Estimate the price impact of a 50-basis point interest rate change using a linear approximation of a 10-year 7% semi-annual coupon bond priced at 97.50.
a. 1.72
b. 3.40
c. 3.44
d. 6.80
e. 6.88
The bond prices have inverse relation with change in interest rate , i.e. the price moves in the opposite direction of the change in interest rates.
Value of bond =
Face Value | $ 100 |
Annual Coupon Rate | 7.000%(annual) 7%/2=3.5%(semi annual) |
Years to Maturity | 10.00 |
Price of bond | 97.5 |
Payment Frequency | 2 |
YTM | 7.36% using rate() function |
Rate | Price of Bond |
7.357% | $97.50 |
7.857% | $94.14 |
7% | $100.00 |
7.50% | $96.53 |
8% | $93.20 |
8.357% | $90.92 |
after running the regression , output for the linear relation establish as
Price of bond = A + B* change in interest
Coefficients | Standard Error | t Stat | P-value | Lower 95% | |
Intercept | 146.7565964 | 0.481033181 | 305.0862 | 6.93E-10 | 145.421 |
Interest rate Variable 1 | -669.075076 | 6.254155755 | -106.981 | 4.58E-08 | -686.439 |
for 50 bps = 0.5%
Change = -669.07 * 0.5% = -3.34
Option C : 3.44
Estimate the price impact of a 50-basis point interest rate change using a linear approximation of...
Estimate the price impact of a 50-basis point interest rate change using a linear approximation of a 10-year 7% semi-annual coupon bond priced at 97.50. a. 1.72 b. 3.40 c. 3.44 d. 6.80 e. 6.88
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