# What happens to convexity of bonds when interest rates rise? Why?

Assume a two-year Euro-note (pays coupon annually), \$100,000 par value, an annual coupon rate of 10 percent and convexity of 2.7.  If today’s YTM is 11.5 percent and term structure is flat,

1. What is this bond’s Macaulay duration?
1. What does convexity measure? Why does convexity differ among bonds? What happens to convexity of bonds when interest rates rise? Why?
1. What is the exact price change in dollars if interest rates increase by 10 basis points (a uniform shift)?
1. Use the duration model to calculate the approximate price change in dollars if interest rates increase by 10 basis points.
1. Incorporate convexity to calculate the approximate price change in dollars if interest rates increase by 10 basis points.
1. Assume the Euro-note is the debt issue of the firm. How should the firm invest the proceeds of the debt issue such that its equity value is immunized against interest rate risk? (i.e. achieve equity dollar duration of zero supposing convexity is ignored).
1. How long is the hedge in part (g) (i.e. the zero duration position) good for? Why? Explain.

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