This dissertation contains three studies relating to executive equity compensation. In the first study (Chapter 2), I investigate whether firms adjust CEO's equity incentives in response to the firms' prior earnings management. I find that the risk-taking incentives from new equity grants are lower for firms with higher prior real earnings management (REM), but not for firms with higher accruals-based earnings management (AEM). My finding suggests that boards perceive the consequences of REM are more value-reducing than AEM and that they take stronger actions against REM by reducing the CEO's risk-taking incentives arising from equity incentives. In addition, I this result is driven by firms with higher institutional ownership, suggesting that institutional investors play an important monitoring role in structuring executive compensation contracts to limit the CEOs' value-reducing behaviors. In the second study (Chapter 3), I investigate how the firm's downside risk and upside potential differentially affect the choice between cash and equity compensation and the choice between stock options and restricted stock compensation. First, I find that, as downside risk (upside potential) increases, boards grant more cash compensation (more equity compensation) and less equity compensation (less cash compensation). This is consistent with the idea that, when downside risk increases, a CEO requires a higher risk premium for equity compensation and, thus, the board shifts compensation away from equity compensation to cash compensation. The reverse is true for the increased upside potential. When upside potential increases, the observed compensation contract will contain less cash and more equity compensation. Second, I find that the proportion of CEO option compensation increases with downside risk and decreases with upside potential. This is because, when downside risk increases, the probability of a stock option finishing out of the money (i.e., zero intrinsic value) increases but restricted stock has positive value as long as the stock price is positive. In contrast, when upside potential increases, because of stock options' leverage effect, a CEO will prefer stock options to restricted stock. In the third study (Chapter 4), I study how executive stock options differentially affect the firm's systematic and idiosyncratic risk by exploiting the passage of Financial Accounting Standard (FAS) 123R as an exogenous shock to CEO option compensation. I find that option-based compensation and the proportion of idiosyncratic risk in total risk is negatively associated. This is consistent with the idea that since, unlike risk-neutral investors, risk-averse CEOs have limited ability to eliminate firm specific idiosyncratic, idiosyncratic risk is unwanted by under-diversified CEOs. Thus, CEO option compensation creates incentives to increase the firm's systematic risk relative to the firm's idiosyncratic risk.