Question

a) Calculate the price, duration and convexity (all based on continuous discounting) of a two-year 14% coupon bond (paid semi-annually) with a face value of $100. Suppose that the yield on the bond is 12% per annum with continuous compounding

b) What would be the estimated change in the value of the bond for a small decrease of 10 basis points in interest rates (using first order derivation only)?

c) What would be the estimated change in value for a larger increase of 200 basis points in interest rates (using second order derivation as well)?

d) The effect of what type of change in interest rates on bond value can be estimated using these methods?

Answer 1

Ans a) Price of bond = 7*e^(-.06*1) + 7*e^(-.06*2) + 7*e^(-.06*3) + 107*e^(-.06*4)

= 6.59 + 6.21 + 5.85 + 84.17 = $102.82

Time	Cashflow	PV	PV* Time
0.5	7	$       6.59	$        3.30
1	7	$       6.21	$        6.21
1.5	7	$       5.85	$        8.78
2	107	$    84.17	$   168.34
		$ 102.82	$   186.62
Maculay's Duration			1.82

Modified Duration = Maculay's Duration/ e^(.06) = 1.71

				Convexity
Time	Cashflow	PV	PV* Time	PV*Time*(Time + .5)
0.5	7	$       6.59	$        3.30	3.30
1	7	$       6.21	$        6.21	9.32
1.5	7	$       5.85	$        8.78	17.55
2	107	$    84.17	$   168.34	420.85
		$ 102.82	$   186.62	$                          451.01
Maculay's Duration			1.82
Convexity				3.89

Formula for convexity = 451.01/102.82 * 1/e^(.06*2) = 3.89

Ans b) Change in bond price = - Bond price * modified duration * basis change

= - 102.82 * 1.71 * (-.001)

= .17582

Ans c) Bond Price Change = Duration * Yield change + convexity adjustment

= 1.71* 2% + .5*3.89*100*(2%)^2

= -3.42% + .08% = -3.34%

Since yield is increasing bond price will be decrease by 3.34%

Ans d) If there is change in yield to maturity then one can find the value of bond using duration and convexity. If yield to maturity will increase then bond prices will decarease and vice versa.