什麼是交易策略回溯測試
回溯測試:藉助歷史數據檢驗交易策略有效性
回溯測試,作爲投資策略制定的重要環節,是一種利用歷史市場數據模擬過往交易情況的驗證方法。這一過程旨在重現過去的投資環境,將您的交易理念與實際發生的市場變化相對照,以科學嚴謹的態度評估交易策略在歷史條件下的表現。
具體而言,在金融投資領域,投資者或交易員在構建新的交易模型或策略時,並非直接應用於實時市場,而是首先通過回溯測試進行“沙盤推演”。它就像一部時光機,載着您的交易邏輯穿越歷史價格波動的迷霧,揭示出該策略在已發生的不同市場情景下可能產生的收益和風險狀況。
通過這種基於歷史數據的模擬實驗,回溯測試能夠提供有力證據,幫助您初步判斷所設計的交易策略是否具備潛在盈利能力,從而爲決定是否將其應用於實戰交易提供關鍵參考依據。
選擇交易類型與準備回溯測試
在進行回溯測試之前,首要任務是明確自身的交易風格,並據此做好相應的準備工作。交易者大致可以分爲兩類:自主決策型和系統型。
對於自主決策型交易者而言,其交易策略的核心在於個人經驗和判斷力,靈活應對市場變化,開倉和平倉時機往往基於對實時市場狀況的主觀評估。這種類型的交易方式雖然開放且自由度高,但由於缺乏嚴格的標準和規則,進行回溯測試時可能面臨結果不一致、可靠性較低的問題。但這並不意味着自主決策型交易者應當完全忽視回溯測試,他們可以通過模擬交易來了解自身決策模式的歷史表現,以優化決策過程並減少情緒化影響。
相比之下,系統型交易者更適合應用回溯測試。這類交易者依賴於一套明確且詳盡的交易規則系統,系統中明確規定了何時買入或賣出的條件(例如,“當A和B兩個條件同時滿足時買進,當X條件出現後賣出”)。此類交易策略通過嚴謹的邏輯和量化標準去除了人爲的情緒干擾,爲盈利提供了更爲合理的預期。因此,系統型交易策略在回溯測試中的效果更爲顯著和可靠,尤其在追求精確和自動化的算法交易領域備受歡迎。
爲了確保回溯測試的有效性,不論是自主決策型還是系統型交易者,在實施測試前都必須確保交易策略具備清晰明瞭的定義和操作規則。系統型交易者尤爲如此,沒有具體規則的策略將導致測試結果的不穩定性。
針對不同需求,交易者可以選擇購買自動化回溯測試軟件,只需輸入相關數據即可獲得系統生成的測試報告。然而,本文將重點介紹手動回溯測試方法,儘管過程相對繁瑣,但無疑能提供更深入的理解和學習機會,而且成本更低廉。
實操指南:手動執行交易策略回溯測試
在進行交易策略的回溯測試時,首先需要創建一個詳盡的數據記錄模板,以便跟蹤和分析歷史交易數據。不論是使用Google試算表提供的模板,還是自行在Excel或Python中編寫代碼實現,關鍵在於確保模板涵蓋了所有必要的信息字段,例如日期、市場、交易方向、開倉價格、止損與止盈點位、風險與潛在收益比率以及實際盈虧情況等。
以比特幣爲例,我們可以設計一種基於移動平均線交叉策略的回溯測試方法。當50天移動平均線上穿200天移動平均線形成黃金交叉時,我們假設在下一個每日收盤價買入;相反,當200天移動均線下穿50天移動平均線形成死亡交叉時,我們設定在下一個每日收盤價賣出。
爲了保證測試的有效性,我們需要明確指出策略適用的時間週期(如日線圖)以及回測的歷史時間段(例如,從2019年初開始)。通過查閱比特幣的歷史價格走勢,我們可以根據策略規則找到相應的交易信號,並記錄在回溯測試表格中:
- 買入 @ ~$5,400(黃金交叉)
- 賣出 @ ~$9,200(死亡交叉)
- 買入 @ ~$9,600(再次黃金交叉)
- 賣出 @ ~$6,700(又一次死亡交叉)
- 買入 @ ~$9,000(隨後的黃金交叉)
這些交易信號落實到圖表上後,我們可以直觀地看到策略的實際表現。計算每一筆交易的盈虧,第一筆交易獲利約$3800,第二筆交易則損失$2900,最終已實現盈虧爲$900。同時,截至特定時間點(如2020年12月),未實現盈利約爲$9000,這意味着如果遵循策略,在下一次出現死亡交叉時平倉離場,將可能實現這部分預期利潤。
進行回溯測試時,務必關注交易頻率、勝率、每筆交易的風險回報比以及整體資產曲線的變化等重要指標。通過系統化地模擬過去的交易場景,可以評估策略在不同市場環境下的適應性和穩定性,從而爲未來的實戰交易提供有力參考依據。
解讀回溯測試結果與優化策略
回溯測試結果分析是評估交易策略有效性和穩健性的關鍵環節。從我們的簡單回測示例中,儘管當前的已實現盈虧並不出色,但透過現象看本質,我們需要深入探究結果背後的市場環境和策略適應性。
例如,在2020年3月新冠疫情引發的市場崩盤期間,未盈利交易反映出策略在極端行情下的表現。這提示我們應考慮黑天鵝事件對策略穩定性的影響,並通過進一步擴大歷史數據範圍進行回測,以判斷虧損是否爲偶發異常或策略內在缺陷。
除了具體的盈虧情況外,回溯測試結果還可以揭示以下重要信息:
1. 波動性測量:最大收益峯值和最大回撤幅度可以幫助您瞭解策略在不同市場週期中的波動特性,以及您可能面臨的心理壓力。
2. 風險敞口:根據回測結果計算所需的風險資本,以便合理分配投資組合資金,控制整體風險水平。
3. 年化回報率:通過計算策略在一年內的平均收益率,可以與市場上其他投資產品或策略進行比較,評估其吸引力。
4. 盈利與虧損比例:觀察策略下盈利和虧損交易的比例及每筆交易的平均盈虧額,有助於判斷策略盈利能力及勝率。
5. 平均成交價格:統計開倉和平倉的平均價格,可瞭解策略執行時點的選擇效果。
然而,真正的價值不僅在於獲取上述指標數值,更在於如何運用這些信息改進策略。對於嚴謹的交易者來說,他們會在回測過程中嚴格記錄各種詳細參數,從而獲得更多學習和調整的機會。
最後,必須注意的是,在解讀回溯測試結果的同時,要警惕過擬合(優化陷阱),即過度依賴歷史數據優化策略,導致未來實際交易效果不佳。爲了確保策略的有效性和前瞻性,需要結合模擬交易(前瞻性測試)進行驗證,確保策略在未知市場條件下的適應能力和持續盈利能力。
結語
在總結全文後,我們可以明確回溯測試是金融投資領域中不可或缺的策略評估工具,它利用歷史數據模擬交易環境,幫助投資者檢驗和優化交易邏輯。不論是自主決策型還是系統型交易者,均能通過回溯測試深入理解策略在不同市場條件下的表現,從而做出更明智的投資決策。
最新的實踐表明,在瞬息萬變的金融市場中,定期進行回溯測試並結合前瞻性測試,可以有效避免過擬合陷阱,提高交易策略的穩健性和適應性。展望未來,隨着人工智能與大數據技術的發展,回溯測試方法將進一步精細化、自動化,爲投資者提供更爲精準和高效的策略驗證手段。
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0.009990 | -7.07% | |
0.4805 | -7.58% | |
5.3380 | 1.22% | |
0.0024972 | 5.86% | |
0.3312 | 5.04% | |
2.017 | 2.59% | |
0.031585 | 11.37% | |
0.017000 | 29.77% | |
0.00000468 | 16.42% | |
3.5480 | -1.75% | |
3.3107 | 1.23% | |
0.8850 | -48.36% | |
0.002069 | -0.81% | |
0.7818 | -7.48% | |
0.388 | -2.02% | |
0.538 | 12.79% | |
0.17980 | 1.77% | |
0.2897 | 163.60% | |
0.000002291 | 7.46% | |
0.015775 | -7.26% | |
0.250454 | -0.14% | |
0.01654 | 7.82% | |
0.48730 | 0.83% | |
0.3555 | 8.38% | |
0.00042 | 5.00% | |
0.00002306 | 1.72% | |
0.0764 | 0.13% | |
0.01538 | 35.63% | |
0.1000 | 0.00% | |
0.00417 | 3.73% | |
