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LUNAR TEST RESULTS
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Tests were run on four entry models: crossover, momentum, crossover with contir mation, and crossover with confirmation and inversions. Each model was studied with entry at open, on limit, and on stop. Table 9-l summarizes the results of all tests, broken down by sample, entry order, and model. For each model, there is a row of numbers containing the annualized portfolio return, and a row with the average portfolio dollar profit or loss per trade. Averages across all order types for in-sample and out-of-sample performance are in the two rightmost columns. The last two rows contain the average across aI models for each type of order.
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Tables 9-2 and 9-3 present information for each of the 12 tests on the specific commodities that the model traded profitably and those that lost, for the insample (Table 9-2) and out-of-sample (Table 9-3) runs. The first column, SYM, is the market being studied. The last column (COUNT ) is the number of profitable tests for a given market. The numbers in the first row are Test identifiers. The last row (COUNZJ contains the number of markets profitable for a given model. Tables 9-2 and 9-3 provide information about which markets are and are not profitable when traded by each model: One dash (-) indicates a loss per trade of $2,000 to $4,000; two dashes (- -) represent a loss of $4,000 or more; one plus sign (+) means a profit per trade of $1,000 to $2,000; two pluses (+ +) indicate gains of $2,00O,or more; a blank cell means a loss between $0 and $1,999 or a profit between $0 and $1,000 per trade. Tests of the Basic Crossover Model A moving average (mnl) was computed for the integrated, price-lie lunar series. A second moving average (ma2) was taken of the first moving average. A buy signal was generated when ml crossed above ma2. A sell signal was generated when ma1 crossed below ma2. This is the same moving average crossover model discussed in the chapter on moving averages, except here it is computed on a lunar series, rather than on prices. The entries were effected by either a market at open (Test l), a limit (Test 2), or a stop order (Test 3). Optimization involved stepping the length of the moving averages (avglen) from 5 to 15 in increments of 5, and the displacement (disp) from 0 to 15 in incre-
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Performance of Lunar Models Broken Down by Model, Order, and Sample
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In-Sample Performance Broken Down by Test and Market
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T A B L E
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Out-of-Sample Performance Broken Down by Test and Market
ments of 1. For entry at the open, the best performance (in terms of in-sample risk-to-reward ratio) was achieved with a moving average length of 15 and a displacement of 8: entry on a limit was best with a length of 15 and a displacement of 6; entry on a stop required a length of 15 and a displacement of 12. No tests showed profits in either sample. In-sample, best performance (least average loss per trade) was with entry on limit; entry on stop produced poorer results; entry at open was the worst. With the limit order, 43% of the 1,759 trades were profitable. Out-of-sample, the limit order produced the smallest average loss per trade and the stop yielded the largest loss. Overall, the system did not do well on the entire portfolio. The relative performance of shorts and longs was inconsistent across orders and samples. In-sample, longs lost substantially more than shorts, the opposite of what was frequently seen in tests of other models. Equity steadily declined from the beginning to the end of the data series for entry at open. For entry on limit, equity was choppy but up, peaking in September 1989. It then declined until July 1992, rose slightly until February 1994, and declined steadily until July 1998, when it suddenly began increasing. With a stop, equity showed a choppy decline from one end of the data series to the other. In-sample, the number of markets with positive returns using a limit, a market-at-open, and a stop were 15, 8, and 7, respectively. Out-of-sample, the limit produced the best results (17) followed by the market-at-open (16), and the stop (14). More market-order combinations produced profits out-of-sample than in-sample; it seems that many markets are becoming more affected by lunar rhythms in recent years. In-sample, only the Deutschemark and Light Crude were profitable across all three entry orders. Out-of-sample, the Deutschemark was highly profitable with limit and stop orders; Light Crude slightly lost with the stop. T-Bonds strongly profitable in both samples with the limit. Pork Bellies was profitable in both samples with entry at open and on limit. Considering only the limit order, profit in both samples was observed for the Deutschemark, Swiss Franc, Japanese Yen, Platinum, Palladium, Sugar, and Cotton. Tests of the Basic Momentum Model A centered moving average smoothed the unintegrated lunar price change series. No lag was induced because the centered average examines as many future (relative to the current bar), as it does past, data points. This smoothing is legitimate because, in the calculations, the lunar estimate at the current bar involves data at least two lunar cycles (about two months) away. For the smoothed lunar price changes, a series of average absolute deviations was computed and a loo-bar simple moving average was taken to produce the desired result. A buy was issued when lunar momentum, at the current bar plus some displacement (d&p), was greater than some multiple (thresh) of the average absolute deviation of the lunar momentum. A sell was issued when lunar momentum, at the same displaced bar,
