Question

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

Answer 1

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 =
Maturity Couponi

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