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This dissertation includes two topics. The first topic focuses on the problem of investor optimization of dynamic asset allocation to maximize expected utility under the value at risk (VaR) constraint. Different to previous researches, this study considers a common realistic case where the VaR horizon is equal to the whole investment horizon without a complete market constraint. Since the problem cannot be solved using the standard dynamic programming method or the martingale method, this study particularly provides an algorithm to solve this difficult problem. Similar to the mean-variance frontier suggested by Markowitz (1952), this study draws the frontiers of dynamic and static asset allocations under the VaR constraint. The analytical results clearly show that the dynamic asset allocations are more efficient than the static asset allocations. The second topic designs an optimal insurance policy form endogenously, assuming the objective of the insured is to maximize expected final wealth under the VaR constraint. The optimal insurance policy can be replicated using three options, including a long call option with a small strike price, a short call option with a large strike price, and a short cash-or-nothing call option. Moreover, expected wealth is increasing and concave in VaR and in significance level. Finally, Mean-VaR Frontiers are drawn, and reveal that the optimal insurance is more efficient than alternative insurance forms.

<p>There are several authors Markowitz (1991), Elton and Gruber (1997) that discuss the main issues that an investor faces when investing, for example how to allocate resources among the variety of different securities. These issues have led to the discussion of portfolio theories, especially the Modern Portfolio Theory (MPT), which is developed by Nobel Prize awarded economist Harry Markowitz. This theory is the philosophical opposite of tradi-tional asset picking.</p><p>The purpose of this thesis is to investigate if an investor can apply MPT in order to achieve a higher return than investing in an index portfolio. Combining a strong portfolio that beats the market in the longrun would be the ultimate goal for most investors.</p><p>The theories that are used to analyze the problem and the empirical findings provide the essential concepts such as standard deviation, risk and return of the portfolio. Further, diversification, correlation and covariance are used to achieve the optimal risky portfolio. There will be a walk-through of the MPT, with the efficient frontier as the graphical guide to express the optimal risky portfolio.</p><p>The methodology constitutes as the frame for the thesis. The quantitative method is used since the data input is gathered from historical data. This thesis is based on existing theories, and the deductive approach aims to use these theories in order to accomplish a valid and accurate analysis. The benchmark that is used to compare the results from the portfolio is the Stockholm stock exchange OMX 30. This index mimics and reflects the market as a whole. The portfolio will be reweighed at a preplanned schedule, each quarter to constantly obtain an optimal risky portfolio.</p><p>The finding from this study indicates that the actively managed portfolio outperforms the passive benchmark during the selected timeframe. The outcome someway differs when evaluating the risk adjusted result and becomes less significant. The risk adjusted result does not provide any strong evidence for a greater return than index. Finally, with this finding, the authors can conclude by stating that an actively managed optimal risky portfolio with guidance of the MPT can surpass the OMX 30 within the selected timeframe.</p>

本研究旨在討探投資型保險之最適退休資產配置，資產配置是決定一個投資組合的報酬與風險的最重要因素。本研究採取五種資產配置策略，包含了BH策略、CM策略、LCF、LCR策略及TRR策略，利用模擬四項投資標的之未來的投資報酬率，在給定之個案設計下進行投資期間分別20、25、30、35年模擬分析，研究結果發現： 1. 當風險性資產所佔之比重愈高對達成目標所得替代率之影響愈明顯， 2. 當投資期間愈長，其愈少投資在風險性資產之策略，在期末終值遠低於於持續持有較高風險資產。 3. 不同投資期間其不同策略在表現各有所不同，LC策略至少投資25年以上會有比較高的所得替代率，保守且投資期間較短的投資人可選擇TRR策略，較積極或投資期間較長的投資人可選擇BH或CM策略以達到較高的所得替代率。 4. CM策略跟BM策略不同之處僅在於有無調整機制，在風險乘數較高的情況下，調整機制對於風險降低有明顯幫助，但對風險乘數為0.1時，其調整機制反而增加了投資組合之波動性。 5. 隨著投資期間的拉長，除了TRR策略外，各策略之結果對所得替代率均有大幅成長。 另就費用與稅賦對投資型保險與「買定期險，差額直接投資在共同基金(Buy Term and Invest the Difference，BTID)」之影響並模擬分析。實證結果發現到只是轉換同基金公司之基金，則必須在投資標的數目較多下，投資型保險才有利基；但若是要轉換不同基金公司之基金，則只要每年轉換一次以上，投資型保險比起BTID策略較有優勢，隨著轉換次數增多及投資金額較大時，此優勢更加明顯；在正常課稅下，隨著投資金額增加，投資型保險帳戶的價值大於BTID策略之年度將遞減。 / This research aims to examine the most appropriate retiring asset allocation of the Variable product. Asset allocation is one of the most important factors to determine the return and risk of a portfolio. This research adopts five asset allocation strategies, including BH strategy, CM strategy, LCF strategy, LCR strategy and TRR strategy. With a given future return on four assets in four different investing durations, which are 20, 25, 30 and 35 years, the results of this current project demonstrates: 1. The likelihood to achieve replacement rate increases with higher risky asset. 2. The longer the period of one’s intended holding period, the less the value of the ending wealth for not pursuing the risky investment. 3. The pattern of these various strategies depends on the investing duration: For the LC strategy, one needs to invest 25 years at least in order to have higher replacement rate. For shorter investing duration, one is advised to choose the TRR strategy whereas the BH or the CM strategy is suitable for longer investing duration in order to attain higher replacement rate. 4. The only difference between the CM and the BM strategies lies in rebalancing. Rebalancing reduces the risk in the higher multiple situation but increases the risk in the lower multiple situation. 5. Except the TRR strategy, the replacement rates of other strategies significantly increased with the investing duration. The result of the analysis on the effects of cost and tax on Variable product and Buy Term and Invest the Difference (BTID) showed that, with more mutual funds, there are advantages when the transferring is within the same company. However, the advantages of Variable product are greater than the BTID strategy if the transferring is under different mutual fund companies. Further, with the increases of the transferring frequencies and the amount of the investing money, the advantages are greater. Under normal taxing and with the increase of the amount of the investing money, the duration of the value on the Variable product which is greater than that of BTID will decrease. That is, the value of the Variable product will be greater than that of the BTID within shorter investing period.

