1. Duration & Convexity Revisited: You have a 4-year 5% coupon bond (annual coupon payments) with a face value of $1,000. The spot rate term structure is shown in the table below.

Maturity	Spot Rate	Discount Factor	Cash Flows	PV Cash Flows	$-Duration	Convexity
1	4.0%	.9608	50	48.04	48.04
2	4.25%	.9185	50	45.93	91.86
3	4.75%	.8672	50	43.36	130.08
4	5.25%	.8106	1050	851.13	3404.52
Ytm =	5.20%

1. Calculate the discount factors, PV of the bond, $-duration (delta), Macaulay Duration and $-convexity. Put the values in the table above.

Use the following formulas to calculate delta (dollar duration), Macaulay Duration and $-convexity:

$ = [1 PV(K1)] + [2 PV(K2)] + [3 PV(K3] + + [T PV(KT)]

DMac = $/

2. Assume the term structure makes a 200 bps shift upward. Estimate the new price of the bond using the duration relationship. Assume the reference rate is the current ytm.

3. For the same 200 bps upward shift, estimate the new price of the bond using your answer in B above and the convexity correction.

The duration relationship with the convexity correction states:

4. Calculate the new price of the bond using the discount function after the term structure shifted up by 200 bps.