A definition of risk must include an investor's own perception of it.

It is common today to find that investment risk is
frequently expressed in terms of the annualized standard deviation
(SD). The usage is so common that in many if not most cases, risk and
standard deviation are used interchangeably. Investors and investment
professionals do not necessarily understand the math underlying the SD
and its concomitant assumptions, yet we continue to use the terms
interchangeably. Because the consequences of such usage are significant
to portfolio construction and investment decision-making, we must
carefully examine our premises and our definitions.

In a recent issue of Philosophy Now the concept of
logical conclusions based on false assumptions was proposed along these
lines:

All dogs are cats.

Fido is a dog.

Therefore Fido is a cat.

We clearly understand the difference in dogs and cats and the fallacy of the previous statement. But it is not that the logic is faulty, but rather the underlying statements. Here is another, more pertinent, logical conclusion, again based on false underlying statements:

Investment risk is measured by SD.

Lower SDs mean lower investment risk.

Fund X has a low SD.

Therefore Fund X has low investment risk.

In his landmark text A Random Walk Down Wall Street (1973), Burton Malkiel defines risk as follows:

"Investment risk, then, is the chance
that expected security returns will not materialize and, in particular,
that the securities you hold will fall in price. ... Thus, financial risk
has generally been defined as the variance or standard deviation of
returns."

In two short sentences this groundbreaking
publication has transferred the concept of risk to a number. It is
interesting to note that even Markowitz (1953), dodged defining
measures of volatility as risk.

It is debatable that this leap from the abstract to
the mathematical was the most blatant of its type. However, it
certainly had a major impact. From Malkiel, Fama and French, Treynor,
Black and Sholes, Sharpe, etc., the study of portfolio construction
centered around enhancing return while decreasing "risk" as defined by
SD. With this model, risk has no decision-making component. "Risk" by
this definition is completely dependent on SD values. Uncertainty is
only a byproduct of the dispersion around a mean.

Unfortunately, investment risk requires a decision
maker-a human, in the case of investing. To the extent that events are
important to the decision maker, one could posit that those events may
impact the likelihood of making an undesirable decision. Because these
events may be entirely unrelated to the underlying investment, risk is
clearly much more than the volatility component of an investment. A
simple-minded example will illustrate. Imagine that an investor
purchases a mutual fund for $10 per share. The next day he dies without
heirs. What is the risk after his death?

While this appears to be an absurd question, if we
as a profession define risk as SD would we not have to conclude that
the risk is equal to the SD of the investment? If this sounds like
semantics, then why do we not describe an investment in terms of its
potential reward and its volatility followed by an in-depth discussion
of the behavioral factors that might impact the decision to buy or sell
at the wrong time. I would propose that it is simply this: It is too
threatening to admit that we really do not know what the "risk" is for
a particular investor.

Addressing FAME in February 2002, Peter Bernstein stated:

"What do we mean by risk? It's a very
messy four -letter word. Volatility is the most popular proxy for risk.
It's a good one. First of all, intuitively, it makes sense. When
something is jumping around, it hits you in the gut, you're not
comfortable, none of us is comfortable with volatility. If we have a
sense something is going on we don't understand, we don't know where
the limits are. There are plenty of intuitive reasons for using
volatility as a proxy for risk. Volatility is also nice because it's a
number, standard deviation or variance, it's a number, and that means
we can manipulate it mathematically. All those beautiful equations
wouldn't be there unless we had a mathematical concept for risk. But
volatility cannot deal with fat tails, with non-normal distributions,
with nonlinear relationships, with nonstationarity, with multiperiod
analysis, and there's more. It gets messed up, it doesn't hold
together. So we have to think about different kinds of risk models, and
more elaborate kinds of risk models, and the more elaborate they get,
maybe the further away we get from the basic ideas. And for long-term,
buy-and-hold investors, volatility is essentially irrelevant. So our
definition of risk, the thing that we use the most, is in a sense a
floating crap game. Uncertainty means-this is what Keynes and Frank
Knight were very clear to explain-uncertainty is something we cannot
quantify, we do not know what is going to happen, we don't know what
the probabilities are."

And later in the same speech:

"How well do we really understand
investor responses and how they weigh the trade-offs between risk and
return? How do we define risk aversion? How variable and how stable are
utility functions? These are very important in making policy decisions
for long-term asset allocation. We need some sense of this, and it's
very slippery because it is so intuitive and so internalized."

Not only does the SD fail to define risk, but the interested observer
can hardly find the basic definition for how annualized standard
deviations are calculated. One need only look at the detailed
definition of standard deviation expressed by Morningstar and that of Smart Money to find that for the exact same periods standard deviations are dramatically different and yet they are defined identically in both publications even to the commas and periods.
When observing such glaring flaws in such popular resources designed to
assist in portfolio construction, how can we continue to rely on such a
concept? And yet, as professionals, we take the SD to be an expression
of risk with which we build portfolios for the investing public. This
seems to be inexcusably shortsighted on the part of our profession.

If the standard deviation does not represent risk
but rather is simply a measure of volatility, what then is risk and how
do we define it, or do we even need to do so? A critical part any risk
definition necessitates that we understand that investment risk
requires human behavior. That behavior is unique to the investor. As
professionals, we do not have the privilege of defining investor
perception. That is the unique property of the owner of the investment.

Put much more eloquently in the words of Glyn Holton (Financial Analyst Journal, Vol. 6, 2004):

"The definition
(of risk) depends on the notions of exposure and uncertainty, neither
of which can be defined operationally. ... All we can hope to define
operationally is our perception of uncertainty. Consequently, it is
impossible to operationally define risk. At best, we can operationally
define our perception of risk. There is no true risk."

So then, we are left with the factors that influence
an investor's perception of his investment risk. This is the embryonic
domain of behavioral finance. It is an area that we must begin to study
so we can understand the complexity of human behavior as it pertains to
investment decision-making. As professionals we must strengthen our
ability to determine the risk for each individual, recognizing that the
same investment has different risks in the hands of different
investors. That determination requires frequent monitoring of the
investor's life status, and their perception of the investment
experience. Because of the extensive dynamics of an individual life,
risk determination is dynamic and potentially complex. Perhaps it is
for this reason that there is such unfounded allegiance to quantifying
risk with the proxy of a standard deviation.

As a point of discussion I would like to propose the following operational definition.

Investment risk
can be defined as the exposure of capital to a future decision based on
the perceived value of an investment at the time of that decision.

Notice that the exposure of capital is to a future decision, not to an investment. Also, that the decision is based on perceived value,
and that perception is based on several factors such as observation
frequency, deviation from expectation, volatility and current life
factors, to name a few.

It is not the purpose of this article to propose a
strategy for assessing risk and recommending investments as a result of
that assessment. Nor is its purpose to address the components
associated with risk and how those components can be impacted by
investment work. That is a job for behavioral finance. What I do hope
to accomplish is to further motivate a dialogue for investment
professionals to open their thinking to other ideas of assessing risk
and to question, (in the words of Ken Fisher), "What is it that I
believe that is wrong?" Maybe one of those beliefs is that SD defines
investment risk.

To quote Bertrand Russell, "In all affairs it's a
healthy thing now and then to hang a question mark on the things you
have long taken for granted."