FX Forward Trader please? Contradicting forward point equations question
Hello Monkeys,
I have one questions related to calculating the forward.
My knowledge:
Let us assumer CCY1/CCY2 is 1. If CCY 1 is 5% in interest rate while CCY2 is flat. The 1y forward should be 1*(1+0.05)/(1+0.0) = 1.05 and the swap point should be +5
interest rate parity:
Forward = Spot(now)*e^(rcc2*t-rccy1*t)
Under this equation, the forward will be lower than 1 and the forward is negative.
I totally understand the logic behind IRP for the no arbitrage calculation. However, wouldnt the first calcualtion make more sense?
Ah, the classic conundrum of FX forward pricing! Let's swing through the trees of finance and break this down, shall we? Based on the most helpful WSO content, it's clear that understanding the nuances of FX forwards is crucial for any trader or enthusiast in the field.
First off, your initial calculation uses a simple interest rate differential method to determine the forward rate. This method is straightforward and intuitive, especially for those just starting to explore the jungle of FX trading. You've correctly calculated that if CCY1 has an interest rate of 5% and CCY2 is at 0%, the 1-year forward rate, assuming a spot rate of 1, would indeed be 1.05. This calculation is based on the principle that money should have the same value regardless of the currency it's in, assuming no arbitrage opportunities.
However, when we swing over to the interest rate parity (IRP) formula, things get a bit more complex. The IRP formula you've mentioned uses continuous compounding (indicated by the exponential function) rather than simple compounding. The formula is:
[ \text{Forward} = \text{Spot} \times e^{(r_{\text{CCY2}} - r_{\text{CCY1}}) \times t} ]
Where: - (e) is the base of the natural logarithm, - (r_{\text{CCY1}}) and (r_{\text{CCY2}}) are the interest rates for currency 1 and currency 2, respectively, - (t) is the time in years.
Using your example, where (r_{\text{CCY1}} = 5\%) or 0.05, (r_{\text{CCY2}} = 0\%), and (t = 1), the formula would give us:
[ \text{Forward} = 1 \times e^{(0 - 0.05) \times 1} = 1 \times e^{-0.05} \approx 0.9512 ]
This result seems counterintuitive at first because it suggests the forward rate is less than the spot rate, even though CCY1 has a higher interest rate. The key here is understanding the effect of continuous compounding, which is a more accurate representation of how interest accrues over time, especially in markets that operate 24/7 like FX.
So, why the difference? The simple interest calculation assumes a one-time compounding at the end of the period, while the IRP formula with continuous compounding reflects a more realistic scenario where interest accrues continuously. Both calculations are valid, but the IRP formula is generally considered more precise in financial markets.
In essence, the first calculation is more straightforward and easier to grasp, but the IRP formula provides a more accurate picture by accounting for the continuous nature of interest accrual in the real world. As you swing through your FX trading journey, it's crucial to understand both methods and know when each is appropriate to use.
Sources: Interest rate curves for dummies, WSO Exclusive: Legerdemath - Anatomy of a Banking Trick, Q&A: First year macro hedge fund analyst, Q&A: Rates & Macro Research/Strategy - Career Path, Technical Topics, Education, etc., Math behind pricing a CMBS loan
I think 1y forward should be -(1-1/1.05)%, which is around -4.76%. You can think of it this way: if I have 100 ccy2 now, ccy1/ccy2 spot is 1 so if I change into 100 ccy1 now to enjoy 5% annual interest rate (while ccy2 has 0% interest rate), when I change from 105 ccy1 into ccy2 in 1y the FX rate should be such that I get the same amount of ccy2 if I were to hold onto my 100ccy2 at the beginning, i.e 100.
We usually say pips so -4.76% will be -476 pips.
I would like to follow up please, so under this case as the forward point is negative, the forward trader should short CCY1/CCY2 in the forward desk?
As far as I know, the forward desk is structured as dealing fx swaps, so they mainly face interest rate risk instead of spot fx risk. If you check the BIS fx turnover survey, fx swap is 50% of the total fx turnover, accounting for a much larger portion of the market than plain forwards. If the client asks for a plain forward, the forward desk will just do a corresponding spot transaction with the spot desk to make sure they still get a fx swap.
You got numerator and denominator flipped in the first scenario
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