81 NTU Management Review Vol. 31 No. 1 Apr. 2021 and σ is the annualized expected stock return volatility. We estimate Vega and Delta as follows: Vega = ( ) ( ) ×0 .01= ( 1) ×0 .01 ' . (2) Delta= ( ) ( ) × 100 = ( 1) × 100 ＝ . (3) Since the data of previously granted options are unavailable, we employ the “oneyear approximation” method (OA method) proposed by Core and Guay (2002) to estimate ESOs incentives for previously granted options. The OA method is convenient and only requires information from the most recent proxy statement. ESOs include new, exercisable and unexercisable granted options. We calculate the vega and delta for each category of ESOs and multiply the numbers of options held by CEOs. We also calculate the delta for restricted stocks and stock holdings by multiplying the year-end market value of the stock portfolio by one percent. Then we aggregate across option and stock holdings for the sum of the delta, and define total vega by aggregating across three categories of options. Finally, we convert both vega and delta from individual-year data into firm-year data for the regression analysis. 3.3 Empirical Models 3.3.1 Bidding Likelihood To examine whether excess cash holdings can amplify the risk incentive effect of ESOs to induce managers to undertake investments associated with idiosyncratic risk via M&As, we adopt and modify the model from Harford and Uysal (2014) as follows: Prob(MAi,t = 1│Xi,t ) = β0+β1Vegai,t-1+β2Deltai,t-1+β3Cashrichi,t-1 +β4Vegai,t-1×Cashrichi,t-1+β5 Deltai,t-1×Cashrichi,t-1 +β6Cashrichi,t-1/ TAi,t-1+β7Salesi,t-1+β8Market leveragei,t-1 +β9Stock returni,t-1+β10Market_to_Booki,t-1 +β11EBITDAi,t-1/ TAi,t-1+β12Industry M&A liquidityi,t-1 +β13Herfindahl indexi,t-1+β14InsideOwni,t-1+εi,t , (4)
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