Daily Volatility

ver the flight to Taiwan, I tried looking at the relationship between price and volatility by looking at price, price+1, intraday high minus low, and 20 day moving average of daily volatility using 30 minute intraday data of SPY.

I first check if there’s any follow through on up and down day with daily volatility higher than two standard deviations.

There are 25 instances of up days which have volatility two standard deviation higher than 20 day moving average of volatility (V>V20) out of 2007 days since 2002. Out of 25 instances, 2 instances occurred in January 2007, 5 instances are from July 2002 to October 2002, 12 instances are from September 2008 to February 2009 which coincides with the steepest drop in recent market history. My take on this phenomenon is that once market becomes hectic, the madness will continue for a while. A true longer term bottom will not be put in on a day of huge rally; extreme up days are rare in a market that’s truly going up. On days with high volatility, 52% is followed by up day. The number is really too low to provide any useful information.

The above chart show volatile up days and SPY daily close price plotted on the same chart. From the chart, it is very clear that in recent market history volatile days (even up days) are associated with weak market.

There are 32 instances of down days which have volatility two standard deviations away from the V20 in the negative side. Out of the 32 instances, 2 instances are from July 2002, 6 instances in second half of 2007, and 19 instances are from September 2008 to April 2009. The extreme negative data also supports the hypothesis that days deviate from the volatility means tend to appear near each other. Out of the 32 instances, 56.2% closed higher than the next day. Once again, the number is really too low be of any significance. However, this finding does confirm with earlier hypothesis that extreme weakness tends to be followed by short term bounce rather than more immediate weakness.

I split data into tow group of V20>2%, and V20>1%, but doing so have not yield much useful data so far.

Movement after Extreme Strong and Weak Day

In the previous two posts I talked about average movements after 1, 3, 5, and 10 days after extreme strong and weak days separately. Here is a chart comparing the result from the posts.

In the chart, red bars red bars represents average movement after extreme weak days and green bars represent what happen after strong days.

From the chart, it is very clear that market tends to consolidate immediately after extreme strength, attempts follow through, reverse after follow through, and eventually value being accepted.

However, market tends to bounce back immediately after extreme weakness and slowly giving back the retracement after the immediate bounce.

From the historical data, the best time to enter long position is after an extreme weak day. As the chance of immediate bounce on the day after is nearly 60%. How does this information help me? Seeing weakness following an extreme day, I imagine that knowing the historical tendency would help me placing a trade against the immediate trend to secure good location and ride out the bounce.

Relevant posts:
<What Happens To SPY After Extreme Weak Day>
<What Happens To SPY After Extreme Strong Day>

What Happens To SPY After Extreme Weak Day

After looking at what happen after a strong day, let's look at what happen after an extreme weak day.

An extreme weak day in this case is defined as a drop more than -2.28%. From 2000, there have been 58 occurrences such drop took place.

• Next Day: SPY average 0.57%, 24 (41.38%) down, 34 (58.62%) up. Down day with average of -1.74%, and up day with average of 2.20%.

• 3 Days later: SPY average 0.58%, 26 (44.83%) down, 32 (55.17%) up. Down days with average of -3.16%, and up days with average of 3.62%.

• 5 Days later: SPY average 0.51%, 28 (48.2%) down, 30 (51.72%) up. Down days with average of -4.1%, and up days with average of 4.82%.

• 10 Days later: SPY average 0.42%, 26 (44.83%) down, 32 (55.17%) up. Down days with average of -5.5% and up days with average of 5.23%.

From this simple test, it is very clear that farther weakness is not likely to follow extreme weakness even when stretched out to 10 day move. The observation holds true even in the drop lasted from 6/6/2008 to 4/20/2009. The day after extreme drop has average gain of 0.5% in the period, only when zooming out to 5 days or more the down trend is clear.

What Happen To SPY After Extreme Strong Day

從學習交易以來，我一直把 Dr. Steenbarger 當成是模仿的對象，再來這一系列的文章是以 Dr. Steenbarger <Consecutive Narrow Days: What Comes Nex> 這種文章為範本，來探討 SPY ETF 的特性。

利用 1/2/2002 到 12/18/2009 每日歷史資料 N=2007，我們來看看當 S&P 上漲超過 2.28% 後，再來 1, 3, 5, 10 天的表現。會選擇 2.28% 是因為它剛好是 2 standard deviations from absolute value of daily move，在過去七年來這種情形發生了 50 次：

• Next Day: SPY average -0.01%，20 (40%) down, 29 (58%) up，1 (2%) flat. Down day with average of -1.67, and up day with average of 1.14%.

• 3 Days later: SPY average 0.46%, 21 (42%) down, 29 (58%) up. Down days with average of -3.31%, and up days with average of 3.19%.

