2012 CFAI AM Q 8A rounding error (dollar duration/beta) (S2000Magician)

I use S2000Magician’s excellent “dollar beta” and "dollar duration method for adjusting beta and duration (see here:


Anyway, in the 2012 AM exam, this would have given an answer inconsistent with CFAI’s answer, as they do the two step method (adjusting the value of the portfolio, then the beta of the portfolio), round each, and then add. Whereas S2000Magician’s method (more correctly) rounds at the end. In this example, you get an answer different by 1 contract.

Do I need to worry about this? You can even see in the guideline answer that CFAI have kind of screwed up because they’re acknowledging that you have to add together the amount of contracts you have to buy for each step, and if you use their unrounded numbers, you get the same answer that I got. It’s just if you round and then add, you get 1 contract fewer.

So, thoughts?

I verified with CFA Institute that if you do as I suggested you will get full marks.

As you mention, their (prematurely rounded) answer is incorrect. And they acknowledge that.

2011 actual paper question 7 part c

the beginning values are 25 for bonds and 10 for equities so a total of 35

ending values are 27.5 and 8 total of 35.5. both in foreing currency terms

so the domestic return on asset is 35.5-35/35=1.43 percent

since we are short in futures we have a gain of .8-.87/.87=8.05 cent

so the total gain should b 1.0143*1.0805=9.59cent

can some one can please illustrate to come up with the profit of 400,000 i personally cant figure it out

much appreciated if someone can help??

Thank you very much.

Love your website.

Can we see that as a general statement? In the answer keys to past exams they always round very early and mostly to one decimal point (if at all). Is there any topic where it might be a problem to round only at the end and leave percentages with 2 decimals? Of course, contracts need to be rounded at the end, cannot buy fractions. But things like required returns, allocations or payments?

so long as you are in the ballpark - they should give you the marks.

I would however suggest against rounding too early. I always kept a 4 decimal point precision on my calculator.

@ Salmanshah - This should help


S2000 - would the formula still work if we assume that a cash position has a 0.25 duration? or does it only hold if we assume a 0 duration?

Works for all durations and betas as long as you correctly specify the dollar duration and dollar beta of the target, the current portfolio, and the forward contract.

So if the cash position has a 0.25 duration, we must take that into account in whichever part of the formula (portfolio, target, or forward) the cash position is relevant for.

The formula of S2000 does not work if you sell bonds and buy equities and the duration of cash is different from zero. I wrote with S2000…

Thank you!

But still: in all other cases the formula should work and you safe a lot of time using it!

i got 64 and 463. is that full marks?

I have a question related to this question. Why we need to adjust the beta of the portfolio. Should we use the notional principal of the original portfolio or including the synthetic one too ?