University of Macau / Faculty of Social Sciences and Humanities / Department of Government and Public Administration

The main objective of this thesis is to build a multi-stage stochastic pro- gram within an asset-liability management problem of a leasing company. At the beginning, the business model of such a company is introduced and the stochastic programming formulation is derived. Thereafter, three various risk constraints, namely the chance constraint, the Value-at-Risk constraint and the conditional Value-at-Risk constraint along with the second-order stochastic dominance constraint are applied to the model to control for riski- ness of the optimal strategy. Their properties and their effects on the optimal decisions are thoroughly investigated, while various risk limits are considered. In order to obtain solutions of the problems, random elements in the model formulation had to be approximated by scenarios. The Hull - White model calibrated by a newly proposed method based on maximum likelihood esti- mation has been used to generate scenarios of future interest rates. In the end, the performances of the optimal solutions of the problems for unconsid- ered and unfavourable crisis scenarios were inspected. The used methodology of such a stress test has not yet been implemented in stochastic programming problems within an asset-liability management. 1

This research examines the role that modern portfolio theory (MPT) plays in current South Africa asset management practice in comparison to other portfolio management techniques and security evaluation methods. The purpose of asset management is to pool complementary financial market expertise, in order to generate returns in excess of the market return on the investments of the owners of financial resources that are entrusted to the firm, since the owners of financial resources might not be able to make superior investment decisions on their own. The research presents and discusses the literature pertaining to modern portfolio theory, traditional portfolio theory (fundamental and technical analyses), and behavioural finance theory. The implication of the efficient market hypothesis in relation to all the portfolio management theories is also presented and discussed. In line with a positivist paradigm, the survey research methodology, which combines both qualitative and quantitative aspects, was adopted. The instrument used for data collection was a questionnaire, which was found to be reliable and valid for this research. The questionnaire encompassed the Lickert scale to measure the data. The results of the analysis were interpreted using descriptive statistics. The results of this research suggest that modern portfolio theory does not play a significant role in the management of portfolios and security evaluation in South Africa. South African asset managers regard fundamental analysis as the most significant method of security evaluation in the management of portfolios. Technical analysis and econometric models are regarded as playing a moderate role and complement fundamental analysis whilst behavioural finance models play the least role. This research recommends an integrated portfolio management strategy that incorporates MPT, traditional portfolio theory and behavioural finance models to enhance investor value and protection.

