投資組合管理：資產最佳配置、保本與套利之模型規劃

Abstract

本論文針對投資組合管理的四項主題進行研究。在積極型投資組合研究中，以均異效率組合為基礎的各種投組最適配置規劃方法，於跨國資產配置中並未考慮當期市場聯動行為、資產間領先-落後期數與投資者的理性預期對於投組規劃的影響，造成資訊不對稱下的前期資產最適配置在後期的績效表現出現落差。為處理上述問題，在第四章中，本文提出一種結合情境分析方法與均異最適規劃法的跨國投資組合規劃模型，該模型透過跨國投資組合內的價先資產與價後資產間的聯動情境分類，導入均異最適規劃模型中，藉以於當期調整於前期求取的投組風險-報酬結構且估計合理之期望報酬水準，作為後期投組資產配置的基礎，期以獲得為符合預期而修正後的投組效率前緣，在資訊不對稱的環境下增加獲取超額報酬之機會。實證結果顯示，與傳統的均異投組規劃進行比較，所提出之情境-均異模型具有使得投組效率前緣依理性預期調整與減少求取風險矩陣資料量與計算成本降低等優點。 相對地，在保守型投資組合研究中，以CPPI以及TIPP為基礎的投組保險策略，該模型中的乘值因子的設定影響其保險期間內的績效表現甚鉅，但目前並無系統性的設定方法。因此本研究提出風險值資產配置保險策略模型，其為以風險值為基礎所推演之動態調整策略模型；該模型利用風險值估計方法以動態調整投組保險策略的乘值因子，達到提升上方報酬捕獲率與強化下方風險規避之目的。研究結果顯示所提模型具有最大化極小報酬的能力，並證明其符合理想投資組合保險策略模型之特性，在實務應用亦具有可行性與有效性。由實證結果中發現，在各型市場趨勢下，可顯著地擊敗主要標竿指數並優於其它傳統之投資組合保險策略；尤其面對市場跳空情境下，風險值資產配置保險策略模型可提供較傳統投組保險策略為佳的保本效果，同時降低破底機率。本研究成果除對理論之推展創新具貢獻外，尤其在面對時值全球性市場向下動盪修正趨勢之金融環境下，對於諸如保本基金、退休基金、平衡式基金與相關之保守型基金等，以資產配置保險策略為基礎之操作經理人或機構績效之提升，具明顯而實質之助益。 另者，在非線性資產積極型投組規劃方面，本研究所提出的是智慧型套利模型。Black-Scholes選擇權定價模型目前廣泛地被應用於各式選擇權合約之設計與交易操作、資產評價與企業價值估計等領域。但由於該理論定價模型的六大假設，使得在實務環境下產生諸多未盡考量之現象，若能充份考慮該現象於模型中，則可創造許多超額報酬的機會。本研究結合在傳統的Black-Scholes模型中尚未考慮，但影響顯著的隱含波幅偏態效用，以及選擇權商品和標的物價格間跳動級距的差異效果，透過基因類網以建立兩階段選擇權套利模型。實證結果顯示所提出的套利模型優於以Black-Scholes為基礎之傳統套利方法並適行於各式選擇權市場。智慧型套利模型有助於選擇權定價模型在實務環境下考慮其它影響評價的變因，提升理論模型與實務應用的配合度，同時強化選擇權市場交易之合理性與效率性。 最後，針對投資組合的績效評估，本研究比較滿意度水準(aspiration level)指標與傳統夏普指標的異同處。該部分的實證研究，是以投資組合決策為核心，主要重點乃在於找出最佳的投資組合；以傳統的均異模型為基礎的處理方式多半是以利潤最大或風險最小為決策目標。但在實際的金融市場中，尚必須考量諸多具有不確定性特質的問題。本部分研究所建構的組合決策分析模式裡，經由各輸入要因歷史的時間序列資料中，不僅考慮獲利最大化，且同時追求風險最小化。研究中利用模糊均異法則作為投資組合決策之分析工具，藉以在滿足報酬最大化、風險最小化的多目標決策前提下，建構模糊多目標投組模型，以找出組合中各要因的最佳配置量；其中，解的評價方式為將目標函數轉換成模糊歸屬函數，使其滿意水準滿足度為最大。研究中以全球主要股價指數為實證案例，比較滿意度水準指標與夏普指標的差異性。

