Share-based pay and its effects on managerial risk-taking

Bachelor Thesis, 2013

53 Pages


Table of contents

List of figures

List of Tables

List of Appendices

List of abbreviations

1 The growing use of stock-based compensation

2 The diverging risk preferences of principal and agent

3 Overcoming managerial risk aversion

4 The risk premium on share-based pay
4.1 The influence of the exercise price, degree of diversification and the risk aversion parameter on the risk premium of the manager
4.2 The importance to distinguish between firm-specific and systematic risk when the market portfolio can be traded
4.3 Implications for the use of share-based pay and research on the effects of share- based pay

5 Theoretical predictions on the risk incentives provided by share-based pay
5.1 The effects of managerial risk aversion and compensation design on risk incentives provided by share-based pay
5.2 The incentives provided by share-based pay regarding total risk
5.3 The effects provided by share-based pay to change systematic risk, firm-specific risk and the correlation between company returns and market returns

6 Empirical findings on the relationship between share-based pay and company risk
6.1 Estimating the sensitivities to stock price and stock volatility of a manager’s portfolio with the “one-year” approach
6.2 The joint determination of firm risk characteristics and share-based pay
6.3 The incentives provided by vega and delta to change the components of risk

7 Descriptive analyses of the pay-performance sensitivities of German DAX and MDAX executives
7.1 Sample description
7.2 Calculation of the pay-performance sensitivity
7.3 The alignment of DAX and MDAX board members

8 Summary of results


List of references

List of figures

Figure 1: Option value to the executive as a function of stock price for different risk aversions and levels of diversification

Figure 2: Plot of the partial derivative of a manager’s expected utility with respect to the standard deviation of stock returns versus the probability of the option finishing “in the money”

Figure 3: The change in total option value for 1 per cent increase in idiosyncratic risk as a function of option wealth as percentage of total wealth

Figure 4: The change in total option value for a 0.1 increase in beta as a function of total wealth

Figure 5: The option value as a function of stock return volatility

Figure 6: Frequency distribution of alignment values

List of Tables

Table 1: Average and median annual alignment values

List of Appendices

Appendix 1: Annual alignment means and medians of DAX and MDAX CEOs and VPs

List of abbreviations

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1 The growing use of stock-based compensation

The leading candidate of the social democratic party Peer Steinbrück has recently stated that the German chancellor does not earn enough compared to the importance of the task and the performance that he or she has to bring.[1] This statement lines up in the long discussion about the appropriateness of top executive compensation, which is a recurring topic in media, politics and the economy itself. However, the discussion has been mainly focusing on compensation of company executives and members of the supervisory board. The main driver of this discussion is the fear that social peace could be endangered when the top earners’ payoff absconds even more from the average wage.

It used to be union leaders and left-wing politicians who demanded that executive compensation should be reduced or at least capped, now even industry-related politicians and company leaders themselves start to argue that a perpetual increase in management remuneration could eventually be harmful to social peace. For example the founder and president of the World Economic Forum Klaus Schwab recently said that astronomically high executive pay is socially not compatible.[2] More surprisingly the supervisory board of the Volkswagen AG wants to restructure the compensation design of its top executives, because CEO Martin Winterkorn will receive total compensation of € 20 millions for 2012 according to current contractual agreements. Member of the supervisory board Bernd Osterloh says that the height of the top executive compensation is not communicable to the public despite the exceptional success of the carmaker.[3]

In the scientific community the discussion about compensation also takes place, but the focus lies on other aspects than the simple height of the compensation.[4] A prevalent topic is the question if share-based pay helps to induce value-maximizing behaviour. The use of share- based pay has increased dramatically since the early 1990s especially with regard to stock options.[5] In 2011, 24 out of the 30 DAX companies used share-based pay.[6] Moreover, stock- based compensation accounted on average for 21.7 per cent of total compensation of executives in 2011.[7] This trend shows that shareholders increasingly believe that share-based pay will motivate management to maximize company value. Company value will be maximized, if all projects that add value are realized. At least some of these projects are characterized by a certain amount of risk. Thus, share-based pay helps to maximize shareholder value, if it alters the risk preferences of risk-averse managers so they do not pass up risky value-adding investment opportunities. In this thesis I aim to identify the effects of stock-based compensation on managerial risk-taking by discussing theoretical and empirical research findings. Moreover, I conduct a descriptive analysis of the pay-performance sensitivity of the portfolios of DAX and MDAX board members in the period of 2006 till 2010.

