Pinning in the S&P 500 Futures

We document that S&P 500 futures finish in the proximity of the closest strike price more often on days when serial options on S&P 500 futures expire than on other days. The effect is driven by the interplay of market makers' rebalancing of delta hedges due to the time-decay of the hedges as well as in response to reselling (and early exercise) of in-the-money options by individual investors. Consistent with limits to arbitrage, we find that the effect is asymmetric and stronger above the strike price. In line with increased options activity, pinning becomes more pronounced in recent years.Pinning, Futures, Options, Option Expiration, Hedging

Incentive Contracts and Hedge Fund Management

This paper investigates dynamically optimal risk-taking by an expected-utility maximizing manager of a hedge fund. We examine the effects of variations on a compensation structure that includes a percentage management fee, a performance incentive for exceeding a specified highwater mark, and managerial ownership of fund shares. In our basic model, there is an exogenous liquidation barrier where the fund is shut down due to poor performance. We also consider extensions where the manager can voluntarily choose to shut down the fund as well as to enhance the fund’s Sharpe Ratio through additional effort. We find managerial risk-taking which differs considerably from the optimal risk-taking for a fund investor with the same utility function. In some portions of the state space, the manager takes extreme risks. In another area, she pursues a lock-in style strategy. Indeed, the manager’s optimal behavior even results in a trimodal return distribution. We find that seemingly minor changes in the compensation structure can have major implications for risk-taking. Additionally, we are able to compare results from our more general model with those from several recent papers that turn out to be focused on differing parts of the larger picture.

Managerial Responses to Incentives: Control of Firm Risk, Derivative Pricing Implications, and Outside Wealth Management

We model a firm’s value process controlled by a manager maximizing expected utility from restricted shares and employee stock options. The manager also dynamically controls allocation of his outside wealth. We explore interactions between those controls as he partially hedges his exposure to firm risk. Conditioning on his optimal behavior, control of firm risk increases the expected time to exercise for his employee stock options. It also reduces the percentage gap between his certainty equivalent and the firm’s fair value for his compensation, but that gap remains substantial. Managerial control also causes traded options to exhibit an implied volatility smile.

Managerial Responses to Incentives: Control of Firm Risk, Derivative Pricing Implications, and Outside Wealth Management

We model a firm’s value process controlled by a manager maximizing expected utility from restricted shares and employee stock options. The manager also dynamically controls allocation of his outside wealth. We explore interactions between those controls as he partially hedges his exposure to firm risk. Conditioning on his optimal behavior, control of firm risk increases the expected time to exercise for his employee stock options. It also reduces the percentage gap between his certainty equivalent and the firm’s fair value for his compensation, but that gap remains substantial. Managerial control also causes traded options to exhibit an implied volatility smile.Risk; Wealth Management; Derivative

Employee Stock Options: Much More Valuable Than You Thought

Previous papers have argued that trading restrictions can result in a typical employee stock option having a subjective value (certainty equivalent value) that is substantially less than its Black-Scholes value. However, these analyses ignore the manager’s ability to (at least partially) control the risk level within the firm. In this paper, we show how managerial control can lead to such options having much larger certainty equivalent values for employees who can exercise control. We also show that the potential for early exercise is substantially less valuable with managerial control. The certainty equivalent value for a European option with managerial control can easily exceed the Black-Scholes value for a comparable option without control. However, it is questionable whether Black-Scholes is an appropriate benchmark for an option where the underlying process exhibits controlled volatility. We show how to obtain a risk-neutral valuation for such an option. That risk-neutral value can be substantially greater or less than the Black- Scholes value. Furthermore, the option’s certainty equivalent value can also be greater or less than its risk-neutral value.

Incentive Contracts and Hedge Fund Management: A Numerical Evaluation Procedure

The behavior of a hedge-fund manager naturally depends on her compensation scheme, her preferences, and constraints on her risk-taking. We propose a numerical method which can be used to analyze the impact of these influences. The model leads to several interesting and novel results concerning her risk-taking and other managerial decisions. We are able to relate our results to partial results in the literature and show how they fit in a more general context. We also allow the manager to voluntarily shutdown the fund as well as enhancing the fund’s Sharpe Ratio through additional effort. Both these extensions generate additional insights. Throughout the paper, we find that even slight changes in the compensation structure or the extent of managerial discretion can lead to drastic changes in her risk-taking.

Incentive Contracts and Hedge Fund Management

We investigate incentive effects of a typical hedge-fund contract for a manager with power utility. With a one-year horizon, she displays risk-taking that varies dramatically with fund value. We extend the model to multiple yearly evaluation periods and find her risk-taking is rapidly moderated if the fund performs reasonably well. The most realistic approach to modeling fund closure uses an endogenous shutdown barrier where the manager optimally chooses to shut down. The manager increases risk-taking as fund value approaches that barrier, and this boundary behavior persists strongly with multiyear horizons.Hedge Fund; Management; Incentive

Improved Portfolio Choice using Second-Order Stochastic Dominance

We examine the use of second-order stochastic dominance as both a way to measure performance and also as a technique for constructing portfolios. Using in-sample data, we construct portfolios such that their second-order stochastic dominance over a typical pension fund benchmark is most probable. The empirical results based on 21 years of daily data suggest that this portfolio choice technique significantly outperforms the benchmark portfolio out-of-sample. As a preference-free technique it will also suit any risk-averse investor in e.g. a pension fund. Moreover, its out-of-sample performance across eight different measures is superior to widely discussed portfolio choice approaches such as equal weights, mean variance, and minimum-variance methods.second-order stochastic dominance, portfolio choice, portfolio measurement

An analysis between implied and realised volatility in the Greek Derivatives Market

In this article, we examine the relationship between implied and realised volatility in the Greek derivative market. We examine the differences between realised volatility and implied volatility of call and put options for at-the-money index options with a two-month expiration period. The findings provide evidence that implied volatility is not an efficient estimate of realised volatility. Implied volatility creates overpricing, for both call and put options, in the Greek market. This is an indication of inefficiency for the market. In addition, we find evidence that realised volatility ‘Granger causes’ implied volatility for call options, and implied volatility of call options ‘Granger causes’, the implied volatility of put option

Recovering Probabilities and Risk Aversion from Option Prices and Realized Returns

This paper summarizes a program of research we have conducted over the past four years. So far, it has produced two published articles, one forthcoming paper, one working paper currently under review at a journal, and three working papers in progress. The research concerns the recovery of market-wide risk-neutral probabilities and risk aversion from option prices. The work is built on the idea that risk-neutral probabilities (or their related state-contingent prices) are an amalgam of consensus subjective probabilities and consensus risk aversion. The most significant departure of this work is that it reverses the normal direction of previous research, which typically moves from assumptions governing subjective probabilities and risk aversion, to conclusions about risk-neutral probabilities. Our work is partially motivated by the conspicuous failure of the Black-Scholes formula to explain the prices of index options in the post-1987 crash market. First, we independently estimate risk-neutral probabilities, taking advantage of the now highly liquid index option market. We show that, if the options market is free of general arbitrage opportunities and we can at least initially ignore trading costs, there are quite robust methods for recovering these probabilities. Second, with these probabilities in hand, we use the method of implied binomial trees to recover a consistent stochastic process followed by the underlying asset price. Third, we provide an empirical test of implied trees against alternative option pricing models (including “naïve trader” approaches) by using them to forecast future option smiles. Fourth, we argue that realized historical distributions will be a reliable proxy for certain aspects of the true subjective distributions. We then use these observed aspects together with the option-implied risk-neutral probabilities to estimate market-wide risk aversion.Risk Aversion; Option; Realized Returns