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Can someone help me understand how to derive the implied interest rate or spot rate in BBG FXFA?

I actually get why the Forward rate, F_Ask and F_Bid are derived using the formula in the picture.

The problems are the other formula. I thought by rearranging the terms in the implied forward rate I can get the implied rate for AUD or USD or spot. But it appears the bid/ask need to be twisted as well.

Can someone help me with this? Probably using N_Bid formula as an illustration for its economic meaning.

Thanks in advance.

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The reason for the bid and ask twisting is that you can think of a long AUD forward as three transactions:

Borrow USD Sell USD, buy AUD spot Lend AUD

As a result, there are three sources of bid/offer cost for a forward. In contrast, for an interest rate, it's just one transaction (borrow or lend). This is why they twist those equations. They are trying to isolate the amount of the bid/offer attributable to that one source.

There will may be a gap between the implied interest rates and what you see for interest rate swaps. Reading about coss currency basis swaps may be of interest to you see here for example. I don't currently use a Bloomberg Terminal, but I think the command to see some of the cross currency basis levels is XCCY.

The above info is for educational purposes only, not investment advice.

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  • $\begingroup$ Thanks for the reply. I am still confused with this part - "In contrast, for an interest rate, it's just one transaction (borrow or lend). This is why they twist those equations. They are trying to isolate the amount of the bid/offer attributable to that one source." I think the relationships should always follow as established in F_Bid and F_Ask formula. Otherwise, won't there be arbitrage opportunities? $\endgroup$
    – pqsn
    Sep 19 '18 at 2:56
  • $\begingroup$ No, let's say you could get mid price for any transaction, but you had to pay commissions instead. Also assume the mid price for the forward is priced relative to the other three according to the standard formula. Also assume the commissions for a spot trade are $2, the commissions for a bond in currency A are $1, and the commissions for a forward trade are $4. In this case, you could say the implied commission for bonds in currency B are $1 (4-2-1). If commissions for the currency B bonds are less than $1, it is cheaper to do three trades to create your own synthetic forward. $\endgroup$
    – Charles Fox
    Sep 19 '18 at 3:14
  • $\begingroup$ If commissions for the B bond are greater than $1, it is cheaper to trade the forward. However, for any non-negative commission, there is no arbitrage. $\endgroup$
    – Charles Fox
    Sep 19 '18 at 3:15
  • $\begingroup$ Thanks for the help Charles. I spoke to traders about this and they think (i am not 100% sure if they do know/care how the math is done) that the bid/ask used in the calculation are different from investment and market making perspective. $\endgroup$
    – pqsn
    Oct 3 '18 at 2:28

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