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證 券分析之計量化技術指標

∼ 2019輔仁大學 股票投資模擬競賽 ∼

王冠倫12

國立臺灣大學

民國 108 年 10 月 23 日

1電子信箱:polyphonicared@gmail.com

2個人網站:https://www.csie.ntu.edu.tw/∼d06922002/

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

自我介紹

研究興趣:

時間序列模型

仿真建模投資組合選取 主要應用:

多資產即時交易

尋找資產間長期均衡

建構可控風險投資組合 目前議題:

共整合檢定 結構性變動分析 均值回復機率之估計

(2)

柴比雪夫的啟示

柴比雪夫不等式 [33]

任意給定 r ∈ N, r > 0,令一隨機變數 Xt且其 E[|X |r]存在。那 麼,對於任意的 c ∈ R 與  > 0,我們有

Pr [|X − c| ≥ ] ≤ E [|X − c|r]

r . 柴比雪夫不等式 (r = 2, c = E[X ])

令有一隨機變數 Xt其變異數有限 (Var[X ] < ∞),則對於任意 的  > 0,我們有

Pr [|X − E[X ]| ≥ ] ≤ Var[X ]

2 .

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

比較同策略僅持倉差異 (1/2)

單位時間下期望報酬為 µ,變異數為 σ2。 總時間為 T ,持倉時間 ∆t1, . . . , ∆tN。 每次報酬 X1, . . . , XN

報酬期望值 ∆t1µ, . . . , ∆tNµ 變異數 ∆t12σ2, . . . , ∆tN2σ2 均時報酬:

平均單位時間報酬 µ≡PN

n=1Xn/T 平均單位時間報酬期望值 E[µ] = µ

平均單位時間報酬變異數 Var[µ] = σ2PN

n=1∆tn2/T2

(3)

比較同策略僅持倉差異 (2/2)

考慮持倉時間均等,則柴比雪夫告訴我們如下:

Pr

"

PN n=1Xn

T − µ

≥ 

#

≤ σ2PN n=1∆tn2

T22 = σ2 N2.

考慮兩策略 X 與 Y ,且 NX > NY,則策略 Y 的平均報酬較不具 有參考性。

同時,我猜測這場比賽如果參加者夠多,則第一名可能是持有期 間較長者或是風險較高者。

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

風險與報酬的兌換性

Figure:風險與報酬

(4)

夏普比率比較好?

夏普比率 (Sharpe ratio) 為一種常見的績效衡量方式,且考 慮風險與報酬的兌換性 [5]。

定義為每單位總波動下的超額報酬,即 S ≡ ¯R/σ。

藉由基本定價方程 (basic pricing equation) 可推論出夏普比 率,意味著夏普比率應適合套用於具有特定效用函數的個人 之上 [8]。

股權溢價之謎 (equity premium puzzle) 的實證顯示夏普比率 仍然有問題 [34]。

風險–報酬的兌換率於風險較高時有較好的兌換比。

未考慮持有期間長短差異。

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

股票市場的困難點 (1/2)

非線性 (non-linear) 與非平穩 (non-stationary) [4]

政治事件、市場新聞、營收報告及國際事件等等 [50]

效率市場假說 (efficient market hypothesis) [5]

弱式 (weak-form)

股價充分反映了過去所有的歷史訊息,包括各種已發生的交 易資訊,如過去的成交價、交易量或短期利率水準等。

半強式 (semistrong-form)

股價已反映所有與公司前景有關的即時公開訊息。

強式 (strong-form)

股價已反映所有與公司有關的訊息,甚至包括內線交易。

相對優勢交易規則 (relative strength trading rules) 無效 [21]

(5)

股票市場的困難點 (2/2)

西元 2000 年時,全球頂尖學術期刊《Fiance》甚至對於技術分析 有如下評論 [32]:

關於基本面分析與技術分析之不同,

如同天文學與占星術的差異一般。

It has been argued that the difference between fun- damental analysis and technical analysis is not unlike the difference between astronomy and astrology.

