Couple of questions re p. 341/342 in CFAI text. 1. I don’t understand where the 87% comes from. If they reduce the position in Bond#2, what are you buying? If you hold cash, doesn’t the dollar duration reduce? And doesn’t the answer depend on how much of Bond1 and Bond2 you buy, which isn’t given? 2. Middle of page 342, “effect due to a change in sector spreads is in addition to the effect…increase or decrease in interest rates”. Did they really mean in addition to effect of general spreads? You can break down price changes for your FI portfolio as follows: - parallel shift - twisting - spread shift - sector spread shift - issue spread shift Seems like CFAI statement is too general. 3. Example 8, #3 – I agree it’s incorrect, but isn’t there also the spread risk?
#1) actually i tried to solve the the equation assuming x+y amount of bond 2 is sold, and the x amount of bond 1 and y amount of bond 2 is bought, but there’s only one equation here and I couldn’t find another equation to solve it, I can e-mail you my work if you want. Seems like only author knows where 87% comes from. I also googled “rebalancing ratio duration” and result is next to nothing, so you are not alone. #2) good question but you think too deep, i’d keep it simple #3) well again you can add the other factors that affect the yields, but i think if they ask a multiple choice question like this the answer will be much clearer.
I think the authors made a mistake here. Selling 87% of Bond#2 and putting about 10% of the proceeds back into Bond 1 with the other 90% in Bond#3 would get your dollar duration back to $111,945. Likewise, selling 80% of bond#2 and putting about 56% of the proceeds back into Bond 1 with the other 44% in Bond#3 would get your dollar duration back to $111,945. There are an infinite number of combinations.
There definitely was an eror on page 341 regarding DD (See CFAI errata). I would avoid that tipic in CFAI altogether.