通常已建立的指數基金，經過一段時間後其追蹤指數的效能已經無法滿足初期建購時的要求，此時管理者便面臨指數基金投資組合的調整問題。本論文融合建構指數基金的方法及最小化交易成本的概念，提出一個新的混合整數線性規劃模型以調整指數基金投資組合。模型亦考慮實務中交易成本、最小交易單位及批量、固定交易費用比率、以及資產總類數等限制。因此，模型包含整數變數及二元變數，求解也較為困難許多。本論文以啟發式演算法增進求解的效率，並以台灣50指數的相關資料做為實證研究的對象。 / The efficiency of index-tracking in index fund, which has been built, has usually been incapable to meet the needs after a period of time. In this moment, the managers have to face with the problems of the adjusting for index fund portfolio. In this paper, we integrate the methods of constructing index fund and the concepts of minimum transaction cost with it, and propose a new mixed integer linear program model to adjust the index fund portfolio. Moreover, the model also considers some limitations, such as the transaction costs, minimum transaction units and lots, fixed proportional transaction rates, and cardinality constraint in practical operating. For this reason, a set of integer variables and binary variables are introduced. However, they increase the computational complexity in model solution. Due to the difficulty of the MILP problem, a heuristic algorithm has been developed for the solution. The computational results are presented by applying the model to the Taiwan 50 index.

本篇論文以分析師對未來公司盈餘預測為基礎，使用剩餘所得模型來對台灣股票市場做實證研究。在這個架構下，我們比較了剩餘所得模型評價法與各種不同的傳統評價法對台灣50成分股的估算表現。 本篇論文的實證發現，內含價值對股票價格比率(intrinsic value to price ratio)對台灣50成分股的預測，在中短期的投資期間內相較於傳統評價法，預測力最高。帳面價值對股票價格比率(book value to price ratio)則在長期的投資期間內，預測力顯著高於其他評價法。盈餘對價格比率(earnings to price ratio)預測力最低。而將所有評價法一同列入考慮時，則發現並沒有任何一種評價法能明顯主宰其他不同的評價法，各種評價方法在預測未來股市表現是互補的。 本篇論文進一步探討剩餘所得模型評價法對台灣50成分股的交易策略，發現以剩餘所得模型估算出的內含價值為標準來進行交易，能得到正報酬。而考慮會計保守原則的模型報酬率能顯著高於沒有將會計保守原則列入考慮的模型。 / We provide an empirical assessment of the residual income valuation model bases on analysts’ forecast data in Taiwan stock market. In this framework, we compare the performance of alternative estimates of intrinsic value with traditional valuation estimates for the component stocks of TSEC Taiwan 50 Index. According to our results, intrinsic value-to-price ratio is a reliable predictor of market returns over short-to-mid period and book-to-price ratios is a reliable predictor over long horizons. Unlike the two ratios, earnings-to-price ratio has little predictive power for returns in Taiwan stock market. Furthermore, intrinsic value-to-price ratio does not dominate traditional valuation but provide another perspective of stock valuation, and we can have a better forecast of future return of Taiwan stock market with consideration of all valuation estimates.

自從槓桿型指數基金於各股票市場發行後，各國主管機關皆紛紛發出聲明表示，該商品並不適合長期持有；因此，該類型投資商品的公開說明書皆會註明不宜長期投資。然而，本研究實證結果發現，持有期間長短並非主要風險來源。雖然，如大家所知，槓桿型指數基金多是以「日」為單位追蹤指數，而導致複利效果 (Compounding Effect) 使基金長期報酬與槓桿倍數不同。 根據算出上述的報酬差異(Return Difference)可以發現不論是正向2倍或是反向1倍皆與台灣50報酬率的標準差有統計上顯著關係。反向1倍皆與台灣50報酬率的標準差有顯著負相關；反之，正向2倍與台灣50報酬率的標準差有顯著正向相關。然而，從已實現乘數(Realized Multiple)的分佈中可發現，不合理值並不隨投資期間越長而越多。意即儘管投資期間越長，並不一定會導致複利效果越大，而與目標槓桿倍數脫節。再者，隨著投資期間越長，波動度(volatility)的對於報酬差異的解釋力越強；因此，若想長期投資槓桿型指數資金，預測標的波動度的能力更顯為重要。 / When we browse the reports about the inverse and leveraged ETF, most of them emphasize that the LETF is not appropriate to long-term investors. However, in this research, we attempt to demonstrate the main factor of the performance of the leveraged and inverse ETF is not how long the LETF we hold, but the volatility of the underlying index or ETF. Observing the empirical test, no matter how long the investment horizon is, the coefficient of the variance of the Taiwan 50 is statistically significant both in the Taiwan 50 Bear -1X and the Taiwan 50 Bull. However, its effect on the Bear -1X is opposite to that on the Bull 2X. First, the relationship between the volatility and the return difference of Taiwan 50 and the Bear -1X is negative. In contrast, the relationship between the volatility and the return difference of Taiwan 50 and the Bull 2X is positive. However, in accordance with the distribution of the realized multiples, the frequency of either the Bear -1X or Bull 2X was not more and more when the holding period is longer. As a result, our research show the variance has a significant effect on both, no matter how long investors hold. If the volatility is moderate, the return difference may be close to zero; then the LETFs would be a convenient way to investors who desire to magnify the market return. Moreover, due to the increasing explanatory power of the volatility, we may make a further inference that whether the compounding effect is positive or negative depends on the volatility, especially within longer holding period. Therefore, without the great ability to forecast the variance, the LETFs are not recommended to the long-term investors.

