Mean variance optimization has shortcomings making the strategy far from optimal from an investor’s perspective. The purpose of the study is to conduct an empirical investigation as to how modern methods of portfolio optimization address the shortcomings associated with mean variance optimization. Equal risk contribution, the Most diversified portfolioand a modification of the Minimum variance portfolio are considered as alternatives to the mean variance model. Portfolio optimization models introduced are explained in detail and solved using the optimization algorithms Cyclical coordinate descent and Alternating direction method of multipliers. Through implementation and backtesting using a diverse set of indices representing various asset classes, the study shows that the mean variance model suffers from high turnover and sensitivity to input parameters in comparison to the modern alternatives. The sophisticated asset allocation models equal risk contribution and the most diversified portfolio do not rely on expected return as an input parameter, which is seen as an advantage, and are not affected to the same extent by the shortcomings associated with mean variance optimization. The paper concludes by discussing the findings critically and suggesting ideas for further research. / Maximering av avkastning i samband med minimering av varians, på engelska kallat Mean variance optimization, är inte optimalt ur en investerares synpunkt. Syftet med denna uppsats är att genomföra en empirisk studie av hur moderna metoder för portföljallokering adresserar de problem som är förknippade med Mean variance optimization. Mer specifikt undersöks allokeringsstrategierna Equal risk contribution, Most diversified portfolio samt en variant av Minimum variance som ersättare till Mean variance optimization. Allokeringsmetoderna beskrivs detaljerat och löses med optimeringsalgoritmerna Cyclical coordinate descent och Alternating direction method of multipliers. Genom implementering och historisk simulering med ett antal index som representerar olika tillgångsslag visar studien att Mean variance optimization innebär hög portföljomsättning och har en större känslighet för ingångsparametrar i jämförelse med de moderna alternativen. De sofistikerade allokeringsmodellerna Equal risk contribution och Most diversified portfolio bygger inte på ingångsparametern förväntad avkastning, vilket ses som en fördel, och drabbas inte i samma utsträckning av problemen associerade med Mean variance optimization. Studien avslutas med att diskutera resultatet kritiskt och ge förslag på vidare studier som bygger på den teori och det resultat som har presenterats.

本研究利用元大台灣50 ETF作為樣本資料，檢測2006年至2016年實證期間風險基礎指數和市值加權指數所分別建構的投資組合，其績效表現、風險表現、分散性表現的優劣性；其中Choueifaty, Froidure, and Reynier (2011) 所建構的最佳風險分散投資組合 (most diversified portfolio) 為近年來新起的風險基礎指數投資組合，我們將證實在獲得良好的投資組合分散性同時，如同其他的風險基礎指數投資組合的目標，同時也能獲得超越以追蹤市值加權指數為標的的投資組合績效。 本研究以夏普比率、信息比率、阿爾法作為衡量績效的指標；以標準差、貝他作為風險衡量的指摽；另以Choueifaty and Coignard (2008) 提出的分散性比率作為分散性衡量的指標。實證結果顯示，在整體實證期間，最佳風險分散投資組合在績效、風險、分散性的指標上皆有超越市值加權指數投資組合的能力，再以年為單位的個別期間，其績效衡量上大致優於市值加權指數投資組合，風險和分散性衡量上則優於市值加權指數投資組合的表現，但論以其整體表現，並非為本研究所提出的風險基礎指數投資組合中最佳者，因此投資人在選擇該類投資組合策略時，建議從該投資組合過去表現中判斷，選擇符合自己投資習慣者為之。 / This article examines the performance, risks and diversification of different types of portfolio strategies such as risk-based indexes and cap-weighted index during 2006- 2016. We introduce the recent most diversified portfolio (MDP), which was proposed by Choueifaty, Froidure, and Reynier (2011) and find the result that like the goal of other risk-based portfolios, which is to improve the risk-return profile of cap-weighted portfolio, MDP surpasses overall performance, risks and diversification compared to cap-weighted portfolio while achieving diversification. We use Sharpe ratio, information ratio and alpha as the performance indicators, use standard deviation, beta as the risk indicators, and adopt diversification ratio (DR), which was proposed by Choueifaty and Coignard (2008), as the diversification indicator in our analysis. The results of this study show that MDP surpasses overall performance, risks and diversification compared to cap-weighted portfolio in the full empirical period. In addition, MDP is generally superior to cap-weighted portfolios in terms of performance in many single years of the whole period, and completely beat cap-weighted portfolios in terms of risks and diversification in every single year of the whole period. Although the ability of exceeding cap-weighted portfolio, MDP do not win first place of mentioned risk-based portfolios in our research. As a result, we suggest investors choose their portfolio strategies refer to its past performance, risks and diversification, and select the best according to their investment preference.