0.002968 | -0.74% | |
0.016806 | -1.68% | |
0.04704 | 34.86% | |
224.895 | 7.09% | |
0.00187 | 96.84% | |
0.002463 | 5.26% | |
0.61302 | -1.54% | |
0.2216 | 3.07% | |
14.1236 | 6.24% | |
0.02334 | -21.76% | |
0.1166 | -42.05% | |
0.0002464 | 9.51% | |
0.0022993 | 0.04% | |
0.12167 | 7.43% | |
0.0028739 | -3.30% | |
0.05399 | -0.02% | |
0.03070 | 10.47% | |
0.00544 | 8.15% | |
0.00014778 | 3.30% | |
0.0000000000948 | -9.46% | |
0.5197 | 7.11% | |
0.3136 | -4.48% | |
0.1389 | 20.57% | |
0.0101 | 4.12% | |
0.0000999 | 0.00% | |
0.0000006427 | 1.37% | |
0.002950 | -0.54% | |
0.00009636 | 17.31% | |
0.038779 | 2.03% | |
4.6771 | 2.34% | |
0.02479 | 6.90% | |
17.1000 | -0.26% | |
0.011530 | 2.78% | |
0.0945 | -0.42% | |
0.0000000058 | 3.57% | |
0.001603 | 0.00% | |
0.000000497 | 12.44% | |
9.8627 | 0.21% | |
0.002969 | 16.52% | |
345.9 | 4.16% | |
0.005709 | -2.09% | |
0.0805 | -0.98% | |
0.4874 | 3.11% | |
0.006643 | -0.06% | |
0.00024 | 0.00% | |
0.815 | 7.24% | |
0.004993 | 7.17% | |
0.9222 | 3.50% | |
1.292 | -0.23% | |
0.0000854 | -0.35% | |
0.4810 | 1.26% | |
34.0260 | -0.07% | |
0.004796 | -0.75% | |
0.0228 | 57.24% | |
0.12114 | -43.31% | |
0.07450 | 28.47% | |
5.3006 | 0.01% | |
0.00219 | 5.29% | |
1.995 | -0.84% | |
2.714 | 4.14% | |
0.004698 | 19.36% | |
166.67 | 8.46% | |
0.3929 | -5.37% | |
0.0000174 | -2.79% | |
5.35 | 4.49% | |
0.0001474 | 2.29% | |
3.4637 | 0.14% | |
0.00000003875 | 4.45% | |
0.008112 | -12.91% | |
0.000692 | -1.42% | |
0.00000004804 | 7.26% | |
0.20082 | 10.96% | |
0.9996 | -0.04% | |
0.0000318 | 0.32% | |
0.00012179 | 10.51% | |
0.0577 | 0.35% | |
3.322 | 0.27% | |
0.01670 | 0.48% | |
105.6199 | -2.84% | |
0.0909 | 4.24% | |
0.00000096 | -67.79% | |
2.821 | 4.10% | |
0.03423 | 3.82% | |
83.10 | 0.00% | |
0.01353 | 4.48% | |
0.00873 | 14.57% | |
0.00017173 | -0.21% | |
0.05715 | 1.13% | |
0.0017 | 0.00% | |
0.000130 | 0.78% | |
0.0006146 | 23.89% | |
0.000456 | -5.79% | |
0.024106 | 102.38% | |
0.00221 | 4.25% | |
4.565 | 2.15% | |
0.7504 | 16.43% | |
0.003002 | 40.87% | |
0.01204 | 14.89% | |
0.8008 | -0.16% | |
0.00004370 | 14.49% | |
0.011350 | 6.56% | |
0.02207 | -3.88% | |
0.001106 | -1.51% | |
0.000184 | -13.21% | |
0.0771 | -0.13% | |
0.012446 | 0.59% | |
2.1111 | 0.00% | |
0.00004372 | 0.41% | |
0.0000890 | -6.41% | |
0.00007202 | 13.36% | |
0.006385 | 48.42% | |
0.00603 | -13.24% | |
0.00000137 | -0.72% | |
0.00644 | 7.87% | |
0.001002 | 10.35% | |
0.000000000317 | -0.94% | |
0.513 | 6.88% | |
0.06080 | -3.80% | |
0.0360 | 11.46% | |
0.000700 | 1.45% | |
1.6093 | 0.28% | |
0.001867 | 26.32% | |
0.02588 | 40.58% | |
0.00013935 | 0.00% | |
6.39 | 8.67% | |
0.740 | 5.71% | |
0.000146 | 15.87% | |
0.955 | -2.65% | |
0.00852 | 5.84% | |
0.000415 | 8.07% | |
0.1576 | 11.06% | |
0.7965 | 4.20% | |
0.004663 | 4.36% | |
0.00000000011977 | -4.55% | |
0.9995 | 5.21% | |
0.00160 | -5.88% | |
0.0000048 | -23.81% | |
0.2355 | -1.34% | |
0.000920 | 1.10% | |
0.000000051538 | 1.23% | |
0.0001750 | 8.02% | |
0.000000002182 | 46.44% | |
0.381 | 1.87% | |
0.005644 | -2.82% | |
6.025 | 6.62% | |
0.6643 | 1.73% | |
0.0643 | -5.16% | |
0.0636 | 9.47% | |
0.07097 | -2.71% | |
3.97 | -2.46% | |
0.00003753 | 1.05% | |
0.005900 | 66.53% | |
0.07962 | 0.95% | |
5.136 | 4.26% | |
0.05192 | 39.80% | |
0.00215 | 4.37% | |
0.00015 | 0.00% | |
0.0037732 | 0.40% | |
0.2401 | 6.62% | |
0.01594 | 13.61% | |
0.00713 | 5.32% | |
