Question

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Problem 1 : Lucky Star Inc. just issued a bond with the following characteristics:

Maturity = 3 years

Coupon rate = 8%

Face value = $1,000

YTM = 10%

Interest is paid annually and the bond is noncallable.

1. Calculate the bond’s Macaulay duration （Round "Present value" to 2 decimal places and "Duration" to 4 decimal place.）
2. Calculate the bond’s modified duration
3. Assuming the bond’s YTM goes from 10% to 9.5%, calculate an estimate of the price change without considering convexity .
4. Calculate the convexity of the bond.

Answer 1

(a) Calculation of Bond's Macaulay duration :

Year (D)	Cashflow	PVF @ YTM =10%	PV (W)	D*W
1	80	0.91	72.80	72.80
2	80	0.83	66.40	132.80
3	1080	0.75	810	2430
			W = 949.20	DW = 2635.60

Macaulay Duration = DW / W

= 2635.60 / 949.20

= 2.7767 Years

(b) Modified Duration = Duration / (1+ YTM)

= 2.7767 / (1+0.10)

= 2.5242 Years or 2.5242 %

(c)

Year	Cashflow	PVF @ YTM =10%	PV	PVF @ YTM = 9.50%	PV
1	80	0.91	72.80	0.91	72.80
2	80	0.83	66.40	0.84	67.20
3	1080	0.75	810	0.76	820.80
		Total	949.20	Total	960.80

Change in Price = 960.80 - 949.20

= 11.60 or 1.22%

(d) Assuming Interest rate shock of 0.50% is given.

Year	Cashflow	PVF @ YTM =10.50%	PV	PVF @ YTM = 9.50%	PV
1	80	0.90	72	0.91	72.80
2	80	0.82	65.60	0.84	67.20
3	1080	0.74	799.20	0.76	820.80
		Total	936.80	Total	960.80

Convexity = (P+ + P- - 2Po) / 2*Po*

Here,

P+ = Higher Price where YTM decreases

P- = Lower Price where YTM Increases

P0 = Original price

    = Change in YTM (shock) used to calculate above P+ & P-

= (960.80 + 936.80 - 2*949.20) / 2*949.20*(0.50%)2

  = -16.86