本論文主要探討時變環境下之最適動態資產配置策略。由於對許多跨期的投資者而言，其所關心的不只是資產當期的報酬與風險，更關心隨著時間的經過，報酬與風險的改變方向。過去許多財務實證利用不同的時間序列模型發現風險性資產，尤其是股票市場存在著某些特性，例如：均數復歸 (Mean-reverting) 與隨機波動等現象，這些實證現象對於跨期的投資者在進行資產配置時尤為重要。本文即在此時變環境架構下探討三個資產配置上的問題。並利用擾動法以求解隨機設定下之封閉解，進而提出直接的資產配置建議。 第二章主要在探討不完全市場與時變環境下，跨期退休基金管理之最適動態資產配置策略。在納入退休基金管理中二項重要的特性：多期投資與退休基金負債的考量後，提出退休基金的最適跨期資產配置策略，本文並同時利用Sharpe and Tint (1990) 所提出的彈性考量退休基金負債的觀念，納入本文之模型設定當中，使本文能同時涵蓋不同退休基金管理者之不同負債考量進入資產配置之最適配置策略。本文所提出之跨期退休基金管理之最適動態資產配置策略，除了包含單期與面對時變環境下之跨期避險成分外，更提出退休基金管理者如何依據其退休基金之特性，如基金負債比率(funding ratio)等來建構其資產配置中之退休基金負債避險成分。 第三章主要在隨機環境設定下利用跨期避險與不可交易資產求解「資產配置的迷思」。Canner, Mankiw and Weil (1997) 指出，一般財務顧問公司對於投資者風險態度的差異所提出之投資建議與財務理論間存在著嚴重的不一致性，其將之稱為「資產配置的迷思(An asset allocation puzzle)」。於第三章中提出一理性的長期投資者模型，在考量投資者之不可交易資產與隨機投資機會下，提出最適動態資產配置策略，並解決了此資產配置的迷思，與現今之一般財務顧問公司對於投資者之投資建議相一致。 第四章主要在探討利率隨時改變下，一持有不動產抵押貸款負債之家計單位或投資者，如何進行跨期的動態資產配置策略。由於購屋置產對許多家庭或個人而言是相當重要的投資決策，但一般由於缺乏足夠的資金或為了維持一穩定的消費過程，一般均會利用不動產抵押取得貸款，但隨著市場利率的越漸波動，投資者如何進行跨期的資產配置以達到獲取報酬並規避利率波動的目的為本章之討論重點。利用可交易資產來對其所持有之不動產抵押貸款負債進行避險，依不同投資者風險態度、跨期偏好、抵押期限等之設定，對於持有不動產抵押貸款負債之投資者提出資產配置及避險的建議。

