A portfolio manager s hired to manage a bond portfolio worth $23m. If the manager were to immunize this portfolio, base on the client’s needs, it would earn 7.5% p.a. over the next 10 years. However, the portfolio manager is allowed to actively manage this portfolio as long as the ave horizon return does not fall below 5.0%. Such being the case, what would be the current dollar safety margin of the portfolio? a) $4,822,415 b) $3,478,331 c) $19,771,193

A. 4822415.00?

A

C

Hmmmm… I got $4,951,420. What’s the answer Kumanal? And can you please provide the calculation workings?

“earn 7.5% p.a. over the next 10 years” necessarily means investing in 7.5% coupon bond ?

To compute the minimum required terminal value: 23m * (1.05)^10 = 37,464,576 Since immunization will yield 7.5%, the assets needed today would be as follows: 37,464,576 / (1.075)^10 = 18,177,585 Dollar safety margin = portfolio market value - required assets today: 23,000,000 - 18,177,585 = 4,822,415

kurmanal, Why not compound semi-annually ? It is compounded semi-annually in CFAI’s text.

The problem does not mention to compound it semi-annually… it just says - over the next 10 years… and i got this problem from another source, not CFAI…

Kurmanal - Thanks. Your workings are exactly the same as mine except you compounded annually and I compounded semi-annually. AMC - I totally agree with you. If you compound semi-annually, your initial dollar safety margin would be $4,951,420. Try calculating it and let me know if you get the same answer. Cheers!

bidder, $4,951,420.

Perfect. Thanks AMC. Next topic now…!