The remainder of the paper is structured as follows. Chapter 2 presents the agency theoretical explanation for the diverging risk preferences between management and shareholders. Chapter 3 establishes the need to differentiate between the cost of the stock-based compensation to the company and the value to the executive. Chapter 4 shows that managers value stock-based compensation below market value and discusses the factors that influence the risk premium that the manager demands. Chapter 5 discusses theoretical considerations on the determinants of share-based pay and its effects on risk-taking. Chapter 6 is concerned with empirical research on the impact of share-based pay on managerial risk-taking. Chapter 7 contains a descriptive analysis of share-based pay programs in the German DAX and MDAX with a focus on the pay-performance sensitivity of managerial wealth. Chapter 8 discusses the results and proposes areas for future research.

2 The diverging risk preferences of principal and agent

In their seminal paper on agency theory Jensen and Meckling (1976) define an agency relationship “as a contract under which one or more persons (the principal(s)) engage another person (the agent) to perform some service on their behalf, which involves delegating some decision making authority to the agent”.[8] The authors claim, that if the principal and the agent both aim to maximize their utility, it is plausible that they will have deviating interests.[9] Clearly, the principal’s primary concern is the maximization of company value whereas the agent will be interested in his own wealth, personal status or non-pecuniary benefits e.g. a lease car or a company jet.

The principal has to incentivize the agent to ensure that he acts in his best interest or monitor the agent’s actions to prevent him from doing something harmful. However, there will always be a reduction of welfare for the principal due to the diverging interests. Thus, the diverging interests lead to costs. Jensen and Meckling (1976) define these costs, which are called “agency costs”, as the sum of the monitoring expenditures by the principal, the bonding expenditures by the agent and the residual loss.[10] The monitoring expenditures include measures to incentivize the agent to act in the principal’s best interest and monitoring costs to monitor the agent to keep him from doing aberrant activities. Bonding expenditures are used to guarantee the principal that the agent will not undertake harmful actions. The residual loss is the “dollar equivalent of the reduction in welfare experienced by the principal as a result of this divergence”.[11]

The problem of incentivizing an agent to act in the principal’s best interest is quite general and occurs in all organizations and collaborations, e.g. companies, universities, governments and schools.[12]

The relationship between shareholders of a listed company and the company’s management fits the definition of an agency relationship.[13] The shareholders maximize their utility when company value is maximized. The managers’ utilities depend on their own wealth and other variables such as power, social status and non-financial benefits. In case of the agency relationship between shareholders and company management these diverging interests between principal and agent are also reflected in differing risk preferences. Based on the assumption that the principal is a diversified shareholder, who wants company value to be maximized, it is obvious that the principal will have a positive attitude towards undertaking risk-increasing positive net present value (NPV) projects. By contrast, the agent, who is tied to the company with his human capital[14] as well as a large portion of future expected earnings, will be less favourable towards risk. This risk aversion prevents the management from maximizing value. Therefore, shareholders have to create incentives for the management to overcome the risk aversion.[15]

3 Overcoming managerial risk aversion

In order to surmount the previously discussed divergence of risk preferences, it is necessary to implement compensation schemes that incentivize the manager to make optimal financing and investment decisions regardless of his or her aversion against risk. A manager will undertake a project that raises company risk, if his utility increases with the increased amount of risk. A formal definition is given on how managers value payoffs to understand how share-based pay can help to incentivize managers.

Pratt (1964) shows that a risk-averse manager is indifferent between a certainty equivalent and a risky payoff, , minus a risk premium:[16] In the context of share-based pay represents the Black-Scholes value of a manager’s stock and option holdings, the risk premium is the discount that the manager puts on his portfolio and the is the subjective value of the portfolio to the manager. This equation can help to assess the value of a portfolio to a manager depending on his risk aversion. But the equation has to be differentiated with respect to firm risk, , to evaluate whether a portfolio creates any incentive to increase risk:[17]

The first component of the right side of the equation, , characterizes the change in expected wealth from a manager’s view when firm risk changes and is therefore called wealth effect. The second component of the right side of the equation, , “captures the influence of risk-aversion on managers’ utility” and is therefore called the risk-aversion effect.[18] The size of the risk-aversion effect depends on diversification in the manager's overall portfolio, manager-specific risk aversion, his total wealth and the design of the compensation scheme.[19] The risk aversion effect of a risk-neutral investor is zero.

