收益差與股票價格之研究

Abstract

在本篇論文研究中，我們利用一套完整的理論架構來做為分析的工具，藉以討論股票價格與短利及長利之間的連動關係。除此之外，更考慮一個離散時間的模型來研究一般投資人關於股票與債券市場的最佳投資組合並且介紹收益差的相關性質。利用我們設定的模型所得到的結果有以下主要三點：首先、研究結果顯示利率水準與股票市場的預期報酬率息息相關並且也受股價波動率的影響，不過，投資者的相對風險規避程度卻關係不大，更進一步地說，利率水準會隨著股票預期報酬率及波動率增加而增加。第二、股價波動越大，利率波動的幅度也跟著變大。此外，也發現當股價上升機率趨向中間時，利率波動率會趨向最大值。最後，也是本篇論文的也就主題，收益差會隨著股票預期報酬率及股價波動率增加而增加。同樣地，來自投資者相對風險規避係數的影響仍然有限。而最後在這個研究架構下，我們將可以再一次地驗證債券預期利率超出即期利率的部分將與其波動率成正比。

In this thesis we explore a theoretical framework to analyze the associations between stock prices, short-term interest rates, and long-term interest rates. In particular, this study considers a discrete time model in which investors have positions of stocks and determine the optimal portfolios of stocks, short-term bonds, and long-term bonds. Several properties of yield spreads are also discussed. The main results are summarized as follows. First, interest rate level correlates closely with the expected rate of return on stock market and the volatility of stock prices, but the extent of relative risk aversion almost does not matter. This paper further indicates that interest rate level increases as either the expected rate of return on stock or the volatility of stock prices increases. Second, the more stock prices fluctuate, the larger volatilities of interest rates become. It also finds that the volatilities of interest rates get toward the maximum as the probability of an upward movement of stock prices tends to the one of a downward movement of stock prices. Third, yield spreads also increase as either the expected rate of return on stock or the volatility of stock prices increases. Similarly, the relative risk aversion does not affect the yield spread significantly, too. Under our framework, it is verified again that the expected rate of return on any bond in excess of the spot rate is proportional to its volatility.