由於許多資產報酬率的分配呈現厚尾的現象，因此，本文探討將最低報酬要求限制條件加入傳統的平均數╱變異數模型中，考慮在分配已知的情形下，假設資產報酬率的分配為t分配及常態分配，來求取最適的資產配置；在分配未知的情形下，利用古典Bootstrap法、移動區塊Bootstrap法及定態Bootstrap法的抽樣方法來模擬資產報酬率的分配形式，並利用模擬的資產報酬率分配求出最適的資產配置。 同時，本文亦探討資產配置在風險管理上的運用，當分配已知時，若對分配參數的估計正確，則使用的最低要求報酬率就是此資產配置的涉險值，反之，若對參數的估計錯誤時，會對資產配置產生很大的影響及風險管理上的不正確；當分配未知時，利用模擬方法來產生分配，則使用的最低要求報酬率可看成是此資產配置的涉險值。 實證部分選取資料分成本國及全球，研究發現對於何種分配或模擬方法的資產配置績效最好？沒有一定的結論。其原因是各種分配或模擬方法皆必須視資料的性質而定，因此，本論文的貢獻僅在建議使用厚尾分配及利用模擬方法，來符合資產報酬率呈現厚尾的現象，並利用此分配，以期在考慮最低報酬要求限制條件下的資產配置更為精確。 / The distributions of many asset returns tend to be fat-tail. This paper attempts to add the shortfall constraint in Mean-Variance Analysis. When the distribution is known, we find the optimal asset allocation under student-t distribution and normal distribution. On the other hand, we use Classical Bootstrap, Moving Block Bootstrap, and Stationary Bootstrap to stimulate the distribution of asset return, and to obtain the optimal asset allocation. We also examine the risk management of asset allocation. When we use the correct estimators of parameters under the known distribution, the threshold in shortfall constraint is the value-at-risk in asset allocation. Otherwise, if using the wrong estimators, we get the incorrect asset allocation and the improper risk management. When the distribution is unknown, using simulation to generate the distribution, the value-at-risk is the threshold. The empirical study is conducted in two parts, domestic and global asset allocation. The results cannot point out which distributions and simulations are suitable. They depend on the data’s property. The contribution of this paper is to introduce some methods to fit the fat-tail behavior of asset return in asset allocation.

資產配置乃是將資金分散投資到主要的資產類別中，諸如股票、債券、現金等。傳統的均數/變異數方法在資產配置上早已被廣泛的運用。但是，現今的金融情勢多變，多期配置的需求提高，傳統均數/變異數方法只處理單一期間的資產配置，且反應未來的能力不佳，顯然已經不適用。 本論文提供一種多期動態的資產配置，可以改良過去單點估計值的缺點，同時能夠將未來情境納入考量，使多期資產配置更富策略性。並實證在兩期的情況下，期中調整資產組合與不調整的差異性。從而瞭解持續的動態規劃，方能提升資產配置的效率性。 / Asset allocation is the process of dividing an investment fund among major asset classes such as equities, bonds, cash, etc. Traditional mean-variance portfolio selection is widely used for asset allocation. However, as time goes by, the financial condition changes rapidly. The method of mean-variance analysis has some limitations. It not only can’t deal with multiperiod asset allocation, but also cannot reflect future economic circumstances, especially for long-term investments. This research tries to use the method of multi-stage dynamic programming for asset allocation. This method can improve the pits of single estimate in using mean-variance analysis, and take future scenarios into account so that the model will become more useful in practice. The two-period empirical results have shown that using continuous dynamic programming to build strategic asset allocation decision can improve the efficiency of asset allocation.

本研究主要探討資產組合是否應隨著景氣循環進行調整的實證，並觀察在不同的景氣狀態下，各類資產的投資報酬率、投資風險、資產間相關係數與配置比例變化情形。實證結果發現： 在投資報酬率分析方面，在景氣時期，權益型資產的投資報酬率確實高過債券型資產的投資報酬率；相對地，在不景氣時期，權益型資產的投資報酬率就低於債券型資產的投資報酬率。再者，權益型資產在景氣時期的投資報酬率的確比不景氣時期的投資報酬率要高。債券型資產雖然在景氣時期的投資報酬率稍微高過了不景氣時期的報酬率，不過高出的差異並不顯著。 在各資產的投資風險分析方面，在本研究中大部分各資產在不景氣時期的標準差都顯著地高過景氣時期的標準差兩倍左右，代表在不景氣時期，投資組合的避險效果較差。 在報酬率相關係數分析方面，權益型資產間的相關程度比其與債券型資產的相關程度來得高，且資產間的相關程度在景氣時期較低、在不景氣時期較高，這代表在不景氣時期多角化投資的避險效果較差，在景氣時期多角化投資的避險效果較好。 在資產配置比例分析方面，在景氣時期，投資組合內權益型資產的配置比例較高；在不景氣時期，投資組合內債券型資產的配置比例較高。 此外，經由本研究實證結果可得到一個較特別的發現，不論是國內或國外的權益型資產，在納入投資組合前除了要注意其與國內景氣循環的相關程度要較低之外，還要不違背「權益型資產在景氣時期的投資報酬率比不景氣時期的投資報酬率要來得高」及「權益型資產在景氣時期的投資報酬率比債券型資產的投資報酬率要來得高；且債券型資產在不景氣時期的投資報酬率比權益型資產的投資報酬率要來得高」的原則，如此才能真正達到納入國外資產至國內資產組合中以趨避國內系統風險的目的。