0.04971 | 6.56% | |
0.3154 | 3.24% | |
0.00992 | 6.21% | |
95.148 | -7.48% | |
0.0050 | -54.95% | |
0.8606001 | 4.52% | |
0.006191 | 19.29% | |
0.01698 | 4.56% | |
9.53 | 6.01% | |
0.6509 | -2.11% | |
0.000000555 | 6.94% | |
0.00096 | -2.04% | |
0.2486 | 4.19% | |
0.0281 | 32.55% | |
0.007777 | 16.86% | |
16.90 | 6.69% | |
0.3203 | 0.03% | |
0.00617 | -0.48% | |
0.00003875 | 2.13% | |
0.00658 | 8.76% | |
4.397 | 3.26% | |
0.00000470 | 0.00% | |
0.619 | 1.81% | |
0.1977 | -10.01% | |
0.2133 | 5.54% | |
0.0116 | -4.13% | |
0.02949 | 11.70% | |
0.0001777 | 5.27% | |
6.00 | 3.99% | |
0.07036 | 0.37% | |
0.550 | 2.42% | |
0.001721 | 2.20% | |
0.000501 | 0.00% | |
0.17084 | 0.75% | |
102.5868 | -1.91% | |
0.0304 | 12.59% | |
0.2954 | 3.32% | |
0.000478 | 0.21% | |
0.0725 | 11.71% | |
0.02121 | 13.30% | |
42.91 | 3.05% | |
0.3505 | -0.45% | |
0.002349 | 0.00% | |
0.014799 | 2.76% | |
0.09190 | -55.52% | |
0.3087 | 2.66% | |
0.0013 | 0.00% | |
0.00228 | 0.00% | |
0.669 | 6.87% | |
0.016265 | 18.01% | |
0.03752 | 4.19% | |
0.4515 | 5.89% | |
0.02569 | 7.58% | |
0.01766 | 9.55% | |
16.77 | 2.69% | |
0.1939 | -7.09% | |
0.00824 | 11.35% | |
0.009135 | -0.47% | |
0.0880 | 7.19% | |
0.0892 | 1.48% | |
0.005150 | 8.54% | |
0.00154 | 0.00% | |
0.1109 | 20.02% | |
0.00084361 | 1.89% | |
0.071715 | 2.43% | |
0.02942 | 26.43% | |
0.002752 | 4.20% | |
0.0565 | -5.99% | |
0.002710 | -0.29% | |
0.00953 | 22.49% | |
0.00001129 | 20.11% | |
0.1406 | 2.63% | |
0.006237 | 8.75% | |
0.1389 | 1.68% | |
0.01264 | 2.27% | |
0.042871 | 1.76% | |
0.00127 | 6.72% | |
0.02978 | 9.77% | |
0.001868 | 8.29% | |
0.006476 | 12.12% | |
0.14872 | 0.82% | |
0.000394 | 31.77% | |
0.04284 | 7.05% | |
0.000123 | -6.11% | |
0.1509 | 3.57% | |
0.003932 | 0.98% | |
0.05626 | -4.21% | |
0.00891 | -2.41% | |
2.792 | 4.45% | |
0.0274 | 5.38% | |
0.6411 | 4.72% | |
0.0823 | -2.26% | |
0.0415 | 1.97% | |
0.00481 | 10.32% | |
0.001750 | 14.53% | |
0.01369 | 9.35% | |
0.06676 | 51.97% | |
0.0409 | 4.87% | |
0.006353 | 12.34% | |
0.001591 | -18.91% | |
3.0250 | 1.49% | |
0.000000205 | -18.97% | |
0.2850 | 3.52% | |
5.117 | -9.32% | |
0.003288 | 6.27% | |
0.000002462 | 6.90% | |
1455 | 2.68% | |
1.0488 | 7.45% | |
0.02641 | -4.62% | |
0.0016317 | 17.86% | |
0.0000518 | 31.47% | |
0.000330 | 2.80% | |
3255.69 | -4.87% | |
0.00003658 | -9.48% | |
0.3888 | -2.43% | |
6.220 | 6.96% | |
0.008742 | -0.79% | |
0.001074 | 11.64% | |
0.00215 | -0.46% | |
0.00280 | -1.75% | |
0.5269 | 1.58% | |
0.000798 | -10.03% | |
0.003877 | 23.55% | |
0.003842 | 13.97% | |
0.00556 | 3.15% | |
0.493 | 2.71% | |
0.000177 | -9.23% | |
0.0161452 | 2.18% | |
0.5353 | 23.57% | |
0.00881 | 4.76% | |
0.010693 | 12.13% | |
0.1196 | -2.69% | |
0.006108 | -26.07% | |
1.6498 | 0.00% | |
0.02589 | 4.44% | |
0.00000013911 | 2.23% | |
0.002659 | -1.01% | |
0.763 | 6.12% | |
0.1518 | 3.27% | |
0.03669 | 21.85% | |
0.0003194 | 5.17% | |
0.004476 | 1.24% | |
0.003125 | 5.04% | |
0.4406 | 2.92% | |
0.2756 | 6.41% | |
0.00390 | -4.88% | |
0.1938 | 5.56% | |
0.1908 | -14.75% | |
0.0810 | 3.85% | |
0.010231 | 2.14% | |
0.0002291 | 11.97% | |
0.02944 | 3.70% | |
0.06357 | 4.33% | |
0.01396 | -0.29% | |
0.0000000419 | 49.11% | |
0.01919 | 3.06% | |
5.0205 | -11.92% | |
0.002231 | 17.42% | |
0.7193 | -3.63% | |
0.1083 | 5.66% | |
0.00028 | -3.45% | |
0.1989 | 4.63% | |
0.00305094 | 9.60% | |
0.00876 | 21.67% | |
0.00004015 | -0.74% | |
0.01043 | 1.07% | |
