The performance of cash protection strategies implemented in the South African market are investigated in order to establish if investors are able to add value through the use of dynamic portfolio insurance methods. The analysis is performed, using monthly data, from January 1961 to August 2014 using six alternative methodologies including both a Fixed Rate and Rolling Average Stop-Loss approach, a Lock-In approach, a Constant Mix strategy, a Constant Proportion Portfolio Insurance ("CPPI") approach and an alternative CPPI approach using a Ratchet mechanism. The results indicate that the use of such cash protection strategies can markedly improve portfolio performance from a risk return perspective compared to a pure diversified investment strategy. Notably, the use of older, simpler trading strategies such as the Stop-Loss and Lock-In approaches at optimum threshold levels can still offer investors higher risk to reward benefits with less commitment required. These strategies, though, lack the flexibility observed with the more recently developed dynamic trading strategies in terms of providing for varying risk appetites.

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.

機構投資者在現今全球的金融市場中佔有舉足輕重的地位，但是在財務理論的領域裡，他們卻是被極度忽略的一群。本文的第一個部分（見第二章）建構在傳統的期望效用理論之下，進而推導出機構投資者的最適動態資產配置模型。研究發現機構投資者的最適動態資產配置乃是由標竿避險元素與跨期-規模避險元素所共同組成。標竿避險元素述說了機構投資者跟隨標竿投資組合的現象，而跨期-規模避險元素除了為資產配置迷思提供了一個可能的解決之道外，更指出機構投資者會隨著所管理的資產增加而趨於保守。再者，近年來傳統的期望效用理論履遭學者們的質疑，許多實證結果均顯示展望理論更能貼切描述人們的行為模式。本文的第二個部分（見第三章）假設機構投資者的行為模式符合展望理論的公理與假說，進而推導出機構投資者的動態資產配置模型。研究發現當機構投資人處於獲利的狀態之下時，其最適動態資產配置和第二章所得到的結果完全相同，但是，當機構投資人處於損失的狀態下時，他會變得比較積極，持有的風險性資產會大於處於獲利狀態之下時所做的決策。雖然行為財務學已行之有年，但是大家對於損失趨避係數對資產配置所造成的影響所卻知極為有限，本文在此提供了一個參考的模型。本研究發現，損失趨避係數對動態資產配置的影響力會被風險趨避係數、個別投資人對機構投資者績效的敏感度以及機構投資者本身所收取的管理費所抵消掉。此外，近年來金融市場巨幅震盪的現象履見不鮮，本文的最後一個部份（見第四章）假設機構投資者的行為模式符合展望理論的公理與假說，進而在跳躍模式下推導出機構投資者的動態資產配置模型。研究發現在跳躍模式下機構投資者的最適動態資產配置乃是由標竿避險元素、跨期-規模避險元素與跳躍避險元素所共同組成。這個新的元素－「跳躍避險元素」，用以描述機構投資者在面對 跳躍模式所帶來的不同衝擊時所產生的不同回應。本研究發現即使面對相同的投資環境，機構投資者仍然會因為本身所處的狀態不同而有不一樣的投資決策，這個結果迥異於傳統的理論模型，是一個相當有趣且值得進一步研究的議題。此外，本研究還發現損失趨避係數在不同的狀況之下會分別發揮不同的影響力，對損失趨避係數在財務理論上的意義提供了另一個新的視野。 / Institutional investors do matter in financial market, but most of the studies on institutional investors have not determined holdings of different assets by institutional investors. Institutional investors who receive payments and deposits from their customers but they are also subject to withdrawals from them. Compared with individual investors, institutional investors do bear the extra risk that evokes from individual investors. Appling dynamic programming approach, we derive the optimal dynamic asset allocation of institutional investors. In chapter 2, we find that the optimal dynamic asset allocation of the institutional investor with exponential utility function contains two components: the benchmark hedge component and the intertemporal-size hedge component. The benchmark hedge component indicates that the institutional investor takes care of the volatility of benchmark portfolio. The intertemporal-size hedge component provides a possible solution to asset allocation puzzle and depicts that the position of risky assets held by the institutional investor is inversively proportional with its total net managed assets. In chapter 3, we take operating cost into account and find that the optimal dynamic asset allocation of the institutional investor with revised value function will hold more risky assets when she is facing losses, and the sensitivity of loss aversion to dynamic asset allocation strategy is inversively proportional with the absolute risk aversion coefficient, the sensitivity of flow to performance, and the management fee charged by the institutional investor. In chapter 4, we consider both the operating cost and the risk of a sudden large shock to security price into account and find that the optimal dynamic asset allocation of the institutional investor has a further component than that in chapter 3. The further component is labeled "jumps hedge component". Besides, the optimal dynamic asset allocation is divided into four situations that figure the institutional investor with different status quo will make different investment decision. It is a very surprisingly result. Furthermore, we find a very interesting phenomenon that the loss aversion coefficient plays different roles in different situations.

