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Dear John,
The lock-in rate is assumed to be the sum of transaction at spot rate +- gain/loss on futures deal.
Is there somewhere mathemetical proof of this statment? Or what is the logic behind it, if it is not precise, but just approximation? It does not seem intuitively easy to grasp. I tried very simple cases and never got the same result with ‘traditional’ and ‘lock-in rate’ way.Thank you!
It does not require a mathematical proof.
If you ignore the fact that we cannot usually hedge the exact amount using futures because of the contract size, then you will see from my lectures that were it not for the basis risk then the futures price would change by exactly the same amount as the spot rate. Therefore, if there were no basis risk, the gain or loss on the transaction would be exactly covered by the gain or loss on the futures – the net result would be fixed.
However in practice the futures price will not move by exactly the same amount as the spot rate – the difference is the basis risk. We assume that the basis falls linearly to zero over the life of the future (which may not be the case in practice, but is an assumption that we always make) and therefore we can predict exactly what the difference will be.
This is what the lock-in rate is doing – predicting exactly what the net effect will be.
Do watch my free lectures on this 🙂
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