本研究針對退休基金管理的兩項重要議題：提撥政策與資產配置作最適規劃之探討。由於傳統退休基金的評價僅考慮單一期間的離散時間模型，不若多期規劃的效率性，因此，本研究考量連續時間下，利用控制理論觀點，將提撥金額與資產配置視為可調節的因子，以風險最小化為最適定義，提供基金多期管理的有效方法。 首先，為充分反映退休基金管理時所面臨的不確定因素，本研究假設資產價值服從幾何布朗運動，並且經由隨機微分方程式描述退休基金所累積資產與應計負債的動態隨機性質。其次，考量基金管理所面臨的提撥風險與清償風險，給定能夠量化這些風險的評估測度，藉以監督退休基金於管理期間的經營績效，並且利用Bellman方程式求出最適的基金提撥與資產配置策略。 最後以勞動基準法規範下的企業退休金計劃為實證對象，透過動態模擬估計模型中之參數，並且利用數值方法求出所需的函數值，將控制理論與情境模擬連結，藉以檢視現行固定給付退休基金之最適策略。由實證結果可知，透過本研究的方法的確可以有效管理基金同時符合財務清償能力的要求。利用動態規劃所得的最適策略與給定的風險評估函數相關，因此，基金決策者可以依據基金的特性給定適當的風險評估函數，依照不同的投資期限擬定合適的基金策略。 / This study explores two critical issues in pension fund management: funding policy and asset allocation. The traditional valuation of pension fund is restricted in one-period setting under discrete-time framework, and it is not efficient comparing to the continuous-time models. Therefore, in this study, control theory is employed to obtain the optimal strategy based on a specific plan dynamics. Employer's contributions and investment proportions are treated as the controllers in our model. Optimal solutions are obtained by minimizing the given risk performance in monitoring the multi-period fund management. First, the stochastic differential equations are constructed to describe the dynamics of the funding levels and the accrued liabilities. Geometric Brownian motions are used to model the assets held by the fund manager. Secondly, a stochastic control model with given risk measurement is formulated in a continuous-time framework to investigate the optimal decisions. In our approach, the plan's normal costs and accrued liabilities are simulated through plausible scenarios while the optimal contribution and asset allocation are solved through Bellman equation. At last, a specific pension scheme under the regulation of the Taiwan labor standards law is studied for numerical illustrations. A monitoring mechanism linking plausible scenarios and the closed-form solutions are employed to scrutinize the funding policy and asset allocation. The optimal strategies are estimated through dynamic programming under realistic workforce scenario. According to the result, it shows that the methodology in this study can assist the fund manager in obtaining the plan's financial soundness. Meanwhile, the optimal strategy can fully incorporate the given risk measurement. Hence, the policy maker can input certain managerial considerations into the performance measure to investigate the stability and solvency issues.

我們利用「台灣地區中老年身心社會生活狀況長期追蹤調查研究」這份資料，以似無關迴歸(Seemingly Unrelated Regression)模型，探討老人的資產持有行為，發現：一般老年人口並不偏好持有股票，持有行為相當少見，但高教育、高所得、都市化地區（尤其是直轄市）的老人，可能分別因為高教育程度、所得效果影響、都市地區資訊流通快速等因素，使得這類型老人明顯較願意持有股票。 另一方面，在台灣，不動產扮演的角色特殊，傳統認為其與家族宗系連結，在持有行為上並非只從風險報酬觀點去看待，通常還與其他考量有關，因此在持有行為上有其特殊模式。 同時，我們也發現，老人婚姻關係的消解(dissolution)，例如離婚/分居，將對資產持有產生負面的財富效果影響，使得這類型老人各項資產的持有都顯著低於已婚/同居的老人；而健康情形越差的老人持有的不動產與存款也越少，應與此類老人有較高的醫療與保健支出，造成負面的財富效果有關。 除此之外，台灣老人平均而言，持有的不動產會隨年紀降低，但持有的存款會隨年紀而上升，主要與台灣老人隨著年紀上升，所得逐漸不足以維生，產生了反儲蓄(dissave)不動產的現象，有所關聯。我們認為台灣確實存在老人「以房養老」的現象。 最後，我們認為很重要的一點是，台灣老人資產的持有行為，並不是使用傳統的風險報酬概念就能解釋，我們必須考量其他可能因素，才能有效分析台灣老人所表現出來的資產持有行為。 / The general elders don’t prefer to hold stocks, but the elders of high-level education, the elders of high-level income and the elders in metropolis are more willing to hold stocks. Besides, the real estate plays a special role. People regard that it is linked up with the family or kindred. We also find out that the dissolution of relationship in elder’s marriage causes negative wealth effect on holding assets. The similar effect exists in much unhealthy elders. The elders hold less real estate as they getting older, but hold more stocks. It might due to that elders dissave their real estate. Finally, besides perspective of risk-reward, it might appropriate that think the behavior of holding assets in other view-points.

