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There are many ways to generate entries based on solar activity. The method used below is a simple variation of a breakout model, applied to sunspot counts, not prices. The rules are: If the current sunspot number is higher than the cument upper threshold, and the sunspot counts for a certain number (I& ) of previous bars were lower than their corresponding thresholds, then either a buy or sell signal (depending on previous market behavior in response to upside breakouts in the sunspot numbers) is issued. If the current sunspot number is lower than the current lower threshold, and the sunspot counts for the same number of previous bars were all higher than their corresponding thresholds, then either a sell or a buy signal (again, depending on previous market behavior) is issued. The signals are not responded to immediately, but only after a specified number of days (disp). The breakout thresholds are determined as follows: The upper threshold, used for a given bar, is the highest sunspot number found in a certain larger number of previous bars (Ibl), while the lower threshold is set at tbe lowest of the sunspot numbers in those previous bars. Previous market behavior refers to whether the market was near the bottom or top of its near-future range when a paaicular kind of breakout occurred. If a given direction of solar brealout is historically associated with the market being near the bottom of its near-future range, a buy signal is generated, on the other hand, if the market is characteristically near the top of its near-future range, a sell signal is generated. Like lunar phenomena and seasonality, entries based on solar activity share the assumption that market behavior is intluenced by external factors and that the independent, influential variable has predictive value, i.e., market behavior is anticipated rather than responded to. As with any predictive system, the forecasts may be more or less correct. Trades resulting from incorrect predictions can be incredibly bad, even if many trades resulting from correct predictions are perfect, as is often the case with predictive systems. Being anticipatory, the models lend themselves to countertrend entries, which means better tills, less slippage, and better risk control, assuming appropriate stops are used (not done here because of the need to maintain the standard exit).
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9 Lunar and mar Rhythms
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The code for these tests is similar to that for lunar analysis and so is not presented here. It is available on the companion software CD (see offer at back of book).
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SOLAR TEST RESULTS
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Tests were performed on the solar entry model using entry at open (Test 1). on a limit (Test 2), and on a stop (Test 3). The breakout look-back (Ibl) was stepped from 25 to 40 in increments of 5; the repeat prevention look-back (lb, ) from 10 to 15 by 5; and the displacement (disp) from 0 to 2 by 1. For entry at the open, the best in-sample performance was with a breakout look-back of 35, a repeat prevention look-back of 15, and a displacement of 2. For the limit, a breakout lookback of 40, a repeat prevention look-back of 15, and a displacement of 0 were optimal. For the stop, the best values were: for the breakout look-back, 35; for the repeat prevention look-back, 15; and for the displacement, 2. Table 9-4 shows both the in- and out-of-sample performance for specific commodities. The columns and rows contain the same kinds of data as in Tables 9-2 and 9-3 above. The solar model performed about as well as the lunar ones and, in sample, did best with a stop order. In-sample, entry at the open was worst (-$I631 per trade); a limit was slightly better (-$1519), substantially so when only long trades were considered. The stop order was the best, losing only $52 per trade; were it not for transaction costs, this order would have been very profitable in-sample. The mode1 required the theoretically expected displacement. The best displacement for the limit was zero, understandable since the goal is to respond quickly, before the market turns, when a limit can enter on the noise. With the stop, a displacement of 2 was best: Movement needs to begin to trigger the stop and cause entry. The average loss per trade worsened, from -$52 to -$2,000, when displacement deviated just one or two bars from its optimal value. This implies a relationship between the timing of the market and solar events otherwise small changes in the displacement should have little or no effect. With the stop order, the highest percentage of wins (in-sample) was obtained and the long side was actually profitable. Out-of-sample, the stop was again best, but the average loss per trade was a substantial $1,329. Equity was examined only for the stop, since the other orders performed so poorly. Equity rose very rapidly until June 1988, then, until October 1990, it was choppy and fairly flat. Between October 1990 and June 1994, equity declined sharply, then was choppy and slightly down. Interestingly, some of our previous findings (Katz and McCormick, September 1997) were confirmed. With the stop, which generally performed best on the whole portfolio, the S&P 500 was very profitable in both samples. The average trade returned $4,991 in-sample: the return was 20.4% annualized; and,
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