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Historical Rate Roll Calculator
What is an HRR ?HRRs (Historic Rate Rolls) or HREs (Historical Rate Extensions) are the same thing. If a corporate has a forward contract where the rate on the deal is not at the current market and wants to extend that deal the normal procedure is to use an FX swap where the near leg uses the current spot rate and the far leg rate is calculated by adding or subtracting the 'market' forward points from the spot rate.
ExampleABC Exports Ltd has a forward contract with a bank maturing at spot [in two days], where they sell (pay) USD 1,000,000 and buy (rec) AUD 1,428,571.43, at a rate of 0.7000. The contract was initiated two years ago and the rate has moved substantially against them. Unfortunately they don't have the USD yet because their US customer has not paid on time and they think they will get the money in two months. Let's assume:
AUD/USD Spot today is: 0.6000
2 month forward pts are: -0.0010
2 month market forward: 0.5990
2 month AUD Interest Rate: 6.60%
2 month USD Interest Rate: 5.50%
2 months from spot = 60 Days
A normal swap would look like this. ABC Exports Ltd would enter a new contract as follows:
a) In 2 days Buy (rec) USD 1,000,000 and Sell (pay) AUD 1,666,666.67 at a rate of 0.6000 and,
b) In 2 months Sell USD 1,000,000 and Buy AUD 1,669,449.08 at a rate of .5990 (0.6000-0.0010).- In 2 days ABC Exports Ltd has no net USD payment or receipt as the new swap cancels the existing swap neatly.
- There is a difference in the AUD amounts in 2 days so ABC Exports pays a net amount of AUD 238,095.24 to the bank.
- The new contract is for ABC Exports Ltd to Sell USD 1,000,000 and Buy AUD 1,669,449.08 in 2 months at a rate of 0.5990.
However when a corporate wants to do an HRR they want the first leg of the swap to be the same as the rate on the maturing deal, in this case .7000. The major attraction of this is that at spot there will be no cash flows, ie the corporate does not have to pay the AUD 238,095.24 payable on the normal swap (which really represents the loss on the original contract as the market moved against ABC Exports Ltd), the loss is rolled into a new contract rather than being paid out.
The rate applicable to the far leg needs to be calculated as the market points of -.0010 are not relevant to a start rate of 0.7000 because of proportionality. Also we need to take into account that ABC Exports are effectively borrowing the loss from the bank for two months, and thus the bank needs to factor in an interest charge.
The CalculationStep 1 - Calculate the profit or loss on the existing dealThe loss on the deal is equal to the difference between the existing rate and the spot rate. In this case the USD amount is being held constant at USD 1,000,000. At the historical rate that amount of USD equals AUD 1428571.43 (1,000,000 / 0.7000). At the spot rate it equals 1,666,666.67. Therefore the loss is AUD 238,095.24.Step 2 - Calculate the interest benefit/cost on the above amountIn this case ABC Exports is retaining AUD 238,095.24 that would otherwise be paid to the bank. The bank will treat this as a loan and charge interest. Let assume the bank chooses to use the market AUD interest rate for 2 months of 6.60% (although its fair if the bank charges ABC Exports Ltd an increased rate due to credit risk just like an ordinary loan). So AUD 238,095.24 * 6.60 / 100 * 60 / 365 = AUD 2,583.17 (and its a cost to the client).Step 3 - Calculate the real value of the forward pointsEven though we have previously stated the forward points as 'points' we can calculate their real value. Based on a spot rate of 0.6000 USD 1 mio = AUD 1,666,666.67 and based on a forward rate of 0.5990 USD 1 mio = AUD 1,669,449.08, the difference is AUD 2,782.41 (and
its a benefit to the client). Step 4 - Putting it all togetherThe existing deal is to sell USD 1 mio and buy AUD 1,428,571.43 at 0.7000. Since we are holding the USD constant we need to adjust the AUD amount by the calculations above. So AUD 1,428,571.43 less interest cost AUD 2,583.17 plus the forward points benefit AUD 2,782.41 equals a new principal of AUD 1,428,770.67.
To calculate the new forward rate is easy, the USD principal / the new AUD principal (1,000,000 / 1,428,770.67) = 0.6999. So the HRR forward points are actually -0.0001.
Other Tips- Steps (2) and (3) above can be confusing, its worth establishing with each number whether it is a benefit or cost to the client, and adding and subtracting accordingly in Step (4).
- In the above example we have just used mid rates for everything. In reality clients will deal on a number of spreads. For example the bank in above case would calculate the AUD interest costs based on the interest rate that they lend at, and would probably add some credit risk margin.
- However if a client is doing an HRR on a deal that is in profit the client is effectively lending the money to the bank therefore there is no credit risk that the bank should charge or price into the calculation.
- HRRs are not favoured by regulators in Australia and many other counties. Banks will often require special approval if a client wants to transact them and may require that the client send the bank a letter signed by the clients senior management that HRRs can be transacted.
- Clients can hold either currency constant but the calculation logic is the same.
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