確定提撥制是現今退休金制度潮流的趨勢，而在這個制度下，勞工最後所能累積的退休金總額及每月所能領到的月退休金額度和個人帳戶的投資結果有很大的關係，所以個人帳戶的投資績效成為勞工退休生活安全性最重要的因素。 本研究的目的在提供一個方法以評量投資績效，使得在每月提撥一定金額到個人帳戶的情形下，對於投資期間的經濟環境以隨機投資模型或情境分析模型加以考量後，可以在不同的投資策略及起始資產配置下，找到適合投資人的最佳投資策略及起始資產配置。在本研究中考慮了股票和長期債券兩種投資標的，而投資標的之投資報酬率變化則以隨機投資模型(Stochastic Investment Model)及情境分析(Scenario Analysis)兩種模擬方式為之，其中在隨機投資模型模擬的部分，不同的隨機投資模型對於經濟環境有不同的設定，也因此將得到不同的投資結果，本研究採用在英國學術上廣為研究的Wilkie投資模型(1986)及黃泓智等人於2005年證券市場發展季刊所推導之台灣投資模型，並利用蒙地卡羅模擬的方式來建構投資標的之報酬率。而在情境分析模擬的部分，則設定三種基本的投資報酬率趨勢，並假設三種投資報酬率趨勢服從均勻分配，而後考慮投資期間分成前後兩個時期，搭配而得九種情境。 本文將觀察不同的起始資產配置(股票資產配置之權重考慮由0%~100%，間隔為1%，共101組；債券資產的權重則為1-股票資產配置之權重，也就是100%~0%)，並以投資組合保險中三種常見的投資策略：買入持有(Buy & Hold；BH)、固定比例混合法(Constant Mixture；CM)及時間不變性投資組合保護(Time-invariant Portfolio Protection；TIPP)，作為投資策略。 在三種投資策略及每種投資策略有101個起始資產配置下，將可以得到303組不同的投資結果，而每一組投資結果中，都可找到個人帳戶於退休時的累積金額、在一定目標所得替代率下之破產機率，以及平均投資報酬率和投資報酬率之標準差，並將所得之投資組合報酬率之平均值為縱軸，標準差為橫軸作圖，找出效率前緣；也就是說，可以依個人帳戶持有人的風險，在其所能忍受的風險下，找到最適的起始資產配置及投資策略，及依這樣的起始資產配置和投資策略下所能得到的平均報酬。另外，更進一步以Sharpe ratio及Reward-to-VaR ratio、Reward-to-CTE ratio三個指標來衡量投資表現，找出在這三個指標下的最適起始資產配置和投資策略。 在前述中，都未考慮到交易成本對於投資結果的影響，但在現實的環境中，交易成本對於投資結果是有影響的，所以本研究也會在考慮交易成本下，找到情境分析和隨機模型下的投資結果及效率前緣，並找出三個投資指標的值來衡量投資表現。 / The defined contribution plan is the trend of retirement pension funds management, but under this plan, the total account values accumulated and the retirement benefits paid each month that labors can get are great related to the investment results of the individual accounts. That's why we said that the investment result of the individual accounts is the most important factor the labors care about. In this article, we will focus on the measure of investment results. We consider bond and stock as our holding assets, and set the investment rate of return in two methods, including scenario analysis and stochastic model. In the scenario analysis method, we set fourteen scenarios to reflect the changes of the investment returns of stocks. In the stochastic model method, we take use of Wilkie investment model to set the investment return rate of stocks and bonds and simulate enormous data to find the average investment rate of return. In each method, we will consider 101 different initial ratio of stock value and three different investment strategies: Buy & Hold(BH)、Constant Mixture(CM) and Time-invariant Portfolio Protection(TIPP). After setting the investment rate of return and investment strategies, we can find 303 different investment results under three investment strategies and 101 initial ratios of stock values. In each result, we can get the accumulated amounts, the income substitute rate and the average rate of return, and use the average rate of return as y-axis, standard deviation as x-axis to find the efficient frontier. That is, we can find the optimal investment strategies and initial ratio of stock value under the risk we can tolerant. We will also use Sharpe Ratio、Reward-to-VaR ratio and Reward-to-CTE ratio to measure the investment results, and find the optimal investment strategies and initial ratio of stock value basic on the three ratios. In practice, the transaction cost is an important factor that will affect the investment results, so we also find the investment results under different situations which had considered the transaction cost.

