Question

There is a 3-year bond available with a face of PLN 500,000, interest 6% pa, coupons paid semi-annually. It is expected that the YTM will be fixed during maturity period at 8% pa. Estimate how would the PVB at issue date change if YTM were to immediately increase to 12% pa and stay fixed during maturity period? Please use the best possible estimation (approximation).

Answer 1

Details available
Yield to maturity r= 8% or 4% semi annually
Bond face value = PLN 500,000
Coupon rate = 6% or 3% semi annually
Period = 3 years

Step 1 Coupon amount of bond
Coupon amount = par value × rate
Coupon amount = 500,000×3%
Coupon amount = 15,000

Step 1 Price and Duration of bond

Period P	A. Cash Flow	B. Dis rate at 4%	C. PV = A×B	D. P×C
0.5	15,000	0.96	14,423.08	7,211.54
1	15,000	0.92	13,868.34	13,868.34
1.5	15,000	0.89	13,334.95	20,002.43
2	15,000	0.85	12,822.06	25,644.12
2.5	15,000	0.82	12,328.91	30,822.28
3	515,000	0.79	407,011.98	1,221,035.94
			473,789.32	1,318,584.64

Price of bond = 473,789.32
Duration of bond D= (sum of PC)/(sum of C)
D = 1,318,584.64 /473,789.32
D = 2.783

Step 2 Price volatility
The yield to maturity of a bond and price of a bond are inversely related which means if the rate goes down the price of the bond goes up and if the rate goes up the price of the bond go down. The relation is calculated as below
Price volatility = D/(1+r)
= 2.783/(1+0.08)
= 2.58

Step 3 Price change
Now change in price if the rate goes up to 12% that is up by 4%
New price = old price-old price(price volatility×increase in rate)
New price = 473,789.32-473,789.32(2.58×4%)
New price = 473,789.32-48,835.40
New price = 424,953.92

Therefore the price will change by PLN 48,835.40 to the new price PLN 424,953.92 if the rate goes to 12%