risk-free interest rate. The profit or loss of the trader on the futures position in period t directly added to or subtracted from the margin account is equal to (Pt-Pt-1) Post.

We will also consider transaction costs. Costs are calculated as a fraction c of the price. Some strategies generate trading signals very often, others not. If a strategy does not generate trading signals very often and a position in the market is maintained for a long time, then there are also trading costs due to the limited life span of a futures contract. In particular, we assume that if a certain position in the market is maintained for 20 days after a roll over date, a trade takes place since the position has to be rolled over to the next futures contract and transaction costs must be paid. This approach leads to a fair comparison of the cost structure of strategies that generate many signals with strategies that generate only a few signals.

Finally, the gross return on time t is calculated as

Mt-1=Pt-1 if there is a trade (i.e. Post ≠ Post-1 )
  else Mt-1 remains the same;
Mt=(1+rtf)Mt-1+(Pt-Pt-1) Post;
1+rt= ⎧
⎪
⎪
⎨
⎪
⎪
⎩
Mt
Mt-1
, if there is no trade;
Mt
Mt-1
1-c|Post-1|
1+c|Post|
, if there is a trade.
    (5)
If no position is held in the market, i.e. Post=0, then according to the formula above a risk-free interest rate is earned. Formula (2.5) represents in the best way the daily return generated by a long as well as a short position in a futures contract. The net return with continuous compounding can be computed by taking the natural logarithm of (2.5). The excess return over the risk-free interest rate and after correcting for transaction costs of trading futures contracts we compute as rte=ln(1+rt)-ln(1+rtf). If we take the cumulative excess return, ∑t=1T rte, to the power e, then we get
A=exp (
T
∑
t=1
rte)=
T
∏
t=1
1+rt
1+rtf
.     (6)
Equation (2.6) determines how much better a technical trading strategy performs relatively to a continuous risk free investment. Hence (A-1)*100% determines how much percent the strategy performs better than a risk free investment.

We take as a proxy for the risk-free interest rates the 1-month US and UK certificates of deposits (COD), which we recompute to daily interest rates. Costs of trading c are set equal to 0.1% per trade, which is close to real transaction costs in futures trading.

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