隨著時間的發展，基金的種類與數量成倍數增長，導致投資人在挑選基金時，亦面臨了選擇股票時的窘境：投資標的數目過多、複雜度高，身陷其中，而不知如何挑選理想的投資組合。目前由於人們對於退休金的相關規劃愈益重視，遂有基金商品針對此概念來設計。 生命週期基金基本上符合這樣的概念，生命週期基金基本上是屬於一種組合型基金，但是並不一定要以組合型基金的型態來顯現，美國80只生命週期基金中將近半數為基金的基金。生命週期基金是為了滿足某個年份左右退休投資者的退休投資目標的基金，如FidelityFreedom系列、FrankRussell Life Points系列、T.Rowe PriceRetirement系列、Vanguard LifeStrategy系列等。例如FidelityFreedom2020是針對2020年左右退休的投資者設計的，為實現投資者退休的投資目標的基金，主要投資在Fidelity旗下股票型基金、債券型基金和貨幣市場基金等各類基金。我們便想要了解此種商品的投資型態下具有何種特色。 我們首先要探討基金在不同投資策略其表現如何，而我們衡量的方式---簡單的說是以是否能夠達到投資人的要求報酬率為基準，以投資報酬率來建構出年金終值，最後以各種投資策略所得到的最終價值之差距做為成本的衡量，之後我們則根據生命週期基金的樣態，自行設計出兩種投資模式同樣來探討不足要求資本的相關概念。 再來以投資聚集效果(pooling effect)為主題，因為在基金存在著不同風險容忍程度的投資人，所以我們希望探討在不同投資策略下所建構的效率前緣對於不同風險忍受程度的投資人是否具有超額報酬。 首先我們就兩種投資標的(股票、債劵)之投資報酬率變化以下列方式作設定---利用隨機模型(Stochastic Model)：並利用蒙地卡羅模擬的方式來建構投資標的之報酬率。 我們觀察不同的起始投資比重(股票資產權重考慮由0%~100%，間隔為1%，共101組；債券資產的權重則為1-股票資產權重，也就是100%~0%)，並以投資組合保險中三種常見的投資策略：買入持有(Buy & Hold；BH)、固定比例混合法(Constant Mixture；CM)及時間不變性投資組合保護(Time-invariant Portfolio Protection；TIPP)，作為投資策略。在完成對投資標的之報酬率變化及投資策略的設定後，就可以在三種投資策略及每個投資策略有101個起始權重下，得到303組不同的投資結果，如此我們就可以得到帳戶的最終價值，就可以針對是否符合投資者要求的報酬率做相關的研究。 同樣的我們可以就個別的投資策略建立個別的效率前緣。之後我們就不同風險容忍程度的投資大眾，以Harry M.Markowitz等人所提出的optimal frontier的概念加以設定風險點(risk point) ，各種不同風險程度的投資人即代表不同的風險點，如此我們便可以就不同的投資模型來探討基金的投資聚集效果(pooling effect) 。 最後我們想探討的部分則是希望讓投資大眾知道如果其處於何種經濟體之下，應該採用何種投資方式，或者是在投資人的不同要求之下，可以知道採取何種投資策略，以求學術上的操作可以應用到實務上，並求取更佳的效果。 / With the development of time, the kind and quantity of the fund become multiples to increase, cause investors to face the awkward situation while choosing the stock when they select funds: There is too much figure of the investment object marking investment complexity more diffcult , and does not know how to select ideal investment combination. Nowdays, people put emphasize on retirement plan more and more. so some mutual funds are designed for this concept. Lifecycle fund is identical to this concept .Lifecycle fund is a kind of Fund of Funds basically, but might not appear like the Fund of Funds , 80 Fund of Funds in U.S.A. nearly half appear like Fund of Funds . Lifecycle fund is for the fund of retired investors' retired investment needs which is different from age-changed , such as Fidelity Freedom series, Frank Russell Life Points series , T.Rowe Price Retirement series , Vanguard Life Strategy series ,etc.. For example Fidelity Freedom2020 is designed for pensioner's investor to retire about 2020 year, the fund that in order to realize the goal of investors when they retired, make an investment in many objectives, such as stock fund ,bond fund and money market fund ,etc. under command of Fidelity mainly. I want to know the characteristic of lifecycle fund and based on this concept to design mutual fund. I will discuss behavior of fund in different investment strategies, and the way which we measure ---It is to set the rate of returns by meeting investor's requirement as the datum, build and pay the end value of the annuity to construct by investing in the rate of returns, for the measurement of " bankrupt " with the disparity of the final value got of various kinds of investment strategies , later I designed two kinds of investment ways according to the concept of lifecycle fund and also discuss the concept of " bankrupt ". This research will also make emphasize on pooling effect , There are a lot of investors of different risk tolerance in the fund ,so I hope to discuss investor of different risk tolerance will have abcdrmal return under different efficiency frontier which are derived by different invest model and strategies. First, two kind investment target (stock, bond) Investment rate of returns by way of the following to settle ---Utilize Stochastic Mode: Wilkie investment model, Taiwan investment model and the rate of returns of the one that make use of simulation that build and construct investment terms. In each method, we will consider 101 different initial ratio of stock value and three different investment strategies: Buy & Hold(BH)、Constant Mixture(CM) and Time-invariant Portfolio Protection(TIPP).According to theses investment combination, I can construct different efficiency frontier under different investment models and strategies. Such final value of the account that we can receive so I can do relevant research to the rate of returns according with investor's request . Later, according to investor of different risk tolerance , set some risk point with the concept of optimal frontier published by Harry M.Markowitz, the investors of different risk degrees represent risk point, I can discuss pooling effect in fund under different investment model and strategies. Finally, the topic I want to discuss is let the investor know at which kind of economy , should adopt the investment strategies , or under investors' different requests, can know which kind of investment tactics are adopted , so that the operation on academy can be applied to the practice , and ask for better result.