INVESTMENT MANAGEMENT Case Solution
INTRODUCTION
This case is about the computation of Treasury bond prices of different maturities, it also includes the computation of forward rates. The case also contains the application of expectation theory on interest rates and yield curve. Furthermore, the case includes the duration of both modified and effective durations and lastly, the hedging of interest rate risk.
ZERO COUPON BONDS
Q1a BASED ON INFORMATION PROVIDED FOR THE TREASURY BONDS, COMPUTE THE BOND PRICES.
In this part, the value of Treasury bond is computed using yield on bonds and the bonds present value and the present value of principle is being computed. The present value of bond is taken as the sum of present values of interest and payments, which are shown below:
| Face value | Yield or market rate | Bond price | Coupon + face |
| 100 | 2.25% | 108.28853 | 104.75 |
| 100 | 1.78% | 103.8961 | 106 |
| 100 | 1.85% | 96.159634 | 104.25 |
| 100 | 1.83% | 95.027321 | 105.5 |
| 100 | 1.79% | 91.179693 | 103.25 |
| 100 | 1.77% | 93.651777 | 105.25 |
| 100 | 1.82% | 82.500501 | 102.75 |
| 100 | 1.84% | 87.196885 | 104.5 |
| 100 | 1.95% | 71.644573 | 101.75 |
| 100 | 1.96% | 80.008752 | 105.75 |
| 100 | 2.12% | 115.60367 | 105.75 |
| 100 | 2.21% | 118.29881 | 105.5 |
| 100 | 2.31% | 103.82485 | 102.75 |
| 100 | 2.36% | 108.63546 | 103.25 |
| 100 | 2.40% | 114.35016 | 104.25 |
| 100 | 2.48% | 116.2901 | 104.75 |
Q1b BASED ON THE CURRENT YIELD CURVE, CALCULATE THE FOLLOWING FORWARD RATES OUT OF 6 MONTHS.
The forward rates on the basis of two scenarios are calculated using yield curve on the bonds of 6 months and one year maturity, the increase was taken as the difference between the two yield rates of two different maturities, which can be seen below. It can be seen that yield rates are increasing in the longer term and showing an increasing trend.
| years | Current yield | Time horizon | Forward rate | Time Horizon | Forward rate |
| 0.5 | 2.25% | 0.5 to 1 year | 1.78% | year 1 to 1.5 year | 1.85% |
| 1 | 1.78% | 0.5 to 1.5 year | 2.25% | year 1 to 2year | 2.25% |
| 0.47% | 0.5 to 2 year | 2.72% | year 1 to 2.5 year | 2.65% | |
| 1.5 | 1.85% | 0.5 to 2.5year | 3.20% | year 1 to 3 year | 3.05% |
| 0.40% | 0.5 to 3 year | 3.67% | year 1 to 3.5 year | 3.45% | |
| 0.5 to 3.5year | 4.14% | year 1 to 4 year | 3.85% | ||
| 0.5 to 4 year | 4.62% | year 1 to 4.5 year | 4.26% | ||
| 0.5 to 4.5 year | 5.09% | year 1 to 5 year | 4.66% | ||
| 0.5 to 5 year | 5.56% | year 1 to 5.5 year | 5.06% | ||
| 0.5 to 5.5year | 6.03% | year 1 to 6 year | 5.46% | ||
| 0.5 to 6 year | 6.51% | year 1 to 6.5 year | 5.86% | ||
| 0.5 to 6.5 year | 6.98% | year 1 to 7 year | 6.26% | ||
| 0.5 to 7 year | 7.45% | year 1 to 7.5 year | 6.66% | ||
| 0.5 to 7.5 year | 7.93% | year 1 to 8 year | 7.06% | ||
| 0.5 to 8 year | 8.40% | year 1 to 8.5 year | 7.46% | ||
| 0.5 to 8.5 year | 8.87% | year 1 to 9 year | 7.86% | ||
| 0.5 to 9 year | 9.35% | year 1 to 9.5 year | 8.27% |
Expectation theory also states that if interest rates rise in future, then yield curve slope goes upward for different maturities, it is expected that the bonds with higher maturities always have higher interest rates as it can be seen below.....................
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