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

股票市場的希望

基本面分析在半強式下仍然有效 [35, 41]。

技術分析具有輔助效果 [6, 18, 32, 45]。

部分技術分析有效。

如,動量交易 (momentum trading) [1]。

嘗試跨領域結合。

用類神經網路 (neural networks) 改善技術分析 [9]。

類神經網路適合小範圍數據處理 [11, 50]。

總體經濟學 (macroeconomic) 數據預測方法與技術分析結

合 [39]。

市場互動技術分析 (Intermarket Technical Analysis) [36, 37]。

以某個市場的資訊分析另一個市場的狀況。

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策略類型的差異

策略 時效 滑價 獲利 獲利趨勢 風險

均值 無 低 低 穩定 低

趨勢 有 高 高 下降 高

Table: 均值回復策略 (mean-reverting strategies) vs. 趨勢型策略 (trend trading strategies) [55]

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

應 用原則與常見判斷依據

應用原則 [52]

選擇適當的技術指標

建立各種技術指標買賣紀錄

時常檢視各種技術指標的使用結果 擬定投資策略及資金管理模式 定期評估投資績效

常見判斷依據 [52]

技術指標交叉點

技術指標上下限值的範圍 技術指標走勢圖

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技術指標分類–描述與刻度

長期 中期 短期

價格 MACD, SAR, BIAS, DMI, RSI, 當日分時走勢圖、

AR, BR, MA TOWER, MTM, 3-6日BIAS, KD, OSC, Qstick, CMO, WMS%R, Kinder%R, CCI Stoch, RSI, CDP 交易量 逆時鐘曲線、 VR, OBV, VAM, VR, OBV, VAMA,

成交量移動平均線 EOM, FI, VK EOM, FI, VK

時間 股市週期循環 ? ?

市場寬幅 ? ADL, ADR, PSY, OBOS ARMS Index, MT,

TO

其他 ? 融資融券餘額表 委託成交筆數(分)、

張數及成交值表、

當日沖銷比例 Table:技術指標分類 [52]

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

技術指標分類–方法與技術 [16]

方法 (methodology)

支援系統 (decision’s support trading system) [7, 12, 46]

計算技術 (computational technique) [56]

圖表型態 (chart patterns) [40, 42]

技術 (operational tools)

隨機線 (stochastic line) [4, 30]

相對強弱指標 (relative strength index) [22, 30, 46]

基因演算法 (genetic algorithm) [7, 9, 12, 38]

加強增強學習 (evolutionary reinforcement learning) [2, 48]

統計分析 (statistical analysis) 移動平均 (moving averages) [47, 49]

計量經濟學模型 (econometric models) [25, 43, 53]

類神經網路 (neural network) [9, 11, 50, 57]

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技術分析前提與調整 (1/6)

布林通道 (Bollinger Bands, BBands) [54]

令一投資組合 A 價格 PriceA(t),定義簡單移動平均

MA(t; N) ≡ 1 N

t

X

t0=t−N+1

PriceA(t)

與其於時間 t 時,近 N 筆之樣本變異數序列為 σ2N(t)。在給定了 簡單移動平均線樣本數 N (觀察範圍) 與標準差數量 K (軌道寬 度)下,BBands 可定義三條軌道 (線) 如下:

middleBB(t) ≡ MA(t; N)

lowerBB(t) ≡ middleBB(t) − K σN2(t) upperBB(t) ≡ middleBB(t) + K σN2(t).

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

技術分析前提與調整 (2/6)

Figure:布林通道 [24]

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技術分析前提與調整 (3/6)

布林通道 (Bollinger Bands, BBands) [54] –續

證券於時間 t 之股價分布有一隨機分佈 D(t),而三條軌道則 提供一個參考範圍。

該 D(t) 應為對稱分佈,或其通常股價範圍應為該二軌道之 間,而於兩軌道區間外則為罕見事件。

分析與調整 [54]

lowerBB(t)與 upperBB(t) 一起向上 (或向下) 調整是可行 的 (兩軌道調整幅度並不一定相等)。

認為分佈不對稱,可對單一軌道或多個軌道進行修改。

middleBB(t)與 σN2(t) 可以替換。

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

技術分析前提與調整 (4/6)

布林通道 (Bollinger Bands, BBands) [54] –續

PriceA(t0) ≥ upperBB(t0) =⇒ PriceA(t1) ≤ middleBB(t1) PriceA(t0) ≤ lowerBB(t0) =⇒ PriceA(t1) ≥ middleBB(t1) 分析與調整

有限時間均值回復

再增加一個上下軌進行停損

藉由計量經濟學模型預測回復時間

無法有效加碼進場 均值趨勢影響獲利

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技術分析前提與調整 (5/6)

注意事項 估計參數

以報酬為目標可能導致交易過長或曝險過高等 回測與未來上線使用獨立

布林通道未描述跨時間變化 直接使用效果差

不如買進持有 [28]

比移動平均差 [29]

反過來交易效果卻意外地不錯 (因單一標的多為趨勢) [28]

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

技術分析前提與調整 (6/6)

所有的方法都有自己前提 以方法的意圖著手修改與改良 必要時使用其他領域技術解釋 需具體描述投資人需求

不是每一種投資人都適用一樣的技術分析

進化

參數藉由類神經網路優化

跨時間變化藉由計量經濟學模型描述 均值回復前提藉由建構投資組合完成

(11)

常 見缺點真的是缺點?