本研究主係探討以投資者持有本國股票作為基礎投資組合，利用台灣五十成份股投資組合及金融期貨指數之月報酬率資料形成效率前緣，然後將本研究所選取之黃金產業GOX指數或以黃金現貨價格兩種黃金商品投資組合分別加入基礎投資組合中，觀察每個投資組合標的加入前後之投資機會集合之變化，是否基礎投資組合之效率前緣進一步向左偏移，並比較其優劣。此外進一步探討在兩種黃金投資組合加入基礎投資組合，分別在股市多頭及空頭市場時會不會產生相同的效果；並且藉由中央大學台灣經濟發展研究中心所調查訂定的消費者信心指數，以中位數區分為信心指數高或信心指數低兩組情境，並將兩種黃金商品投資組合在不同的情境依序分別加入基礎投資組合中，其基礎投資組合之效率前緣是否皆仍進一步向左偏移。實證結果發現，黃金現貨帶給基礎資產投資機會集合的貢獻，明顯優於黃金產業GOX指數，當檢定資產為黃金產業GOX指數時，「切點投資組合」差異W_1統計值上皆不具統計顯著性，整體而言當黃金產業GOX指數在加入投資組合之後，我們認為大部份的效果是來自分散原有的投資組合風險；然而黃金現貨在改善投資機會集合的貢獻上，來自「最小變異數投資組合」及「切點投資組合」的改善皆有顯著的效果。

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.

本文以摩根台指與台灣50指數成分股調整的股價效應做比較，兩者對於成分股調整的宣告及生效是否存在異常報酬，而異常報酬的不同是否與其指數編制方式有關。實證結果發現摩根台指新增股具有 顯著正報酬、剔除股具有顯著負報酬，且在宣告日二十天後價格呈現反轉，符合價格壓力假說。而台灣50指數新增股異常報酬則不顯著異於零，兩種指數的新增股在宣告成份股調整後皆有超額成交量、流動性持續增加。再者摩根台指的宣告效果比台灣50指數強，且透過加權的方式較能表現出指數成份股調整所帶來的現貨價格影響。 / The study examines both the price and volume effect of stock additions or deletions on both the MSCI Taiwan index and Taiwan50 index. We document significant abnormal returns of stock additions and deletions for the MSCI Taiwan Index both on the announced period or on the effective period. In addition, we also find a significant abnormal return of stock deletions for Taiwan 50 Index either announced period or the effective period. While we do not find any significant abnormal return of stock additions. Further more, both the announced date effect and the effective date effect for MSCI Taiwan Index are stronger than those for Taiwan 50 Index. Our results support the price pressure hypothesis.

有別於國內現有相關研究文獻，本研究首度將台灣50股價指數報酬率及區分多頭市場、空頭市場後之每日台灣加權股價指數報酬率、台灣50股價指數報酬率分別與相對應之每日外資買賣超金額納入研究，並以2002年1月至2008年12月底止之這一段時間為研究期間，從其間所經歷之數個多頭、空頭起伏波段，以瞭解外資之累積性淨買超或淨賣超行為對台灣股價指數報酬率所產生之影響，藉由實證數據探知外資於我國股市是否有洞燭先機，居證券市場領先者之能力，抑或僅是市場之追隨者。 經以因果關係檢定發現，就研究期間內所有樣本資料而言，在台灣加權股價指數方面，台灣加權股價指數報酬率與外資買賣超金額間呈具反饋互為因果之關係，但在落後期數加長後，加權股價指數報酬率對於外資買賣超金額仍維持相當顯著之影響關係，而外資買賣超金額對於加權股價指數報酬率影響之顯著性則有減弱現象。在台灣50股價指數部分，檢定結果則與台灣加權股價指數報酬率之情形有別，台灣50股價指數報酬率對外資買賣超金額存在著明顯之單向影響關係，即外資買賣超金額係隨著台灣50股價指數報酬率漲跌幅之高低而變動。 若將研究樣本資料分為多頭及空頭兩部分，經因果關係檢定發現，台灣加權股價指數與台灣50股價指數無論是在多頭市場或空頭市場，所呈現之結果均相同，即當市場處於大多頭時，外資買賣超金額單向的隨著加權股價指數報酬率及台灣50股價指數報酬率之變動而變動，但在市場處於小多頭或空頭時，外資買賣超金額與加權股價指數報酬率及台灣50股價指數報酬率間之因果關係並不顯著。