FX Forward Contract - Marking to Market/Closing Out

[VaR_99]

Can someone take a peek at at volume 1, p.499, question 5 in the CFAI texts and explain to me how to get the correct answer using the formula for marking to market a forward:
(FP -FPt)(contract size)/(1 + (rate*(days/360))
I have figured it out using the ‘longer way’ of simply calculating the individual cash flows, but not using the formula since the question is buying the price currency, not the base currency. I can’t quite figure out how to adjust the formula in this case. I’ve take the inverse of price quotes, etc, but can’t get the answer.
Thanks for the help.

 

[Aether]

I ended up spending quite a bit of time trying to figure this out when I was on V1. This stuff is evil .
The key is to properly account for the conversion of the three-month forward points when you go to the indirect quote (i.e. from USD/NZD to NZD/USD).
1) The initial all-in forward rate is 0.7900. This converts to 1/0.7900 = 1.2658.
2) Your indirect quote of 0.7825/0.7830 becomes {1/0.7825}/{1/0.7830} = 1.2771/1.2780.
3) This was the most time-consuimg piece for me: obtaining the indirect quote of the three-month forward points. The USD/NZD quote is -12.1/-10.0. I was confused because I was trying to find the reciprocal of the three-month forward points. Which is arcane! Instead of thinking in terms of reciprocals, the easiest way to convert this quote is to start from the original USD/NZD quote. So we have, {0.7825 - 12.1/10000}/{0.7830 -10.0/10000} = 0.7813/0.7820. Now take the inverse of this to directly get to the ending quote. That is, when you reciprocate these numbers, you will end up the NZD/USD inclusive of the three-month forward points.
So we have {1/0.7813}/(1/0.7820} = 1.2788/1.2799.
4) Since we’re buying back USD, we use the 1.2799 ask price. Now we have 1.2799 - 1.2658 = 0.0141.
5) Multiplying the above result by 10M, should give you 141180. The present value of this at 3.31% using the 90/360 discount window is 141180/1.0083 = 140022.
There is a difference of around $60 due to rounding, I think. Note that once you understand the above process, step 2 is not required. I covered it here because I think that’s how most of us are going to begin thinking about solving such problems.
Hope this helps. And I really hope we don’t see this kind of stuff on the exam!

 

[VaR_99]

Man, thanks for working this out…I was close to what you had! I noticed a couple of things in your above calculations after I went through and tried your method:
1. The result should be negative, since were originally short USD, and USD subsequently appreciated (implied by the orignal contract rate of 0.79 vs. the forward rates of 0.78129/0.7820, in USD terms). This would require switching (FP - FPt) to (FPt - FP) in the equation.
2. Since the result we want is in NZD, we would want to discount at the NZD risk-free rate of (1 + (0.0031*(90/360)) = 1.00078. It is confusing since they quote the risk-free rates so similarly at 3.31% and 0.31%
So then I get:
((1.26582-1.27993)(10,000,000))/(1 + (0.0031*(90/360)) = -140,990, which is about 130 NZD off from the book answer.
I could still be off someplace, but man, you are right. I hope they don’t unleash this shit on the exam….WAY too time consuming.
Thanks agian, I appreciate the assist!

 

[Aether]

As far as the sign goes, I believe you don’t need to “rework” the numbers. Basically, since you’re reciprocating everything else, the final answer’s sign would also “flip.” I didn’t mention in my original post since I thought it was so obvious after all that work (sarcasm!). Hah.