0.000186 | -30.08% | |
0.4498 | 1.60% | |
0.001800 | 13.28% | |
2.572 | 1.34% | |
0.002293 | 10.61% | |
0.002252 | -0.18% | |
0.537 | 2.48% | |
0.00006368 | 2.53% | |
7.67 | 9.57% | |
0.008000 | -3.64% | |
28.29 | 4.78% | |
0.05639 | 10.98% | |
0.1950 | 3.23% | |
1923.19 | 4.95% | |
0.004314 | 29.74% | |
0.003076 | 32.19% | |
0.09855 | 0.45% | |
0.000635 | 12.99% | |
0.00000001473 | 16.17% | |
0.006430 | 4.77% | |
0.004530 | 17.63% | |
0.2093 | 0.05% | |
0.01638 | 7.34% | |
0.000000001275 | 0.00% | |
0.01891 | -3.37% | |
0.000165 | 22.22% | |
0.001218 | -36.79% | |
0.004940 | 2.49% | |
0.002280 | 1.83% | |
0.00002380 | 11.68% | |
0.1246 | 10.07% | |
0.00933 | 3.44% | |
0.2382 | 3.84% | |
0.002528 | -1.48% | |
0.000636 | 4.61% | |
0.000479 | -0.62% | |
0.527 | 6.46% | |
0.06407 | 66.72% | |
2.221 | 13.66% | |
0.1601 | 6.24% | |
0.0277 | 14.94% | |
0.0001616 | -1.64% | |
0.00000445 | -19.09% | |
0.2448 | -1.65% | |
0.00714 | 0.00% | |
0.00000007350 | 119.34% | |
14.76 | 8.13% | |
0.01874 | 19.82% | |
0.00558 | 24.28% | |
0.2532 | 10.37% | |
0.00411 | -0.24% | |
0.01017 | 3.78% | |
0.000796 | -4.44% | |
0.00196758 | 4.04% | |
0.01663 | 1.84% | |
0.00020860 | 14.62% | |
0.000500 | 1.42% | |
0.5135 | 15.50% | |
0.005780 | 25.84% | |
2.1416 | 2.18% | |
0.0127 | 23.30% | |
0.01533 | 5.07% | |
0.590 | 8.66% | |
0.0548 | 3.40% | |
0.0000078 | 0.00% | |
0.00001067 | -4.99% | |
15.22 | 5.77% | |
0.00006688 | 6.18% | |
0.0000170 | -0.58% | |
0.2577 | -0.39% | |
0.000839 | 20.03% | |
0.02425 | -12.45% | |
0.0000568 | 7.58% | |
0.00000878 | -7.19% | |
1.7011 | 3.92% | |
0.027943 | 7.71% | |
0.005600 | 191.97% | |
72.0 | 4.50% | |
0.002110 | 32.62% | |
0.0813 | -2.28% | |
0.02636 | 10.80% | |
0.01303 | 5.59% | |
0.2807 | 16.52% | |
0.0000000212 | -0.93% | |
0.0068 | -35.24% | |
0.02898 | 0.66% | |
0.00215 | 8.04% | |
0.002414 | 15.78% | |
1.173 | 6.15% | |
0.004685 | -9.94% | |
0.00450 | 4.41% | |
0.0003692 | 18.87% | |
0.1117 | 2.29% | |
0.0060 | 22.45% | |
0.0785 | 5.37% | |
0.581 | 10.88% | |
0.00330 | 1.54% | |
0.0123 | 0.00% | |
0.9405 | 5.91% | |
0.005769 | 23.51% | |
8.023 | 2.35% | |
0.0063 | 0.00% | |
0.03954 | 16.40% | |
0.17164 | 1.48% | |
0.029956 | 0.01% | |
0.1828 | 7.15% | |
0.00009 | -35.71% | |
0.01151 | 1.59% | |
0.0000000371 | 12.08% | |
0.0030192 | -0.97% | |
0.09010 | 0.41% | |
11.71 | 1.39% | |
0.0000000597 | 6.23% | |
0.001339 | 23.18% | |
0.00639 | 1.59% | |
8.07 | 4.26% | |
0.0000003179 | 11.15% | |
0.00103 | 4.04% | |
358.9 | 1.18% | |
0.000532 | 18.75% | |
0.75092 | -0.65% | |
0.8199 | 1.90% | |
0.55589 | 4.38% | |
0.02673 | 12.22% | |
0.004784 | 18.53% | |
0.000001397 | 5.91% | |
0.0539 | 19.25% | |
0.00971 | 4.41% | |
2.508 | 3.98% | |
0.001074 | 34.08% | |
0.0437 | 10.63% | |
0.2920 | 5.99% | |
0.01422 | 11.18% | |
0.03242 | 31.26% | |
3.286 | -2.81% | |
0.00607 | 14.53% | |
0.004015 | 71.14% | |
0.5565 | 2.68% | |
0.2130 | -2.52% | |
0.003724 | 24.92% | |
0.000472 | -21.20% | |
0.0896 | 6.79% | |
6.52 | 10.51% | |
0.12316 | 14.46% | |
0.004912 | -14.28% | |
0.1490 | 8.05% | |
0.1106 | 8.11% | |
0.00038154 | 66.63% | |
0.0079 | -10.23% | |
0.000669 | -15.74% | |
0.06044 | 1.41% | |
0.008363 | -3.32% | |
0.04964 | 1.97% | |
0.00000685 | 13.04% | |
0.09264 | 2.93% | |
0.0000536 | 3.47% | |
0.1321 | 0.76% | |
0.00000001260 | 2.11% | |
0.0000000452 | 8.39% | |
0.1450 | 2.47% | |
0.003226 | 2.94% | |
0.000001247 | 9.10% | |
