以凱利公式建構週選擇權價差交易策略之績效探討

本文提供一種以資金管理為核心思考所建構的選擇權交易策略。以凱利公式 (1956) 為基礎並解析其假設與真實世界之間的差距和限制，搭配選擇權價差交易策略包含bull spread、bear spread、long butterfly以及short butterfly可以預先鎖定損益區間，並引用R. Vince (1990) 提出的延伸想法來處理多種賠率分配的情形，計算出最適投資比例，再實證研究策略的投資績效報酬。研究期間自2019年1月2日至2021年2月24日，由買權及賣權價內三檔到價外三檔組成上述四種價差交易策略。結果顯示bull spread策略表現最佳，大多數履約價組合年化報酬率表現優於大盤，且勝率平均約60%，符合指數長期處於成長趨勢的預期。

關鍵字

凱利公式；週選擇權；價差交易

並列摘要

This article provided an option trading strategy by managing capital size for investment. Based on Kelly Criterion (1956) to construct the strategy, author analyzed restrictions and differences between the criterion’s hypothesis and trading in real world. Using option spread trading strategy, which including bull spread, bear spread, long butterfly and short butterfly to establish the bound of consequence. R. Vince (1990) proposed a concept about Kelly Criterion to calculate possible multiple outcomes. It helped us to obtain the optimal fraction for investment. And we took this optimal fraction to do empirical study. The portfolio was composed of calls or puts which exercise price from in the money third strike price to out of the money third strike price. Study period was from January 2, 2019 to February 24, 2020. The result shows that bull spread strategy had the best performance. Most of the portfolio showed that annualized rate of return beyond the market and the winning percentage was approximately 60%. This consequence was in line with expectations when market was growing up in long term.