Question

Given a 9-year bond with YTM of 4% and a duration of 7.5, what is the expected percent price change/return for a 0.05% (5 basis-point/bps) shift up in market yields?

Given 1-year ZCB securities with 5.2% yield in GBP and 4.5% yield in EUR, and a spot exchange rate of GBP/EUR at 1.5408, what expected spot ex- change rate in 1-year would result in a break-even between the two instruments? Which bond would be a better investment given a 1Y forward exchange rate of GBP/EUR 1.4120?

Answer 1

In this case, Modified Duration = Duration/(1+YTM) =7.5/(1+0.04) = 7.2115

So, for 0.05% increase in market yields , the bond price should change by

= -modified duration* change in yield

= -7.2115 * 0.05%

= -0.36%

The bond price is expected to decrease by 0.36% (which is the expected price change)

From Interest rate parity

Expected Spot exchange rate in 1 year (GBP/Euro)

= Spot exchange rate today * (1+interest rate in Euro)/(1+interest rate in GBP)

= 1.5408*1.045/1.052

=1.5305

So,expected spot ex- change rate in 1-year of GBP/Euro 1.5305 would result in a break-even between the two instruments

Given a 1Y forward exchange rate of GBP/EUR 1.4120, Euro is more valuable than the breakeven rate

So, Euro bond is a better investment

(Sell GBP ZCB worth 1 million today, get GBP1 million/1.052 , Convert to Euro to get Euro 1 million/1.052*1.5408

=Euro 1,464,638.78 and buy Euro ZCBs at 4.5% to get Euro 1464638.78*1.045 =Euro 1530547.53 at maturity

Simultaneously sell Euro 1530547.53 forward at GBP/EUR 1.4120 to get GBP 1083957.17 after one year, pay GBP 1 million for short ZCB and make GBP 83957.17 as arbitrage income)

Thus , Euro bond is a better investment