In the first essay, I decompose inflation risk into (i) a part that is correlated with real returns on the market portfolio and factors that determine investor’s preferences and investment opportunities and (ii) a residual part. I show that only the first part earns a risk premium. All nominal Treasury bonds, including the nominal money-market account, are equally exposed to the residual part except inflation-protected Treasury bonds, which provide a means to hedge it. Every investor should put 100% of his wealth in the market portfolio and inflation-protected Treasury bonds and hold a zero-investment portfolio of nominal Treasury bonds and the nominal money market account. In the second essay, I solve the dynamic asset allocation problem of finite lived, constant relative risk averse investors who face inflation risk and can invest in cash, nominal bonds, equity, and inflation-protected bonds when the investment opportunityset is determined by the expected inflation rate. I estimate the model with nominal bond, inflation, and stock market data and show that if expected inflation increases, then investors should substitute inflation-protected bonds for stocks and they should borrow cash to buy long-term nominal bonds. In the lastessay, I discuss how heterogeneity in preferences among investors withexternal non-addictive habit forming preferences affects the equilibrium nominal term structure of interest rates in a pure continuous time exchange economy and complete securities markets. Aggregate real consumption growth and inflation are exogenously specified and contain stochastic components thataffect their means andvolatilities. There are two classes of investors who have external habit forming preferences and different localcurvatures oftheir utility functions. The effects of time varying risk aversion and different inflation regimes on the nominal short rate and the nominal market price of risk are explored, and simple formulas for nominal bonds, real bonds, and inflation risk premia that can be numerically evaluated using Monte Carlo simulation techniques are provided.

[pt] Nesta tese buscamos fornecer duas diferentes abordagens para a otimização de carteiras de ativos sob incerteza. Demonstramos como a incerteza acerca da distribuição dos retornos esperados pode ser incorporada nas decisões de alocação de ativos, utilizando as seguintes ferramentas: (1) uma extensão da metodologia Bayesiana proposta por Black e Litterman através de uma estratégia de negociação dinâmica construída sobre um modelo de aprendizagem com base na análise fundamentalista, (2 ) uma abordagem adaptativa baseada em técnicas de otimização robusta. Esta última abordagem é apresentada em duas diferentes especificações: uma modelagem robusta com base em uma análise puramente empírica e uma extensão da modelagem robusta proposta por Bertsimas e Sim em 2004. Para avaliar a importância dos modelos propostos no tratamento da incerteza na distribuição dos retornos examinamos a extensão das mudanças nas carteiras ótimas geradas. As principais conclusões são: (a ) é possível obter carteiras ótimas menos influenciadas por erros de estimação, ( b ) tais carteiras são capazes de gerar retornos estatisticamente superiores com perdas bem controladas, quando comparadas com carteiras ótimas de Markowitz e índices de referência selecionados. / [en] In this thesis we provide two different approaches for determining optimal asset allocation portfolios under uncertainty. We show how uncertainty about expected returns distribution can be incorporated in asset allocation decisions by using the following alternative frameworks: (1) an extension of the Bayesian methodology proposed by Black and Litterman through a dynamic trading strategy built on a learning model based on fundamental analysis; (2) an adaptive dynamic approach, based on robust optimization techniques. This latter approach is presented in two different specifications: an empirical robust loss model and a covariancebased robust loss model based on Bertsimas and Sim approach to model uncertainty sets. To evaluate the importance of the proposed models for distribution uncertainty, the extent of changes in the prior optimal asset allocations of investors who embody uncertainty in their portfolio is examined. The key findings are: (a) it is possible to achieve optimal portfolios less influenced by estimation errors; (b) portfolio strategies of such investors generate statistically higher returns with controlled losses when compared to the classical mean-variance optimized portfolios and selected benchmarks.

增強式學習（Reinforcement Learning）透過與環境不斷的互動來學習，以達到極大化每一期報酬的總和的目標，廣泛被運用於多期的決策過程。基於這些特性，增強式學習可以應用於建立需不斷動態調整投資組合配置比例的動態資產配置策略。 本研究應用Deep Q-Learning演算法建立動態資產配置策略，研究如何在每期不同的環境狀態之下，找出最佳的配置權重。採用2007年7月2日至2017年6月30日的美國中大型股的股票ETF及投資等級的債券ETF建立投資組合，以其日報酬率資料進行訓練，並與買進持有策略及固定比例投資策略比較績效，檢視深度增強式學習在動態資產配置適用性。 / Reinforcement learning learns by interacting with the environment continuously, in order to achieve the target of maximizing the sum of each return. It has been used to solve multi-period decision making problem broadly. Because of these characteristics, reinforcement learning can be applied to build the strategies of dynamic asset allocation which keep reallocating the mix of portfolio consistently. In this study, we apply deep Q-Learning algorithm to build the strategies of dynamic asset allocation. Studying how to find the optimal weights in the different environment. We use Large-Cap, Mid-Cap ETFs and investment-grade bond ETFs in the U.S. to build up the portfolio. We train the model with the data of daily return, and then we measure its performance by comparing with buy-and-hold and constant-mix strategy to check the fitness of deep Q-Learning.