2.6006 | 0.02% | |
0.0003033 | 3.09% | |
0.0195 | 3.72% | |
0.05311 | 16.55% | |
0.003156 | 31.99% | |
0.07640 | 16.22% | |
0.000271 | 1.12% | |
0.2024 | 1.45% | |
0.000505 | -5.43% | |
0.1313 | -1.65% | |
0.0465 | 1.09% | |
0.7001 | 1.79% | |
0.02979 | 7.43% | |
0.396 | 3.13% | |
0.2497 | 13.60% | |
0.000942 | 9.28% | |
0.000255 | 54.55% | |
0.614 | -0.65% | |
0.02434 | 0.00% | |
14.274 | -6.84% | |
0.000613 | 0.49% | |
0.000461 | 2.22% | |
0.01708 | 13.11% | |
3.6146 | 0.46% | |
14.85 | 4.14% | |
0.0000377 | 1.34% | |
12.3877 | -3.22% | |
0.002733 | 11.92% | |
0.0190 | 1.60% | |
0.1168 | -0.26% | |
0.0764 | 1.06% | |
0.00009923 | -0.77% | |
0.000094 | -5.05% | |
0.00885 | 0.80% | |
0.003792 | -0.11% | |
0.2008 | 18.40% | |
0.00900 | 0.56% | |
0.0609 | 5.36% | |
0.0120 | 1.69% | |
0.0000532 | -6.01% | |
0.0436 | 4.31% | |
0.0001600 | 2.89% | |
0.455 | 2.25% | |
0.0901 | 2.50% | |
0.002330 | 12.24% | |
0.0000015451 | 12.10% | |
0.001457 | 40.23% | |
15.70 | 5.09% | |
0.728 | 2.68% | |
1010.00 | -8.56% | |
0.0429 | 6.98% | |
0.000788 | -9.22% | |
0.03746 | -9.21% | |
0.1998 | 5.38% | |
2.219 | 1.88% | |
0.8784 | 6.41% | |
0.022148 | 4.45% | |
0.001649 | -13.21% | |
3.710 | 6.76% | |
0.11561 | 3.14% | |
0.2388 | -3.05% | |
0.15184 | 6.58% | |
0.004310 | 74.99% | |
18.90 | 3.90% | |
0.00528 | -7.37% | |
0.1314 | 3.30% | |
0.10001 | 8.97% | |
0.0040 | -2.44% | |
0.001279 | -24.23% | |
4.8791 | 18.97% | |
0.05257 | -6.79% | |
0.00999 | -26.97% | |
0.00178 | -11.00% | |
0.0289 | -3.99% | |
0.3281 | 8.18% | |
0.02992 | 9.24% | |
0.0803 | 2.03% | |
0.00002950 | 7.31% | |
0.0678 | -8.63% | |
0.000001752 | 4.47% | |
0.0000000000000164 | 6.49% | |
0.0005899 | 0.68% | |
0.00018231 | -4.76% | |
0.0003450 | -5.22% | |
0.00327 | -0.61% | |
0.01708 | -0.23% | |
11.48 | 4.17% | |
0.01952 | 1.99% | |
0.000966 | 9.28% | |
0.0170 | 6.25% | |
0.0000000654 | 1.08% | |
0.000699 | 91.51% | |
0.0763 | -2.43% | |
0.2602 | 5.99% | |
2.777 | -1.42% | |
0.001051 | 3.14% | |
0.3112 | 5.10% | |
0.001335 | 13.62% | |
0.004145 | 1.07% | |
0.000000000001140 | 5.26% | |
0.00003238 | 4.28% | |
23.617 | 0.10% | |
0.001338 | 13.97% | |
0.0612 | 3.55% | |
0.2411 | -2.03% | |
0.2016 | -6.84% | |
0.00003 | 50.00% | |
0.0000512 | 2.40% | |
1.802 | -0.72% | |
0.00000000000162 | -8.47% | |
0.0462 | 0.22% | |
0.0001868 | 4.77% | |
0.0713 | 6.26% | |
0.000058420 | -7.01% | |
0.2514 | 8.22% | |
0.002977 | 1.33% | |
0.0595 | 2.59% | |
0.693 | 7.11% | |
0.389 | 16.47% | |
0.00697 | 7.40% | |
0.00972 | 6.35% | |
0.9485 | 0.35% | |
0.000820 | 16.81% | |
0.1780 | 1.02% | |
0.001211 | 0.58% | |
0.0002584 | -19.25% | |
0.001649 | -2.43% | |
4.2512 | 1.95% | |
0.003187 | -3.28% | |
0.1776 | 5.40% | |
0.0542 | 6.07% | |
0.1100 | -28.06% | |
5.681 | 6.39% | |
0.000000000236 | -3.28% | |
0.2830 | 117.52% | |
0.0592 | 4.04% | |
0.0007081 | 4.04% | |
0.308 | 0.33% | |
0.000304 | 11.36% | |
0.002443 | 1.71% | |
0.6150 | 0.99% | |
0.1877 | 3.30% | |
0.0009 | -50.00% | |
0.0000000035 | 0.00% | |
0.3278 | 2.15% | |
0.0001900 | 89.81% | |
0.000412 | 13.50% | |
0.560 | 0.72% | |
0.006296 | -21.85% | |
0.0152 | 2.01% | |
2.6665 | 8.54% | |
0.0582 | 1.93% | |
0.01064 | 16.79% | |
0.0790 | 6.61% | |
0.0001568 | 9.57% | |
2.088 | 6.69% | |
0.7440 | 6.61% | |
0.2473 | -0.32% | |
0.0000017 | 13.33% | |
1.709 | 11.41% | |
0.0145 | 0.00% | |
0.001585 | 6.38% | |
0.6643 | 4.43% | |
0.1120 | 1.45% | |
15.35 | 3.79% | |
