You've learned how to compute price elasticity with respect to changes in interest rates (modified duration) of a bond under the flat term structure of interest rates, and parallel shifts in the term structure. In this problem, you are asked to compute the price elasticity of a bond under a non-flat yield curve. The present value (price) of a bond is

B=Tt=1CFt(1+rt)t.

Now consider the parallel shift of the yield curve by x, i.e. rtrt+x, t. Then the price elasticity of the bond with respect to parallel shifts in the yield curve can be written as

PE=1BdBdx=1BTt=1tCFt(1+rt)t+1.

We can now approximate price changes in response to a small parallel shift r in the yield curve as

BB|PE|r

Note that when the yield curve is flat, the absolute value of price elasticity |PE| equals modified duration.

Consider the following term structure, which is upward sloping:

1-yr	2-yr	3-yr	4-yr	5-yr
2.21%	2.53%	2.82%	3.04%	3.22%

A 5-year Treasury note (T-note) has a face value of $100 and a 4.25% coupon rate (assume annual payments).

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(a) Compute the price of the T-note.

unanswered

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(b) Suppose that the yield curve suddenly shifted down by 0.9% (this is a parallel shift, all points on the yield curve shift by the same amount). Compute the new price of the T-note and report the difference between the new price and the original price computed in (a), i.e., BnewBold.

unanswered

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(c) Compute the absolute value of price elasticity |PE| of the T-note as defined above.

unanswered

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(d) Compute the approximate price change based on the price elasticity.

unanswered

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Food for Thought: Compare the exact price change that results from the parallel shift in the yield curve to the approximate change, using the approximation BB|PE|r. How accurate is the duration-based approximation? You may want to experiment with larger and smaller shifts to get a better sense of how reliable the duration-based approximation is in this context.