• 5 Days later: SPY average -0.4%, 27 (54%) down, 23 (46%) up. Down days with average of -4.2%, and up days with average of 4.06%.

• 10 Days later: SPY average 0.29%, 21 (42%) down, 29 (58%) up. Down days with average of -5.68% and up days with average of 4.27%.

From the first glance, strength seems to have follow through in the immediate three days after the big move, peters out after stretched out to five days, and gaining back strength after ten days.

Cumulative TICK 的研究

NYSE 指標當中有一個叫做 TICK 的東西，它是 NYSE 股票交易在 uptick 和 downtick 的差別，一搬來講它的值在 1000 到 -1000 中，而 cumulative TICK 則是把一分鐘內 TICK 的高、低、收三個值的平均值加起來的總合。

我採用的資料是 4/30/2007 到 11/20/2009 647 天的一分鐘 TICK 。而這個研究的目的是要看是否能用前十五分鐘 cumulative TICK 來判斷今天是否會成為 trend day。

首先我先算 median，standard deviation (stdev)；

• median = 143, mean = 106
• stdev = 2882
• 1 stdev up = 3025, 1 stdev down = -2739

以這個數據我假設說假如 8:45 分 cumulative TICK 在 1 stdev 以上 SPY 收盤的價錢也應該是同樣的方向。

首先我們先來看 TICK 為正數的天數，以下這個 table 可以看的出來 TICK 在過去兩年內，市場是比較偏向於 mean reversion，當 cumulative TICK 超過 1 stdev 但是沒有超過 4000，市場當天上漲的機會比下跌的機會多，但是下跌的幅度比較大。 TICK 必須超過 4000 才勉強算是有 small edge，不過發生的機率實在太低了。

	Close Higher	Close Lower	Winning %	Average % Change	Positive Average % Change	Negative Average % Change
Less Than 4000	29	26	52.73%	-0.12%	0.95%	-1.28%
4000 ~ 5000	13	8	61.9%	0.16%	1.01%	-1.34%
5000 ~ 6000	12	7	63.16%	0.47%	1.29%	-0.92%
6000 ~ 7000	7	1	87.5%	1.49%	1.73%	-0.22%
7000 ~ 8000	1	0	100%	1.10%	1.10%	0

在來我們看看假如 cumulative TICK 是 1 stdev 往負數的結果。在以下這個表裡，我們可以再次看到市場 reversion to means 的傾向，市場在 cumulative TICK 沒有達到 -4000 的情況下，當天不但上漲的機率較高，上漲的百分比也較多。

	Close Higher	Close Lower	Winning %	Average Change %	Positive Average % Change	Negative Average % Change
Greater Than -3000	8	4	33.33%	1.11%	1.96%	-0.59%
Neg. 4000 ~ 5000	8	13	61.90%	-0.42%	1.20%	-1.41%
Neg. 5000 ~ 6000	5	15	75%	-1.17%	2.43%	-2.37%
Neg. 6000 ~ 7000	1	6	85.71%	-1.04%	0.9%	-1.37%
Neg. 7000 ~ 8000	0	4	100%	-2.29%	0	-2.64%

依照這次的數據，於是我又發展了兩個簡單的交易規則：

• Cumulative TICK 在 8:45 AM 之前達到 -4000 或 4000，除非當天有新聞公佈，continuation 可能性較高。
• Cumulative TICK 若未在 8:45 AM 達到 -4000 或 4000，除非當天有新聞公佈，reversion 可能性較高。

Advance Decline Line 的一些研究

Advance Decline Line 來判斷是否當天真的會有趨勢。$ADD 基本上告訴你今天上漲股票與下跌股票支的差，假如是 1500 表示今天上漲的股票比下跌的多 1500 支。 詳細的解釋可以在<財金商業科技辭典>找到。

這個週末回顧時看到 Dr. Steenbarger 部落格這篇 <The NYSE Advance-Decline Line: Identifying Trending and Range Environment>，他說的一些數據我覺得還滿值得研究的；

By the end of the first half hour of trade, again going back to October, 2008, we find that the median value for $ADD has been -346, with a whopping standard deviation of 1378. That tells us that, within the first 30 minutes of trading, much of the issue of whether or not we're in a trending environment has been sorted out. (My next post will explore this issue more specifically). If we're seeing $ADD between -1000 and +1000 by the end of the first half hour of trade, we're much less likely to be in a trending environment than if we have readings of +1500 or more or -1500 or less.

Will a break above or below a range lead to a directional, trending move? It's likely that the participation of the NYSE advance-decline line will provide some clues. If, for instance, a break above a market's opening range (say, its range for the first 15 minutes of trade) occurs with $ADD well below +1000 and with mixed sector strength, we might be much less likely to go with that move than if the breakout vaults $ADD above +1500 with strong sector participation and leadership.