Various models driven by a hidden Markov chain in discrete or continuous time are developed to capture the stylised features of market variables whose levels or values constitute as the underliers of financial derivative contracts or investment portfolios. Since the parameters are switching regimes, the changes and developments in the economy as soon as they arise are readily reflected in these models. The change of probability measure technique and the EM algorithm are fundamental techniques utilised in the optimal parameter estimation. Recursive adaptive filters for the state of the Markov chain and other auxiliary processes related to the Markov chain are derived which in turn yield self-tuning dynamic financial models. A hidden Markov model (HMM)-based modelling set-up for commodity prices is developed and the predictability of the gold market under this setting is examined. An Ornstein-Uhlenbeck (OU) model with HMM parameters is proposed and under this set-up, we address two statistical inference issues: the sensitivity of the model to small changes in parameter estimates and the selection of the optimal number of states. The extended OU model is implemented on a data set of 30-day Canadian T-bill yields. An exponential of a Markov-switching OU process plus a compound Poisson process is put forward as a model for the evolution of electricity spot prices. Using a data set compiled by Nord Pool, we illustrate the vast improvements gained in incorporating regimes in the model. A multivariate HMM is employed as a framework in providing the solutions of two asset allocation problems; one involves the mean-variance utility function and the other entails the CVaR constraint. Finally, the valuation of credit default swaps highlights the important considerations necessitated by pricing in a regime-switching environment. Certain numerical schemes are applied to obtain approximations for the default probabilities and swap rates.

Each of the three essays in this dissertation deals with asset timing or allocation using technical techniques and pattern recognition. The first essay uses a technical indicator, the stochastic oscillator, for market timing in the bond market. The trading strategy using this technical indicator is optimized using a genetic algorithm The second essay finds that a measure of market chaos improves the performance of a simple trend-following technique in the stock market. The last essay uses technical analysis for asset allocation. A neural network with technical indicator inputs outperforms both a passive asset mix strategy and a neural network with economic data as inputs.

Submitted by Regis Baratti Lima Salgado (regiss@fgvmail.br) on 2012-10-09T13:30:32Z No. of bitstreams: 1 TeseRegisBarattiLSalgado_VFim.pdf: 861409 bytes, checksum: 48cbf91a3e1e3ed3d3c91940bfde85ac (MD5) / Approved for entry into archive by ÁUREA CORRÊA DA FONSECA CORRÊA DA FONSECA (aurea.fonseca@fgv.br) on 2012-10-22T19:15:00Z (GMT) No. of bitstreams: 1 TeseRegisBarattiLSalgado_VFim.pdf: 861409 bytes, checksum: 48cbf91a3e1e3ed3d3c91940bfde85ac (MD5) / Made available in DSpace on 2012-10-23T18:23:36Z (GMT). No. of bitstreams: 1 TeseRegisBarattiLSalgado_VFim.pdf: 861409 bytes, checksum: 48cbf91a3e1e3ed3d3c91940bfde85ac (MD5) Previous issue date: 2012-08-22 / This thesis extend the theoretical dominance of annuities over non-contingent discount notes; under standard assumptions, we show that full annuitization is optimal even in incomplete annuity markets. Through numerical simulations, we scrutinize factors a ecting annuitization decision, consolidating and extending previous research by taking into account unfair prices, bequest motives, and out-of-pocket medical expenses. We also take into consideration the insurer's risk of default, and relax an implicit assumption in most past models and detach annuitization from retirement, i.e.: we do not presume that consumers are already retired from work when they decide whether or not to annuitize. In line with previous literature, our results originate very high levels of annuitization. Yet, we show that the demand for annuities drops sharply, if preferences are such that the implied optimal consumption path decays with age. We also show that optimal annuitization timing is closely related to the endowments pattern. / A inconsistência entre a teoria e o comportamento empírico dos agentes no que tange ao mercado privado de pensões tem se mostrado um dos mais resistentes puzzles presentes na literatura econômica. Em modelos de otimização intertemporal de consumo e poupança sob incerteza em relação ao tempo de vida dos agentes, anuidades são ativos dominantes, anulando ou restringindo fortemente a demanda por ativos cujos retornos não estão relacionados à probabilidade de sobrevivência. Na prática, entretanto, consumidores são extremamente céticos em relação às anuidades. Em oposição ao seguro contra longevidade oferecido pelas anuidades, direitos sobre esses ativos - essencialmente ilíquidos - cessam no caso de morte do titular. Nesse sentido, choques não seguráveis de liquidez e a presença de bequest motives foram consideravelmente explorados como possíveis determinantes da baixa demanda verificada. Apesar dos esforços, o puzzle persiste. Este trabalho amplia a dominância teórica das anuidades sobre ativos não contingentes em mercados incompletos; total na ausência de bequest motives, e parcial, quando os agentes se preocupam com possíveis herdeiros. Em linha com a literatura, simulações numéricas atestam que uma parcela considerável do portfolio ótimo dos agentes seria constituída de anuidades mesmo diante de choques de liquidez, bequest motives, e preços não atuarialmente justos. Em relação a um aspecto relativamente negligenciado pela academia, mostramos que o tempo ótimo de conversão de poupança em anuidades está diretamente relacionado à curva salarial dos agentes. Finalmente, indicamos que, caso as preferências dos agentes sejam tais que o nível de consumo ótimo decaia com a idade, a demanda por anuidades torna-se bastante sensível ao sobrepreço (em relação àquele atuarialmente justo) praticado pela indústria, chegando a níveis bem mais compatíveis com a realidade empírica.

