Economics & Finance
• 7 minute read
Sure Win: New Study on Option Pricing Suggests Arbitrage Opportunities
A cutting-edge option pricing research reveals flaws in the derivatives markets. The results have turned heads on Wall Street and may rewrite the manual on trading strategies
By Jason Y. Ng
A cutting-edge option pricing research at CUHK Business School reveals flaws in the derivatives markets. The study not only challenges our fundamental understanding of how these markets operate, but it also opens the door to sustainable and predicable profit-making opportunities. The results have turned heads on Wall Street and may rewrite the manual on trading strategies.
It is said that there is no such thing as a free lunch, least of all on Wall Street. Conventional wisdom tells us that financial markets operate efficiently, and that securities – whether it is stocks, bonds, or the derivative instruments they underlie – are priced tightly to eliminate any arbitrage opportunity that may generate risk-free profits.
But a recent finance research by the Chinese University of Hong Kong (CUHK) Business School throws a spanner into those long-held views, specifically in the option markets. The results of the study entitled Option Return Predictability reveal that sustained returns from trading delta-hedged options are not only possible, but they are also predictable using basic stock fundamentals such as market capitalisation and return on equity.
Leading the research was Associate Professor Cao Jie of CUHK’s Department of Finance and his former PhD student Zhan Xintong who joined Erasmus University Rotterdam as Assistant Professor in Finance this August, alongside Bing Han of the University of Toronto and Qing Tong of Singapore Management University.
The team conducted extensive regression analyses using monthly option data of over 5,000 underlying stocks between 1996 and 2012, which amounts to nearly 160,000 data points. The model focused on actively traded stocks in the United States across a broad range of industry sectors, screening out small, highly illiquid ones that could potentially skew results.
A delta-hedged or delta-neutral option position involves longing and shorting options and underlying stocks in such a way that the overall payout is the same regardless of stock volatility. The position has to be rebalanced on a regular basis to adjust for fluctuating stock prices. Delta-hedged options are priced using traditional models such as Black-Scholes and stochastic volatility to eliminate any arbitrage gains.
The central question is whether a relationship exists between delta-hedged option gains and well-known stock characteristics used by financial analysts and investors. Of the 12 characteristics studied by the research team, eight of them, namely market capitalisation, cash-to-asset ratio, return on equity, new issuance, idiosyncratic volatility, monthly returns, annual returns and the dispersion of analyst forecast, show a strong correlation with delta-hedged option returns.
That means long-short trading strategies involving delta-hedged options based on those eight stock characteristics can yield stable, predictable profits over time. Their Sharpe ratios – a commonly used measure of risk-adjusted return – ranged from 0.63 to 2.00 (for perspective, a portfolio of U.S. Treasury bills has a Sharpe ratio of exactly zero). The correlation remains robust regardless of seasonality and market conditions. For instance, the profitability of the option trading strategies did not diminish during the 2008-2009 subprime mortgage crisis.
The predictive power of these stock fundamentals suggests one of two things: either conventional pricing models are flawed, or the option market – with all its modern innovations and the rise of high-frequency algorithmic trading – is not as efficient as previously thought.
While further studies are necessary to understand the exact cause of the abnormal returns, Prof. Cao’s research team believes that one possible source of market inefficiency is the insufficient cross-sectional arbitrage activities in the option market. More specifically, trading frictions created by regulatory limits to arbitrage may have played a key role in, ironically, spawning the delta-hedged arbitrage.
Until this anomaly is corrected, arbitrage opportunities continue to exist and risk-free profits in the option market – the proverbial free lunch – are there for the taking. That’s why Wall Street traders and fund managers have taken notice of the startling results.
Last October, Prof. Cao presented his research findings to a captivated audience at the Third Deutsche Bank Annual Global Quantitative Strategy Conference in New York. He was subsequently invited to speak at a seminar at Morgan Stanley’s head office, hosted by Dr. Peter Carr, the investment bank’s Global Head of Market Modelling. Within the same month, his PhD student Zhan Xintong gave similar presentations to a number of New York-based hedge funds and investment firms, including OptionMetrics, Cubist Systematic Strategies, and Two Sigma.
What followed were other high profile speaking engagements, including the 10th Advances in the Analysis of Hedge Fund Strategies Conference in London; the Sixth Risk Management Conference in Mont-Tremblant, Canada; the Fourth Chicago Quantitative Alliance Asia Conference in Hong Kong; and a presentation at Menta Capital LLC in San Francisco.
“As more traders start to take advantage of our trading strategy. We expect the arbitrage to narrow. It may eventually disappear.” – Prof. Cao Jie
More recently, in May this year, Prof. Cao presented his research at the 4th annual Asia Bureau of Finance and Economic Research Conference in Singapore, one of the largest events of its kind in Asia Pacific. In June, he presented it at Macquarie Global Quantitative Research Conference, a leading conference for finance industry, and in August, at European Finance Association Annual Meeting in Oslo, Norway, a leading conference for finance academic researchers.
Reactions from the financial community have ranged from excitement and intrigue to amazement and disbelief. To answer the sceptics, Prof. Cao and his team continue to test the robustness of their theory by controlling for ‘noise’ such as stock volatility risk factors and adjusting for transaction costs resulting from the spread between bids and ask option prices. So far, the findings have held up and the research remains on firm ground.
There have also been questions of a more pragmatic nature: how big the potential market is and whether option traders can make fortunes by replicating the trading strategy on a large scale.
“Our research is relatively new and Wall Street has yet to test it in the actual derivatives markets,” says Prof. Cao. “But based on the presentations we have done to date, there is a lot of interest in our discoveries on the streets,” he says.
When it comes to risk-free gains, however, popularity can be a double-edged sword.
“As more traders start to take advantage of our trading strategy,” Prof. Cao offers a reality check, “we expect the arbitrage to narrow. It may eventually disappear.”
That sentiment may have answered, if only preliminarily, the question of what causes the abnormal returns in the first place. Prof. Cao’s prediction of narrowing arbitrage suggests that the anomaly uncovered by the study may have far less to do with flaws in the conventional pricing models than market inefficiency and regulatory frictions.
While the study is being discussed and debated in the real world, Prof. Cao has already moved on to analyzing other derivative instruments. He is expanding his research from delta-hedged options to raw options and straddles – longing a call and a put option with the same strike price and expiration date – in hopes of discovering a similar pattern.
“We’ve dug up something interesting and opened a door to a new area of research,” says Prof. Cao. “More broadly speaking, our study forces us to examine how much we actually understand option valuation and trading. We hope our work will attract attention from both practitioners and researchers so that more people will focus on this area.”
It appears that the professor does not have to wait long for his hope to materialize. His research has already drawn praise from heavyweights in high finance.
“I just wanted to say how impressed I was with your new papers,” wrote Euan Sinclair, option trader and author of such definitive treatises as Volatility Trading and Option Trading: Pricing and Volatility Strategies and Techniques, in a congratulatory email to Prof. Cao. “For a few years I’ve been convinced that the next frontier in option trading is using factors like [the ones referenced in your research].”