0.0683 | 2.86% | |
0.00001000 | 23.15% | |
0.04193 | 3.43% | |
5.47 | 3.40% | |
0.00005 | -77.27% | |
0.2817 | 7.19% | |
0.0000670 | 6.52% | |
0.00012 | 9.09% | |
0.001134 | 6.98% | |
0.001009 | -0.20% | |
0.8512 | 3.75% | |
0.003597 | -3.69% | |
0.0494 | -5.54% | |
0.000278 | 52.75% | |
0.02927 | 3.06% | |
0.002189 | 0.97% | |
0.1025 | 2.50% | |
0.04659 | 2.60% | |
0.007202 | -25.49% | |
0.00949 | 4.98% | |
0.000227 | 7.08% | |
0.234 | 4.93% | |
0.002607 | 1.40% | |
0.002615 | 7.66% | |
0.0000070 | -14.63% | |
0.002899 | -0.07% | |
0.000000000000798 | 4.18% | |
0.0878 | 5.15% | |
0.5378 | 2.97% | |
0.00009165 | 1.38% | |
0.0034 | -2.86% | |
0.05113 | 8.72% | |
0.0086 | 11.69% | |
0.0663 | 17.35% | |
0.6000 | 50.00% | |
0.000000000537 | 15.73% | |
0.0872 | 6.86% | |
0.004477 | 12.86% | |
0.00002185 | 1.11% | |
0.1225 | 5.60% | |
0.002584 | -5.24% | |
0.00242 | 2.11% | |
101.67 | 0.95% | |
6.47 | 8.38% | |
0.00000000001183 | -13.96% | |
0.0000165 | -2.37% | |
0.801 | 12.03% | |
0.000000001893 | 4.59% | |
0.0230 | 7.48% | |
0.00171 | -10.00% | |
0.002350 | -10.00% | |
0.1192 | 2.05% | |
0.0000001935 | -6.34% | |
0.3470 | -0.52% | |
0.001543 | -1.84% | |
0.045125 | 0.00% | |
0.00127 | 47.67% | |
0.000031 | -6.06% | |
0.0011 | -15.38% | |
0.010840 | -1.04% | |
0.00000444 | 8.29% | |
0.000000000210 | -15.32% | |
0.1783 | 5.63% | |
0.1759 | -2.11% | |
0.003867 | 5.68% | |
0.1104 | 3.95% | |
0.0000320 | 0.31% | |
0.04597 | -0.45% | |
0.06713 | 11.47% | |
0.0119 | 1.71% | |
0.0006158 | 8.88% | |
1.0943 | 13.38% | |
0.00013 | -40.91% | |
9.075 | 0.55% | |
0.00040000 | -20.00% | |
0.0016 | -23.81% | |
0.0637 | -1.85% | |
0.00150 | 8.70% | |
0.5990 | 2.78% | |
13.35 | 9.97% | |
0.0040 | -59.60% | |
0.0715 | 5.15% | |
0.0055 | -3.51% | |
0.868 | 3.95% | |
0.0003370 | 9.03% | |
0.000015 | 25.00% | |
0.0286 | 2.88% | |
0.00000000000088 | 3.53% | |
0.0000000043869 | 0.00% | |
0.0092 | -16.36% | |
0.0782 | -6.12% | |
0.0008250 | -0.06% | |
0.000208 | 0.00% | |
0.005136 | 4.86% | |
0.0807 | -0.12% | |
0.000000000004500 | -0.82% | |
0.02960 | 10.82% | |
0.0000000270 | 48.35% | |
0.2500 | 79.86% | |
0.0000482 | -3.41% | |
0.04499 | 10.30% | |
1.273 | -0.55% | |
0.00000397 | 39.79% | |
0.43900 | -2.44% | |
0.9995 | 0.00% | |
0.2374 | 3.58% | |
1.293 | 4.27% | |
0.001070 | 0.66% | |
0.001978 | 4.66% | |
0.299 | 2.40% | |
0.03463 | 3.10% | |
0.00000000001064 | 12.24% | |
0.001000 | -33.33% | |
1799.00 | -5.27% | |
0.000099 | 65.00% | |
0.00350000 | 0.00% | |
0.001200 | 0.00% | |
0.01806 | 5.68% | |
0.0007910 | -1.03% | |
0.0000000054 | 0.00% | |
0.01550 | 1.84% | |
0.00005182 | 0.00% | |
0.00280 | 0.00% | |
0.000706 | 7.79% | |
0.02459 | 2.80% | |
34.33 | 10.96% | |
2.365 | 2.69% | |
1.163 | 0.26% | |
0.03191 | -6.15% | |
0.0000007393 | 13.79% | |
0.0015 | -46.43% | |
0.0306 | 0.66% | |
0.0000000000000168 | 4.35% | |
0.00000341 | 3.65% | |
0.01192 | 3.20% | |
0.00000000000251 | -3.46% | |
0.0168 | 16.67% | |
0.0510 | -1.92% | |
0.00002753 | -6.71% | |
0.0006 | -45.45% | |
0.0000207 | 0.00% | |
0.00010 | 0.00% | |
8.83 | 1.96% | |
0.00000035 | 0.00% | |
4.44 | 0.23% | |
0.00000000003915 | 0.10% | |
0.00689 | 2.68% | |
0.000003156 | 3.82% | |
0.00000000001509 | -1.44% | |
0.4344 | 6.94% | |
0.0005 | -16.67% | |
0.000020 | -25.93% | |
0.000042 | -65.00% | |
0.000415 | 1.22% | |
0.968 | 0.73% | |
0.001904 | -13.30% | |
0.0892 | 8.38% | |
0.1883 | -3.53% | |