動態規劃的問題並不一定都存在封閉解(closed form solution)，即使存在，其過程往往也相當繁雜。本研究擬以 Gerrard & Haberman (2004) 的模型為基礎，並使用逼近動態規劃理論解的數值方法來求解，此方法參考自黃迪揚(2009)，其研究探討在有無封閉解的動態規劃下，使用此數值方法求解可以得到 逼近解。本篇嘗試延伸其方法，針對不同類型的限制，做更多不同的變化。Gerrard & Haberman (2004)推導出退休後投資於風險性資產與無風險性資產之最適投資策略封閉解， 本研究欲將模型投資之兩資產衍生至三資產，分別投資在高風險資產、中風險資產與無風險資產，實際市場狀況下禁止買空賣空的情況與風險趨避程度限制資產投資比例所造成的影響。並探討兩資產與三資產下的投資結果，並加入不同的目標函數:使用控制變異數的限制式來降低破產機率、控制帳戶差異部位讓投資更具效率性。雖然加入這些限制式會導致目標函 數過於複雜，但是用此數值方法還是可以得出逼近解。 / Dynamic Programming’s solution is not always a closed form. If it do exist, the solution of progress may be too complicated. Our research is based on the investing model in Gerrard & Haberman (2004), using the numerical solution by Huang (2009) to solve the dynamic programming problem. In his research, he found out that whether dynamic programming problem has the closed form, using the numerical solution to solve the problems, which could get similar result. So in our research, we try to use this solution to solve more complicate problems. Gerrard & Haberman (2004) derived the closed form solution of optimal investing strategy in post retirement investment plan, investing in risky asset and riskless asset. In this research we try to invest in three assets, investing in high risk asset, middle risk asset and riskless asset. Forbidden short buying and short selling, how risk attitude affect investment behavior in risky asset and riskless asset. We also observe the numerical result of 2 asset and 3 asset, using different objective functions : using variance control to avoid ruin risk, consideration the distance between objective account and actual account to improve investment effective. Although using these restricts may increase the complication of objective functions, but we can use this numerical solution to get the approximating solution.

已開發國家中，無論個人或是法人所擁有之財富大多透過金融中介機構管理，因此，財富委由他人管理衍生出現代資本市場中重要的委託關係。委託人與基金管理人產生委任契約時，也必然產生代理問題，即雙方利益不一致所額外增加的成本。為降低代理成本，於委任合約加入對管理人下檔投資風險的要求成為降低代理成本的重要機制。本研究因此探討當基金管理人面對契約存在最低報酬要求時，如何進行最適資產配置決策，並同時分析下檔風險限制改變時對管理人投資行為的影響。研究結果顯示，委任合約增加經理人最低保證收益時，基金管理人傾向增加持股，而經理人風險趨避程度增加時，將減少風險性股票資產，進而持有債券；如果投資目標收益於受委託期間皆不改變，將造成經理人持有債券組合以規避下檔風險，同時卻喪失追求資本利得。 / In most developed countries, financial wealth is not managed directly by the investors, but through a financial intermediary. Hence, the delegated portfolio management is one of the most important principal-agency relationships in the current economy. In addition to that, the principal-agency relationships between the investor and portfolio manager must produce agency cost. In order to reduce these costs, the mandates in the contract become an important factor in reducing the principal-agent problem in a delegated portfolio management framework. In this research, we study how fund managers do asset allocation when they face some guaranteed returns and the relationships between the choices of mandates and the behavior of fund managers. We suppose that the objective of the delegated fund managers is to maximize the expected utility of wealth of the long-term fund at the end of each period and fund managers also have to fulfill some constrains given at the beginning. Finally, we explain how fund managers do optimal asset allocation by our model and some numerical analysis.

