Reading 30 Example 10 into, maintain, equation, reading

bolligerallstar

In reading 30, on page 112 of the CFAI text there is an example to calculate the par value needed to maintain the duration of a portfolio when adding a bond. To calculate this they use the equation:
Dollar Duration of the portfolio / Dollar Duration of the new bond * 100
However, in the equation given above the example in the text it states taht the equation should be:
Dollar Duration of the portfolio / Duration of the new bond * 100
Can someone please look into this and tell me if I am missing something?
Thanks,
TheChad

infinitybenzo

TheChad
Hope the following detailed calculation explains what you are asking
Existing bond
Total market value = 5 500 000 (given)
Market value/bond = 80 (given)
Number of bonds = 68 750 = 5 500 000/ 80
Total par value = 68 750 * 100 = 6 875 000
Duration = 4 (given)
Dollar duration = 5 500 000 *4 / 100 = 220 000
New bond must have the same dollar duration, i.e., 220 000
Duration = 5 (given)
Total Market value = 220 000/5 * 100 = 4 400 000
Mkt value/bond = 90 (given)
Number of bonds = 48 889 = 4 400 000/ 90
Total par value = 48 889 * 100 = 4 888 889 (as given as answered)
Master this well since you will encounter this equal dollar duration again and again (in risk management and portfolio management)

Darien

Thank you for the explanation, it helped a lot.
Best,
TheChad