Yisong S. Tian

Managerial Incentives and Corporate Fraud: The Sources of Incentives Matter*

Operating performance and stock return results imply that managers who commit fraud anticipate large stock price declines if they were to report truthfully, which would cause greater losses for managerial stockholdings than for options because of differences in convexity. Fraud firms have significantly greater incentives from unrestricted stockholdings than control firms do, and unrestricted stockholdings are their largest incentive source. Our results emphasize the importance of the shape and vesting status of incentive payoffs in providing incentives to commit fraud. Fraud firms also have characteristics that suggest a lower likelihood of fraud detection, which implies lower expected costs of fraud. Copyright 2009, Oxford University Press.Executives at fraud firms face greater financial incentives to commit fraud than do executives at industry- and size-matched control firms. After controlling for various firm, governance, and CEO characteristics, the likelihood of fraud is positively related to incentives from unrestricted stock holdings and is unrelated to incentives from restricted stock and unvested and vested options. Executives at fraud firms exercise larger fractions of their vested options, sell more stock, and receive greater total compensation during the fraud years than the control executives. Operating performance measures suggest executives commit corporate fraud following declines in performance. Stock prices fall approximately twenty percent on average upon the disclosure of potential fraud, which suggests that frauds inflated stock prices during the fraud period. Our results imply that optimal governance measures depend on the strength of executives’ financial incentives, especially following periods of poor performance, and that restrictions on an executive’s ability to sell shares could deter fraud. Corresponding author: Prof. Shane A. Johnson Dept. of Finance—MS 4218 Mays Business School Texas A&M University College Station, TX 77843-4218 Tel: (979) 862-3318 Email: sjohnson@mays.tamu.edu Acknowledgements: We thank Hao Li, Huihua Li, Stephen Smith, and Brooke Stanley for excellent research assistance, and Andrew Christie, Jay Hartzel, Jayant Kale, Omesh Kini, Scott Lee, Adam Lei, Kevin Murphy, Steve Smith, Bob Parrino, Jeff Pontiff, and seminar participants at the University of Arizona, Georgia State University, Notre Dame University, University of Waterloo, Queens University, McMaster University, and Drexel University for helpful comments. Johnson and Tian thank the Social Sciences and Humanity Research Council of Canada for financial support.

The Value and Incentive Effects of Nontraditional Executive Stock Option Plans

We examine the value and incentive effects of six nontraditional executive stock options: premium options,performance-vested options, repriceable options, purchased options, reload options, and indexed options. With reasonable parameter values, four options have lower value than a traditional option when granted, and large differences in value are evident across the types. Holding option value constant, five options create stronger incentives than traditional options to increase stock price, five create stronger incentives to increase risk, and three create stronger incentives to reduce dividend yield. Changing various option-specific parameters can produce large changes in incentive strengths.

Indexed executive stock options

We design and derive a pricing model for an executive stock option with a strike price indexed to a benchmark and investigate its valuation and incentive implications. In both up and down markets, the indexed option filters out common risks beyond the executives control, thereby increasing the efficiency of incentive contracts. The indexed option has a different payoff structure and much lower initial value than a traditional option. Incentive effects of the indexed option also differ from those of traditional options. We design an optional penalty function to reduce the payoff if executives manipulate specified model parameters such as volatility.

Arbitrage and Valuation in the Market for Standard and Poor's Depositary Receipts

This paper examines pricing in the market for depositary receipts, securities designed to track the performance of a stock index that trade like shares of stock. Arbitrage costs are low because these assets have low fundamental risk, low transactions costs, and high dividend yields. We find that Standard and Poor’s Depositary Receipts (SPDRs), or spiders, do not trade at economically significant discounts, unlike closed-end mutual fund shares. Although individual investors invest much more heavily in SPDRs than in S&P500 stock, investor sentiment is not an important determinant of the discount. The SPDRs redemption feature facilitates arbitrage so that sophisticated traders can take advantage of and eliminate mispricing. However, we also report a larger, economically significant discount for MidCap SPDRs. MidCap SPDRs are designed to track the performance of the S&P MidCap 400 index, an index of moderate capitalization firms, and are expected to have higher arbitrage costs. Finally, we find that SPDRs and MidCap SPDRs returns are not excessively volatile, also unlike closed-end funds.

