Serving the Quantitative Finance Community
Problem on Duration
A fixed-rate bond with a market value of 20 million and a duration of 4 is separated intothree bonds. Two of the bonds are floaters and the third is an inverse floater.You are given the following information with respect to the floaters:Floater Market Value Duration A 16 million 1 B 2 million 0.5Calculate the duration of the inverse floater.
Problem on Duration
Think about it this way. If interest rates go up one basis point, the original bond will decline in price by four basis points or $8,000. Floater A will decline in price by 1 basis point or $1,600. Floater B will decline in price by 0.5 basis points or $100. So the inverse floater must decline in price by $8,000 - $1,600 - $100 or $6,300.The market value of the inverse floater is $20 million - $16 million - $2 million = $2 million. $6,300 / $2,000,000 = 0.00315 = 31.5 basis points. So the duration of the inverse floater must be 31.5.
Problem on Duration
Duration of a portfolio is the weighted average of durations of its constituents.