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.

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.

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.

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

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

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.

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

Recovering Delisting Returns of Hedge Funds

Numerous hedge funds stop reporting to commercial databases each year. An issue for hedgefund performance estimation is: what delisting return to attribute to such funds? This would be particularly problematic if delisting returns are typically very different from continuing funds’ returns. In this paper, we use estimated portfolio holdings for funds-of-funds with reported returns to back out maximum likelihood estimates for hedge-fund delisting returns. The estimated mean delisting return for all exiting funds is small, although statistically significantly different from the average observed returns for all reporting hedge funds. These findings are robust to relaxing several underlying assumptions.

Recovering Delisting Returns of Hedge Funds

Numerous hedge funds stop reporting to commercial databases each year. An issue for hedgefund performance estimation is: what delisting return to attribute to such funds? This would be particularly problematic if delisting returns are typically very different from continuing funds’ returns. In this paper, we use estimated portfolio holdings for funds-of-funds with reported returns to back out maximum likelihood estimates for hedge-fund delisting returns. The estimated mean delisting return for all exiting funds is small, although statistically significantly different from the average observed returns for all reporting hedge funds. These findings are robust to relaxing several underlying assumptions.Hedge Funds