Derivatives still winds me up

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pissed-level3

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Could someone please explain the solution for the problem below. in simple baby language the solution…..I someknow the fomular but cant intutivelly make sense of it.
You are told that John enters into a six-month forward contract to deliver CAD 1,000,000 for dollars with counterparty. The current 6-month forward rate is $1.1050/CAD. Three months into the contract, the spot rate is $1.018/CAD, the U.S. interest rate is 3.5%, and the foreign interest rate is 3.2%.
Calculate the amount at risk from a credit loss on the contract. Determine which party bears the credit risk.
 
Value the contract first, remember that you are short the contract, so you would want the current present value to be more than the value of the spot rate today.
If the value of the contract is negative, then you are profiting, and you bear the credit risk, and the opposite is true.
 
Is the answer $85,520, credit risk to John?
I’m not great with these either but if I’m right, here’s how I understand it:
Credit Risk is borne by the party who has positive value on the contract. This is because the party who has positive value (or is owed) is at risk of the counterparty not paying. In this case, John is delivering CAD, which is also the same thing as buying USD. Therefore, he is long USD. He enters into a forward contract to buy USD at $1.1050/CAD. Three months later the spot rate is $1.018/CAD. The CAD has depreciated because 1 CAD buys less USD now. Because the CAD has depreciated, the USD has appreciated. John is long the USD and so has a gain on his forward contract. Therefore, he bears credit risk. Now you have to figure out how much credit risk that is. To do that, you set up the Value to long formula that was in Level 2:
Value to Long =
For the denomiator, the way I understand it is base currency (CAD) is before the price currency (USD) in the value to the long formula.
What comes out of this formula is a negative number, but you know John was long USD and it appreciated, so he has a gain. You could think of it like Mr. Smart has framed it too: he is short CAD so the negative value is a gain.
Hope I am right and that makes sense.
 
Thanks Smart
But my main problem is with the formula.
Price of the forward discounted at 3 months = 1,000,000 x 1.050 x (1+0.035)^0.25)/(1+0.032)^0.25
Spot = 1,000,000 x 1.018
Net = $87,802
I know the answer above is wrong but i cant figure out why my reasoning is wrong.
 
Yes. correct the answer is $85,522 but i dont understand why my intuitive reasoning/ formuls above is wrong.
 
are you sure you’re discounting the 6mo fwd back to calculate PV at 3 months time?
 
yea –first part of my solution - Price of the forward discounted at 3 months = 1,000,000 x 1.050 x (1+0.035)^0.25)/(1+0.032)^0.25
 
nope. you should divide to discount the fwd back.
so using the handy formula: it should be 1.105 / (1+0.035) ^0.25 <— this is discounting the fwd back to time t
1.018 / (1+0.032)^0.25 - (above)
will get you value to long which is - 0.08552
and then multiply by notional principle. which is 1 million
 
I get the handy formula -its just that it doesnt make sense to me:
Value of contract = current price of the asset less the present value of the forward price (at expiration).
Current price = 1.018
present value of the forward price = 1.050 x (1+0.035)^0.25)/(1+0.032)^0.25
Surely the price of the contract after 3 months (now) is 1.050 x (1+0.035)^0.25)/(1+0.032)^0.25 and the spot rate is 1.018 (now); why should i further discount the spot rate since i am valueing the contract NOW (spot time) ???
 
its a forward rate not a spot rate. and its 1.105? I hope a typo isnt messing up your calculation?
 
I understand what he is trying to say. Hopefully this helps, read carefully:
The [forward]price, which is actually an exchange rate, of a forward contract on a currency is the spot rate discounted at the foreign interest rate over the life of the contract and then compounded at the domestic interest rate to the expiration date of the contract.
https://takloo.wordpress.com/2011/04/12/cfa-reading-on-derivatives-forwa...
I think he is trying to compare what the forward rate would be in 3 months (based on the spot now) and the orginal forward contract. But I don’t think that’s how you calcuate the gain or loss on a forward contract. I believe you calculate gain or loss based on the spot rates.
 
pissed-level3 wrote:
I get the handy formula -its just that it doesnt make sense to me:
Value of contract = current price of the asset less the present value of the forward price (at expiration).
Current price = 1.018
present value of the forward price = 1.050 x (1+0.035)^0.25)/(1+0.032)^0.25
Surely the price of the contract after 3 months (now) is 1.050 x (1+0.035)^0.25)/(1+0.032)^0.25 and the spot rate is 1.018 (now); why should i further discount the spot rate since i am valueing the contract NOW (spot time) ???
Click to expand...
MAGICIAN where art thou brother?
 
I believe that the problem is that you’re not discounting the spot rate using the foreign currency risk-free rate.
You reason that the spot price is the contract value (in CAD) times the spot rate (for which I believe you have a typo).
In fact, the spot price is not the contract value (in CAD); it’s the present value of the contract value (in CAD): it’s 1,000,000 / 1.032^0.25.
“Why?” you ask?
Because the CAD1,000,000 isn’t going to be delivered for 3 months, and currencies always grow at their own risk-free rates. Today, that CAD1,000,000 isn’t worth CAD1,000,000; it’s worth PV(CAD1,000,000).
Give that a try.
 
OP - where did you get this question from? Which reading? Risk Management?
 
ltj wrote:
OP - where did you get this question from? Which reading? Risk Management?
Click to expand...
Found the question on http://www.analystninja.com , risk management mocks section. There is a similar question in the EOC of the curriculum. Its also level 2 material but i wanted to get the intuition right.
 
My friend… Read the qn properly: three months into the contact, the spot rate is $1.018/CAD and the rates correspond to that time. You’re valuing the position in the third month. Now you’re valuing a contact whichll terminate in three months (a six month contract where three months have passed). Value the contract as of that date.
The forward rate is fixed at 1.105/CAD.
At the end of six mos: the spot rate will be (1.018*(1.035/1.032)^(3/12)) = 1.0187/CAD
From John’s angle: 1000000*(1.105 - 1.0187)
= $86261 he’ll receive at the end of the contract (6 months from initiation; 3 months from now)
The current value is 86261/(1.035^(3/12)) = $85522.
Thus John gains since he booked the forward to receive more dollars/CAD. He bears the risk that the counterparty will fail.
 
AmruthSundarkumar wrote:My friend… Read the qn properly: three months into the contact, the spot rate is $1.018/CAD and the rates correspond to that time. You’re valuing the position in the third month. Now you’re valuing a contact whichll terminate in three months (a six month contract where three months have passed). Value the contract as of that date. The forward rate is fixed at 1.105/CAD. At the end of six mos: the spot rate will be (1.018*(1.035/1.032)^(3/12)) = 1.0187/CAD From John’s angle: 1000000*(1.105 - 1.0187) = $86261 he’ll receive at the end of the contract (6 months from initiation; 3 months from now) The current value is 86261/(1.035^(3/12)) = $85522. Thus John gains since he booked the forward to receive more dollars/CAD. He bears the risk that the counterparty will fail.
Click to expand...
AmruthSundarkumar where have you been??. Brilliant explanation! You are a star!
 
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