You own a 30-year bond issued by Apple.

You own a 30-year bond issued by Apple. The yield is 2.75%. 30-year Treasury rates are at 1.3%. The price is at par (100). What is its duration? Estimate from the duration what happens to its price if Treasury rates decline by 20 bps, but credit spreads widen by 30 bps.

Since the price is equal to par value, coupon rate is equal to YTM which is 2.75%

Duration of the bond is assessed at 20.8062 years. (Calculation is appended below)

As a general rule, for every change of 100 basis points in interest rate, present value will change, in the opposite direction, by approximately 1% for every year of modified duration

In the given case, Treasury yield declines by 20 bps but credit spread increase by 30 bps. As a result, there is a net increase of 10 basis points (0.1%) in yield

Consequently, price will fall by Duration*0.1% = 20.8062*0.1% = 2.08062%

New price= 100*(1-2.08062%) = 97.9193

Calculation of Duration as below:

Comment （转载自info.gandue.net）