The purpose of this paper is to determine whether the adoption of a simple trend-following quantitative method improves the risk-adjusted returns across various asset classes within a South African market setting. A simple moving average timing model is tested since 1925 on the South African equity and bond markets and within a tactical asset allocation framework. The timing solution when applied to the JSE All Share Index, RSA Government Bond Index and within an equally weighted portfolio improved returns, while reducing risk. Testing the model within sample by decade highlighted periods of inferior return performance providing evidence to support prior research (Faber, 2007) that the timing model acts as a risk reduction technique with limited to no impact on return. / Dissertation (MBA)--University of Pretoria, 2012. / Gordon Institute of Business Science (GIBS) / unrestricted

is worldwide concern that people do not save enough towards retirement. To stimulate savings, tax incentives are a method employed by governments to encourage retirement savings. In this context, the asset allocation decisions that individuals make and the asset allocation restrictions that are imposed by regulators in an attempt to protect retirement savings, potentially impact the retirement ending wealth, which could be accumulated in the pre-retirement phase of an individual. The objective of the study was to determine the impact of tax legislation, Regulation 28 of the Pension Funds Act (24/1956) and asset allocation choices on accumulated retirement ending wealth and what could be deemed appropriate for most individuals considering different time horizons. Therefore, the aim of this study was two-fold: to determine whether pension fund legislation which limits the exposure to risky asset classes resulted in sub-optimal accumulated retirement ending wealth despite the associated tax savings; and to determine whether life cycle retirement funds, as opposed to different balanced retirement funds, were appropriate for most individuals. The study did not find support for the notion that direct investment funds dominated high equity balanced retirement funds that complied with Regulation 28 as measured by firstorder and almost stochastic dominance. Despite the higher asset allocation to equities that was possible with direct investments, this benefit was outweighed by the tax savings attributable to retirement funds. Additionally, the results of the study refuted the notion that a direct investment fund could be optimal over a long investment horizon. The implication of the finding was that an individual saving for retirement should, firstly, do so by taking full advantage of the tax savings that retirement funds offered. Hence retirement funds are an effective retirement saving tool despite the limitations on high-risk asset class allocations. The study found only limited support for the hypothesis that a theoretical retirement fund with a 100 per cent allocation to equities dominated a high equity balanced retirement fund that complied with Regulation 28 (particularly in the case of a 100 per cent local equity retirement fund compared with a Regulation 28 high equity balanced fund with no foreign equity exposure). Because the South African equity asset class was very volatile (annualised standard deviation of 19.8 per cent against 17.4 per cent for local against foreign equity in the data used in the study), a high exposure could lead to very low accumulated retirement ending wealth values; the intent of Regulation 28 was to protect the retirement savings of individuals against such adversity. Despite being perceived as very restrictive on the individual, the findings could not conclude that Regulation 28 restrictions on asset classes were inappropriate. This study provided no support for the notion that a life cycle fund dominated a balanced fund with similar starting asset allocation from the perspective of accumulated retirement ending wealth. This raised the question whether life cycle funds, which are often included as default options for members of retirement funds, have a place. Hence they were likely not the optimal choice compared with a balanced fund counterpart with similar starting asset allocation. However, they could be attuned to the preferences of the individual (such as risk and personal preferences) rather than a rational objective assessment of one fund compared with another. The study provided mixed support for whether a life cycle fund dominated a balanced fund with dissimilar starting asset allocations. This indicated that whether there was a place for a life cycle fund in any retirement fund default options, or whether it was optimal compared with an alternative balanced fund, strongly depended on the underlying asset allocations of the funds while the length of the glide path, the investment horizon as well as the risk and return characteristics of the investable universe could also influence the conclusion. The study uniquely contributed to the retirement savings question with evidence that did not support the notion that Regulation 28 of the Pension Funds Act was necessarily inappropriate to serve the purpose of protecting retirement savings. The study also showed how the lower risk attribute of life cycle strategies impacted on accumulated retirement ending wealth, how it compared with balanced funds and which choice would be appropriate for most individuals. Because the life cycle industry is a fast-growing portion of the retirement fund market and becoming more popular as default options in retirement funds, the study contributed by contrasting life cycle funds with balanced funds and showed that the choice of which fund was optimal, was driven by the different characteristics of the funds such as investment horizon, starting and ending asset allocations as well as the length of the glide path. / Thesis (PhD)--University of Pretoria, 2015. / tm2016 / Financial Management / PhD / Unrestricted