La présente thèse s’intéresse aux modèles d’allocation stratégiques d’actifs et à leurs applications pour la gestion des réserves financières des régimes de retraite par répartition, en particulier ceux partiellement provisionnés. L’étude de l’utilité des réserves pour un système par répartition et a fortiori de leur gestion reste un sujet peu exploré. Les hypothèses classiques sont parfois jugées trop restrictives pour décrire l'évolution complexe des réserves. De nouveaux modèles et de nouveaux résultats sont développés à trois niveaux : la génération de scénarios économiques (GSE), les techniques d’optimisation numérique et le choix de l’allocation stratégique optimale dans un contexte de gestion actif-passif (ALM). Dans le cadre de la génération de scénarios économiques et financiers, certains indicateurs de mesure de performance du GSE ont été étudiés. Par ailleurs, des améliorations par rapport à ce qui se pratique usuellement lors de la construction du GSE ont été apportées, notamment au niveau du choix de la matrice de corrélation entre les variables modélisées. Concernant le calibrage du GSE, un ensemble d’outils permettant l’estimation de ses différents paramètres a été présenté. Cette thèse a également accordé une attention particulière aux techniques numériques de recherche de l'optimum, qui demeurent des questions essentielles pour la mise en place d'un modèle d'allocation. Une réflexion sur un algorithme d’optimisation globale d’une fonction non convexe et bruitée a été développée. L’algorithme permet de moduler facilement, au moyen de deux paramètres, la réitération de tirages dans un voisinage des points solutions découverts, ou à l’inverse l’exploration de la fonction dans des zones encore peu explorées. Nous présentons ensuite des techniques novatrices d'ALM basées sur la programmation stochastique. Leur application a été développée pour le choix de l’allocation stratégique d’actifs des régimes de retraite par répartition partiellement provisionnés. Une nouvelle méthodologie pour la génération de l’arbre des scénarios a été adoptée à ce niveau. Enfin, une étude comparative du modèle d’ALM développé avec celui basé sur la stratégie Fixed-Mix a été effectuée. Différents tests de sensibilité ont été par ailleurs mis en place pour mesurer l’impact du changement de certaines variables clés d’entrée sur les résultats produits par notre modèle d’ALM / This thesis focuses on the strategic asset allocation models and on their application for the financial reserve management of a pay-as-you-go (PAYG) retirement schemes, especially those with partial provision. The study of the reserve utility for a PAYG system and of their management still leaves a lot to be explored. Classical hypothesis are usually considered too restrictive for the description of the complex reserve evolution. New models and new results have been developed over three levels : economic scenario generation (ESG), numerical optimization techniques and the choice of optimal strategic asset allocation in the case of an Asset-Liability Management (ALM). For the generation of financial and economic scenarios, some ESG performance indicators have been studied. Also, we detailed and proposed to improve ESG construction, notably the choice of the correlation matrix between modelled variables. Then, a set of tools were presented so that we could estimate ESG parameters variety. This thesis has also paid particular attention to numerical techniques of optimum research, which is an important step for the asset allocation implementation. We developed a reflexion about a global optimisation algorithm of a non convex and a noisy function. The algorithm allows for simple modulating, through two parameters, the reiteration of evaluations at an observed point or the exploration of the noisy function at a new unobserved point. Then, we presented new ALM techniques based on stochastic programming. An application to the strategic asset allocation of a retirement scheme with partial provision is developed. A specific methodology for the scenario tree generation was proposed at this level. Finally, a comparative study between proposed ALM model and Fixed-Mix strategy based model was achieved. We also made a variety of a sensitivity tests to detect the impact of the input values changes on the output results, provided by our ALM model

論文摘要: 本研究以現金餘額計劃（Cash Balance Plan）及確定提撥退休金計劃（Defined Contribution Pension Plan）建構出公務人員退撫基金之建議機制，建構之主要目的在於透過第一層現金餘額計劃之利息給付機制降低退休基金利率風險，同時由第二層確定提撥計劃獲取額外退休所得，使雇主與員工在双層式退休金計劃下，同時承擔投資風險，以降低基金利率風險並同時滿足適當退休所得保障。本文在現金餘額計劃不同控管年限及利息給付假設下，模擬超額積蓄（Overfunded）基金與不足額積蓄（Underfunded）基金執行資產負債管理（Asset Liability Management）所需存續期間，同時模擬双層式退休金計劃提供員工之退休所得替代率，研究結果發現： 1、超額積蓄基金及不足額積蓄基金均可以在目前資本市場中找到符合所需存續期間之資產投資。在控管20年限內，超額積蓄基金所需存續期間在-1.71年到0.39年之間；不足額積蓄基金所需存續期間在4.68年到8.31年之間。 2、退休基金越接近超額狀態越有利於資產負債管理。當基金積蓄狀態越接近超額積蓄時，基金負債與資產的比例較不足額積蓄基金低，故資產負債管理所需存續期間較短，對於基金能夠控管的年限也越長。 3、雇主可透過現金餘額計劃利息給付機制執行百分之百免疫策略。雇主可利用現金餘額計劃利息給付依據外部債券利率為參考依據的特性，鎖定債券利率，達到資產負債管理百分之百免疫效果。 4、現金餘額計劃執行百分之百免疫策略情況下，45歲以下公務人員採行自動選擇投資基金（Default Fund）為高風險投資基金，自動選擇提撥率（Default Rate）為每月薪資5.08﹪，可使員工達到適當所得替代率保障水準。 / Abstract This thesis proposes an new alternative two-tier pension composed of Cash Balance Plan (CBP ) and defined contribution pension plan to the traditional defined benefit pension plan of Taiwan Public Employee Retirement System(TPERS). In order to decrease the interest-rate risk of the pension fund and to provide additional retirement income protection, we utilize the credit rate mechanism of CBP and supplement CBP with additional defined contribution plan. We investigate the Asset-Liability Management (ALM) for TPERS and calculate the liability duration under different time horizons, interest credits of CBP. We also simulate the replacement rate of the two-tier pension plan under different contribution rates, and investment returns. The results are as follows: 1、Given the twenty-year time horizons, the asset duration of overfunded plan ranges between –1.71 years and 0.39 years, whereas that of underfunded plan varies from 4.68 years to 8.31 years. In this case, the requirements of asset duration can be satisfied in the Taiwan Capital Market. 2、The overfunded pension plan has higher probabilities to meet the requirements of asset duration. Therefore, we suggest that the fund manager can increase the asset allocation percentage of external fund management in order to improve the long-term returns. 3、Perfect matching of pension fund can be achieved by matching the yield of securities to interest credit under CBP . In addition, we suggest that the interest credit of the new labor contracts should take the trend of the current interest rate into consideration. 4、Replacement rates provided by CBP for woman range from 19.05﹪ to 45.70﹪and from 20.86﹪to 50.05﹪for man assuming the interest credit rate is 5.2%. To increase the retirement income, the defined contribution plan provide additional replacement rate between 13.56﹪and 162.96﹪for woman and between 14.85﹪and 178.42﹪for man assuming the employee can contribute 3.08 percent to 13.37 percent of regular salaries and investment returns are from 4 percent to 8 percent .

