I just got a question and I’ve been stumped on it for awhile.
This question relates to currency differentials and calculation of the profit and loss on a futures hedging situation.
Step 1: Let’s say we have 100,000 Australian Dollars (AUD).
Step 2: Let’s say we convert this 100K AUD into US Dollars (USD)
Step 3: Let’s say the following are the exchange rate inputs that we see today and “expect” in future:
Current & future AUD/USD rates:
AUD/USD Spot rate today: 0.9100 … AUD/USD Spot rate in 1 year = 0.9400
USD/AUD Spot rate inverse: 1/0.91 = 1.09890 … USD/AUD Spot rate inverse in 1 year: 1.06383
Step 4:
(i) Profit/Loss from AUD/USD difference 1 year from today = 0.9400 - 0.9100 = 0.003000
(ii) Profit/Loss from USD/AUD difference 1 year from today = 1.06383 - 1.09890 = -0.03507
Now, going back to Step 1 if we convert 100K AUD today we get:
100,000 x 0.91 = 91,000 USD
Let’s say we leave that 91,000 USD as it is for 1 year.
At 1 year’s time, we convert it back to Australian dollars at the spot rate that exists at THAT TIME i.e USD/AUD = 1.06383:
91,000 USD x 1.06383 = 96,808.53 AUD
Obviously with the strengthening in the AUD and the fact that we have kept our money parked in USD for one year, we have seen a bit of a loss.
My question is, why is the -0.0319147 from our most recent calculation (iii) different to the exchange rate differentials we got from the above prior calculations of (i) and (ii)??
Shouldn’t they be the same?? We did not do anything to the US Dollar amount of 91,000 USD once we converted it, we just left it there.
If anyone can help with this it would be great.
If there is a reference to a text book I can find great.
I think it has something to do with the base currency in which we calculate the profits/losses which determines the difference.
There is an arithmetic error in Step 4: 0.9400 - 0.9100 = [B]0.0300[/B] (not 0.003000, as you stated).
You asked why your calculations in (i) and (ii) do not match your calculation in (iii). There is a logical error in your question.
In (iii) you are calculating [B]a percentage loss[/B]. In (i) and (ii) you are calculating [B]the difference between two exchange rates[/B].
Maybe looking at it this way will help.
In your hypothetical transaction, you spent 100,000 AUD to purchase 91,000 USD.
At that point you owned 91,000 USD, each U.S. dollar having a value of 1.098901 AUD. Total value 100,000 AUD.
After 1 year, you owned 91,000 USD, each U.S. dollar having a value of 1.0638297 AUD. Total value 96,808.50 AUD.
Over the course of 1 year, you took a loss of -0.0350713 AUD on each of the 91,000 USD that you owned.
Your percentage loss was -0.0350713 / 1.098901 = [B]-0.0319148[/B] = -3.19148% loss — which is the loss you calculated in (iii).
Edit: The calculation originally appearing here contained a conceptual error, and has been removed.
See post #6, on this thread, for the corrected calculation.
If one were to hedge this 100K AUD position, while the portfolio is in USD, would we need to take into account the conversion back to AUD to take into account the full dollar value of the hedge??
What I mean is shown below, I have left out cost of carry and basis risk for simplicity:
Because the money of the entire portfolio is in USD, and we are using the USD in the portfolio to hedge (i.e. buy a 100K Australian dollar futures contract with the UD dollars in the current portfolio) we are only getting $3000 from the hedge in USD. Only when we take into consideration the conversion back into AUD do we fully hedge out the position.
Another thing I’d like to ask is about the mechanics of the futures hedge. If we have USD, and we are shorting one 100,000 AUD futures contract … are we actually selling 100K Australian dollars?? Or is it just a derivative contract, and we just participate in the profit/loss of the contract and if so … I presume that the profit/loss is considered in USD not Australian dollars as aforementioned above???
The scenario you have outlined is getting pretty far away from the spot forex domain of this website and this forum,
in two important ways:
[B]1. Babypips deals with margined transactions in the spot forex market.[/B] These transactions behave, in effect, like very short-term (2-day) futures contracts; but, they are not “futures contracts” as traded on a regulated futures exchange. In the scenario you have described, you have (hypothetically) made a cash purchase of U.S. dollars, paid for with Aussie dollars. And this cash transaction has converted your brokerage account from one denominated in Aussie dollars to one denominated in U.S. dollars. This sort of transaction can be accomplished through any forex broker; but, this is not a spot forex transaction, as defined here.
[B]2. Exchange-traded currency futures and currency options are outside the scope of this website. [/B] The spot forex market is an off-exchange market, consisting of retail brokers and institutional brokers (most of whom are market-makers), and their liquidity providers (banks in the worldwide interbank network).
I will try to tackle your questions. But, please understand that you are venturing rather far afield of what we normally do here.
As I understand your scenario, it goes like this:
[ul]
[li]You start with an account denominated in Aussie dollars. Your starting balance is 100,000 AUD.
[/li]
[li]Then, you convert the entire account balance to U.S. dollars, not as a margined forex transaction, but as a direct currency conversion. The AUD/USD exchange rate at the time of this conversion is 0.9100. After the conversion of your entire account to U.S. dollars, your account balance is 91,000 USD.
[/li]
[li]Next, you use your U.S-dollar-denominated account to enter into a currency futures contract, going LONG the Aussie dollar, in order to hedge your “short” Aussie dollar cash position. It is your intention to put on a “perfect” hedge, such that gains in your LONG futures position will exactly offset losses in your short cash position.
[/li]
[li]Finally, over the course of 1 year, the AUD/USD exchange rate changes from 0.9100 to 0.9400.
[/li][/ul]
You have asked whether going LONG 1 contract of the Aussie dollar (100,000 AUD) will provide the perfect hedge you desire.
And you have asked about the nature of a futures contract.
I hope I have correctly understood your scenario, and your questions. Here are the short answers to your questions:
[B]
(1) [/B] A 100,000 LONG position in the futures market will perfectly hedge your “short” cash position, ASSUMING (1) you ignore commissions on your futures contract, and (2) the notional value of your distant futures contract (one year, or more, out) moves pip-for-pip with changes in the spot price of the AUD/USD.
[B]
(2)[/B] Regarding the mechanics of a futures contract, by taking a LONG position in the AUD/USD, say 13 months out, you are agreeing to take delivery of 100,000 AUD 13 months from now, and to pay for them in USD. If you liquidate your futures position prior to its expiration (13 months from now), the contract will be settled in cash — in this case, in USD — based on the change in the notional value of the contract. That is, if the exchange rate changed by 0.0300 (from 0.9100 to 0.9400) during the time that your futures contract was open, then the notional value of your futures contract will have changed by 3,000 USD.
[B]Here is a step-by-step accounting of your scenario:[/B]
[li][B]After account conversion from AUD to USD[/B]
[/li]AUD/USD = 0.9100
cash account = 91,000 USD (equivalent to 100,000 AUD)
[li][B] At the time the futures contract is opened [/B]
[/li]AUD/USD = 0.9100
cash account = 91,000 USD (equivalent to 100,000 AUD)
futures contract (100,000 AUD @ 91 cents U.S.): P/L = zero USD (no gain or loss)
