Question

Question 3 Suppose you observe the following market data on debt securities: Security Coupon (p.a.) Yield to maturity (p.a. continuously compounded) n.a. 2.00% 6-month Treasury Bond 1-year NZ Government Stock 10%, semi-annual 4.00% Note: Data deviates from the current market conditions as it simplifies the calculations. Required: (a) What are the continuously compounded zero-coupon yields for 6 months and one year, respectively? Report your answer in percentage (%) with 4 dps. (4 marks) (b) What is the duration of the following default-free bond portfolio? (4 dps) Time to maturity Number held 1 year 60,000,000 Coupon rate (p.a.) 8.00% 6.00% 1 year 75,000,000 Note: Each bond has a face value of $1.00 and coupons are paid semi-annually. You should assume the zero-coupon rate calculated in part a above. Note: Use the following formula to measure the duration of the bond portfolio, i.e., —, where ti, c, and r, denote for term, cash-flows, and zero-coupon yield for the ce ih period.

Answer 1

In the above question , we need to find continuous compounding and portfolio duration. Attaching two JPEG image for the work out of those two problems
a) Given - contina YTMIP. A coupon Security compared 2.00l. 6-month deasury bond 1-yeau NZ. Government Stock MA 107. SEMP.ANNUAL 40%. our objecture is to find the continously compounded nero coupon yields for 6 months and a year respectively continens componending to to. In fett N = peried R . intetatarea interest Rate Plugging the YTM in above mentioned formula i continous compound for 6 month Treasury boud for | : : In. I 1+ 1.4.) inlto.o1) 0.009950 0.9990% - continous compound for 1 year NZ. Government ا ین در مره اند تا با Inllooh 0:03 92207 Hence continous coumpound for 6 month Preamry .انه 45ة. وما لهما - and Continous compound for Stock is 9 2 21% 1 year NZ Governs Scanned with CamScanner

al 10 maksity Coupe batu Number - 60.000.000 75,000,000_ 1 year - CL. It is also given that each bond has a face nale of $1.00 and coupons are paid lemi- annually our objective is to find the duration of the above nuntiand default free land portfolio by using the Det 19 ; cieniti ciet where t, e and ni denote for term, coth flang and yero-coupon yield for the period folla me patfelis dili is w.b - We Dot & WNDN where wi full price of bond i divided by the total natue of the posfolio dustin M bend N no y loses in the posetio - -R 60.0oo.. N 220.03.-t Poufle dute b o.000.0 12 + TSDOCCO 2 3 SOOS + 0.55SCA2 5 . 442 1919 7 years