none

The purpose of the study is to investigate optimal asset allocation as a means of minimising the investment risk, drawdown risk and longevity risk associated with an investment linked living annuity. The three risk elements were tested for various categories of retirees investing the full retirement savings amount in a living annuity. At first the paper examines the South African public's current pre-retirement savings habits, propensity to save and knowledge on the financial industry. The literature concludes that very few people are saving adequately for retirement, thus leaving a gap between required retirement savings capital and accumulated retirement savings capital. As a consequence, retirees have to take on more risk, usually in the form of equity exposure, (only available in an investment linked living annuity) or delaying retirement, to try and breach the gap. Secondly the paper examines the constructs in developing an optimal asset allocation. An analysis of the constructs includes risk versus return relationships for retirees, various unit trust sectors and portfolios within the South African financial market, the investment horizon also stated as the life expectancy of a retiree and withdrawal strategies applied by investors or retirees. The practical data and theory from the literature study formed the basis of the empirical study where different retirement savings balances were tested at various drawdown rates and asset allocations in an investment linked living annuity. The study concluded that retirees have to consider, among other factors, the required standard of living (stated as a net replacement ratio), the need to withdraw one third of the retirement capital and life expectancy before investing in an investment linked living annuity. These factors will have the biggest influence on the risks associated with an investment linked living annuity. Furthermore, the study concluded that an optimal asset allocation would be able to support a retiree during the post-retirement phase. A well diversified portfolio with a minimum of 50% allocation towards equity and property assets seems to be optimal. / Thesis (M.B.A.)--North-West University, Vaal Triangle Campus, 2010.

The purpose of the study is to investigate optimal asset allocation as a means of minimising the investment risk, drawdown risk and longevity risk associated with an investment linked living annuity. The three risk elements were tested for various categories of retirees investing the full retirement savings amount in a living annuity. At first the paper examines the South African public's current pre-retirement savings habits, propensity to save and knowledge on the financial industry. The literature concludes that very few people are saving adequately for retirement, thus leaving a gap between required retirement savings capital and accumulated retirement savings capital. As a consequence, retirees have to take on more risk, usually in the form of equity exposure, (only available in an investment linked living annuity) or delaying retirement, to try and breach the gap. Secondly the paper examines the constructs in developing an optimal asset allocation. An analysis of the constructs includes risk versus return relationships for retirees, various unit trust sectors and portfolios within the South African financial market, the investment horizon also stated as the life expectancy of a retiree and withdrawal strategies applied by investors or retirees. The practical data and theory from the literature study formed the basis of the empirical study where different retirement savings balances were tested at various drawdown rates and asset allocations in an investment linked living annuity. The study concluded that retirees have to consider, among other factors, the required standard of living (stated as a net replacement ratio), the need to withdraw one third of the retirement capital and life expectancy before investing in an investment linked living annuity. These factors will have the biggest influence on the risks associated with an investment linked living annuity. Furthermore, the study concluded that an optimal asset allocation would be able to support a retiree during the post-retirement phase. A well diversified portfolio with a minimum of 50% allocation towards equity and property assets seems to be optimal. / Thesis (M.B.A.)--North-West University, Vaal Triangle Campus, 2010.

