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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.

本文係針對臺灣50指數期貨與基金於2003年6月30日上市之後，臺灣期貨及現貨市場報酬率間領先落後關係與波動性的變化來進行探討。研究分為兩部份，第一部份是觀察臺灣50指數期貨與現貨之間的關聯性，並探討臺灣加權股價指數、金融保險類股股價指數及電子類股股價指數期貨與現貨市場間的變化；第二部份是採用可模擬現貨走勢的臺灣50指數基金、國泰金及臺積電的股價來做為現貨的替代變數，觀察其與期貨之間的關連性是否與第一部份的結果類似，若是實證結果極為相同，則相關機構與一般投資人將可運用各期貨與其標的指數中市值最大的股票來進行套利操作。此外，本文在進行模型估計時，首度採用一階段估計法，來聯合估計雙變量GARCH模型中的條件平均數方程式與條件變異數方程式，以避免過去相關文獻將兩條方程式個別估計時所造成的估計誤差。 實證結果所獲得的重要結論如下：首先，臺灣期貨市場的發展仍未趨成熟，並不具有價格發現的功能，在考慮風險溢酬方面，僅有臺灣50指數期貨與現貨的投資人會在報酬率之外，額外要求用以補償的風險溢酬，再者，臺灣50指數期貨與基金的上市，並沒有對臺灣現有的期貨與現貨市場造成顯著的影響，然而，替代變數並不能完全取代現貨指數，但相較之下，國泰金在臺灣50指數期貨與基金上市之後的那段期間模擬成效最好。 / This paper investigates the change of lead-lag relationship in returns and volatilities in Taiwan futures and spot markets after the introduction of Taiwan 50 Futures and Taiwan Top50 Tracker Fund (TTT) on June 30, 2003. The study divides into two parts. The first part examines the relationship between Taiwan 50 Futures and spot markets, and also discusses the change of Taiwan Stock Exchange Capitalization Weighted Stock Index, Taiwan Stock Exchange Banking and Insurance Sector Index, and Taiwan Stock Exchange Electronic Sector Index in futures and spot markets. Another part uses the stock price of TTT, Cathay Financial Holding Company and Taiwan Semiconductor Manufacturing Company as the substitutive variables of spot index and goes a step further to examine the relationships between them and futures individually. Additionally, this research used One-Pass Method for first time to estimate jointly the conditional mean equation and conditional variance equation of Bivariate GARCH Model to avoid estimating error in previous relative studies with Two-Pass Method. The major empirical results are as follows: first, the development of Taiwan futures market is incomplete. The futures market does not play the price discovery role to the spot market. Second, under the consideration of risk premium, only investors in Taiwan 50 Futures and spot markets would ask for compensated risk premium excepting returns. Third, the opening of Taiwan 50 Futures and TTT does not influence significantly Taiwan futures and spot markets. Last but not least, these substitutive variables can not replace spot index perfectly. However, comparing with others, the stock price of Cathay Financial Holding Company is the very model of Taiwan Stock Exchange Banking and Insurance Sector Index after the introduction of Taiwan 50 Futures and TTT.