馬可夫轉換模型是Hamilton(1989)所提出，他應用此模型的非線性特性研究美國的景氣循環。本文將此模型應用到財務領域當中，希望能從財務報表所揭露的某些訊息來掌握該公司在不同期間的報酬率變化，本文選用價值資產效果及公司規模效果，這兩各種效果對資產報酬率的解釋能力最為顯著，假使運用的得宜，模型的預測能力高，則投資者根據不同的資產特性轉換投資策略，長期間能獲得較佳的投資報酬率。同時，應用平滑過程使模型對狀態的認定更為精確，但在公司規模效果得到的成效明顯優於價值型資產效果，離群值的影響明顯對模型的推論造成嚴重的影響，最後，本文也就補救方法的可行性與否做為結論。

本論文使用大中取小原則及目標規劃技術，提出建構投資組合的數學規劃模型。要求此投資組合面對於不確定的股市，能夠在控制風險最小的情況下穩定且具有成長性的獲利。論文內探討如何透過數學的限制式來控制風險，而又能兼顧穩定且具有成長性的獲利，同時模型也可針對不同投資者的需求設定其數學規劃模型。最後以台灣股票市場做為實證分析的對象，給予不同的參數設定來驗證投資組合的表現。實證發現若以期初的配置比重持有到投資期間結束，此投資方式的績效欠佳。因此論文中進一步探討最佳的調整週期，實證顯示每經過8週，根據最新的資訊，重新調整建立新的投資組合，投資績效最好。 / This thesis proposed a mathematic programming model to construct a growth portfolio by using the mini-max principle and goal programming technique. The constructed portfolio is required to minimize the risk and to earn a stable profit under uncertain market. In the thesis, we discussed how to control the risk and maintain the growth of the portfolio by using the linear constraints. The proposed model also provides several parameters setting to meet the different investors' requirement. Finally, an empirical study will be provided by using the data from Taiwan’s stock market. The portfolios are constructed by giving different parameters and the performances are reported. The empirical study showed that holding a portfolio through the entire investment period without rebalance yield the performances that are not good. Therefore, the rebalance timing is investigated and the empirical study showed that a portfolio with rebalance strategy by every 8 weeks yield the best performance.

本研究探討長期信託基金（諸如退休基金，人壽保險公司等）之固定收益債券多期資產配置，利用時間可加性之效用函數描述投資者於投資期限時對財富大小之風險偏好程度，滿足基金之長期最適效益目標，為避免模型過於複雜，本文假設於動態完備市場中針對基金所持有之資產執行動態資產配置，建立財務動態調整機制以評量基金到期之獲利表現。為實際反應市場之風險程度，持有資產將利用隨機擴散過程表示，短期市場利率採用單因子Vasicek隨機模型表示，本文以給定金融市場之情境假設，說明不同到期日之債券為適當之獲利投資及避險工具，本研究之多期資產配置模型主要參考Cox與Huang (1989, 1991)與Sorensen (1999)，將未來財富過程利用平賭過程表示，給定不同投資限制條件、風險偏好程度與市場系統風險，以擬似動態規劃實際計算與比較每期之最適資產配置。 / This study attempts to investigate the hedging behavior through multi-period asset allocation strategy for the long-term fund manager, i.e., pension fund managers, life insurers, etc. Time additive utility function is employed to depict the risk preference of the investors during his investment time horizon. Based on their long-duration liabilities, assets held by the fund manager are employed in hedging and speculating under dynamic complete market assumption. To fully reflect the financial risks from the market, a risk management mechanism is implemented to monitor the long-term financial soundness. Short-term interest rate model proposed by Vasicek is employed to characterize the diffusion pattern of the invested assets. Current financial market information are incorporated and investigated to portray the hedging strategy through fixed income securities with various maturities. The quasi-dynamic approach proposed in Cox and Huang (1989, 1991) and Sorensen (1999) are implemented to construct the optimal asset allocation model. The optimal strategy is examined through maximizing the indirect utility function through the optimal growth portfolio. Finally, the hedging behaviors are compared and fully explored under various market scenarios.

Bakgrund: Det finns många aktier att välja mellan på aktiemarknaden. För en person som aldrig tidigare har handlat med aktier kan det vara svårt att veta vilken investering som efter en tid kan generera ett högre värde än det satsade kapitalet. Relativvärdering är en investeringsstrategi som kan tillämpas för att identifiera dessa aktier. Syfte: Syftet med studien är att undersöka om värdemultiplarna P/E-talet, P/BV-talet och direktavkastning kan generera överavkastning genom investeringar i undervärderade aktier i finansbranschen. Om så är fallet, därefter påvisa vilken av värdemultiplarna som genererar högst avkastning. Metod: Studien har att tillämpat en kvantitativ metod med deduktiva inslag. Värde- och tillväxtportföljer har komponerats med värdemultiplarna P/E-talet, P/BV-talet och direktavkastning. Värdemultiplarna har beräknats fram med sekundärdata från databasen Thomson Reuters EcoWin Pro och årsredovisningar. Resultat: Studiens resultat påvisar att det går att generera överavkastning med relativvärdering som investeringsstrategi. Majoriteten av värdeportföljerna presterade bättre än tillväxtportföljerna. Portföljen som hade den högsta överavkastningen var värdeportföljen baserat på P/BV-talet. / Background: The capital stock market consists of many different shares. For a person who has never acted in shares, it can be difficult to know which investment over time that could generate a higher value than the invested capital. Relative valuation is an investment strategy that can be applied to identify these shares. Objective: The aim of this study is to investigate whether key ratios P/E-ratio, P/BV-ratio and dividend yield can generate excess returns by investing in undervalued stocks in the financial industry sector. If so, then demonstrate which of key ratios that generates the highest return. Method: This study has applied a quantitative approach with deductive features. Value and growth portfolios have been composed by key ratios P/E-ratio, P/BV-ratio and dividend yield. Key ratios have been calculated on secondary data from the database Thomson Reuters EcoWin pro and annual reports. Results: Our results demonstrate that it is possible to generate excess returns with the relative valuation as an investment strategy. The majority of the value portfolios performed better than the growth portfolios. The portfolio that had the highest excess return over the total period was the value portfolio that consisted of P/BV-ratio.