本研究探討長期投資人在面臨通貨膨脹風險時的最適投資決策。就長期投資者而言，諸如退休金規劃者等，通貨膨脹是無可避免卻又不易被數量化之風險，因為各國僅公布與之相關的消費者物價指數而沒有公布真實通貨膨脹數值，因此我們延伸Campbell和Viceira(2001)及Brennan和Xia(2002)的模型假設，以消費者物價指數的資訊來校正原先假定符合Vasicek模型之通貨膨脹動態過程。本研究之理論背景為：利用貝式過濾方法(Baysian Filtering Method)，將含有雜訊之消費者物價指數，透過後驗分配得出通貨膨脹動態過程。利用帄賭過程(Martingale Method)求解資產之公帄價格。再引進定值相對風險趨避(Constant Relative Risk Aversion，CRRA)的效用函數，求出最適投資組合下之期末累積財富、各期資產配置以及效用值。 / 本研究歸納數值結果如下： 一、投資期間越長，通貨膨脹學習效果越顯著。投資期間達25年以上時，有學習效果之累積財富為無學習效果時兩倍以上，25年為2.36倍；30年為2.18倍。此外，學習效果對投資人效用改善率於長期投資時也較顯著，投資10年效用改善率為35%，而投資30年則高達1289%，呈非線性成長。以上結果顯示：資產在市場上累積越久，受到通膨影響越明顯，更需要以學習方式動態調整資產配置進行通貨膨脹風險管理。 / 二、風險較趨避之投資人，CRRA參數值越大；於最適投資組合下之期末財富較少，因為風險較趨避投資人偏好低波動度資產組合。風險容忍度低之投資人較需要通貨膨脹之學習，否則效用減損過高，例如CRRA參數為1.5之投資人30年後效用減損65%，CRRA參數為4之投資人效用減損達96.5%。以上數據顯示：風險趨避投資人對風險關注程度較高，考慮學習效果時，較能根據目前通貨膨脹調整資產配置。 / This study examines the optimal portfolio selection incorporating inflation risk learning adjustments for a long-term investor. For long-term investors, it is inevitable to face the uncertainty of inflation. On the other hand, quantifying inflation risk needs more effort since the government announced the information on Consumer Price Index (CPI) rather than the real inflation rates. / In order to measure the inflation rate in planning the long-term investment strategies, we extend the works in Campbell and Viceira (2001) and Brennan and Xia (2002) to construct a stochastic process of the inflation rate. The prior distribution of inflation rate process, which is not directly observable, is assumed to follow the diffusion process. Based on the information of CPI, we then employ the optimal linear filtering equations to estimate the posterior distribution of the inflation rate process. Through these mechanisms, the inflation rate process is closer to reality by learning from CPI. We also construct the optimal portfolio strategy through a Martingale formulation based on the wealth constraints. The optimal portfolio strategies are given in closed-form solutions. / Furthermore, the importance of learning about inflation risk is summarized through the numerical results. (1) When the investment interval is longer, the learning effect becomes more significant. If the investment horizon is longer than 25 years, the wealth accumulation under learning will be twice more than that without learning effect, e.g., the wealth accumulation is approximately 2.36, 2.18 folds at the end of 25, 30 years. Utility increase under learning also become larger for long-term investor, e.g., the utility values will improve 35% after considering learning ability on inflation from 10-year interval, improve 1289% from 30 years. / (2)When the CRRA parameter increases, the investor have lower risk tolerance; and their wealth accumulation become less due to the lower volatility portfolio. A conservative investor requires more learning ability given the inflation, otherwise their utility value will be reduced, e.g., the utility values will be reduced 35% when CRRA=1.5 after 30 years’ investment, 96,5% when CRRA=4.

本研究主要是針對投資型年金之資產負債管理作探討，其中是就規避利率風險對於資產負債管理上的影響以及分析資產配置最適化作為研究的架構，而所利用的研究方法乃是取決於建構利率隨機模型並輔以免疫理論與Markowitz投資組合理論，以期在規避利率風險的同時，亦能將資產配置達至最佳化。 首先，為實際模擬出符合現實經濟環境變動下的隨機利率期間模型，本研究利用C.I.R利率期間結構模型來建構年金保單期間的利率結構，並且由於投資型年金之保單價值的累積特性，因此本研究同時亦建構出連接保單價值的投資資產之報酬率型態，進而模擬出各期之現金流量以及各項投資資產的存續期間；再者，藉由Markowitz投資組合理論，以在免疫條件之限制下進行最適資產配置之評估。 最後，以某知名的保險公司所推出的投資型年金商品作為本研究之實證對象，透過模擬之方法，將研究模型中之各項參數予以評估，並且根據上述之研究過程將免疫理論與投資組合理論相連接，以檢視投資型年金商品在規避利率風險的狀態下，其最適之資產配置比例是否與現行法令之規範相牴觸，而能給予適時之建議。另外，由本實證結果可知，經由本研究的分析流程，可以有效地給予年金管理者規劃出年金資產負債管理時的最適投資組合比例，並且在增加外國投資資產時，更能有效的增加年金資產之報酬，同時也不影響保險法對於投資資產的比例與總金額之限制。再者，對於探討規避利率風險前後之資產組合之資產報酬之變化時，可以進一步了解到，當年金管理者在運用免疫策略來規避利率風險時，其所面對的風險成本之多寡，以作為制定避險決策時的依據。 / This research explores the asset-liability management (ALM) for the Investment-Link-Annuity. Two aspects investigated in this research are the interest rate risk and the optimal asset allocation. Moreover, the major issue investigated here is the trade-off between the optimal investment return and the hedge of interest rate risk. We refer this trade-off as ALM cost. By using stochastic interest rate model, Immunization theory and Portfolio Selection Model, we construct an ALM model to achieve the optimal asset allocation given on hedging the interest rate risk under the immunization strategies for the insurance company. First, we utilize the public trading data for investment market in Taiwan and in USA from 1985 to 2000 and the investment-link annuity product of a well-know insurance company in Taiwan to simulate the cash flow and demonstrate the implementation of our model. By analyzing different simulations under various scenarios, the empirical results are as the followings: 1.The ALM cost for immunization strategies is very small, and is estimated to be about 1% to 2%. Therefore, we suggest that insurance companies should start to undertake the asset liability management as soon as possible. 2.If relaxing the investment restrictions of Insurance Law or allowing insurance company to invest in foreign investment market, the overall investment return will be increased and the ALM cost will be reduced effectively.

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.