Information Content Of Right Option Tails: Evidence From S&P 500 Index Options

American University of Sharjah

October 17, 2015

Abstract:

In this study, we investigate how useful the information content of out-of-the-money S&P 500 index call options is to predict the size and direction of the underlying index for the period 2004-2013. First, based on the results of Orosi (2015), we demonstrate that behavior of the right tail of the option implied risk-neutral distribution can be characterized by a single parameter. Subsequently, we find that weekly changes in the tail parameter can be used to devise trading strategies that outperform the underlying index on a risk adjusted basis. In particular, two strategies that have comparable drawdowns to the S&P 500 index, have cumulative returns of 370.67% and 324.42%, while the index has a cumulative return of 60.16%.

Information Content Of Right Option Tails: Evidence From S&P 500 Index Options – Introduction

The idea that option prices contain information about future density of the underlying asset has been understood since the work of Black and Scholes (1973). It is now well established that option-implied information can be used to construct portfolios with improved risk-return characteristics (see for example DeMiguel et al. (2013)). Moreover, Audrino et al. (2014) find that profitable trading strategies can be devised by estimating the physical density from the risk-neutral one.

In this study, we propose a trading strategy that relies on the information content of out-of-the-money S&P 500 index call options to predict the future change in the underlying index. First, based on the results of Orosi (2015), we demonstrate that a single parameter characterizes the behavior of the right tail of the option implied risk-neutral distribution implied by option prices. Subsequently, we find that this parameter contains predictive information about the S&P 500 index and that it can be used to devise trading strategies with improved risk-return characteristics.

The remainder of the paper is organized as follows. In Section 2, we summarize the findings of Orosi (2015), and introduce the trading strategies. In Section 3, we present the results of our empirical study and discuss our findings. Finally, Section 4 presents our conclusions.

The Trading Strategy

In this section, we review the work of Orosi (2015) and point out that the behavior of the right tail of the distribution is determined by a single parameter. Moreover, we illustrate how trading strategies can be developed using these results.

Trading Strategies

It is well known there is a difference between real-world parameters and risk-neutral ones that are derived from option prices. Although studies attempting to recover the physical density or moments from the risk-neutral ones rely on restrictive assumptions (see for example Aït-Sahalia and Lo (2000), Ross (2013), and Ghysels and Wang (2014)), some empirical evidence indicates that these approaches can be useful to practitioners. For example, Audrino et al. (2014), using the recovery theorem of Ross (2013), extract the market’s forecast of the physical density and use this to develop trading strategies that outperform the S&P 500 index.

Based on the above results, we consider two trading strategies. The first strategy (referred to as Strategy 1 hereafter) takes both long and short positions and is based on the following rule: if the value in parameter is larger than it was the week before, we go long the S&P 500 index for one week; otherwise we short the index for one week. The idea behind the strategy is that when the right tail of the risk-neutral density (and hence distribution) gets fatter or thinner, investors expect the market to rise or fall, respectively. Therefore, it takes advantage of the information content of option prices by extracting the market’s current expectation about the change in the underlying. The second strategy (referred to as Strategy 2 hereafter) only takes on long positions and is based on the following rule: if the value in the parameter is larger than it was the week before, we go long the S&P 500 for one week; otherwise we do not take on a position. Note Strategy 2 is similar to Strategy 1, and it avoids shorting the index because the historical weekly change in the S&P 500 index is positive more often than negative.