The willingness of a manager to increase risk depends upon the order of magnitude of both the wealth and risk-aversion effect. The manager will only be willing to increase risk, if the wealth effect is dominating, because then is positive and the agent’s certainty equivalent increases with rising company risk. This predicates that it is attractive for the manager to raise company risk, because if he does so his utility, which is derived from the payoff, increases.

As discussed before, diversified shareholders want managers to undertake all available positive NPV projects, regardless of the risk that is associated with them. Hence, to align interests between shareholders and managers the wealth effect has to dominate the risk- aversion effect.

Agency theorists argue that stock options help solving the problem of aligning interests between managers and shareholders, because the value of stock options increases with company risk according to the Black-Scholes valuation.[20] Black and Scholes (1976) argue that their valuation formula can also be used to value stocks, because a stock is essentially a call option to buy back the company’s assets with an exercise price that is equal to the face value of corporate debt, which is basically a stock option with strike price zero.[21] Galai and Masulis (1976) show that stock value is also increasing with company risk.[22] Thus, both stock and options have a convex payoff scheme[23], though Guay (1999) finds empirically that the convexity provided by stocks is not economically relevant for most CEOs.[24]

The Black-Scholes valuation takes the perspective of a risk-neutral investor, i.e. the risk aversion effect is considered to be zero. In contrast, managers are generally considered to be risk-averse and they are usually restricted from trading or hedging their stocks and options, thus, they will value them lower than the Black-Scholes model does, because they subtract a premium for bearing risk, or in other words their risk aversion effect is larger than zero. The premium they subtract depends on several factors and affects the risk incentives.

4 The risk premium on share-based pay

A company manager cannot sell the stocks and options he receives.[25] Moreover, he is restricted from hedging by short selling company stock, since this would “defeat a primary purpose of the option grants, which is to align the financial interests of the managers with those of the shareholders”.[26] Moreover, company executives are tied to their company with

their human capital, which leaves them by far less diversified than an outsider.[27] So, it makes sense to assume that company executives will value their stock and option holdings below market value. In contrast, if managers would value “options at their cost to the company, (…) (they) should be paid entirely in options rather than cash as long as options offer any positive incentive benefits“.[28]

The first part of this chapter explains the influence of exercise price, diversification and risk aversion on the risk premium. The second part establishes the importance to distinguish between systematic and idiosyncratic risk, if the market portfolio can be traded. The third part derives implications for the use of share-based pay and the research on the effects of stock- based compensation.

4.1 The influence of the exercise price, degree of diversification and the risk aversion parameter on the risk premium of the manager

Hall and Murphy (2002) use a “certainty-equivalence” approach to estimate the value of a non-tradable option to an undiversified risk-averse executive by determining the amount of cash the executive would exchange for the option.[29] They define the executive’s wealth at time T as follows.W is the amount of non-firm related wealth that is invested at the risk-free rate rf, s is the number of shares held by the executive,n is the number of options awarded to the manager with exercise price X and PT is the stock price at time T:

illustration not visible in this excerpt

If he would receive the amount of cash that is also invested at the risk-free rate his wealth at time T would be:

illustration not visible in this excerpt

The executive’s utility as a function of his wealth is defined as U(W) . The value of the options to the manager is defined as the certainty equivalent that equates the utilities:

illustration not visible in this excerpt

This means V is the amount of cash that is of equal value to the executive owning options.[30]

Hall and Murphy (2002) conduct a numerical analysis[31], which means they analyse how the certainty equivalent behaves as a function of one of the input variables e.g. exercise price or the risk aversion parameter.

illustration not visible in this excerpt

Figure 1: Option value to the executive as a function of stock price for different risk aversions and diversification levels[32]