This thesis examines four issues in asset allocation. The research on active portfolio, in which the traditional asset allocation method based on mean-variance efficient portfolio when forming portfolios does not take into account the linkage behavior, lead-lags or rational expectations of investors. That caused the unexpected result of performance on next-period while using allocations from the previous period in asymmetric information situations. To attack this bottleneck, we propose a multinational portfolio allocation model that integrates the mean-variance optimization with a scenario approach, which derives the linkage scenario classifications of assets in multinational portfolio in order to estimate rationally the expected return and risk matrix on next-period by modifying the previous-period periods so as to reallocate the weights of assets, thus increasing the opportunity to earn profits in an asymmetrical information situation. By using the Morgan Stanley country indices of global markets as the empirical evidence of portfolio content, we show that the proposed scenario- based mean variance model can serve as an efficient frontier to correspond with rational expectation of investors, decrease the data samples for calculating risk matrix. In addition, there will be less computation cost to solve mean-variance optimization. In contrast, the research on passive portfolio consists of linear assets, in which the original portfolio insurance model based on constant proportion portfolio insurance (CPPI) and time-invariant portfolio protection strategies (TIPP) strategies. The multiplier factor of CPPI or TIPP model significantly influences the performance of insurance. However no systematic tuning method has been presented to date. Thus, we propose a value-at-risk based asset allocation insurance model (VALIS), which is a novel dynamic strategy derived from the theorem of value- at-risk control. For this, we derive a dynamic tuning model for the multiplier in portfolio insurance strategies, considering of estimation of value-at-risk. The proposed model also improves the capability of capturing upside profits and enhances the ability to avoid downside losses. This research shows that the VALIS model seems a Min-Max style insurance strategy and demonstrates that this model fits in with the concept of portfolio insurance properties proposed by Rubinstein. Simulations and empirical study show the proposed model is superior to conventional portfolio insurance strategies such as buy and hold, constant-mix, the fixed multiplier CPPI and TIPP. Furthermore, the VALIS model also decreases the probability of failure to insurance. This research would contribute to the innovation of CPPI portfolio insurance based models and would be very helpful to passive investors or foundations for managing portfolios in the real world market, especially for the Asian markets or others in financial turmoil. Furthermore, this research on active portfolio, we proposed an intelligent arbitrage model. The Black-Scholes options pricing formula is widely applied in various options contracts, including contract design, trading, assets evaluation, and enterprise valuation, etc. However, this theoretical model is bounded by the influences of phenomenon caused in real world considerations by six unreasonable assumptions. Therefore, if we take into account the phenomenon of linkage behavior soundly, the opportunity to gain excess return would be created. This research combines both the remarkable effects caused by implied volatility smile (or skew), and discrepancy of both the underlying and derivative tick price movement limitation to form a two-phase options arbitrage model using genetic-based neural network. Evidence from the plain vanilla options in Taiwan indicates that the proposed model is superior to the original Black-Scholes based arbitrage model and is suitable to be applied to various options market in practice. The proposed model would help to coordinate the theoretical model and real world considerations. Finally, for performance evaluation, we compare the aspiration level index with the Sharpe ratio, emphasizing their differences. We begin with portfolio decision-making for which is placed on how to obtain an optimal solution under given circumstance, maximizing returns or minimizing risk. However, in real situations of management under uncertainty risk must be considered to make decisions. In this part, a decision-making method for portfolios is proposed to both maximize returns, and also minimize the risk of portfolios. The fuzzy mean-variance technique employed here is used to analyze the maximum return under minimum risk in market using the proposed model, called the fuzzy multi-objective portfolio (FMOP) model. It does so by setting up optimal weights for each of the portfolio factors. Aspiration level is represented in FMOP model using fuzzy membership functions to obtain feasible solutions, which are evaluated by the vague aspiration level of investors’ decisions. The cases study of global portfolio demonstrates the difference between the aspiration level index and Sharpe ratio.