CFA 2012 AM - Multiple routes to same answer?

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banjo711

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In Question 8A, the solution illustrates decreasing the equity allocation, then beta. Also, it shows increasing bond allocation, then decreasing it’s modified duration.
My question is: Can we perform these calculations in the reverse order? Then end result is more or less the same, but of course the CFAI solution only indicates the previous sequence of events. For example, if you decrease beta first, then the equity allocation, the # of contracts to sell for each calculation is different, but adding them together lands the same end result.
CFAI = sell 242, then sell 222 for a total of 464. I got sell 262, then sell 201 for a total of 463 (seems like a rounding error)
Same sort of result for the change in bonds.
Did anyone else stumble on to this conclusion?
 
Good question. Would be interested in the answer.
 
On this particular question I did it the CFA way - sell 242 to reduce exposure then sell 222 to reduce beta on remaining equity exposure. However for the Bond part I reduced duration first then increased bond exposure and ended up with buy 63 contracts when the answer specifies 64. What I gathered from that is the CFA way is to increase/decrease exposure first then increase/decrease Beta/Duration. However, I then did the question again - when I added the two answers without rounding until the end (for the bond: sell 148.28 contracts to reduce duration, buy 211.83 contracts to increase bond exposure) I got the same answer = buy 64 bond contracts. So by not rounding until the end, it doesn’t matter which way around you do it you will still come up with the correct answer. Try it for the equity part and you will also come up with buy 464 contracts
 
I suppose the only reason this is even a question I would pose is the fact that it appears as a short-answer Q in the AM portion. If it were a PM question, it wouldn’t make a difference how one ended up with a correct answer. What’s at stake is the partial points a person may or may not receive doing the question one way or the other.
I would like to believe that if we can discover another route to the answer, an exam grader would be able to follow the same logic and award points along the way.
I’ll probly just try to follow the sequence of events the same way it’s presented in the question next time and move on with my life haha.
 
Any order you do this in is perfectly valid.
The equation sets give the exact same result if you do not round in between, by definition if A = 464 and B = 464 then A = B.
Think back to basic math, the order in which you do multiplications doesn’t really matter, and that’s all you are doing here, changing that order.
 
Do we need to break it into 2 steps? You can get the answer by adjusting beta/duration and setting the notional as the difference between target and current notionals in one formula.
 
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