Question

For the following bond,

Par value: $1,000

Coupon rate: 8% paid annually

Time to maturity: 3 years

Interest rate: 3%

What is the convexity? Also, if the interest rate increases from 3% to 4%, what is the price change due to the convexity?

Select one:

a. Convexity: 9.7806; price change: $.7087

b. Convexity: 11.125; price change: $.6402

c. Convexity: 10.2961; price change: $.5876

d. Convexity:11.925; price change: $.8887

Answer 1

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =3

Bond Price =∑ [(8*1000/100)/(1 + 3/100)^k]     +   1000/(1 + 3/100)^3

k=1

Bond Price = 1141.43

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc	Convexity Calc
0	($1,141.43)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period	=duration calc*(1+period)/(1+YTM/N)^2
1	80.00	1.03	77.67	77.67	146.42
2	80.00	1.06	75.41	150.82	426.47
3	1,080.00	1.09	988.35	2,965.06	11,179.41
			Total	3,193.54	11,752.31

Convexity =(∑ convexity calc)/(bond price*number of coupon per year^2)

=11752.31/(1141.43*1^2)

=10.2961

Using convexity adjustment to modified duration

Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price

0.5*10.3*0.01^2*1141.43

=0.5876

C is correct