# Dollar duration - Maintaining portfolio duration in changing portfolio holdings

Please see page 112 on Vol 4 Based on the formula provided, new bond market value = dollar duration of old bond / DURATION of NEW BOND * 100 Yet in the example 10 (on the page), they use this equation instead, new bond market value = dollar duration of old bond / Dollar DURATION of NEW BOND * 100 How come?

I struggled with this one too. Anyone has a good explanation?

suppose bond X has market value of 8 mn (par value 10 mn) and duration = 5. suppose bond 9 has market value of 9 mn (par value 10 mn) and duration = 4. DD of bond X for 100 bp change in yield = .01 * 8,000,000 \* 5 = 400,000 DD of bond Y for 100 bp change in yield = .01 * 9,000,000 \* 4 = 360,000 if he portfolio manager has desire to maintain the same interest rate exposure for bond Y (that he’s considering to exchange for Bond X) as bond X, she’ll buy market value of bond Y that has same dollar duration as bond X. MV of bond Y = DD of bond X / (Duration of bond Y * 0.01). in this case its 400,000 / .04 = 10,000,000 \$ MV of bond Y will be purchased. 10mn mkt value of bond Y has same DD as 8mn mkt value of bond X Amt of par value of bond Y that must be purchased given its price of 0.90 per 1 par value = \$10,000,000/\$0.90 = \$11.11 mn

rf040234 Wrote: ------------------------------------------------------- > Please see page 112 on Vol 4 > > Based on the formula provided, new bond market > value = dollar duration of old bond / DURATION of > NEW BOND * 100 > > Yet in the example 10 (on the page), they use this > equation instead, new bond market value = dollar > duration of old bond / Dollar DURATION of NEW BOND > * 100 > > How come? Must be a typo - dollar duration is always multiplied by .01, not 100, to my knowledge. Also, I came across a CFAI EOC question today which stated that you take the higher of the two durations for your denominator…*Skillionaire leaves the comfort of the couch to grab his books*…nevermind, was a spread widening question, but I was confused nonetheless - Volume 4, page 154, #22, for all those playing along at home.

I have not looked at the example so specifically but in general Dollar Duration = Duration*Market Value Therefore MV of new bond = Dollar Duration of Old Bond/Duration of New Bond*100 I think the second equation may be a typo.

skillionaire Wrote: ------------------------------------------------------- > rf040234 Wrote: > -------------------------------------------------- > ----- > > Please see page 112 on Vol 4 > > > > Based on the formula provided, new bond market > > value = dollar duration of old bond / DURATION > of > > NEW BOND * 100 > > > > Yet in the example 10 (on the page), they use > this > > equation instead, new bond market value = > dollar > > duration of old bond / Dollar DURATION of NEW > BOND > > * 100 > > > > How come? > > Must be a typo - dollar duration is always > multiplied by .01, not 100, to my knowledge. > > Also, I came across a CFAI EOC question today > which stated that you take the higher of the two > durations for your denominator…*Skillionaire > leaves the comfort of the couch to grab his > books*…nevermind, was a spread widening > question, but I was confused nonetheless - Volume > 4, page 154, #22, for all those playing along at > home. Yield differentials can be eliminated from both countries: increase in yield in country A, or a decrease in yield in Country B. Using the highest of both durations makes common sense to me, as you want to approximate what increase in spread will eliminate the advantage, a conservative approach is the use the highest duration…

I did some resarch on this and found that the righ answer will be #Market Value of new bond portfolio =( DDo/DDn)*100 #Compare Page 112 example 10 with Q9 of page 60 CFAI Volume 4 #The numerator (DDo) is for the entire portfolio of single bond whereas denominator(DDn) is DD of new bond (Notportfolio) #You are not using price of old bond if market value is given . If par value is given then you have to multiply par value with price to get market value to calculate DDo

I guess some of you have answered it in the above posts, but just to reiterate: Example 10 is correct. It asks about the “par” value of the new bond. The duration formulas are generally all for market value. So a more straight-forward way to get to the answer would be to use the formulas in the text to determine the market value of the new bond of \$4.4MM (\$220,000/5*100). Then to determine the par value, multiply with \$100/\$90 -> \$4.889MM.