本研究探討通貨膨脹風險下長期投資人之最適資產配置。由於長年期通貨膨脹之估計誤差於投資決策上容易產生顯著差異，我們延伸 Brennan and Xia (2002)的模型，嘗試以消費者物價指數預估及修正通貨膨脹率，利用貝氏過濾方法預估未來通貨膨脹率。以平賭過程描述基金的限制條件，最適化投資人之效用值求得加入可預測性效果後之最適多期資產組合模型。研究結果顯示，長期投資人之最適策略可表示為固定比例股票指數基金及不同存續期間固定收益基金之組合。以不同存續期間之固定收益債券可以有效建構規避通貨膨脹風險之避險組合。本研究並提供數值計算與分析。 / This paper examines the optimal portfolio selection for a long-term investor. In order to consider the uncertainty of inflation rate, we extend the work in Brennan and Xia (2002) and use the consumer price index (CPI) to estimate and update the inflation rate through the filtering mechanism. The stochastic real interest rate is assumed to follow the Vasicek-type model. The investor’s optimal portfolio selection is solved through the Martingale method. The result is given in a simple closed form solution. We show that the optimal strategy for the fund manager in hedging the inflation uncertainty is to incorporate a dynamic fixed income portfolio with different durations. Numerical illustration is provided to clarify our findings.

The paper investigates dynamic optimal portfolio strategies of utility maximizing portfolio managers in the presence of risk constraints. Especially we consider the risk, that the terminal wealth of the portfolio falls short of a certain benchmark level which is proportional to the stock price. This risk is measured by the Expected Utility Loss. We generalize the findings our previous papers to this case. Using the Black-Scholes model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results.

本論文含蓋三篇文章，分別從評價、避險和風險控管三方面，分析上限型股權連結保本票券。 第一篇文章為上限型股權連結保本票券之設計、評價和比較。本文考量投資人保守的投資行為與設限型股權連結票券所存在的delta跳躍(delta jump)現象，延伸Brennan and Schwartz (1976)模型，提出一個能在股價波動之際，使發行的避險部位delta呈現平滑變動且兼具保本(protected principal)功用的一般化模型(general form)。相較於一般的設限型股權連結保本模型，本模型具有以下特色。第一，加入股價成長率的調整因子(adjustable factor)，當景氣低靡，股價不停下跌時，正的調整因子可減緩股價下滑之勢，進而增加投資人在票券到期日時獲取更多資本利得(capital gain)的機會。同時，調整因子縮小了當期股價成長率與股價上限成長率(capped stock growth rate)之間的差距，繼而減緩delta 跳躍的幅度，降低發行者的避險成本。並且在HJM利率模型下，delta隨股價與股價波動度的變化更顯平滑(smooth)。第二，在保本率(protection rate)和參與率 (participation rate)不變之下，本模型的期初合理價格(fair price)較低，投資人能以較低的成本取得同等的投資保障。第三，若將本票券的名目面額(notional principal)視作共同基金(mutual fund)的淨值(net value)，而該淨值與股價連動，則本模型即成為股權連結的保本型基金(principal-protected fund)。 第二篇文章是路徑依賴之上限型股權連結保本模型之評價和風險測量。該文是擴展Brennan and Schwartz (1976)模型發展一個路徑依賴之上限型股權連結保本模型，並且提出一個比二元數模型更精確的封閉解。此外，也對七個時間序列進行股價波動度之精確檢定，得知AR-ARCH(1)模型對上限型股權連結保本票券而言，較其它時間序列模型，更能有效估計股價之波動度。 第二篇文章是外國資產的風險管理。目前在國內金融市場上，國外金融商品很多，大都以外幣計價，因此匯率風險是投資人不可忽視的因子。本文拓展Kupiec(1999)模型，將匯率風險加入模型中，使投資人更有效進行風險管理。 / This thesis studies valuation, hedge and risk management of capped equity-linked and principal-protected notes by means of the following essays: (1) Design, Valuation and Comparison of Capped Equity-linked and Principal-protected Notes (2) Valuation and Risk Measurement of Capped Equity-linked and Principal-protected Notes with Path Dependence (3) Risk Management of Foreign Assets Capped equity-linked and principal-protected notes are similar with barrier options. There exists delta jump as stock price or growth rate reaches the barrier. But previous studies about equity-linked and principal-protected notes with a restricted growth rate of stock price never explicitly discussed how the delta jump could be solved. In my first essay, I present a new design for capped equity-linked and principal-protected notes and add an adjustable factor to growth rate of stock price in such a way that the adjustable factor narrows the gap between the current stock growth rate and the capped stock growth rate and thus really reduces the magnitude of the delta jump and hence lowers the hedging cost for brokers. Recently, the focus of previous studies about principal-protected notes has been on either the restriction on the rate of stock return or the path dependence on the underlying asset, but not both in the same context. In my second essay, I develop a model on the capped, equity-linked and principal-protected notes with path dependence. There are two issues in this article. The first issue is valuation on the capped, equity-linked and principal-protected notes with path dependence. I find a closed-form approximation using the 2nd-order Taylor approximation and the method of Vorst (1992) that has higher accuracy than binomial tree model as maturity time or volatility becomes large. The second issue is risk measurement. I use VaR model to evaluate market risk of the principal-protected notes, and employ seven univariate time series models to forecast volatility and examine the accuracy. Additionally, investors may well encounter potential loss as the prices of financial products are reduced in the secondary market. The VaR is mainly concerned with the downside risk and becomes a standard measure of financial market risk that is increasingly used by investors. But if we want to apply 〝textbook〞formulation to risk management of foreign assets, there leaves exchange rate risk out of consideration. Therefore, I extend the work by Kupiec (1999) to present VaR formula with exchange rate risk for foreign assets and then to manage market risk usefully.