也就是說 $ADD 在開盤後半小時幾乎已經成了定局，而判斷是否有突破為真正的突破則可以參考 $ADD 是否超過 1500。我用 2007 年 12/13 到 2009 年 11/13 的數字，出來的數在和史丁巴格博士得數據稍有不同，不過大致上還滿類似的。在我找到的數據裡，開盤時的 median 是 66，standard deviation 是 762，十五分鐘後 median 為 -69，standard deviation 為 1235，半小時後，median 為 -97，standard deviation 為 1217，收盤時 median 為 -3，standard deviation 為 1341。開盤十五分鐘後大局以定。開盤時 ADD 與收盤時 ADD 的 correlation 為 0.53，開盤後十五分鐘 ADD 與收盤時 ADD 的 correlation 為 0.62，

由此可見假如開盤後十五分鐘假如 ADD 超過 1200 或者小於 -1300，表示這一天趨勢還滿強的，必須要注意今天成為 trend day 的可能信還滿高的。從 2007 年十二月到今天只有 37% 的天數是從一開盤就有可能成為 trend day，所以在還未確認前假設今天是 range day，是個正確的假設。

另一個還滿有趣的數據，有 197 天一開盤的 $ADD 是在 1 個 standard deviation 之外 (>882 或者 <-697)。三十分鐘後，還能為在 882 之上或者是 -697 之下的有 82%，但是過了十一點之後只剩 62% 還在這個範圍之外。這樣表示就算一開盤的氣勢很強，但是能維持的只有六成左右，再一次確認假設為 range day 是正確的。最後，一整天都能維持在之前提到的範圍內是所有天數的 25%。 由這個 counting excercise，可以發展出兩個簡單的交易規則：

• 所有的天數有趨勢的日子不到四分之一，因為我用的趨勢定義已經很低了。
• 當 $ADD 在開盤後十五分鐘，假如超過 1200 或小於 -1314，今天發展成為趨勢日的機率有四成，比平常高。Fade the market 時要非常小心。

2X IBH 不同的獲利目標與三點停損

2X IBH 不同的獲利目標與三點停損

Instrument	Performance	Target	Total Net Profit	Max. Drawdown	Sharpe Ratio	Percent Profitable	# of Winning Trades	# of Losing Trades
ES 12-10	2.25	76	3450	-12	0.92	0.4722	17	19
ES 12-10	2.22	72	3375	-12	0.93	0.4722	17	19
ES 12-10	2.17	68	3225	-12	0.93	0.4722	17	19
ES 12-10	2.14	84	3162.5	-12	0.9	0.4722	17	19
ES 12-10	2.14	88	3137.5	-12	0.91	0.4722	17	19
ES 12-10	2.14	52	3137.5	-12	0.84	0.4722	17	19
ES 12-10	2.14	92	3137.5	-12	0.91	0.4722	17	19
ES 12-10	2.14	100	3137.5	-12	0.91	0.4722	17	19
ES 12-10	2.14	96	3137.5	-12	0.91	0.4722	17	19
ES 12-10	2.13	80	3112.5	-12	0.91	0.4722	17	19
ES 12-10	2.11	64	3075	-12	0.93	0.4722	17	19
ES 12-10	2.1	56	3037.5	-12	0.86	0.4722	17	19
ES 12-10	2.06	60	2925	-12	0.92	0.4722	17	19
ES 12-10	2.05	48	2887.5	-12	0.83	0.4722	17	19
ES 12-10	1.97	44	2687.5	-12	0.83	0.4722	17	19
ES 12-10	1.86	40	2387.5	-12	0.8	0.4722	17	19
ES 12-10	1.76	36	2087.5	-12	0.74	0.4722	17	19
ES 12-10	1.65	32	1787.5	-12	0.67	0.4722	17	19
ES 12-10	1.59	24	1537.5	-9	0.66	0.5	18	18
ES 12-10	1.54	28	1500	-12	0.58	0.4722	17	19
ES 12-10	1.58	12	1137.5	-9	0.42	0.6389	23	13
ES 12-10	1.37	20	962.5	-9	0.45	0.5	18	18
ES 12-10	1.27	16	662.5	-9	0.24	0.5278	19	17
ES 12-10	1.22	8	387.5	-12	0.15	0.6667	24	12

這張表則是今年一月到十月二十七號在 IB x2 的地方放空的結果。從這一張圖再次看到 scale-out 的重要性。獲利的多寡與 scale-out 的比率到15 S&P 點幾乎是成正比 (15 點為 60 ticks)，15 點之後則是有點看運氣了。