The results are depicted in figure 1. The solid black line is the Black-Scholes “cost” of the option. It approximates the opportunity cost to the company of granting an option. The solid grey line is the “intrinsic value” of the option, which is defined as the difference between stock price and exercise price. The four “executive value” lines plot the certainty equivalent values as a function of stock prices for varying pairs of risk aversion and diversification. The parameter of risk aversion is either 2 or 3, because „these estimates are at the low end of the reasonable range of estimates in the literature“.[33] [34] The executives have either 50 per cent or 67 per cent of their wealth invested in company stocks.[35] The executives have $ 5 millions in [31] For the numerical analysis it is assumed that the agent has constant relative risk aversion so when and when . The distribution of stock prices in years is assumed to be lognormal with volatility and the expected value equal to , where is the firm’s systematic risk and is the return on the market portfolio. In the analysis is equal to one, the risk- free rate is set to 6 per cent, the volatility is equal to 30 percent and the market premium is 6.5 per cent initial wealth split between company stocks and safe cash, and he receives an option grant to purchase one share of stock at an exercise price of $ 30.

The executive values are lower than the Black-Scholes “cost” whether they are “in the money”, “at the money” or “out of the money”. But, the ratio between executive value and Black-Scholes cost increases with stock price[36], because the payout probability of an option, i.e. the likelihood of an option to end up “in the money”, increases with share price,[37] and, in turn, the discount that the agent puts on the option decreases.

The option value is negatively correlated with the amount of wealth that is invested in company stock instead of the risk-free asset, because a higher investment in company stocks exposes a larger portion of the manager’s wealth to company risk. The risk aversion parameter captures the variances in the perception of risk depending on personal attributes such as the agent’s cultural background, religious beliefs, age and marital status.[38] If two agents with the same option portfolio and the same degree of diversification value their option holdings differently, the one that values the options lower has a higher risk aversion parameter. The results of Lambert, Larcker and Verrecchia (1991) are in line with this definition.[39]

Kahl, Liu and Longstaff (2003) study the value of stocks to inside holders who are restricted from selling them. They find that the subjective value of the stock holdings has a negative relationship with the risk aversion coefficient, stock return volatility, length of lockup period and the percentage of his total wealth, which is illiquid. Thus, the same factors that influence the premium on options also influence the premium on stock. The magnitude of the discount on stocks is similar to the one on stock options.[40]

To sum up, the magnitude of the discount that managers put on stock-based compensation varies greatly with risk aversion, diversification and stock price respectively exercise price.[41] Thus, research that does not account for the risk-averse perspective of the manager is likely to introduce a measurement error.

4.2 The importance to distinguish between firm-specific and systematic risk when the market portfolio can be traded

If a manager can trade the market portfolio, he can protect his wealth from systematic risk and only has to bear the firm-specific portion. So it can be expected that the subjective option value will increase, because the manager does not have to bear total company risk any more, but only the firm-specific portion.

Tian (2004) estimates the option value to the executive with a certainty equivalent approach that is based on the model of Hall and Murphy (2002). However, Tian (2004) allows the executive to allocate his unrestricted wealth between the market portfolio and the risk-free rate. The executive’s terminal wealth at option maturity is defined as follows:

illustration not visible in this excerpt

N is the number of options held,Wc is the unrestricted wealth, is the risk-free rate, T is option maturity, H(0) and H(T) are the value of the market portfolio today and at option maturity, is the amount of unrestricted wealth that is invested in the market portfolio and is the option payoff at maturity, which is defined as:

illustration not visible in this excerpt

S(T) is the stock price at maturity and is the exercise price of the options.[42] Similar to Hall and Murphy (2002) it is assumed that stock price and unit value of the market portfolio at option maturity are lognormal distributed.[43] The manager aims to make optimal investment decisions to maximize his expected utility[44] at maturity:

Abbildung in dieser Leseprobe nicht enthalten

The value of the stock option is now defined as the amount of cash that the executive is[45] indifferent to. This means the amount of immediate cash payment that creates the same expected utility for the manager as the option package.

illustration not visible in this excerpt

[illustration not visible in this excerpt] is defined as:

illustration not visible in this excerpt

The executive does not have any restricted wealth when options are exchanged for an immediate cash payment, thus he is free to allocate all his wealth between the risk-free asset and the market portfolio.[46] It should be mentioned that earlier studies that allow the executive to only invest in the risk-free rate are a special case of this model where

