Convex payments Flashcards
What is the basic Principal - Agent problem?
The shareholder (owner) of a firm wants to incentivize the manager / CEO to put in sufficient effort, but the effort is not directly observed by the shareholder, or the cost of monitoring would be too high.
In what does the basic Principal - Agent problem result?
Asymmetric information and moral hazard.
After signing the contract the manager would rather put in less effort than more.
What can you observe as a shareholder?
The output (or profits). Higher effort e usually results in higher output, however there’s also a random factor c(e) determining the output (Y = e+ c)
What does concavity implies?
Risk aversion: would rather receive a fixed wage than a variable wage with the same expected value.
Disutility (cost) from effort c(e) is
Convex and increasing in effort e.
The marginal disutility is increasing. Hence after working as much as 80 hours you would like to spend time outside work
Holmstrom showd that the optimal incentive-compatible contract would be
A compensation rule w(y) depending output y such that:
- The manager accepts the offer (Participation Constraint, PC): EUmanager >û (the outside option of the manager)
- The manager prefers to put in high effort rather than low effort (Incentive Compatibility Constraint, ICC): EUmanager High >= EU manager Low
The basic Principal - Agent problem suggests that executive compensation should have
- Fixed part - high enough to satisfy Participation Constraint
- Variable part - pay that depends on the output. High enough to induce high effort, but not transfer too much risk to the agent.
The value of a convex payoff function increases with
uncertainty / volatility
Example: call option
When does Convex payoff function value volatility becomes a problem?
When the person on the receiving end of the convex payment function can actually influence the underlying riskiness. Examples: CEO, fund manager
Most financial incentives are
Convex
Convex incentives have mostly … and very little if any …
Convex incentives have mostly upside potential and very little if any downside
Short term incentives
Receiving a bonus when outperforming, but now the equivalent if under performing. Bonuses are rarely clawed back when performance declines afterwards.
Example of short-term incentives
Fund fees as a share of (positive) returns
Long-term incentives
Share call options allow CEO to benefit from the upside without downside risk.
Equity holdings themselves have unlimited upside, but only limited downside risk (share price cant go below 0)
Example of long-term incentives
convex fund inflows in investment fund
Incentives for fund managers are
Usually convex:
The 2-20 rule: 2% of AUM, 20% on excess returns.
Rewards gains, but does not symmetrically punish losses.
What does the 2% fee on AUM do?
Incentivizes managers to grow AUM
Fund inflows depend on
Previous year’s performance. Empirically, in a convex way:
Large inflows into funds that outperformed.
Not equivalent outflows out of funds that under performed.
What usually happens if people miss their target in the first half of the year? Found by Brown, Harlow and Starks
They increase their risk-taking in the second half.
Lin found that fund managers that are lagging start investing more in …
And the other way around?
- If underperform - Positively skewed assets (lottery-like)
2. If overperform - Negatively skewed assets