A newly issued bond has a maturity of 10 years and pays a 7.5% coupon rate (with coupon payments coming once annually). The bond sells at par value. a. What are the convexity and the duration of the bond? Use the formula for convexity in footnote 7.

Bond

Explanation:

Bond price = B = Face value = F = $100 (Because the bond sells at par value.)

Time to maturity = n = 10 years

Number of periods in a year = p = 1 (annual coupon payments)

Coupon rate = C = 7.5% = 7.5%*100 = $7.5

Yield = r = 7.5% (since bond is selling at par hence the coupon rate = yield)

Duration and Convexity:

Duration is a used as a measure of risk because it provides the average length of time by when the bond holder will receive their payments made. Longer the duration, longer is the time to receive the payments and hence higher the risk.

Expanding the summation and solving for Convexity, we get,

Period (t)Cash FlowPV = Cash Flow / (1+r/p)^(t*p)(t^2+t)*PV

17.56.9767441860465113.953488372093

27.56.4899945916711738.939967550027

37.56.0372042713220272.4464512558643

47.55.61600397332281112.320079466456

57.55.22418974262587156.725692278776

67.54.85971138848918204.107878316546

77.54.52066175673412253.157058377111

87.54.20526675045035302.779206032425

97.53.91187604693056352.06884422375

107.53.63895446226098400.284990848708

1010048.51939283014645337.13321131611

Sum of (t^2+t)*PV7243.91686803787

Convexity = sum/(B*(1+r)^2)62.6839750614418

Convexity = 62.6839750614418 = 62.684 (rounded to 3 decimal places as requested in the question)

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