Rounding Rules in Retail Foreign Exchange Interfaces: Evidence from CNY and HKD Quotes
This paper analyzes retail foreign exchange interfaces at mainland Chinese banks and Hong Kong institutions to demonstrate how cent-level rounding rules, such as half-up rounding, create measurable cumulative arithmetic discrepancies between aggregated and individual transaction costs.
Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
When you exchange money at a bank, whether you are buying Japanese yen with Chinese yuan or selling US dollars for Hong Kong dollars, the computer does a simple multiplication: it takes the amount of foreign currency you want and multiplies it by the current price. Often, the result of that math is not a whole number of cents. It might be a fraction, like 7.164 or 8.049. Because money in these systems is usually counted in whole cents, the computer must decide how to handle that tiny leftover fraction. It has to round the number up or down to the nearest cent. This decision, which seems trivial for a single transaction, becomes important if you make many small trades. If a bank rounds down every time you buy a small amount, you might pay slightly less than the exact mathematical cost for each one, but if you were to buy that same total amount in one big lump sum, the rounding might happen differently, changing the final price you see. This is the quiet arithmetic of retail banking, where the rules for handling fractions determine the exact cost displayed to a customer before they click a button.
A researcher named Ruirui Deng investigated exactly how two major banks in mainland China and a mobile banking app in Hong Kong handle these fractions. The study focused on the public calculators that customers use to check prices before making a trade. By entering specific amounts of foreign currency into the Industrial and Commercial Bank of China's online tool, the researcher tested how the system rounded the results. The tests showed that the calculator follows a standard rule known as "rounding half up." This means that if the fraction is exactly halfway between two cents, or if it is slightly more than halfway, the system rounds up to the next cent. If it is slightly less than halfway, it rounds down. The researcher confirmed this by entering numbers that produced results just below and just above the halfway point. For instance, when calculating the cost of a specific amount of Indonesian rupiah, the exact math resulted in a value just under the halfway mark, and the calculator correctly displayed the lower cent value. When the input was adjusted slightly to push the result just over the halfway mark, the calculator displayed the higher cent value.
The study also looked at how this rounding behaves across different currencies, such as the Japanese yen, the Korean won, and the Indonesian rupiah. Even though these currencies have very different values relative to the Chinese yuan, the bank's calculator applied the same rounding logic to all of them. The researcher found that for certain amounts, the difference between the exact mathematical cost and the displayed cost could be as high as nearly half a cent. While this difference is tiny for a single transaction, the study simulated what would happen if a customer made the same small purchase one thousand times. In one specific test involving the Japanese yen, buying 189 yen at a time resulted in a displayed cost of 8.04 yuan. If a customer repeated this small purchase one thousand times, the total displayed cost would be 8,040 yuan. However, if the customer bought all 189,000 yen in a single transaction at the same rate, the calculator showed a cost of 8,044.22 yuan. The difference of 4.22 yuan arose entirely because the bank rounded the cost down for each of the one thousand small orders, whereas the single large order was rounded only once at the end. This demonstrates that the way a bank displays a price can change the total cost depending on whether the customer breaks the trade into many small pieces or does it all at once.
The researcher also examined the mobile banking app of HSBC in Hong Kong, which displays exchange rates for US dollars to Hong Kong dollars. The app showed rates with four decimal places, but this level of precision was not enough to reveal exactly how the app rounded the final cent. Because the displayed rate might hide a few more digits that the computer uses internally, the researcher could not determine with certainty whether the app rounded up, down, or used a different method. In one instance, the app showed a result that did not match the math based on the visible numbers, suggesting that the internal calculation might be using a rate that is slightly different from what is shown on the screen. This highlighted a key limitation: when a bank shows a rate with limited precision, it is difficult for a customer to know exactly how the final price will be calculated.
The findings confirm that the two mainland bank calculators use a consistent, predictable method for rounding, which is a standard practice in banking systems. The study does not claim that this rounding creates a massive financial risk or that banks are losing money; rather, it shows that the arithmetic rules are real and measurable. The difference of a few yuan in a simulated scenario is small, but it illustrates a clear mechanism: the location where the rounding happens matters. If a bank rounds the price for every small order separately, the total cost can differ from rounding the total amount once. This is an example of an operational control, a rule built into the system to handle fractions. The research provides a way for anyone to check these rules by testing specific numbers and watching how the displayed price changes. It shows that while the numbers on the screen are usually very close to the true mathematical value, the tiny fractions that are cut off can add up in specific ways, and understanding those rules helps explain exactly what a customer is being charged.
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