本研究著重於分析發行大量長年期利率敏感型契約、高財務槓桿比例的人壽保險業中公司經理人之投資決策，發現台灣壽險業亦存在Canner et al.(1997)提出之資產配置迷思，亦即風險性資產中債券與股票之比率於不同壽險公司間有差異，與共同基金分離理論中陳述之風險態度不同之投資人所持有之債券與股票比率應相同不相符。本文嘗試以Sorensen(1999)提出之擬似動態規劃法(Quasi- dynamic Programming)最適化到期之效用函數，試算經理人於股票及不同到期固定收益債券之最適持有比例。且詳細探討不同風險偏好及投資期限對於壽險公司投資組合之影響。將業主權益之最適投資策略加上負債之複製投資組合成為策略性資產配置結果，並將其與目前台灣壽險公司之資產配置做比較。研究結果顯示： 1.以擬似動態規畫法求得之最適投資組合於不同風險態度下皆為長期債券以及股票。當經理人之風險趨避程度增加時，投資於股票之比例會減少、投資於債券之比例會增加。 2.比較台灣壽險公司之債券與股票配置比例與本研究之結果發現，本資公司之風險態度較外資公司積極，本資公司應提高其債券之持有比例。 本研究最後以Bajeux-Besnainou et al. (2001)提出之資產配置迷思解釋說明本資公司與外資公司持有之債券與股票比率之所以不同非因資產配置迷思之存在，本資公司與外資公司於風險性資產中持有之債券與股票比率是相同的，但因風險態度較為趨避之公司，投資於風險性資產比率下降、提高避險部位之配置，導致整體之股票與債券比率增加。 關鍵字：資產負債管理、策略性資產配置、擬似動態規劃法。

The diploma thesis deals mostly with interest rate risk issue. It describes the basic methods of interest rate risk measurement with use of analyses executing by Asset Liability Management department in banks. Such analyses as repricing GAP, net interest income analysis, market value of equity and sensitivity analyses to interest rate movements. There is an analysis of Czech crown yield curve as well, in order to deeper insight of its probability behaviour. Results of this analysis are used for advanced techniques in ALM. Especially knowledge of volatilities of particular yield points and theirs relations is used in these methods. There was also a multi equation model for predictions of yield curve development created. One of the variables in the model there is the 2-week repo rate of Czech National Bank included.

This master thesis deals with the area of external audit of the bank in the Czech Republic. Its goal is to identify and describe the specifics making the procedures during bank's financial statements audit different from those applied by non-financial commercial subjects. The first part is focused on the general framework of the external audit. The second part describes main features of the bank identifying several risks connected with the business which have a significant influence on the approach used by the auditors. The third part describes the methodology applied by auditors during the audit of the bank.

