Assuming a 1 US$ investment per trading signal and excluding the reinvestment of speculative profits, our profitability calculations take three components into consideration: the absolute return, the interest rate differential and transaction costs. 1) The absolute return is calculated as the cumulative sum of single returns, pi, where single returns are measured as the log-ratio of the exchange rate between opening, st0, and closing, st1, a foreign currency position27:
pi=ln(st1/ st0)
Since the trading models are active for different time spans, the absolute returns are made comparable by calculating an annualised rate of return:
where a year is taken to comprise 262 business days and Di denotes the cumulative duration of all open positions in days; 2) The net interest rate effect accounts for the fact that a dollar Long position earns dollar interest, pays DM interest in the case of USDDEM, and pays Yen interest in the case of USDJPY.
The net interest effect of opening in a dollar Long position in USDDEM consists of the interest rate differential (r usd-r dem). The net interest effect of a Short position is given by -(r usd-r dem). Following Schulmeister (1986), the overall interest effect Ii of holding currency positions in USDDEM can be approximated as28:
Using 3 month Eurocurrency market rates, the interest differential for USDDEM averaged 1.93 % over the out-of sample period and 5.01% for USDJPY, thus resulting in a discount to the total annual rate of return for trading models with more Short than Long positions and in a premium in the opposite case. 3)
The level of the transaction costs is estimated in line with other studies as the percentage bid-ask spread of interbank quotes. The interbank quotation of bid and ask rates for USDDEM and USDJPY shows a usual spread of 3 base points (BP), i.e. 1.5560-1.5563 DM or 104.30 to 104.33 YEN per US$. Given an exchange rate of 1.50 DM and 100 Yen per 1 US$, estimated transaction costs per round trip, and thus per trading signal, are 0.02% for USDDEM and 0.03% of USDJPY29.
The level of transaction costs assumed here are slightly lower than the figures used by Sweeny (1986), Schulmeister (1987) and Menkhoff (1995), reflecting the declining spread in foreign exchange markets. However, they are still higher than figures quoted by bankers who told us in interviews that transactions costs average around 100 DM per spot transaction and around 200 DM per forward transaction for USDDEM as well as USDJPY30,31.
27 We follow the traditional practice in the field and measure returns in log-forms.
28 The overall interest effect of holding currency positions in USDJPY is likewise calculated as
29 According to Demsetz (1968) the bid-ask spread corresponds to the costs of two transactions. Since the trading strategies investigated here involve switching from Short to Long position or vice versa, i.e. a neutral positions are excluded. Each trading signal involves the closing of the starting position and the opening of the opposite at the same point in time. Thus each trading signal requires tow transactions.
30 Assuming transaction costs of 100 DM, selling or buying of 5 bn US $ thus amounts to 0.0014% , i.e. not even 1 BP. This might explain the custom of foreign exchange dealers to quote sometimes a zero spread to good customers. Since the level of transaction costs can be crucial for the profitability of a trading model, the returns of the different trading models are calculated inclusive and exclusive of transaction costs.
31 Thiessen (1995) reports similar figures. According to Thiessen, the transaction costs lie between 80-120 DM per transaction, if a broker is involved, additionally 20DM per 1bn US$ have to be paid.
Prof. Ronald MacDonald, Prof. Norbert Fiess
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