The Cross-Market Premium

The cross-market premium is defined as the percentage difference between the dollar price of the stock in the domestic market and the price of the corresponding depositary receipt (DR). Depositary receipts (also known as American Depositary Receipts or ADRs) are shares of non-U.S. corporations traded in the U.S. (and denominated in dollars), while the underlying shares trade in the domestic market of the issuer. A depositary receipt represents a specific number of underlying shares remaining on deposit in a so-called custodian bank in the issuer’s home market. A new DR can be created by depositing the required number of shares in the custodial account in the market. The dividends and other payments will be converted by this bank into U.S. dollars and provided to the holders in the U.S. The process can simply be reversed by canceling or redeeming the DR. In this way, an underlying stock can easily be transformed into a DR and vice versa.

The cross-market premium (or discount) thus reflects the deviation between the home market price of the stock and its price in New York. It can be computed by converting the local currency price of the underlying stock in dollar prices, multiplying this by the number of underlying shares one DR represents, and then dividing their value by the DR price. Or, π_t = S_trP_t^und - P_t^dr ÷ P_t^dr with π_t representing the premium at time t, S_t the spot exchange rate expressed in U.S. dollars per local currency, r the number of underlying stocks per unit of DR, P_t^und the price of the underlying stock in local currency, and P_t^dr the price of the DR in New York in U.S. dollars.

When assets can be transferred freely between the domestic market and the U.S., transaction costs are negligible, and the two markets close at the same time, arbitrage should be instantaneous and costless. If the return of the underlying stock is higher than the return of the DR, investors can make an instant profit by buying the DR, transforming it into the underlying stock and selling this stock. This will drive the price of the underlying stock down and the premium back to zero. The reverse story holds when the return of the DR is higher. In principle, the premium will be equal to zero. If a shock occurs too late during the day to be arbitraged away, closing prices will differ, but this difference will disappear quickly the next trading day.¹⁴

In reality, however, there is no instantaneous and costless arbitrage. If an investor decides to transform underlying stocks into DRs and sell them in the U.S., he has to incur transaction costs. These typically include a broker’s fee and a transaction fee to buy the underlying stock and transform it into the DR, plus a second broker’s fee to sell the DR. Additional transaction costs might be the cost of opening a bank account in the U.S. or a tax that needs to be paid to transfer the funds back to the domestic market. A U.S. investor would face similar transaction costs. Furthermore, since settlement in equity markets typically takes place a number of days after the transaction, there is also a foreign exchange risk unless the stock trade is matched with a forward exchange rate contract. These transaction costs incurred include both fixed as well as variable costs. While the fixed costs can be dwarfed by increasing the transaction size, the existence of variable costs can generate a “no-arbitrage band” within which price deviations are not large enough to induce arbitrage. Higher (variable) transaction costs induce the widening of the no-arbitrage band and, thus, weaker integration.

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