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Profitability of technical stock trading: Has it moved from daily to intraday data, страница 6

The single rates of return can be considered as absolute returns in cents if one assumes that there is always 1$ in the game (value of any open position). The sum of all positive (negative) returns gives the gross profits (losses). The gross rate of return (per year) is then the difference between gross profits (per year) and gross losses (per year). If one subtracts transaction costs one gets the net rate of return (the number of transactions is always twice the number of open positions and, hence, of the single returns).

The gross rate of return (GRR) of any technical trading model can be split into six components, the number of profitable/unprofitable positions (NPP/NPL), the average return per day during profitable/ unprofitable positions (DRP/DRL), and the average duration of profitable/unprofitable positions (DPP/DPL). The following relationship holds:^{^[9]}

GRR = NPP4DRP4DPP − NPL4DRL4DPL

Table 1 Components of the profitability of 2580 trading system by subperiods and classes of the t-statistic.
		Number of models Mean for each class of models
		Absolute	Share Gross rate t-statistic Profitable positions ^{in % of return}Number per year Return per day Duration in days	Unprofitable positions
		Absolute		Number per year Return per day	Duration in days
1960–1971		2580	100.0 8.6 2.30 6.8 0.08 44.2	8.7 −0.12	13.3
1972–1982		2580	100.0 2.0 0.45 6.7 0.10 40.9	11.5 −0.16	12.8
1983–1991		2580	100.0 −0.0 −0.01 6.4 0.11 40.3	12.9 −0.16	13.5
1992–2000		2580	100.0 −5.1 −1.12 6.3 0.09 40.2	14.1 −0.16	12.8
2001–2007		2580	100.0 −0.8 −0.15 6.4 0.09 43.3	12.6 −0.15	13.5
1960–2007		2580	100.0 1.5 0.74 6.5 0.09 42.1	11.7 −0.15	13.1
t-statistic b0		888	34.4 −1.2 −0.61 5.7 0.09 40.1	10.1 −0.15	14.2
0–b1		803	31.1 0.9 0.46 4.7 0.08 51.9	8.8 −0.13	16.1
1–b2		449	17.4 3.1 1.47 6.1 0.09 45.6	11.7 −0.14	12.6
2–b3.0		217	8.4 5.0 2.43 9.5 0.11 28.9	16.4 −0.17	7.2
>3		223	8.6 8.3 4.07 14.2 0.13 21.2	23.4 −0.20	4.7


Table 2 Components of the profitability of 2580 trading systems by subperiods and classes of the t-statistic.
Number of models Mean for each class of models
	Absolute Share in % Gross rate t-statistic Profitable positions ^{of return}Number per year Return per day Duration in days			Unprofitable positions
				Number per year Return per day	Duration in days
1983–1991	2580 100.0 −5.1 −0.97 6.4 0.11 39.3			14.0 −0.17	13.7
1992–2000	2580 100.0 −6.7 −1.59 6.5 0.08 38.6			14.4 −0.16	13.0
2001–2007	2580 100.0 1.6 0.32 6.6 0.09 43.7			11.9 −0.14	13.5
1983–2007	2580 100.0 −3.7 −1.34 6.5 0.09 40.5			13.5 −0.16	13.3
t–statistic b0	2361 91.5 −4.1 −1.48 6.6 0.09 39.2			14.1 −0.16	12.6
0–b1	217 8.4 0.6 0.21 4.7 0.08 53.8			7.4 −0.12	20.6
1–b2	2 0.1 2.8 1.04 5.2 0.09 40.1			7.1 −0.12	17.3

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