was less than minus the same multiple of the average absolute deviation. Entries were executed at the open (Test 4), on a limit (Test S), or on a stop (Test 6). Optimization was for the length of the moving averages (stepped from 5 to 15 in increments of 5), the displacement (1 to 10 in steps of l), and the threshold (1.5 to 2.5 in steps of 0.5). Best results were achieved with the length, displacement, and threshold parameters set to 10, 10, 2 for the market-at-open and 15, 9, 1.5 for the limit and stop. Overall, results were worse than for the crossover model. Heavy losses occurred in both samples across all order types. The same poor performance was observed when seasonal effects were analyzed with the momentum model. Longs again performed better than shorts. With entry at open, portfolio equity declined smoothly and severely, with the rate of loss gradually decreasing over time. With a limit order, equity steadily decreased. With a stop, equity dropped sharply from the beginning of the sample until August 1988, then declined gradually. In-sample, the S&P 500, NYFE, Deutschemark, and Swiss Franc were somewhat profitable across all orders. Out-of-sample, the S&P 500 and NYFE neither profited nor lost, but the Deutschemark did well with entry at open, and the Swiss Franc with entry on limit and on stop. As with the crossover model, there were many more profitable market-order combinations. Tests of the Crossover Model with Confirmation This is identical to the basic crossover model except that entries were only taken when an appropriate reading of the Fast %K Stochastic confirmed lunar market behavior. Specifically, if the lunar crossover suggested a buy, it was only acted upon if Fast %K was below 25%; before a buy occurred, the market had to be down or near a bottom, as expected on the basis of the lunar rhythm. Likewise, a lunar sell was not taken unless the market was near a possible top, i.e., Fast %K greater than 75%. Entries were at the open, on a limit, or a stop (Tests 4 to 6, respectively). The length of the moving averages (avglen) was optimized from 3 to IS in increments of 3, and displacement (disp) from 0 to 15 in increments of 1. Best performance was achieved for entry at the open, and on a limit, with a moving average length of 15 and a displacement of 12; the best stop entry occurred with a length of 12 and a displacement of 5. In-sample, the results were somewhat better than the basic crossover model: When combined with the stop, the crossover with confirmation yielded about $234 per trade. Out-of-sample, however, the average loss was more than for either of the previous two models, regardless of order. The stop showed the smallest loss per trade and was best. This is another system not profitable on a whole portfolio basis. The equity curves showed nothing but losses across all three orders.
In-sample, the JapaneseYen, Heating Oil, Soybeans, and Soybean Meal were profitable with all three orders; out-of-sample, only losses or, at best, unprofitable trading occurred in these markets. Kansas Wheat showed consistent behavior across samples: Results were profitable with entry at open and on limit, and unprofitable with entry on stop. Across samples, the British Pound and Swiss Franc were profitable, as was the Canadian Dollar, Eurodollar, and Pork Bellies with entry on a stop. Since the number of trades was fairly small for many markets and the whole portfolio, results are probably not trustworthy. Tests of the Crossover Model with Confirmation and Inversions This is the same as the crossover model with confirmation, but additional trades were taken at possible inversions. If a lunar buy was signalled by a crossover, but the market was high (Fast %K being greater than 75%), a sell (not a buy) was posted; the assumption is the usual lunar cycle may have inverted, forming a top instead of a bottom. Likewise, if the crossover signalled a sell, but the market was down, a buy was issued. These signals were posted in addition to those described in the crossover with confirmation model. Entries occurred at the open (Test lo), on a limit (Test ll), or a stop (Test 12). The length of the moving averages (avg2en) was stepped from 3 to 15 in increments of 3, and the displacement (disp) from 0 to 15 in increments of 1. For entry at the open, the best moving average length was 15 and displacement, 12; entry on a limit was best with a length of 15 and a displacement of 8; entry on a stop required a length of 12 and displacement of 15. This model lost heavily across samples and orders. As with seasonality, inversions did not benefit performance. The equity curve paints a dismal picture. In-sample, the NYFE was profitable across all three orders, but the S&P 500 lost for two of the orders and was flat for the other. The Swiss Franc was also profitable in-sample across all three orders; out-of-sample, it was very profitable for entry at open, but lost for the other two orders. There was a great deal of inconsistency in results between the samples.
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