0.00027 | -3.57% | |
0.00003720 | -58.61% | |
0.1381 | 3.83% | |
0.0006219 | 7.24% | |
0.00003564 | 4.33% | |
0.008612 | -0.29% | |
0.00000000000968 | 23.94% | |
0.00000036 | -2.70% | |
0.901 | 4.89% | |
0.0000001528 | -0.26% | |
0.0006 | 0.00% | |
0.0309 | 6.19% | |
0.000000001178 | 0.00% | |
0.001000 | -41.18% | |
0.001962 | -0.05% | |
0.03315 | -0.39% | |
0.0219 | -43.56% | |
0.000168 | 41.18% | |
0.5085 | 6.31% | |
0.00000000000012 | 0.00% | |
0.00000000000215 | -5.70% | |
0.0000000198 | -20.48% | |
0.00000019857 | -0.01% | |
0.00000000076 | -5.00% | |
187.00 | 19.87% | |
0.0000363 | 19.02% | |
0.001100 | -26.27% | |
0.0000112 | 0.00% | |
0.008200 | -45.33% | |
0.2994 | 0.00% | |
0.0988 | -0.20% | |
0.004000 | 3.55% | |
0.004788 | 16.41% | |
0.000096 | -2.04% | |
0.2322 | 1.80% | |
0.04335 | -1.83% | |
0.002779 | 2.17% | |
0.000531 | -0.38% | |
0.6005 | 0.25% | |
0.06191 | -1.01% | |
0.04478 | 9.86% | |
0.0001323 | -1.71% | |
0.000000000810 | -7.43% | |
0.000057 | -27.85% | |
0.1084 | 19.65% | |
0.000027 | -25.00% | |
0.00336 | -4.00% | |
0.1108 | 0.36% | |
0.00461 | -56.39% | |
0.0000210 | 0.00% | |
0.000032 | -3.03% | |
0.002609 | 0.00% | |
0.02486 | 10.88% | |
0.000025 | -21.88% | |
0.0000164 | 0.00% | |
0.001210 | 0.00% | |
0.00000000000029 | 0.00% | |
0.001102 | 0.00% | |
0.0109 | 0.00% | |
0.00231 | 0.43% | |
0.0434 | 5.34% | |
0.003421 | -34.21% | |
0.01983 | 50.00% | |
0.00018 | 0.00% | |
0.000000012 | -40.00% | |
0.00908 | 7.58% | |
0.0000003 | 0.00% | |
2.42 | 4.31% | |
0.0009192 | 0.31% | |
0.00113 | -0.88% | |
0.0001564 | 49.95% | |
0.0083 | 84.44% | |
0.000599 | 65.01% | |
0.000039 | 44.44% | |
0.0039 | -36.07% | |
0.00000000000113 | 2.73% | |
0.00000050 | 0.00% | |
0.00000008 | 14.29% | |
0.00013050 | 0.00% | |
0.00000000017849 | -6.36% | |
0.00000005 | 0.00% | |
0.00000006 | 20.00% | |
0.0000041 | -59.00% | |
0.000882 | -1.67% | |
0.00023 | 76.92% | |
0.0471 | -3.48% | |
0.00852 | 5.71% | |
0.0360 | 2.86% | |
0.01482 | 3.35% | |
0.0005202 | 2.70% | |
0.00587 | 4.63% | |
0.6447 | 5.26% | |
0.001894 | 6.82% | |
58.5600 | 0.00% | |
0.2223 | 4.27% | |
0.0003023 | 0.00% | |
0.05877 | 3.74% | |
0.0007993 | 0.00% | |
5.851 | 1.51% | |
0.0000457 | 5.06% | |
0.0000557 | 0.00% | |
0.000012 | 0.00% | |
0.01502 | 1.62% | |
0.0000699 | 0.00% | |
0.008778 | 0.99% | |
0.0002484 | 0.24% | |
0.0765 | 1.73% | |
0.603 | 4.33% | |
0.01915 | 7.34% | |
0.5093 | 3.94% | |
1.337 | 0.30% | |
0.0921 | 3.83% | |
3.1006 | 0.00% | |
0.441 | 3.04% | |
0.3771 | 0.00% | |
0.5732 | 0.00% | |
52.060 | 0.68% | |
1.940 | 5.49% | |
2.869 | 5.83% | |
0.6625 | 9.54% | |
0.0134 | 0.00% | |
0.00000000000047 | -2.08% | |
1.0001 | 0.00% | |
3.9889 | 0.00% | |
0.000080 | 0.00% | |
0.4424 | 0.00% | |
0.0337 | 5.31% | |
0.000191 | 13.02% | |
0.9748 | 0.00% | |
0.0073 | 0.00% | |
0.3111 | 1.43% | |
0.230 | 0.00% | |
0.000100 | 0.00% | |
1.418 | 1.87% | |
0.0442 | 1.14% | |
0.2007 | 1.98% | |
0.000000002178 | 0.46% | |
0.000111478 | -3.19% | |
0.1204 | 0.00% | |
0.984 | 4.02% | |
0.004000 | 0.00% | |
0.0000985 | 0.00% | |
0.000300 | 0.00% | |
0.00035 | 0.00% | |
0.000000035 | 0.00% | |
0.00100 | 0.00% | |
0.0000101 | 0.00% | |
0.001329 | 8.76% | |
0.000990 | 0.00% | |
0.0016 | 0.00% | |
0.0000002593 | 0.00% | |
0.00001584 | 0.00% | |
0.0000001014 | 0.00% | |
0.00032989 | 0.00% | |
0.00006187 | 0.00% | |
0.000000000015 | 0.00% | |
0.001405 | 0.00% | |
0.2592 | -0.08% | |
