Among the formulas below pick the one which is correct given the currencies A, B, and C. Select one – the most appropriate answer.

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BlackTom AI · Accepted Answer

Question restatement: Among the formulas below pick the one which is correct given the currencies A, B, and C. Select one – the most appropriate answer.

Option 1: (A / B)BID = (A / C)ASK × (C / B)BID.
This is incorrect because it mixes ASK and BID quotes in a way that breaks the standard cross-rate relationship. The left side is a BID rate, and the right side uses (A/C)ASK multiplied by (C/B)BID, which does not maintain a consistent quote convention across the multiplication. In practice, cross-rate derivations should use BID quotes consistently when forming a BID cross, or consistently use ASK if you’re deriving ASKs; mixing them as shown is not valid for a BID cross.

Option 2: (A / B)BID = (C / A)BID × (B / A)BID.
This is incorrect because the factors on the right do not multiply to give a straightforward (A/B)BID cross. (C/A)BID and (B/A)BID correspond to different currency pair directions and, when multiplied, do not yield the correct (A/B)BID due to misalignment of base/quote currencies and the implied reversals. The algebra does not support this decomposition for a clean BID cross.

Option 3: (A / B)BID = (A / C)BID × (C / B)BID.
This is correct. The cross-rate identity (A/B) equals (A/C) × (C/B) holds for BID quotes when you keep the same quote convention on all legs. In other words, the BID quote for A/B is the product of the BID quote for A/C and the BID quote for C/B, since A/B = (A/C) × (C/B) algebraically and BID quotes are multiplicative in the same convention.

Option 4: (A / B)BID = (A / C)BID × (C / B)ASK.
This is incorrect because it mixes BID on the left with an ASK on the right for the second factor. Using (C/B)ASK would not preserve the BID cross-rate arithmetic and would yield an inconsistent or erroneous cross-rate. Consistency of quote type (BID with BID or ASK with ASK) is essential for valid cross-rate calculations.

Option 5: (A / B)ASK = (A / C)BID × (C / B)ASK.
This is incorrect for two reasons. First, the left-hand side is an ASK quote, while the right-hand side uses a BID quote for (A/C) and an ASK quote for (C/B). Mixing BID and ASK across the terms breaks the internal consistency required for a proper cross-rate derivation. Second, even if you attempted to align types, the standard cross-rate identity in the sense of A/B = (A/C) × (C/B) applies to the same quote type, not a mixture of BID and ASK.

Summary: The only option that maintains consistent quote conventions and correct cross-rate algebra is Option 3, which expresses the cross-rate as (A / B)BID = (A / C)BID × (C / B)BID. The other choices fail due to inconsistent quote types (BID vs ASK) or incorrect multiplicative structure that does not conform to standard cross-rate derivations.

Among the formulas below pick the one which is correct given the currencies A, B, and C. Select one – the most appropriate answer.单项选择题

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