常見缺點 [52]

技術指標間常矛盾

不同指標前提不同自然會矛盾。

資料過期

估計需求樣本,以防使用過久以前的資料。

說服力低

使用統計分析評估可信度,如多重檢定方法。

歷史不一定重演

考慮使用具有時間序列的方法,如傳統的計量經濟學。

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

上市股價分佈 (1/2)

(a)全體股價分佈 (b) 150元以下股價分佈

Figure: 民國107年股價分佈

(12)

上市股價分佈 (2/2)

最小 5% 10% 50% 90% 95% 最大 價格 1.71 8.13 10.08 26.24 94.65 147.43 3940.2

(a)價格分位表

1萬 2萬 5萬 10萬 20萬 30萬 50萬 分位 10% 38% 73% 90% 97% 98% 100%

(b)投資分位表 Table: 分位表

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

組合的好處

讓風險成為可控

特定組合方法可有效避免市場風險 (market neutral) 特定市場甚至可以達成零本金 (money neutral) 達成現有交易策略的前提

對投資人偏好客製化投資組合 (下頁圖)

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投資流程 (1/3)

定 投 資 策 略 發 展 投 資 決 策 製 作 投 資 組 合

Figure: 投資流程圖 [14]

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

投資流程 (2/3)

確 認 條

限制 偏好 目標

形成策略

環 境 考 量

市場預期 資金配置

發展策略

挑 選 配 件 完 成 組 合

選擇工具 挑選時機

多角化 需要?

Figure: 投資流程圖 [14]

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投資流程 (3/3)

投資人的目標、限制與

偏好的規範及量化值 投資組合的方針與策略 監測影響投資人進 行投資的相關因素

建構及修正投資組合,

包括資產配置、投資 組合最佳化、有價證券

的挑選、轉換及買賣

量投資績效表現 以達成投資人目標

監 測 影 響經濟與 市 場 的 相關因素 資 本市 場 的預期

對經濟、社會、政治 及產業的各種考量

Figure: 投資流程圖 [5]

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

組合範例

考慮單因子如下

priceA(t) = βA0+ βA1factor(t) + A(t) priceB(t) = βB0+ βB1factor(t) + B(t) 顯然存在組合消除因子

priceC(t) ≡ βB1priceA(t) − βA1priceB(t)

= (βA0βB1− βA1βB0) + (βB1A(t) − βA1B(t))

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配對 交易的類型 [26]

距離 (distance) [13, 17]

共整合 (co-integration) [44, 51]

時間序列 (time series) [10, 15]

隨機控制 (stochastic control) [23, 31]

機器學習 (machine learning) 與綜合預測 (combined forecasts) [19, 20]

耦合 (copula) [27, 44]

主成分分析 (principal components analysis) [3]

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

組合+技術指標

Figure:共整合+布林通道

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策略的測試

以組合各種模型測試現有策略,用以了解該策略不適用的場合。

迴歸:y(t) = X (t)β + (t)

平滑移動迴歸:y(t) = X (t)(tβ/T ) + (t)

向量自我迴歸:y(t) = µ(t) + Ppi =1Aiyt−1 + (t) ν(t) = 0, ν, ν1+ ν2t, . . ..

結構性變動:

(y (t) = f1(t) + (t), t ≤ t y (t) = f2(t) + (t), t > t

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

測試 範例

以測試 共整合+布林通道 於具趨勢的自我迴歸上為例。

以向量錯誤修正模型估計自我迴歸係數 加入趨勢項於向量自我迴歸模型之中 隨機生成股價

拿現有策略應用並觀察報酬

若有淨利,則適用所加入之趨勢。

若有虧損,則不是用該情況。

詢問該情形出現時,是否有對應的處理方式。

如,即時停損或替換執行新的策略。

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Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

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Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

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Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

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[24] Kabasinskas, A. and Macys, U. (2010). Calibration of Bollinger bands parameters for trading strategy development in the Baltic stock market. Inzinerine Ekonomika-Engineering Economics, 21(3):244–254.

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[31] Liu, J. and Timmermann, A. (2013). Optimal convergence trade strategies. Review of Financial Studies, 26(4):1048–1086.

Kuan-Lun Wang Introduction to Technical Analysis

Chebyshev Technical Pairs References

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