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Assume a $2-$year Euro$-$note, with a $$200,000$ face value, a coupon rate of $10\%$ and a convexity of $4\mathrm{.}53.$ If today$$s YTM is $11\mathrm{.}5\%$ and term structure is flat. Coupon frequency and compounding frequency are assumed to be annual.

$1.$ What is the Macaulay duration of this bond?

$2.$ What does convexity measure? Why does convexity differ among bonds? What happens to convexity when interest rates rise? Why?

$3.$ What is the exact price change in dollars if interest rates increase by $10$ basis points $($a uniform shift$)?$

$4.$ Use the duration model to calculate the approximate price change in dollars if interest rates increase by $20$ basis points.

$5.$ Incorporate convexity to calculate the approximate price change in dollars if

interest rates increase by $20$ basis points.

We consider the following zero$-$coupon curve:

Maturity $($Years$)$ Zero$-$ Coupon Rate $\%$

$14\mathrm{.}0$

$24\mathrm{.}5$

$34\mathrm{.}75$

$44\mathrm{.}90$

$55\mathrm{.}0$

$1.$ What is the price of a $5-$year bond with a $$100$ face value, which delivers a $5\%$ annual coupon rate?

$2.$ What is the yield to maturity of this bond?

$3.$ We suppose that the zero$-$coupon curve increases instantaneously and uniformly by $0\mathrm{.}5\%.$ What is the new price and the new yield to maturity of the bond? What

is the impact of this rate increase for the bondholder?

$4.$ We suppose now that the zero$-$coupon curve remains stable over time. You hold the bond until maturity. What is the annual return rate of your investment? Why

is this rate different from the yield to maturity?