Lexi owns a portfolio of 3 bonds with modified durations of 4.25, 6.80, and 9.50 years, respectively. The proportion of her portfolio wealth invested in the short duration bond is 20%, and she wants to keep it that way. If her desired portfolio duration is 7.50 years, what should be her investment proportion in the long-duration bond? All of her money is invested in the three bonds; she does not hold any cash.

Group of answer choices

38.68%

44.81%

20.00%

55.19%

61.32%

Part II

An 8% coupon bond with 15 years to maturity has a yield (YTM) of 10% today and a Macauley duration of 8.45 years. If the bond yield increases by 25 basis points this afternoon, the bond price will approximately:

Group of answer choices

increase by 4%

decrease by 2%

increase by 2%

decrease by 4%

decrease by 16%

Challenge question: In the previous problem #36, suppose the yield increase is 100 basis points instead of 25. Calculate the actual return on the bond, and by doing so, quantify the benefit for this bond's owner of the positive convexity effect.

Group of answer choices

2.93 basis points

0.67 basis points

11.72 basis points

20.12 basis points

45.18 basis points