In the standard models analysing the optimal contract for a risk averse man- ager, the manager can affect the stock price of the firm in an ad hoc fashion by exerting effort. These standard models predict that the optimal incentive for the manager is decreasing in the level of volatility. However, unlike the present situation, in these models the shareholder can only observe a noisy signal of the manager’s effort.
Efforts to separate the effect of idiosyncratic and systematic risk have shown that it is idiosyncratic risk that matters when a manager is constrained to hold the stock of his firm but can trade the market portfolio.8 The effect in these models is still the same though because the more volatile a firm’s share price is, the more likely it is that the manager’s effort just gets “lost in the noise”. This result is however driven by the assumption that effort is unob- servable. Crucial to our results is the assumption that effort is observable.9
Given the typically ad-hoc nature of the manager’s assumed impact on the firm, we attempted to provide a more detailed analysis of the manager and his impact on the firm. By starting from the firm’s cashflows we are able to introduce the manager’s valuation problem and the implications that this has for the shareholder. Allowing effort to reduce the cost of investment means we now have an explicit relationship between effort and the value of the firm that can be analysed in detail.
With respect to the previous literature on executive compensation, the pri- mary finding of this chapter is that α∗ does not unambiguously decrease with the level of the firm’s volatility (σy). We find that when the manager’s
subjective valuation and an explicit channel for effort are acknowledged, the effect of volatility on α∗ depends crucially on the sign of ρ as this determines
8See Jin (2002).
9As discussed in Section 3.3, this is a weakness of our setup. It does however allow us
the impact of volatility on the manager’s valuation of the firm. Analysis of the impact that the manager’s level of skill and the scope for cost reductions have on the optimal contract also yields some interesting insights. Unsur- prisingly the lower the investment cost can be driven, the higher the optimal incentive level. More interesting though is that the optimal contract is prac- tically insensitive to the ceiling on the investment cost (i.e the cost when no effort is exerted). The finding that a more skilled manager (high λ) is given a lower level of α is also initially surprising, until one considers that this means he can achieve cost reductions with less effort and thus needs less incentive to work hard.
The personal characteristics of the manager also yield some surprising results. The relationship between the manager’s risk aversion and the optimal level of managerial ownership is very complex. Despite this, optimal firm ownership for a low γ manager is not that different from that for a high γ manager. This suggests that the real world un-observability of managerial risk aversion is not of critical importance when determining managerial compensation.10
The fact that the more a manager dislikes effort, the more incentive he needs to exert effort is unsurprising. Similarly, rich managers need more incentive to exert effort than poor managers, because the financial benefit of effort in utility terms is much lower when you have more money.
The key message of this chapter is that determining the optimal amount of the firm a manager should own in order to maximise the value for shareholders is a very complex problem. It requires specific examination of the project the manager will be managing as well as the personal characteristics of the manager - managerial share ownership is not a one size fits all proposition.
Chapter
7
Effort and the Timing Option
7.1
Introduction
The analysis of the manager’s investment decision has so far been in a static setting, in which the manager makes a “now or never” decision of whether or not to invest. The literature on real options has shown that investment decisions can be quite different from what static models of investment predict. Specifically in an environment of uncertainty there is “value in waiting” as this allows the agent to gain new information and thus resolve some of the uncertainty around the profitability of investment.
As discussed in Chapter 2, the majority of the work acknowledging the role of managers has focused on the information asymmetry between shareholders and managers, rather than the positive impact a manager can have. Given the significant and independent impacts that effort and the ability to wait have on investment behaviour, we will now extend the framework of Chap- ter 5 in order to determine whether the interplay of these factors has any interesting implications for managerial behaviour.
This chapter thus allows us to analyse how the manager’s decision of whether
Chapter 1: Introduction
Part 2: The “clean path” Chapter 4: CARA valuation
of SBM cashflow
Chapter 5: Managerial Effort
Chapter 6: The Shareholder's Static Hiring Decision
Chapter 7: Effort and the timing option
Chapter 8: The Shareholder's Dynamic Problem Chapter 9: CRRA valuation
of GBM cashflow
Chapter 10: Conclusion Chapter 2: Literature Review
Chapter 3: General Setup
Part 1: Introduction/ Motivation Part 3: Direct wealth effects Appendices Part 4: Conclusion & appendices
to invest or wait is affected by the ability to exert effort.
The rest of this chapter is set out as follows: Section 7.2 sets up the model, Section 7.3 outlines the numerical solution method used to solve the model, Section 7.4 discusses the results of the model and Section 7.5 summarises the results of this chapter.
7.2
Setup
In this situation the manager is waiting to invest and thus at every point in time he chooses his consumption, portfolio investment and whether or not the firm will invest. If the manager decides to invest he pays his proportion of the investment cost (αI[e]), exerts the optimal level of effort determined by Equation (5.4) and moves to Stage 2 (i.e. the post-investment state). Thus the investment payoff is simply the Stage 2 value function when the manager can exert effort that we analysed in Chapter 5. Therefore the investment payoff is simply Equation (5.3) evaluated at ˆe
Je(W, Y ) = − 1 γre
−γr(W −αI+αG[Y ]+ Φ2
2γr2)− θˆe (7.1) Conversely if the manager chooses to defer the firm’s investment, his in- tertemporal budget constraint is given by Equation (3.7). Following the same process as for Stage 2 and using the 1 superscript to denote the Stage 1 value function we can simplify the General HJB (Equation (3.9)) down to the following when the manager is waiting to invest
βJ1(W, Y ) = max C,π [− 1 γe −γC + Jt1+ Jw1(rW + π (µm− r) − C) + Jy1µy +1 2J 1 ww(πσm)2+ 1 2J 1 yy φ 2+ ρ2σ2 y + J 1 wy(πρσyσm))] (7.2)
with the following first order conditions F OCC : C∗ = −
ln(J1 w)
F OCπ : π∗ = − J1 w(µm− r) J1 wwσm2 − ρJ 1 wyσy J1 wwσm
Therefore at every point in time the manager will compare the solution to the HJB (Equation (7.2)) with the payoff from investment (Equation (7.1)) and if the payoff is greater he will invest, otherwise he will wait. Given the non-linear nature of the HJB for this problem, it must be solved numerically.