Question

You are about to purchase a 10-year par bond with a 5% coupon rate paid annually.

1.What are the duration and the convexity of this bond? [4 marks] Using first derivative with formula

2. Assume that right after you purchase the bond an economic announcement drives the YTM to 7%. What is the new price of the bond? [1 mark]

3. What price would be predicted by the duration rule after the YTM increases to 7%? Is this answer the same as the one reported in part (2)? Why? [2 marks]

4. What price would be predicted by the duration-with-convexity rule after the YTM increases to 7%? Is this answer the same as that reported in part (2i)? Why? [2 marks]

Answer 1

Solution Given that purchase bond = 10 years Coupon rate = 5% Teff Duration (pv-)-(Pvt) ] _ 2 x Change in yield xpro - convexity = ((PV-) + pvt) - [ex Pvo] (change in yield]2x (Pro) > PAS = 100 No lo yeary YTM25% PVO = 100 ( since trading at par) Let change in yield 1% [PV- when yTM is 4% I Pvt when yTM is 6% N -10 y using a financial Calculator or ercel we get 1 PV = $ 108.11 ) IPvt = $92.64 1 change in yield is 1% ov10.0]] Duration using above formula = 7.7 years Convenity using above formula : 75 =) FV=100 coupon=5 Ratero% N=104 - using a financial calculator Camis.PV = $85,95

Let the change in yield = 2% PN- When yTM a 3% Pva When YTM 27% Naloy coupon 25 Using a financial Calculator. TPV- - $117.06 - Pvt = $85.95 . Change is yield is 2% or 0.02. - Duration Using above formula = 7.7 yeary Convenity Using above formula? 75 Both duration and convenity remains same. = The End CS Scanned with CamScanner