Do Calls Make Managers Less Risk Averse?
Kevin Du told me about a good Stephen Ross 2004 article on risk
aversion and call options as compensation. It’s an example of how
top scholars can think of seemingly obvious ideas for articles that
nobody else thinks of. This article could have been written any time
since 1970, but only now does it appear.
… many authors take it for granted that giving options to executives
makes them more willing to take risks. DeFusco, Johnson, and Zorn
(1990, p. 618), for example, note that “The asymmetric payoffs of call
options make it more attractive for managers to undertake risky
projects.” In fact, contrary to their intuition, my intuition, and
that of most observers, without further conditions on utility
functions beyond monotonicity and risk aversion, this is not correct.
Surprisingly, it is not the case that a convex compensation schedule
makes an agent more willing to take risks, that is, less risk averse;
nor does a concave compensation schedule make an agent more risk
averse.The common folklore clearly has its genesis in the observation from
option pricing theory that an increase in the volatility of an option
makes it more valuable (see, e.g., Haugen and Senbet (1981), Smith and
Watts (1982), and Smith and Stultz (1985)). This is, however, not the
same as making the option more desirable to a risk-averse investor.
One clear problem with the intuition of folklore is that compensation
schedules move the evaluation of any given gamble to a different part
of the domain of the original utility function where the utility
function can have greater or lesser risk aversion.(From Stephen Ross, “Compensation, Incentives, and the Duality of Risk
Aversion and Riskiness,” The Journal of Finance,2004 vol:59 iss:1
pg:207.)
It makes me feel good about my own options paper too.
Eric Rasmusen, “When Does Extra Risk Strictly Increase the Value of
Options?” Forthcoming in The Review of Financial Studies. It is well
known that risk increases the value of options. This paper makes that
precise in a new way. The conventional theorem says that the value of
an option does not fall if the underlying option becomes riskier in
the conventional sense of the mean-preserving spread. This paper uses
two new definitionsg of “riskier” to show that the value of an
option strictly increases (a) if the underlying asset becomes
“pointwise riskier,” and (b) only if the underlying asset becomes
“extremum riskier.”
http://www.rasmusen.org/papers/options_rasmusen.pdf.