Synthetic Cross Rate and a Mispriced SGD/JPY Quote
A Singapore-based treasurer has USD 50m to convert into SGD and JPY for payments. The interbank market shows USD/SGD 1.3475/1.3480 and USD/JPY 151.20/151.25. A dealer quotes SGD/JPY 112.35/112.45. The treasurer needs to sell SGD 50m against JPY and notices the dealer's quote looks out of line with the two USD legs. The dealer says the quote is firm for SGD 5m only, although it will consider a larger ticket on a best-efforts basis. The treasurer's compliance team requires that any cross-currency execution be done with approved counterparties and that all legs be booked simultaneously. Settlement is T+2, and the JPY leg will settle in Tokyo while the SGD leg settles in Singapore. The treasurer wants to know whether there is an arbitrage, how much it is worth, and what could go wrong.
1. Calculate the synthetic SGD/JPY bid and ask and identify the arbitrage.
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SGD/JPY = (USD/JPY) ÷ (USD/SGD). The synthetic bid is the rate at which the market buys SGD and sells JPY: bid USD/JPY ÷ ask USD/SGD = 151.20 ÷ 1.3480 = 112.166. The synthetic ask is the rate at which the market sells SGD and buys JPY: ask USD/JPY ÷ bid USD/SGD = 151.25 ÷ 1.3475 = 112.245. The fair cross is therefore 112.17/112.25.
The dealer quotes 112.35/112.45, which is above the synthetic ask. Arbitrage: buy SGD synthetically at 112.245 (sell JPY for USD at 151.25 and sell USD for SGD at 1.3475) and sell SGD to the dealer at the dealer's bid of 112.35, locking in 0.105 JPY per SGD. The direction is 'buy synthetic, sell dealer.' A common error is to compare the dealer's ask with the synthetic ask, which would miss the trade; the correct comparison is dealer bid versus synthetic ask.
2. Calculate the gross profit on SGD 50m and explain why the profit may not be achievable. List the execution and settlement risks.
Read the worked answer
Gross profit on SGD 50m = 50,000,000 × (112.35 − 112.245) = 5,250,000 JPY, about USD 34,700 at 151.25. But the dealer's quote is firm for only SGD 5m; on that size the profit is 525,000 JPY, about USD 3,470. For the larger ticket the dealer will widen or decline, and the treasurer must execute three legs (USD/JPY, USD/SGD, SGD/JPY) with possible leg risk: the cross quote may move before the USD legs are filled.
Settlement is T+2 in two centers, so a Tokyo holiday or a Singapore cutoff can create a failed delivery and overdraft. Counterparty credit lines, transaction costs, and the compliance requirement for simultaneous booking further reduce the edge. The apparent arbitrage is compensation for liquidity and execution risk, not a free lunch. The treasurer should also check whether the dealer's quote is indicative or firm and whether the bank has approved the counterparty for the full notional.