傳統的資產負債管理(Asset-Liability Management，ALM)研究大多強調數量分析方法，並未考慮資料來源的問題。然而在銀行實務上，資產負債管理人員卻必須根據現有內外部資料來釐定資產負債組合的整体政策。在決策支援系統中，模式整合的功能包含模式之組合及連結等，可用以整合數量分析模式與相關資料。本研究運用人工智慧技術來探討資產負債管理中模式整合之問題。藉此可以明瞭ALM的分析流程，以作為銀行人員訓練之參考。另一方面由於應用黑板架構發展系統，也可以提供一個有彈性的整合環境，以反應使用者需求及資料異動狀況，亦可彈性新增、刪除及修改模式整合過程中的資料結構與知識內涵，以為未來連接理論技巧與實務環境之參考。 / The computer support for Asset Liability Management (ALM) in the literature emphasizes on the mathematical analysis and does not address the data source problems. In the practical banking environment, however, ALM decisions are made based on the dynamic internal and external data changes. Therefore, an ideal ALM decision support system has to consider the integration of data sources and mathematical analysis. Traditional Decision Support Systems (DSS) rely on the expert's assistance to understand the problem and formulate or integrate appropriate models. There is a growing recognition that incorporates Artificial Intelligence techniques (Al) into the DSS can enhance the acceptance of these decision aids by management. 　　This paper intends to develop an Intelligent Decision Support System (TDSS) and addresses the model integration concept for the ALM. In the paper, model integration is defined as a series of processes from which important decision making information is inferred through automatic data model mapping and mathematical model conversion. The investigation of model integration concept helps the ALM analysis process understanding which can be useful for baaldng personnel training. On the other hand, the IDSS provides a flexible integration environment in which the system can flexibly response to the user's analysis request with the updated data situations. Since the blackboard architecture used for the system development supports the modularization structure, its inherent maintainability aLows a flexible update of the domain knowledge and data structure, and can therefore serve as a testbed to evaluate the potential integration approaches of various ALM data and mathematical models.

本研究的目的是針對退休金的長期負債以資產負債管理的方式提出有效的投資避險策略建議。在過去，傳統精算的資產負債管理大多採用確定投資模型（Deterministic Model），即以過去的經驗設立「精算假設」，但是這樣的假設無法精確的呈現未來的趨勢，所以本文的第一部份，便是根據過去的台灣總體經濟資料，建構一個退休基金的隨機投資模型（Stochastic Investment Model）。首先，我們以ECM（Error Correlation Model）模式建構出第一個投資模型，之後在精簡參數的考量下，建構第二個以因果關係為基礎的Causality投資模型，再以模型配適能力與預測能力比較兩模型，結果顯示Causality投資模型優於ECM投資模型。 　　有了投資模型，我們設定不同的退休金負債形式，如固定成長型負債MF、隨通貨膨脹成長M^R負債及隨max{固定成長比例，通貨膨脹}而成長的退休金負債M^L，以靜態避險的方式去求得各資產的最適配適比例。從模擬的結果中發現隨著到期日的增長，投資在風險性高報酬率佳的投資標的物上的比例也越來越高。另外，隨著負債固定成長比例f的增加，其M^L負債之期初資產配置額便越接近M^F負債之期初資產配置額。整體而言，我們由模擬中可得出，使用投資組合的投資方式優於單一資產投資的結論。 / In this study, we investigate the hedging strategies for pension liabilities by using Asset-Liability Management method. In the past, the traditional actuarial valuation usually does not take account of market value for both assets and liabilities. Most of the traditional actuarial valuation adopted the Deterministic Model, that is, setting the assumptions based on the experiences. However, it can not exactly show the trend in the future. In part one of this study, we build a stochastic investment model for the pension funds based on Taiwan Market data. First, we apply the first model : ECM( Error Correlation Model ). And then, we apply the second model : Causality Model under considering parsimonious parameterization. Finally, we compare the results of ECM with Causality Model on fitting and forecasting efficiency, and we find that Causality Model is better than ECM. With the investment model, we set some formulas of pension liabilities calculated to obtain the best fit proportion of each valuation by the static hedging. This involves finding optimal static hedging strategies to minimize riskiness of the investment portfolio relative to the liability. Overall, from the simulation results, for static hedging in these kinds of liabilities, investing in all three assets is a better strategy than investing in a single asset class. This confirms that the more assets we use, the more effectively we can hedge.