date | 0.15 |
| 6-month Nominal T-bill Rate on that Date | 0.2 |
| 1-year Nominal T-note Rate on that Date | 0.27 |
| 5-year Nominal T-note Rate on that Date | 1.76 |
| 10-year Nominal T-note Rate on that Date | 3 |
| 20-year Nominal T-bond Rate on that Date | 3.77 |
| 30-year Nominal T-bond Rate on that Date | 3.97 |
Answer the following questions:
On your selected date was the yield curve rising, falling, or flat? What explanation(s) would you give for this shape?
From my selected date, the yield curve is rising. This is due to the fact that the longer money is invested the more youâre compensated and earn due to the fact that the interest rates being higher.
Assume that two U.S. Treasury securities were purchased at par ($1000) on your selected date five years ago: 1) a 10-year T-note and 2) a 20-year T-bond. Also assume that for each of the two securities the reported nominal rate that you found above was the coupon rate at issuance.
Assuming semi-annual coupon payments, calculate the value of each bond today after 5 years based on the current 5-year Treasury constant maturity nominal rate for the original 10-year note and a current 15-year rate (assume it is the average of the current Treasury constant maturity nominal 10- and 20-year rates) for the original 20-year bond at http://www.federalreserve.gov/releases/h15/data.htm.
Complete the following tables (see example below):
10-Year Bond Purchased for $1000 5 Years Ago
| Original Value | $1000 |
| Coupon Rate (From table you completed above at the chosen date from 5 years ago, the original 10-year Nominal T-bond Rate divided by 2 for semi-annual payments) | |
| Current 5-Year Yield to Maturity (The most recent 5-year Nominal T-note Rate reported at the Fed site divided by 2 for semi-annual payments) | |
| Number of Semi-Annual Periods Remaining | |
| Current Value* | |
| Gain or Loss on the Bond over the 5 years |
20-Year Bond Purchased for $1000 5 Years Ago
| Original Value | $1000 |
| Coupon Rate (From table you completed above at the chosen date from 5 years ago, the original 20-year Nominal T-bond Rate divided by 2 for semi-annual payments) | |
| Current 15-Year Yield to Maturity (Take the average of the most recent 10- and 20-year Nominal T-bond Rates reported at the Fed site, and then divide this average rate by 2 for semi-annual payments) | |
| Number of Semi-Annual Periods Remaining | 30 |
| Current Value* | |
| Gain or Loss on the Bond over the 5 years |
*Current Value = PVBond = Coupon Payment +
b) Did you gain or lose more on one bond relative to the other? Explain.
