The most thought provoking comment in the paper is the following:
[CEO Pay Slice] is negatively correlated with the firm-specific variability of stock returns over time. This association could be due to a greater tendency of dominant CEOs to play it safe and avoid firm-specific volatility (which would impose risk-bearing costs on them but could be less costly to diversified investors).
Rarely does anyone take on the serious implications of this observation: CEOs and the Boards that oversee them must strike a balance between taking idiosyncratic risk that differentiates them from the rest of the marketplace and taking incremental diversifying risks that reduces firm specific volatility.
I served on the board of a public reinsurance company. Reinsurers take very risky bets by insuring, typically, catastrophic disasters. Catastrophic insurance has a particular type of risk I'll call short volatility: They collect insurance premiums and pay out very large claims. The claims are nowhere near normally distributed in the world of catastrophes. This means that writing "cat" reinsurance has very high returns on equity, although they aren't normally distributed. Also, cat reinsurers have ratings (A- or better, typically. See AM Best, for example.) This means they write protection on more risks than they can pay, because (re)insurance buyers accept a rating as evidence of ability to pay.
The first problem this raises for the Board is whether the board should be maximizing the expected return on equity of the company or maximizing the return to holding the stock of the company, or even maximizing the return on equity of the company subject to some limit on the risk of losing the rating and therefore destroying the enterprise value of the company.
At the time I served on the Board, I happened to also "control" more than 10% of the stock. However, that 10% of the stock was of little consequence to my firm's total risk. This gave me a serious conflict to address: As a Board member, what did I assume the shareholders of the company wanted me to do? I knew I was not necessarily a typical shareholder. Did I assume they held uncomfortably large blocks of stock, (which we all should view as irrational,) and therefore would want me to not risk the disaster of losing the rating? Was my goal to maximize the "value" of the rating, meaning the ability of the company to default on claims if something truly catastrophic happened, which is perfectly sensible if no one holds large positions in their own portfolio?
These are the interesting questions most boards, I suspect, spend too little time addressing.
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