Question: A five-year step-up note pays coupons semiannually and has the following coupon rate structure: the annual coupon rate is 4% in year 1 and rises

A five-year step-up note pays coupons semiannually and has the following coupon rate structure: the annual coupon rate is 4% in year 1 and rises by 50 basis points (bps) every year over the next four years. The par value of the note is $100.

(a) If this note is selling at $102, what is its YTM?

(b) Use a 25-bps rate shock to compute the duration of the note. Then use the duration just calculated to approximate the dollar price change of this note if the yields increase by 150 bps.

(c) Compute the exact dollar price change of this note when the yields rise by 150 bps. Compare the exact dollar price change to the price change in part (b) above, what might you conclude?

(d) Use a 25-bps rate shock to calculate the convexity of this note. Next, use both duration and convexity to approximate the dollar price change of this note for an increase of 150 bps in yields and compare the result to the exact dollar price change in part (c) above. Please briefly comment on your findings.

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