Yield Curve and Bond Valuation - Math Problem Example

? Yield Curve and Bond Valuation Lecturer: Yield Curve and Bond Valuation Question and 2 Based on the information retrieved from the Board of Governors of the Federal Reserve System on a 1-month business day, the following information concerning historical dairy interest rates on the U.S treasury was obtained. The rates were picked from the current dates (1st January2012) back to five years a go (1st January 2007). Whereby, if that date was not a business date the preceding date was selected as shown in the table below. Business Date chosen Five Years Ago 1st January 2007 1-month Nominal T-bill Rate on that date 5.02% 3--month Nominal T-bill Rate on that date 4.79% 6-month Nominal T-bill Rate on that date 5.11% 1-year Nominal T-note Rate on that Date 5% 5-year Nominal T-note Rate on that Date 4.68% 10-year Nominal T-note Rate on that Date 4.68% 20-year Nominal T-note Rate on that Date 2.68% 30-year Nominal T-note Rate on that Date 0.81% The yield curve in action: US Treasuries, 1St Februry2007 Yields 6% 5.5% 5% 4.5% 4 % 3.5% 3% 2.5% 2% 1.5% 1% 0.5% 1m 3m 6m 1yr 10yrs 30yrs maturity Source: Author 3. on your selected date what was the yield curve rising, falling, or flat? What explanation would you give for this shape? Between the first months to the third month, there was a slight fall on yield. The yield started rising slightly by the end of sixth month. Additionally, another decline was scrutinized between sixth month maturities the fast year. Additionally, the yields remain constant between year one and tenth year maturity. In above connection, a significant decline was scrutinized between tenth year maturities to the 20th year. The curve further indicates that there was a substantial decline in maturities up to the 30th year maturity. The above observation indicates that there were higher fluctuations of yields to maturities (Parameswaran, 2007). The fluctuations may be attributed to the following factors; investor’s anticipation that future interest rates may fall may cause the above decline (Parameswaran, 2007). Additionally, a rise on the above yield curve between fast and the third month may be attributed to investor anticipation that interest rates may rise in the future. (Parameswaran, 2007) Connectively, long term anticipations that interest rates may decline may have brought a substantial decline of maturities by the end of 30th year (Parameswaran, 2007). 4. Completing the tables Table 1 Ten (10) year bond Purchased for $1000 five (5) years ago Original Value $1000 Coupon Rate(From the table above at the chosen date from 5 years ago, the original 10-years nominal T-bond Rate divided by 2 for semi-annual payments) 4.68%?2=2.34% Current 5-year Yield to maturity(The most recent 5-years Nominal T-note Rate reported at the federal site divided by 2 for semi-annual payments) 0.89%?2=0.445 Number of semi-Annual Periods Remaining 10 Current value Computed below Gain or loss on Bond over the five years Determined as shown below (a)Current Value=PVBond=Coupon Payment 1- 1 + 1000 (1+i)N (1+i) N i Current Value=PVBond= (2.34%?10) 1- 1 + $1000 (1.00445)10 (1.00445)10 0.00445 Current Value=PVBond= $238.3+ $956.6=$1194.9 Current Value=PVBond=$1194.9 (b)Compare the above value with the initial investments of $1000 It can be scrutinized that the current value of bond above is slightly higher than the initial outlay of $1000. This indicates that the bond increase it’s value by $194.9 derived by finding the difference between the initial investment and the current value (Fabozzi, 2001). This increase may be as a result of decrease in interest rates (Fabozzi, 2001). Table 2 Twenty (20) year bond Purchased for $1000 five (5) years ago Original Value $1000 Coupon Rate(From the table above at the chosen date from 5 years ago, the original 20-years nominal T-bond Rate divided by 2 for semi-annual payments) 2.68%?2=1.34% Current 15-year Yield to maturity(Take the average of the most recent 10- and 20-years Nominal T-bonds Rate reported at the federal site divided by 2 for semi-annual payments) (1.97%+2.67%)?2=2.32% Therefore semi-annual interest rate=2.32%?2 =1.16% Number of semi-Annual Periods Remaining 30 Current value Gain on Bond over the five years Computed below Gain or loss on Bond over the five years Determined as shown below (a)Current Value=PVBond=Coupon Payment 1 - 1 + 1000 (1+i)N (1+i) N I Current Value=PVBond= $13 1- 1 + $1000 (1.0116)10 (1.0116)10 0.0116 Current Value=PVBond= $125.80 + $891.1 Current Value=PVBond= $1016.9 (b)Compare the above value with the initial investments of $1000 Based on the above computation it can be scrutinized that there was an increase in the value of bond from the initial investment of $1000 to the current value of $1016.9. This indicates that there was an increase of $16.9 in the value of bond. The above increase may be attributed to three factors namely; prepayments, credit rating and interest rates (Fabozzi, 2001). Research indicates that decrease in interest rates may lead to an increase in value of the bond (Fabozzi, 2001). Therefore, the above research findings confirmed with the above calculations. References Fabozzi, F. J. (2001). Bond portfolio management. New Hope, Pa: Frank J. Fabozzi Assoc. Parameswaran, S. K. (2007). Bond valuation, yield measures and the term structure. New Delhi: Tata McGraw-Hill. Read More