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研究生： 彭婕妤
Chieh-yu Peng
論文名稱： 資產配置的學習效果與其實證研究
The learning effect of an asset allocation and its empirical study.
指導教授： 繆維正
Wei-cheng Miao
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
畢業學年度： 95
語文別： 中文
論文頁數： 49
中文關鍵詞： 短視近利權重 、資產配置 、動態規劃
外文關鍵詞： asset allocation, myopic weight, dynamic programming
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    • 本研究旨在探討只有一個風險資產與一個無風險資產所構成的簡單的投資組合，隨著時間的變化，投資在風險資產上的權重(weight)應該如何選擇，才可以使投資者在投資期間做適當的資產配置，使投資者的期末期望效用最大化。在本文中，我們主要是探討投資人除了在期初做資產配置之外，在到期前的各期也可根據所獲得的先驗資訊，重新更改原有的投資組合。此外，我們運用動態規劃(dynamic programming)與貝式模型的觀念來學習投資在風險資產上的短視近利權重(myopic weight)。實證的部分採用臺灣加權指數、日本Nikkei 225指數與美國S&P 500指數的報酬率，觀察後驗分配的平均數、變異數與投資在風險資產上的短視近利權重隨著時間經過所產生的變化。

    The purpose of this paper is to investigate a simple portfolio problem with one risky asset and one risk-free asset: how we choose the weight on the risky asset in order to maximize the expected utility.We consider an investor who rebalances his portfolio continually as more and more information is acquired till the end of the investment horizon. In particular,the investor learns about the parameter values via a Bayesian model and determines the portfolio weight by dynamic programming principle.Empirically,we adopt the return of Taiwan Stock Index,Nikkei 225 Index and S&P 500 index to see the mean and variance of the posterior distribution and the weight on the risky asset as time passes.

    1. 研究動機........................................................................................................................................1 2. 文獻回顧........................................................................................................................................2 2.1 平均變異數最佳化（Mean-Variance Optimization，MVO）....................................................3 2.2 戰術性資產配置（tactical asset allocation）...............................................................................4 2.3 動態規劃（Dynamic Programming）..........................................................................................5 2.4 貝式模型在投資組合上的選擇與修正.......................................................................................6 2.5 無資訊先驗分佈（non-subjective prior）...................................................................................8 2.6 常態貝式估計（Normal Bayes estimators）之分佈..................................................................13 3. 投資者的決策問題.......................................................................................................................15 3.1 離散時間.....................................................................................................................................15 3.2 連續時間.....................................................................................................................................18 3.2.1 風險資產上的短視近利權重..................................................................................................18 3.2.2 風險資產上經由學習所得到的權重......................................................................................22 4. 實證研究與模擬...........................................................................................................................27 4.1 資料來源與檢定.........................................................................................................................27 4.1.1 資料來源..................................................................................................................................27 4.1.2 檢定資料的常態性..................................................................................................................31 4.2 日本Nikkei 225指數...................................................................................................................32 4.2.1 採用先驗分佈與非主觀先驗分佈,平均數與變異數的後驗分配的參數的變化.................32 4.2.2 變異數已知與未知時短視近利的風險資產投資比重的差異..............................................33 4.3 模擬日本Nikkei 225指數............................................................................................................35 4.3.1 採用先驗分佈與非主觀先驗分佈,平均數與變異數的後驗分配的參數的變化..................35 4.3.2 變異數已知與未知時短視近利的風險資產投資比重的差異.36 4.4 美國S&P 500指數......................................38 4.4.1 採用先驗分佈與非主觀先驗分佈,平均數與變異數的後驗分配的參數的變化.............................................38 4.4.2 變異數已知與未知時短視近利的風險資產投資比重的差異.39 4.5 模擬美國S&P 500指數..................................41 4.5.1 採用先驗分佈與非主觀先驗分佈,平均數與變異數的後驗分配的參數的變化.............................................41 4.5.2 變異數已知與未知時短視近利的風險資產投資比重的差異.42 4.6 日本與美國結果的比較.................................44 5. 結論..................................................46 參考文獻.................................................47

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