0.001000 | 0.00% | |
0.0216 | 2.86% | |
0.0001 | 0.00% | |
0.0009 | 0.00% | |
0.00000000027 | 0.00% | |
0.00000000001604 | 0.00% | |
0.000900 | 0.00% | |
0.0000000021 | 0.00% | |
0.000000000199 | 0.00% | |
0.000000008300 | 0.00% | |
0.0071 | 57.78% | |
0.000409 | 0.00% | |
0.0022 | 0.00% | |
0.0048 | 0.00% | |
0.000405 | 0.00% | |
-- | -- | |
0.001000 | 0.00% | |
1.6799 | 0.00% | |
0.0050574 | 0.00% | |
0.00000000002387 | 0.00% | |
0.00425 | 0.00% | |
0.000118 | 0.00% | |
0.0008 | 0.00% | |
0.00050 | 0.00% | |
0.00000120 | 0.00% | |
0.00006767 | 0.00% | |
0.0025 | 0.00% | |
0.001263 | 0.00% | |
0.00166 | 0.00% | |
0.000000000136 | -8.72% | |
0.05056 | 0.00% | |
0.0000600 | 0.00% | |
0.000030 | 0.00% | |
0.000044 | 0.00% | |
0.001234 | 0.00% | |
0.0003 | 0.00% | |
0.0006 | 0.00% | |
0.0240 | 0.00% | |
0.016735 | 0.00% | |
0.000363 | 0.00% | |
0.0019 | 0.00% | |
1.0487 | 0.00% | |
0.000420 | 0.00% | |
0.03520 | 0.00% | |
0.0786 | 0.00% | |
0.00000000000541 | 0.00% | |
0.000024 | 0.00% | |
0.001104 | 0.00% | |
0.0200 | 0.00% | |
0.0087 | 0.00% | |
0.0006 | 0.00% | |
65.1101 | 0.00% | |
3.7189 | 0.00% | |
0.002955 | 0.00% | |
0.000082 | 0.00% | |
0.0035 | 0.00% | |
0.020001 | 0.00% | |
4.1000 | 0.00% | |
0.0484 | 0.00% | |
0.00005177 | 0.00% | |
0.0440 | 0.00% | |
0.053000 | 0.00% | |
4.4022 | 0.00% | |
0.0745 | 0.00% | |
0.002302 | 0.00% | |
0.001275 | 0.00% | |
0.3882 | 0.00% | |
0.001000 | 0.00% | |
0.000118 | 0.00% | |
0.0081 | 0.00% | |
0.0036 | 0.00% | |
0.1770 | 0.00% | |
0.0000897 | 0.00% | |
2.2869 | 0.00% | |
0.0005 | 0.00% | |
0.000202 | 0.00% | |
0.01459 | 0.00% | |
0.03000 | 0.00% | |
0.000946 | 0.00% | |
0.0490 | 0.00% | |
0.0096 | 0.00% | |
0.00501 | 0.00% | |
0.000046 | 0.00% | |
0.003697 | 3.79% | |
1.76670591 | 0.00% | |
0.0040 | 0.00% | |
1.4998 | 0.00% | |
0.000399 | 0.00% | |
0.6700 | 0.00% | |
0.00005 | 0.00% | |
0.000593 | 0.00% | |
0.01989 | 0.00% | |
0.0018 | 0.00% | |
0.0013 | 0.00% | |
0.2888 | 0.00% | |
0.00501 | 0.00% | |
0.01250 | 0.00% | |
0.0650 | 0.00% | |
0.00277 | 0.00% | |
1.0100 | 0.00% | |
0.010200 | 0.00% | |
0.0047 | 0.00% | |
0.88686 | 0.00% | |
0.022415 | 0.00% | |
0.1722 | 0.00% | |
0.0000063 | -4.55% | |
0.04851 | 0.00% | |
0.001790 | 0.00% | |
0.000001000 | 0.00% | |
0.00232 | 0.00% | |
0.0000008 | 0.00% | |
1.3297 | 0.78% | |
0.00274 | 0.00% | |
0.0000162 | 0.00% | |
0.0000325 | 0.00% | |
0.34150 | 0.00% | |
0.00119 | 0.00% | |
0.001021 | 0.00% | |
0.000000002 | 0.00% | |
0.00578 | 0.00% | |
0.000958 | 0.00% | |
0.00700 | 0.00% | |
0.0036 | 0.00% | |
0.0007000 | 0.00% | |
0.00200 | 0.00% | |
0.0900 | 0.00% | |
0.000513 | 0.00% | |
0.0003000 | 0.00% | |
0.00040 | 0.00% | |
0.0000000500 | 0.00% | |
0.000071 | 0.00% | |
0.001250 | 0.00% | |
0.000426832 | 0.00% | |
0.00639 | 0.00% | |
0.0400 | 0.00% | |
0.21670 | 0.00% | |
0.0000227 | 0.00% | |
0.0702 | 0.00% | |
0.00027 | 0.00% | |
0.000003240 | 0.00% | |
12.3888 | 0.00% | |
0.000128 | 0.00% | |
0.000070 | 0.00% | |
0.01428 | 0.00% | |
0.2200 | 0.00% | |
0.00091 | 0.00% | |
0.00075 | 0.00% | |
0.000179 | 4.68% | |
0.00269 | 0.00% | |
0.0000000222 | 0.00% | |
0.05513 | 0.00% | |
0.022501 | 0.00% | |
0.250 | 0.00% | |
0.791 | 3.13% | |
0.000406 | 0.00% | |
0.0120 | 0.00% | |
0.4758 | 0.00% | |
0.5124 | 3.70% | |
0.01257 | 0.00% | |
0.00250 | 0.00% | |
14.94 | 0.00% | |
0.00447 | 0.00% | |
0.4379 | 6.21% | |
0.0015 | 0.00% | |
5600.00 | 0.00% | |
0.0091 | 0.00% |