At first Tian (2004) examines “at the money” stock options, since most executive stock options are granted “at the money”.[47] Like Hall and Murphy (2002) he finds, that the value of the options to the agent is negatively related to the risk aversion coefficient. Furthermore, he finds that the executive’s discount increases with the fraction of total wealth that consists of options and the firm volatility, which is intuitive because these two variables increase the volatility of the expected payoff. Option value also decreases with higher time to maturity.[48]

Tian (2004) also finds that a higher beta decreases the discount, which is due to two reasons. Beta describes the correlated volatility between company stock and the market. First, a higher beta stands for a higher correlation between the volatility of company stock and the volatility of the market. An outside investor can protect himself against firm-specific risk by diversifying his portfolio, thus, he will only ask for a premium to bear systematic risk. Consequently, a higher beta raises the expected return of an outside investor, when keeping volatility constant; this leads to a higher option value.[49] Second, a higher beta results in a higher correlation between the company stock and the market portfolio. Therefore, the executive can hedge a larger amount of risk by trading the market portfolio, which also raises his perceived option value.[50]

To give further evidence on the benefit of hedging Tian (2004) examines the optimal holdings in the market portfolio for the agent, i.e. the holdings that maximize his subjective value. He finds, that the optimal amount of wealth invested in the market portfolio is almost insensitive to frictional option wealth when the firm’s stock is not correlated with the market portfolio, because then an investment in the market portfolio only smoothens future returns. However, if [illustration not visible in this excerpt] option holders will start to short the market portfolio at a frictional option wealth of 30 per cent to hedge their exposure to systematic risk.[51]

Then Tian (2004) looks at the option value at different levels of option moneyness.[52] In line with Hall and Murphy (2002), Tian (2004) finds that the discount executives deduct from options constantly increases with the ratio of exercise price over strike price.[53] This makes sense because the higher the exercise price, the higher the probability for the option to not end up “in the money”.

The subjective value of stock is positively related to beta when the market portfolio can be traded, which is also due to the protection against systematic risk, and the negatively related to the portion of wealth that is illiquid.[54] Kale, Liu and Longstaff (2003) argue that stockholders invest in the market in the portfolio to either smoothen future returns when company risk is purely idiosyncratic or to hedge systematic risk when there is a correlation between company stock returns and market returns.[55]

To sum up, if an agent can trade the market portfolio, he will use it to hedge his exposure to systematic risk to increase his utility. In this situation the subjective value of stocks and options is positively related with the correlation between market risk and company risk, and negatively related with time to maturity respectively the lockup period and the portion of wealth that is illiquid.


[1] See o.V. (2012).

[2] See Meck (2013).

[3] See o.V. (2013).

[4] For example Friedl et al. (2012) argue that the public discussion overemphasizes top executive compensation, since it only accounts on average for 0.33 per cent of total personnel costs in German DAX companies (see Friedl et al. (2012), p. 6).

[5] The value of an average stock option grant of an S&P 500 CEO in 2002 was $ 7.2 millions, which is an increase of 800 per cent compared to 1992 (see Hall and Murphy (2003), p. 51).

[6] See Friedl et al. (2012), p. 31.

[7] See Friedl et al. (2012), p. 30.

[8] Jensen and Meckling (1976), p. 308.

[9] See Jensen and Meckling (1976), p. 308.

[10] See Jensen and Meckling (1976), p. 308-309.

[11] Jensen and Meckling (1976), p. 308.

[12] See Jensen and Meckling (1976), p. 309.

[13] See Jensen and Meckling (1976), p. 309.

[14] That means when the company performs poorly, he has to fear to be replaced. Also his status as a successful manager depends on company performance.

[15] This paper focuses on the theoretical predictions on behaviour by agency theory. Wiseman and Meijia (1998) argue that agency theory is limited due to its simplistic assumptions on risk aversion. They develop the behavioural agency model, which strives to extend agency theory with views from prospect theory, which was developed by Kahnemann and Tversky (1979).

[16] See Pratt (1964), p. 124.

[17] In the literature various measures are used to evaluate firm risk e.g. volatility of stock returns or proxy variables measuring research and development (R&D) expenditures, financing decisions and investment decisions.

[18] Guay (1999), p. 47.

[19] See Guay (1999), p. 47-48.

[20] See Merton (1973), p. 149.

[21] See Black and Scholes (1976), p. 649-650.

[22] See Galai and Masulis (1976), p. 57.

