市值加權的投資組合方式一直廣為投資者所接受，其誘人之處莫過於集合前幾大市值的公司，並依據市值加權分配權重。在Markowitz(1952)提出的投資理論基礎下，討論了能夠在最小風險下獲得較高的預期報酬，應用在資產配置上即為最小變異數投資組合的投資策略。此觀念出現時，造成了市值加權投資組合其投資效率性受到質疑；由於影響市場變動的因子複雜性高，報酬率並不容易預測，因此出現了不少以最小風險為主要投資目標，而非追求高的預期報酬為主要目的之投資觀點。 本研究以市值加權投資組合為比較對象，探討最小變異數投資組合是否為更有效率的投資組合。以台灣50為市值加權投資組合，運用台灣50資料以滾動視窗的方式估計出最小變異數之權重，以此為最小變異數投資組合，比較兩者間的投資報酬率、績效表現。此外，本研究也將同時探討3種滾動視窗的期間長短，配合4種權重持有時間策略，以期了解參考資訊的時間長短、以及持有權重長短的策略是否會影響最小變異數投資組合的報酬率表現；最後，再運用迴歸分析，了解最小變異數投資組合與Fama-French三因子和動能因子之間的關聯性。 研究結果指出，當參考資訊越長期的滾動視窗估計方式，最小變異數投資組合會有較穩定的投資報酬率；若搭配長期的權重持有期間，能運用在長期投資。欲投資短期則可運用滾動視窗較短的估計方式，其在更新資訊較迅速的優勢之下，擁有較極端的報酬率的機率大，同時績效表現也較佳，此也代表最小變異數投資組合的權重估計若適當，則報酬率表現相當傑出；反之則有相當可觀的損失。觀察影響因子層面，最小變異數投資組合主要受到市場溢酬因子的影響，但根據短期權重持有的策略來說，則是動能因子影響越趨顯著。

資產配置問題與方法一直是投資人所關心之重要課題。藉由不同之建構投資組合的方法尋找資產的最適權重分配，可使得投資人對所持有資產的管理變得更容易且具效率。在這些方法當中，最小變異數投資組合可滿足追求風險極小化之需求。本文亦從此出發，探討一種特殊的最小變異數投資組合：加權範數最小變異數投資組合，並以台灣50作為實證資料，運用十個績效指標來衡量加權範數最小變異數投資組合、其他三種標竿投資組合與指數型基金台灣50之表現。 結果發現本研究所選取之台灣市場資料在運用加權範數最小變異數投資組合下，確實可以打敗其他大部分投資組合以及台灣50基金，並且在以下兩論點與過往文獻之敘述一致：加入報酬限制條件無法改善績效、使用替代參數亦可提供相稱績效。 / The asset allocation problem has always been an important issue on which investors concern. It is easier and more efficient for investors to manage their assets through constructing their portfolios in different methods to find the most optimized weight of assets. This essay explores a special portfolio, Weighted-Norm Minimum Variance Portfolio (WNMVP), which can minimize the risks of investment, and use Taiwan stock market data to undertake empirical study. The research measured the performance of WNMVP, other three benchmark portfolios, and Taiwan Top 50 ETF (0050) by using ten indicators, bringing three findings. First, WNMVP performs better than most of other portfolios do. Second, adding estimated mean return vector into the WNMVP does not improve performances. Third, three alternative norm penalties provide comparable performance as parameters in WNMVP do. The second and third findings are consistence with previous literature.

Most indexes use a cap-weighted strategy as the asset allocation method. Many researchers suggest that although the cap-weighted strategy often serves as an appropriate surrogate to the market portfolio, it cannot consistently outperform other portfolio weighting strategies. The main reasons behind it would be related to the market movement and the underlying volatility. It is possible to narrow down the scope of the research by focusing on an industry index as was done in this research. The focus would be on the mining index of Indonesia. Comparisons will be done between the established index to other portfolio weighting schemes, namely the equally weighted portfolio and the minimum variance portfolio. The results of the research was that the index was not quite efficient, both on the returns and the Sharpe or information ratio aspect. There are many possible reasons behind this, but the most possible reasons would be that the stocks included do not contribute to diversification, over focus on the coal industry, lack of rebalancing or restructuring, in addition to the market itself. The implication of this research would be that stock exclusion might also contribute to risk minimization.