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# Fixed Income Risk and return

Hello,

Thank you for your help in advance. May i ask you a question as to why in the solution has it in the effective duration formula as the 0.001 rather then using 0.5%. what indicated 0.001?

The price of a bond is equal to \$101.76 if the term structure of interest rates is flat at 5%. The following bond prices are given for up and down shifts of the term structure of interest rates. Using the following information what is the approximate percentage price change of the bond using effective duration and assuming interest rates decrease by 0.5%?

Bond price: \$98.46 if term structure of interest rates is flat at 6%

Bond price: \$105.56 if term structure of interest rates is flat at 4%

A) 0.174%.

B) 1.74%.

C) 0.0087%.

Explanation

The effective duration is computed as follows:

Effective duration =

105.56 - 98.46/2 × 101.76 × 0.01= 3.49

Using the effective duration, the approximate percentage price change of the bond is computed as follows:

Percent price change = -3.49 × (-0.005) × 100 = 1.74%

• Because your effective duration is calculated on the change in yield of 1% (i.e. bond price when yield is at 6% and 4%, vs. 5%).

In the formula:

105.56 is the price when yield is at 4%

98.46 is the price when yield is at 6%

And your PV0 is when yield is at 5%

So the change in yield is 1% (vs. 5%)

Does this make sense?