[23] Convex payoff means that the value increases as risk increases.

[24] See Guay (1999), p. 54.

[25] Managers are forbidden to sell their stocks and options during a certain vesting or lockup period. An empirical study finds that the average minimum holding period for stock lies between 31 and 74 months (see Kole (1997),

p. 99) and the average waiting period before the stock options can be exercised is 23.6 months (see Kole (1997),

p. 96).

[26] Hall and Murphy (2002), p. 8.

[27] See Hall and Murphy (2002), p. 8.

[28] Hall and Murphy (2003), p. 55.

[29] See Hall and Murphy (2002), p. 9.

[30] See Hall and Murphy (2002), p. 9-10. (see Hall and Murphy (2002), p. 9).

[32] See Hall and Murphy (2002), p. 11.

[33] Hall and Murphy (2002), p. 10.

[34] Friend and Blume estimate that the risk aversion is at least 2 (see Friend and Blume (1975), p. 920-921.). Also Bliss and Panigirtzoglou find that risk aversion coefficients have modest values when forecast horizon increases (see Bliss and Panigirtzoglou (2004), p. 429).

[35] See Hall and Murphy (2002), p. 10.

[36] If the agent has a risk aversion coefficient of and has invested 50 per cent of his wealth in stock. He values an option with strike price $ 30 at 24.5 per cent of its Black Scholes value when stock price is $ 5 and at

71.9 per cent when stock price is $ 60 (see Hall and Murphy (2002), p. 12).

[37] An option with strike price $ 30 has a payout probability of 12.1 per cent when stock price is $ 5 and 93.3 per cent when stock price is $ 60 (see Hall and Murphy (2002), p. 12).

[38] See Halek and Eisenhauer (2001), p. 22.

[39] See Lambert, Larcker and Verrecchia (1991), p. 135.

[40] See Kahl, Liu and Longstaff (2003), p. 395-396.

[41] Hall and Murphy (2002) find discount values between 97.8 and 28.1 per cent for stock options (see Hall and Murphy (2002), p. 12); Kahl, Liu and Longstaff (2003) find discount values between 89.2 and 1 per cent for stock (see Kahl, Liu and Longstaff (2003), p. 396).

[42] See Tian (2004), p. 1229.

[43] For assumptions on the distributions of stock price and the unit value of the market portfolio (see Tian (2004), p. 1229-1230). The executive is expected to be risk averse with a constant relative risk aversion . The manager’s utility function is defined as for , and for (see Tian (2004), p. 1228).

[45] See Tian (2004), p. 1231.

[46] See Tian (2004), p. 1230.

[47] See Hall and Murphy (2003), p. 50.

[48] See Tian (2004), p. 1232.

[49] Option value may actually decrease, if the increase in stock return volatility is not purely firm-specific. An increase in systematic risk results in a lower share price, because the future dividends are discounted at a higher rate according to the so-called volatility feedback effect. And in turn the lower share price, may causes a lower option value. The overall change in option value depends on the magnitude of the volatility feedback effect and the contrary effect resulting from the improved possibility to hedge (see Kanniainen (2010), p. 8-9 (cited after Black (1976)).

[50] See Tian (2004), p. 1232.

[51] See Tian (2004), p. 1232-1233.

[52] Option moneyness is the ratio between stock price and exercise price.

[53] See Tian (2004), p. 1233-1235.

[54] See Kahl, Liu and Longstaff (2003), p. 396-397.

[55] See Kahl, Liu and Longstaff (2003), p. 399-400.

[56] The manager cannot diversify his wealth by investing in the risk-free asset or the market portfolio and he cannot sell his stock options.[57] The value of contract as perceived by the manager is defined as the amount of cash that creates the same utility for him as ,

[56] See Lambert, Larcker and Verrecchia (1991), p. 131-132.

[57] See Lambert, Larcker and Verrecchia (1991), p. 134.

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Share-based pay and its effects on managerial risk-taking
Technical University of Munich
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share-based pay, managerial risk-taking, manager, shareholders, agency theory, compensation, risk premium, risk incentives, stock-based compensation, pay-performance, stock, option, portfolio, board members, DAX, MDAX
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Patrick Gebhard (Author), 2013, Share-based pay and its effects on managerial risk-taking, Munich, GRIN Verlag,


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