2X IBL 不同的獲利目標與三點停損

2X IBL 不同的獲利目標與三點停損

Instrument	Performance	Target	Total Net Profit	Max. Drawdown	Sharpe Ratio	Percent Profitable	# of Winning Trades	# of Losing Trades
ES 12-10	1.31	148	837.5	-24.25	0.1	0.3571	10	18
ES 12-10	1.3	24	675	-12	0.24	0.4643	13	15
ES 12-10	1.29	172	775	-24.25	0.1	0.3571	10	18
ES 12-10	1.29	184	775	-24.25	0.1	0.3571	10	18
ES 12-10	1.29	196	775	-24.25	0.1	0.3571	10	18
ES 12-10	1.29	160	775	-24.25	0.1	0.3571	10	18
ES 12-10	1.27	12	487.5	-9	0.27	0.5714	16	12
ES 12-10	0.85	8	-262.5	-13	-0.13	0.5714	16	12
ES 12-10	0.85	48	-412.5	-24.25	-0.12	0.3571	10	18
ES 12-10	0.83	44	-462.5	-24.25	-0.13	0.3571	10	18
ES 12-10	0.82	4	-212.5	-11.25	-0.12	0.7143	20	8
ES 12-10	0.81	40	-525	-24.5	-0.15	0.3571	10	18
ES 12-10	0.77	36	-625	-25.5	-0.19	0.3571	10	18
ES 12-10	0.73	32	-725	-26.5	-0.22	0.3571	10	18

這是在 2x IBL 做多用今年的歷史資料回測的結果，在這個回測中我固定用三點作為停損，來看那一個獲利點的損益最好。從結果中看的到滿有趣的一點，trade manage 在損益上可以造成很到的影響。效益第二好的與最差唯一不同的地方在於獲利點兩點的差別，但是這 S&P 兩點卻造成了將近一口一千六百美金的獲利差別。這個表中也可以看到 scale-out 重要的地方。效益最好的前幾名，分除了 24 這個獲利點外，其他皆是採用超大獲利點為出口。仔細看了一下交易明細，發現造成這個現象的原因是在一月二十一號有一比三十多點的交易。由此可見放長線釣大魚重要的地方。

1.5 IBL 回測

在另外一篇文章中有提到幾個使用 IB 來入場，這兩天做了更多關於這方面的回測，今天我把在 1.5 IBL 做多的會測結果放在這。

第一張圖可以很明顯的看出來在今年這將進十一個月的交易日中，1.5 IBL 這個方法在不設停損的狀況下獲得 20 ticks 的機率有 60.34%，圖裡的百分比有點標錯，就將就一下吧。這個回促的狀態並非建議大家不設停損，而是要看在這個位子放空的潛力有多少。假如一個交易法在不設停損狀況下無法賺錢的話，應該不是很值得研究。



第二張圖則是時間和勝率的表較。也就是說在建立部位後的x分鐘後清倉的話，勝率是多少。很有趣的，在三十分鐘內清倉，時間和勝率是反比。但是過了三十分鐘到一百二十分鐘，勝率和時間則成正比。所以這個交易法需要耐心。



第三張圖則是這個交易機會在每個不同時段出現的次數。F,G,H 以及 I, J 出現的次數最多次。因為新聞通常在早上會發布，所以 F,G,H 這三個時段會出現高次數並不意外，但是中午出現這麼多次數我則是有點意外。



第四張圖則是每個時段達到五點獲利的百分比。由此圖可見假如不是新聞一發布後就達到的話，早上這個交易法成功率不高。中午這數字則有點怪，I 和 J 的成功率差很多，值得更多的研究。



第五張圖則是每一個 IB的大小，交易出現次數與成功率。5-9 IB 成功率居然比 9-12 高，這點也讓我覺得非常的意外，必須花更多時間來研究是否為怪異現象。



第六張圖則是被停損的交易每一個 MFE 的比率。由這一張圖可以看的出來所有被停損的交易，只有百分之五十的機會不會達到我的第一個獲利目標，我覺得知道這一點很重要，因為在做交易時最需要的就是信心，因為我知道在今年的市場狀況下在這個位置做多，不管最後這個交易是賺是賠，我有百分之六十四的機率我一口會賺兩點，百分之五十的機率我一口會賺三點，在這麼高的機率下這個 setup 是值得使用的。

因為還是有百分之三十五的機率在這個位子或完全賺不到錢，所以要能夠真正獲利，就必須要有完善的 scale-in 以及 scale-out。

相關文章:
< 初始平衡的回測結果 >

「初始平衡」的回測結果

上週花了些時間做了些回測，以下幾張圖是以不停損只對於獲利點做最佳化的結果。這個測試最主要是看這幾個 setup 的 scale out。從這幾張圖可以看的出來這個 setup 在五點以下勝率都還算高，在五點以上則是差不多有一半的機會獲利。