# Question 15.1, Schweser Exam 3 Afternoon

When calculating the dollar duration of bond Q below, why do they divide the price by 100? I thought dollar duration here was just -(ED)*(80 bps)*(104.98)*(\$10 million). In the book they list DD=(-ED)*(0.01)*(Price)… Bond Q has face amount \$10 million, Price 104.98, Duration Today: 10.32, Duration in 1 year: 9.46. The manager wants to completely hedge bond Q for an expected 80 bp change in interest rates. Dollar duration of the CTD bond for a 100 basis point change in rates is \$13,245.46. and the conversion factor is 1.3698. The number of futures contracts required is closest to: A. 82 B. 99 C. 112

because otherwise you’d be overestimatig the value of the position - it’s 10m worth at face value and EACH of that is priced at 104.98/100 or in other words each \$100 is priced at 104.98…make sense?

I’m sorry I don’t get it. Each \$100 is priced at \$104.98? I don’t know what that means. I know that since the change is 80 bps, the Dollar Duration of Q=(10.32)*(.008)*(104.98) which is \$8.6671 per \$100 of par. I know that’s related to what you said, grgkir001; could you take me the rest of the way?

sorry i just mean that the par value is \$100 but the current price is \$104.98. if you multipy the face value of 10m by the current price of 104.98 then you are overinflating it as you are multiplying each of the face value by the price of 100 not the price of each . not sure if i’m making myself any clearer or just making it worse as my brain’s a little fuzzy doing schweser’s online essay questions… basically the bond is trading at above par value (\$104.98 v \$100) - a premium of 4.98% so the value of the \$10m is \$10m x 1.0498 (or \$104.98/\$100) think of it more as the \$D is based on value of the position rather than just price x face value and the value is 10m x 1.0498

from your calc in your response - if the \$D = 8.6671 per \$100 then for \$10m it would be mulyiplied by 10m/100 so 8.667x100000 not by 10m

rellison Wrote: ------------------------------------------------------- > I’m sorry I don’t get it. Each \$100 is priced at > \$104.98? I don’t know what that means. I know that > since the change is 80 bps, the Dollar Duration of > Q=(10.32)*(.008)*(104.98) which is \$8.6671 per > \$100 of par. I know that’s related to what you > said, grgkir001; could you take me the rest of the > way? One thing to notice is Schweser (at least in the examples I have seen) define DD inconsistently with CFAI. As in this case, it says Dollar Duration for a yield change of xx%. As you wrote above, CFAI defines DD as for 100 bps ONLY. Normally, it will give you the same number of futures requires since Schweser applies the xx% both on the denominator and nominator (i.e., xx% yield change applies both for the bond and the hedge). However, you give wrong answer if you are given xx% yield change, market value, dollar duration and try to find out the duration of the bond. IN this case, you need to IGNORE the xx% given and only use 1% (100bps) as per CFAI definition.

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When he says that each 100 is priced at 104.98 that is the % of par it actually trades at. So you can take the 10M face value times 1.0498 in order to get market value. Same thing if it trades a 99, that is % of par the market is trading at. So this will be the price in teh formula for price of instrument to be hedged…

elcfa Wrote: ------------------------------------------------------- > One thing to notice is Schweser (at least in the examples I have seen) define DD > inconsistently with CFAI. As in this case, it says Dollar Duration for a yield change of xx%. > > As you wrote above, CFAI defines DD as for 100 bps ONLY. > > Normally, it will give you the same number of futures requires since Schweser applies > the xx% both on the denominator and nominator (i.e., xx% yield change applies both for > the bond and the hedge). > > However, you give wrong answer if you are given xx% yield change, market value, dollar > duration and try to find out the duration of the bond. IN this case, you need to IGNORE > the xx% given and only use 1% (100bps) as per CFAI definition. elcfa, Ya, I was much confused by Schweser, thanks for your clarification. BTW, would you please take a look at my messages under the title of “R37 : Table 1 (P.145) & EOC Q3/Q5” and please give me some advices regarding my questions posted there. TKVM !