*3.4. Control Variables*

The motivations of corporate hedging have been well examined in the literature; thus, we follow the previous studies to incorporate those important drivers of hedging as control variables. Below we briefly discuss the motivation of including those control variables. We first control for CEO equity-based compensation, which is based on stocks and options granted to the executives: One is the change in stock price, which affects the value of stock holding and value of options, and the other is the volatility of stock return, which mainly affects the value of options. Guay (1999) highlights the difference between these two measures, with the former notated by delta and the latter by vega. More incentives from

delta expose more firm risk to managers and cause them risk averse, while compensation with vega incentive helps offset the problem of underinvestment due to the risk aversion that arises from delta incentive. In addition, Rogers (2002) argues that it has more explicitly economic sense to measure the CEO risk-taking incentive per dollar of value-increasing incentives, namely, the ratio of vega to delta (vega/delta). We expect a negative relation between the ratio of vega/delta and hedging since a stronger risk-taking incentive from compensation makes executive more aggressive and are consequently less likely to hedge.

Smith and Stulz (1985) suggest that hedging reduces the volatility of corporate performance, resulting in a lower bankruptcy risk. The probability of bankruptcy or financial distress is considerably higher when a firm's leverage is higher, or when interest coverage or percentage of tangible assets is lower. Therefore, there is a negative relation between interest coverage or tangible assets and hedging, and a positive relation between leverage and hedging. Froot et al. (1993) theorize that hedging can curtail the underinvestment problem (Myers 1977) when a firm faces potential growth opportunities but suffers a high cost of external financing. Following Gay and Nam (1998), we use the correlation between cash flow and firm investment to gauge the underinvestment problem and expect a positive relation between this measure and hedging, indicating that firms with a severe underinvestment problem tend to hedge. In the case of a progressive (convex) tax schedule, marginal tax rate increases with taxable income. Hedging reduces the expected tax liability by smoothing taxable income. Therefore, a positive relation between tax benefit and hedging is predicted. We adopt two measures of tax benefit: a dummy variable indicating positive tax credit and a continuous variable of tax convexity, which measures the expected tax savings from a 5% reduction in the volatility of taxable income (Graham and Smith 1999). Cash holdings are regarded as a natural mechanism to alleviate the negative impact of uncertainty. In addition, convertible bonds can be also used to reduce the agency cost of debt. As both are potential alternatives of hedging, we include them and expect a negative relation between these substitutes and hedging.
