本文以配方實驗設計與神經網路來更有效率地建構多因子選股模型。本文用六個選股概念：大淨值股價比(B/P)、大股東權益報酬率(ROE)、大營收市價比(S/P)、大季報酬率、大總市值、小市場風險beta，建立加權評分法選股模型。模型中的選股概念權重可視為配方中的成份，因此採用單體形心設計(Simplex Centroid Design)得到63個實驗。再模擬回測這63個加權評分法選股模型在股市歷史資料庫的績效。本研究的股票樣本為自1990年Q4起至2010年Q3，共80季的美國所有上市股票。研究結果顯示 (1) 在概念權重與投組績效的關係中發現，股價便宜、公司獲利良好的小型股報酬較高，而公司獲利良好的個股有較高的絕對勝率、相對勝率，以及股價便宜的個股有較低的系統風險與總風險。(2) 在最大化年化報酬率最佳化模式中，大ROE和小beta概念是最重要的選股概念。(3) 在最大化超額報酬率α最佳化模式中，大B/P、大ROE與小beta是最重要的選股概念。(4) 在不同風險限制下報酬最大化最佳化模式中，當總風險限制嚴格時，選股模型以大總市值為最重要的選股概念；當總風險限制寬鬆時，以大ROE與小beta概念為最重要的選股概念。(5) 在各預測因變數的準確度方面，超額報酬率α比年化報酬率更好預測，總風險σ比系統風險β好預測，而相對勝率比絕對勝率更好預測。其原因可能是基本面分析只能選股，不能擇時。

This study used mix experimental design and neural networks to more efficiently construct multi-factor stock selection models. In this paper, we used six stock selection concepts, including large book value to price ratio (B/P), large return on equity (ROE), large sale to price ratio (S/P), large quarter return, large total market capitalization, and small systematic risk β, to build stock selection models based on weighted scoring method. The concepts of the stock selection model can be regarded as ingredients in a mix formula; therefore, we used the simplex centroid design to get 63 sets of weights. And then we simulated the 63 sets of weights under the Compustat North American version database to evaluate their performance. The backtest period is from 1990 Q4 to 2010 Q3 (80 quarters). The results show that (1) the small-cap stocks with cheap price, high company profitability has higher returns. The stocks from the company with high profitability has higher absolute winning rate and relative winning rate. The stocks with cheap price has lower systematic risk and total risk. (2) In the optimization model maximizing the annualized rate of return, the concepts of large ROE and small beta were the most important concepts of stock selection. (3) In the optimization model maximizing the excess return α, the concepts of large B/P, large ROE, and small beta, were the most important concepts of stock selection. (4) In the optimization model maximizing the annualized rate of return under different risk constraints, when the risk constraints are very strict, the concept of large total market value was the most important concept of stock selection; when the risk constraints are very loose, the concept of large ROE and small beta were the most important concepts of stock selection. (5) In the terms of prediction accuracy of various dependent variables, the excess return alpha is more accurate than the annualized rate of return, the total risk is more accurate than the systematic risk (beta), and the relative winning rate is more accurate than the absolute winning rate. The reason may be that the fundamental analysis can work well for stock selection, not for market timing.

第一章 導論 1
1-1 研究動機 1
1-2 研究方法 2
1-2-1 證券投資決策系統 2
1-2-2 配方實驗設計 (Mixture Design) 3
1-2-3 以配方實驗設計建構證券投資決策系統 3
1-3 研究內容 4
第二章 文獻回顧 6
2-1 前言 6
2-2 選股因子之研究 6
2-3 實驗計畫法與神經網路 9
第三章 選股因子權重與績效之實驗模擬 11
3-1 前言 11
3-2 績效指標 11
3-3 因子篩選 12
3-4 實驗設計 14
3-5 實驗實施 15
3-6 績效的正規化 18
3-7 選股模型與績效之間的關係之持續性 18
第四章 選股因子權重與績效之模型建構 21
4-1 前言 21
4-2 訓練與測試data的分割：移動時框法 21
4-3年化報酬率平均值之神經網路模型 23
4-4季報酬率alpha值之神經網路模型 24
4-5季報酬率beta值之神經網路模型 26
4-6季報酬率標準差之神經網路模型 27
4-7季報酬率絕對勝率之神經網路模型 28
4-8季報酬率相對勝率之神經網路模型 29
4-9 結論 30
第五章 選股因子權重與績效之參數優化 31
5-1 前言 31
5-2模式一：無限制下各目標最佳化 31
5-3模式二：不同風險限制下報酬最大化 34
5-4 模式三：不同風險限制下報酬最大化，並限制總市值因子的權重≧0.5 37
5-5模式四：不同市值因子權重限制下報酬最大化 38
5-6 結論 40
第六章 選股模型最佳化之實證 42
6-1 前言 42
6-2 模式一：無限制下各目標最佳化 42
6-3 模式二：不同風險限制下報酬最大化 48
6-4 模式三：不同風險限制下報酬最大化，並限制總市值因子的權重≧0.5 55
6-5 模式四：不同市值因子權重限制下報酬最大化 62
6-6 結論 69
第七章 結論與建議 71
7-1 結論 71
7-2 建議 72
參考文獻 74

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