"What's the difference between
a risk and a gamble? You can rescue yourself from a risk. If a gamble goes
wrong, the consequences are irrevocable. I first learned this distinction from
a battalion commander who had served several tours in Afghanistan. I interviewed
him for a series of articles I wrote about risk."
That quote is from John Dickerson of
Slate discussing the firing of UVA President Theresa Sullivan. Apparently
the plot to unseat Sullivan was hatched by UVA rector Helen Dragas.
While trying to convince other decision makers to back her coup attempt she
provided the transcript of a commencement address by Atul Gawande. In his
address to Williams College graduates Gawande had discussed risk, failure, and
recovering from failure. Dickerson suggests that perhaps Dragas had
missed the point of the Gawande's speech - the importance of being able too
rescue oneself when a risk goes wrong. Dragas's plan did go wrong (as
protests broke out until Sullivan was reinstated) and Dragas and her co-conspirators
had not planned for that eventuality. While discussing Dragas et als
mistake Dickerson makes the above comparison between risk and gamble.
I am going to show my ignorance here
- I am a risk manager by profession and I have never heard this definition of
risk versus gamble before and frankly it sounds strange to me. However
when I started thinking about why it was wrong I realized that "risk"
is a hard word to define - possibly because the word is used in multiple ways.
Let's see what Websters
has to say
"risk
noun \'risk\
1
possibility of loss or injury: PERIL
2 someone
or something that creates or suggests a hazard
3a: the
chance of loss or the perils to the subject matter of an insurance contract;
also: the degree of probability of such a loss
3b: a
person or thing that is a specified hazard to an insurer
3c: an
insurance hazard from a specified cause or source <war risk>
4: the
chance that an investment (as a stock or commodity) will lose value"
I don't think that any of the
other definitions really express the word risk in a way that I know it.
Let's see what Wikipedia
has to say
"Risk is the potential that a chosen action or activity
(including the choice of inaction) will lead to a loss (an undesirable
outcome). The notion implies that a choice having an influence on the outcome
exists (or existed). Potential losses themselves may also be called
"risks". Almost any human endeavor carries some risk, but some are
much more risky than others."
Wikipedia also provides a number of
alternative definitions of "risk" prefaced by "The many
inconsistent and ambiguous meanings attached to "risk" lead to
widespread confusion and also mean that very different approaches to risk
management are taken in different fields." Ok so that may explain why I have
trouble defining "risk". It appears that there are multiple
manners in which the word "risk" is used.
First "risk" can be used
as a synonym for probability or hazard. As in "what is the risk of
getting hit by a truck?" In this case we assume that the
implication of the event occurring is very negative and the word
"risk" just denotes the probability of the event occurring.
Furthermore when used in this context there are usually phrased as there being
two distinct possibilities - getting hit by a truck or not getting hit by the
truck.
Second "risk" can refer to
a listing of possible bad states without assigning probabilities to them.
An example would be "What is the risk if you were to contract the
flu?" In this case the reference is not to the probability of the
event occurring but rather to what the possible outcomes are. If
you are healthy then the "risk" is that you feel crappy, or be in bed for
a week, whereas if you have a compromised immune system the "risk" of
catching a flu is that it could be fatal. I guess one could attach
probabilities to each possible outcome conditional on the initial health status
of the person in question but that would be an atypical response to the
question.
But how do the above uses of the
word "risk" apply to this statement "what is the risk of holding
one share of IBM stock for a week". Well obviously the
"risk" is that the price of the stock could drop but that is pretty
uninformative. Someone who asks that question wants to know how much the
price of IBM could fall and what probability you would assign to each of those
falls. Just saying how much the price of IBM could fall is nearly
tautological. It "could" fall to zero but that not
likely. So this use of the word "risk" asks for both the
possible outcomes as well as the probability of each occurring.
The case of getting hit by a truck
is really just a special case of this third meaning of "risk".
And it is one where the "risk" is easy to understand since there are
only two outcomes. But once we start assigning probabilities to multiple
outcomes then "risk" becomes difficult to define. Is
"risk" the probability of the worst possible case? or the probability
of being significantly worse off? or the probability of being any any worse
off? should every outcome get the same weighting? We could present
the "risk" as a distribution over possible outcomes - for example the
left hand tail of a t-distribution with mean of 0.5% and standard deviation of
5% and 3 degrees of freedom. That fully enumerates the probabilities of
different negative outcomes but does it tell us what the "risk"
is? That tells us what the probabilities are.
I think of risk as having three
distinct parts (1) a set of possible outcomes (2) a probability distribution
over those outcomes (3) and a valuation or utility measure which assigns a
value to each possible outcome. Assuming the outcomes are distinct we can
then construct a single measure of the "risk" of any situation by
summing over the probability weighted valuations of the outcomes - similar to
expected utility.
For example one possible valuation
could be assign 0 to any outcome except the worst and assign 1 to the worst
possible outcome. Weighting each valuation by its respective probability
and summing over our measure of risk would then be the probability of the worst
case outcome. There are literally an infinite number of possible
weighting schemes one could come up with for different outcomes.
Now back to Dickerson's statement. "What's the difference between
a risk and a gamble? You can rescue yourself from a risk. If a gamble goes
wrong, the consequences are irrevocable." I don't see anything in the definition of risk which alludes to the ability of one to rescue oneself or not. The point of his article may be correct but that is not the definition of risk.