隨著市場上金融創新的日新月異，越來越多的交易者應用商品的槓桿操作，在追求那令人稱羨超額報酬。在理論和實務上，凱利策略是一個頗具盛名但也有相當爭議的操作方法。其核心概念為極大化資本的長期成長率，在過去的歷史上被稱之為凱利準則，甚至被稱之為財富的公式。凱利準則為報酬率和風險的抵換關係，用來決定每次交易操作的槓桿或者是部位的大小。在實證方法上，我們分別報酬的對殘差分配使用 Normal , Generalized Hyperbolic , Generalized Error 這三種不同假設的EGARCH模型，並用其報酬的條件平均數和變異數計算預期的最適操作槓桿。在實務上，資金操作的風險管理比起交易策略是否有擇時能力來的更為重要。因此在本文中我們使用市場上S&P 500 指數的槓桿型ETF 回測了凱利策略在過去十年的表現和風險管理的控制以及其不同策略之間的比較。

While the much more use of leverage could be effective in generating alpha o investment, the Kelly strategy is an attractive approach to capital creation and growth. It is originated from the Kelly criterion dubbed “ fortunes formula “ which maximizes the long run growth rate of wealth. There is a tradeoff of rate of return versus risk/volatility as a asymptotic function solution of leverage or position size determined by the application of EGARCH model in the different residual assumptions given by the Normal, Generalized Hyperbolic, and the Generalized Error distributions. No matter there is any timing ability in any strategy, risk management is much more important especially with many repeated trading. We present the performance and risk control of the leveraged ETFs tracked the S&P 500 index in the past ten years using optimal leverage strategy derived by the full Kelly and fraction Kelly criterion.

中文摘要 ii
ABSTRACT iii
1. INTRODUCTION 1
2. RELATED LITERATURES 10
3. METHODOLOGY 15
4. DATA 22
5. EMPIRICAL RESULTS 39
6. CONCLUSION 65
REFERENCE 67

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