本研究以Plantinga（2010）對退休金基金所提出之績效歸因模型應用於臺灣的壽險公司，並檢定每單位負債下，壽險公司的資產負債配置不匹配是否會影響到公司的投資收益；以及檢定在公司規模及壽險公司負債成本兩因素做為控制變數之下，資產負債不匹配程度是否會影響到壽險公司的投資報酬率的部分，得到以下結果： （一） 在2007年至2012年間，每單位負債下，壽險公司的資產負債配置不匹配會影響到公司的投資收益，且影響為負。 （二） 壽險公司的盈餘資產積極投資報酬率，與其負債成本間有顯著的正向相關；和公司規模間有正向相關；而與資產負債不匹配程度無明顯的相關性。 （三） 壽險公司的名目資產積極投資報酬率，與其資產負債不匹配程度有正向相關，但並不非常顯著；而與公司規模無明顯的相關性；與負債成本相關性之間的關係，亦不是非常顯著。 此研究應用Plantinga（2010）的內部績效衡量的模型，其以每單位負債表示報酬率，更能清楚看出，若在不增加自有資本的前提下，每個績效歸因對公司負債的影響大小，可以做為業界之參考。 關鍵字：資產配置、內部績效、追蹤資料、資產負債不匹配程度 / This research of pension fund is conducted based on Plantinga’s (2010) performance attribution model and applied to insurance companies in Taiwan; The research tested how insurance companies investment return per unit of liability and investment rate of return would be affected would be affected under the circumstance of asset-liability-mismatch based on two variables: company size and cost of capital. The result is shown below: （i） Under unit liability, the asset-liability allocation has negative effect on the return of insurer during 2007 to 2012. （ii） There is a significant positive relationship between insurer’s cost of liability and surplus asset active return rate; positive relationship between insurer’s liability scale and surplus asset active return rate; no significant relationship between asset-liability mismatch level and surplus asset active return rate. （iii） There is a positive but not significant relationship between asset-liability mismatch level and nominal asset active return rate; no significant relationship between insurer’s liability scale and nominal asset active return rate; no significant relationship between insurer’s cost of liability and nominal asset active return rate, either. The research, which is based on Platinga’s (2010) internal performance measurement model, demonstrates the degree of influence on company’s liability disregard of any capital injection. The result can be used as industry reference. Key words：asset-liability allocation, internal performance measurement model, asset-liability mismatch level, panel data

隨著國民所得水準及個人知識水準的提升，再加上人口結構的高齡化，國人財富管理的需求逐漸浮現，而如何依據個人的財務狀況，建構一套穩健成長的個人理財規劃，以實現家庭資產的經濟效益最大化，就成為當前財富管理市場面臨的重大議題。 然而，台灣的財富管理市場才剛萌芽，故綜觀現有文獻及實務上之論述，有關記載個人理財規劃服務的相關報導實為有限，且多屬片段，缺乏完整性之服務模式及可支援計算的理財軟體，因此，本研究之目的即針對個人理之需求建構一套理財服務模式及軟體，並透過此服務模式及軟體的實地操作，為投資人建立一套最適化的個人理財規劃。 本研究首先根據相關文獻，對個人理財規劃的理論架構進行完整的介紹，其次討論台灣目前財富管理事業的現況，接著以個人理財規劃的理論為基礎，建構一套理財規劃服務模式及軟體，驗證所提出的架構、流程、模式與方法的可行性與績效。最後，可以藉由本文研究，提供金融機構之財富管理部門在建置理財規劃服務模式及相關理財系統開發作為一個參考依據。

過去的文獻中，資產配置的方法不外乎效率前緣、動態資產配置等方式，但是，單獨針對銀行探討的文章並不多見，所以本文的貢獻在於單獨針對銀行的資產配置行為進行研究，希望能利用『演化策略演算法』，進行『模擬最佳化』來解決銀行資產配置的問題。基本上這個方法是由兩個動作結合而成，先是模擬，再來尋求最佳解。所以，資產面我們選擇了現金、債券、股票、不動產四項標的，而負債面則模擬了定存、活存與借入款這三項業務，然後透過重複執行模型的方式來求出最適解。並與單期資產配置方法下的結果作一比較，發現運用演化策略演算法有較佳的結果，此外，在不同的亂數下，仍具有良好的穩健性，可作為一般銀行經理人參考之用。 / We focus on the bank’s asset allocation problem in this thesis. We use simulation optimization to solve the problem by evolution strategy, which is relatively new in the financial field. Simulation optimization consists of two steps: simulate numerous situations and search for the optimal asset portfolios. In the simulation, we set up four assets, including cash, bond, stock, and real estate and three business lines, including demand deposits, time deposits, and borrowings. Then we search for the optimal solution by running the ES algorithm. The results show that simulation optimization generates better results than one-period asset allocation. Furthermore, the evolution strategy method generates similar results using different random numbers.