整合貨幣套利與投資組合模型之研究

A Study of Integrating Currency Arbitrage and Portfolio Selection Models

高瑋均(Wei-Chun Kao)

指導教授 ： 蔡榮發

國立臺北科技大學/管理學院/經營管理系碩士班/碩士(2014年)

https://doi.org/10.6841/NTUT.2014.00219

摘要

為了找出在給定風險情形下達到投資組合的獲利最大，亦或者是在給定投資組合獲利的情形下，達到風險最小的分散投資組合，投資組合選擇的問題通常被建構成一個二次規劃的問題。模型中可限制住分散的財富值、交易成本與邏輯限制。雖然許多模型都曾提出投資組合最佳化的問題，但在平均數變異數的模型中貨幣市場的波動很少被討論到。然而，貨幣匯率的波動可能會顯著地影響到所選擇的投資組合的獲利，因此，本研究參考了貨幣套利與投資組合模型，推導整合的確定性模型。根據貨幣市場中的即期匯率和遠期匯率，修改投資組合的模型，以得出最佳化的投資組合問題，本研究也考慮了交易成本、貨幣套利以及風險偏好。舉出實際的數值案例說明結果，呈現所提出的模型的有效性，以及更有效率的求解過程。分析的結果也對問題提供了有用的見解。

關鍵字

投資組合 ； 貨幣套利 ； 確定性最佳化

並列摘要

Portfolio selection problems are usually formulated as a quadratic programming program for finding a diversified portfolio that has the highest return for a given risk or the lowest risk for a given return. The formulated model can handle discrete assets, transaction costs, and logical constraints. Although many models have been proposed to investigate the portfolio optimization problems, the fluctuation in the currency market is rarely discussed in the mean-variance portfolio model. However, the currency exchange rates may affect the return of the selected portfolio dramatically. This study therefore considers currency arbitrage and portfolio selection optimization models to derive integrated deterministic models. According to spot exchange and forward exchange rates of the currency market, a revised portfolio selection model is constructed to derive an optimal portfolio. The model also considers transaction costs, currency arbitrage, and risk preferences. Numerical example results illustrate the effectiveness and efficiency of the proposed model and solution processes. Analysis results also provide useful insights into the problem.

並列關鍵字

Portfolio selection ； currency arbitrage ； deterministic optimization

參考文獻

6. 張志福(2011)。求解投資組合問題之全域最佳化方法。臺北科技大學經營管理系碩士班學位論文，1-7。

5. 黃梓蒼、扈永安(2008)。台灣金融市場套利方式分析與比較。會計研究月刊， 271，76-77。

2. 呂敏鳳 (2012)。貨幣套利交易模型之研究。臺北科技大學經營管理系碩士班學位論文，15-25。

10. Buhl, H. U., Fridgen, G., & Konig, C. (2013). Using financial derivatives to hedge against market risks in IT outsourcing projects–a quantitative decision model. Journal of Decision Systems, 22(4), 249-264.

11. Clark, E., & Ghosh, D. K. (2004). Arbitrage, Hedging, and Speculation: The Foreign Exchange Market. New Hampshire: Greenwood Publishing Group.