Extracting Model-Free Volatility from Option Prices

The CBOEs VIX index is a measure of the implied volatility (IV) in 30-day stock index options. Originally constructed as a weighted average of Black-Scholes IVs from 8 at the money calls and puts, the VIX was redesigned in 2003. The new VIX uses a nonparametric procedure to extract an IV from out of the money calls and puts over the full range of strikes. Implementation of the theoretical procedure, however, requires several approximations, for example to deal with the fact that only a discrete set of strikes are traded in the market, rather than a continuum over the full range from zero to infinity, as required by the theory. In this article, Jiang and Tian look carefully at the new VIX algorithm to assess the impact of these approximations on its accuracy. They find that some of them may produce substantial errors, even in simply recovering the volatility input from a set of options in a pure Black-Scholes world. They then propose a modified calculation technique using a smoothing algorithm, that can almost entirely eliminate the errors.

An explicit finite difference approach to the pricing of barrier options

A modified explicit finite difference approach to the pricing of barrier options is developed. To obtain accurate prices, the grid is constructed such that the barrier is located in a suitable position relative to horizontal layers of nodes on the grid. This means that the barrier passes through a horizontal layer of nodes for continuous-time barrier options and is located halfway between two horizontal layers of nodes for discrete-time barrier options. Both single and double barrier cases can be accommodated. The option price at each node on the grid may be obtained by implementing a standard trinomial tree procedure. As the initial asset price will generally not lie exactly on the grid, the current value of the option is obtained using a quadratic interpolation of the option prices at the three adjacent nodes. The approach is shown to be robust and to provide accurate option prices and hedge ratios (such as delta, gamma, and theta) regardless of whether or not the barrier is close to the initial asset price, and it works effectively for both continuous-time and discrete-time barrier options. This device of adjusting the grid so that the barrier and the asset price lie on the grid is well known in the numerical analysis area.

Too much of a good incentive? The case of executive stock options

Using a utility-maximization framework, I show that the incentive to increase stock price does not always increase as more options are granted. Keeping the total cost of his compensation fixed, granting more options creates greater incentives to increase stock price only if option wealth does not exceed a certain fraction of total wealth. Beyond this critical level, granting more options actually reduces incentive effects and becomes counterproductive. In addition, stock options also create incentive to reduce (increase) idiosyncratic (systematic) risk. These incentive effects are sensitive to the choice of exercise price.

Efficiency in Index Options Markets and Trading in Stock Baskets

Researchers have reported mispricing in index options markets. This study further examines the efficiency of the S&P 500 index options market by testing theoretical pricing relationships implied by no-arbitrage conditions. The effect of a traded stock basket, Standard and Poors Depository Receipts (SPDRs), on the link between index and options markets is also examined. Pricing efficiency within options markets improves, and the evidence supports the hypothesis that a stock basket enhances the connection between markets. However, when transactions costs and short sales constraints are included, very few violations of the pricing relationships are reported.

Arbitrage, Liquidity, and the Valuation of Exchange Traded Funds

This paper investigates the performance of U.S. and country exchange traded funds currently traded in the United States and provides new insight into their pricing. While the U.S. funds are priced closely to their net asset values, the country funds are not and can exhibit large, positive autocorrelations in fund premium. The mispricing of country funds is related to momentum, illiquidity, and size effects. We also find an inverted U-shaped relationship between fund premium and market liquidity, which suggests that more active trading does lead to lower mispricing but only after a certain level of liquidity is reached.

Optimal Contracting, Incentive Effects and the Valuation of Executive Stock Options

In this paper, I examine the optimal contracting problem between a firm and its chief executive officer in a principal-agent framework with information asymmetry. The firm (principal) selects the size and composition of the agents (executives) compensation in order to maximize firm value. Given a compensation contract, the risk-averse and effort-averse agent in turn maximizes his own expected utility by optimizing his effort at the firm and the allocation of his outside investments. Using parameters consistent with average CEO pay of S&P 500 companies, I find that market performance (stock price) based incentive pay represents an important part (14 to 100%) of the optimal compensation contract between the firm and its executive. However, the optimal contract includes stock option grants only if the executive is at most modestly risk averse (with coefficient of relative risk aversion