January/February 1999

13

The Three P’s of Total Risk Management

Andrew W. Lo

Current risk-management practices are based on probabilities of extreme
dollar losses (e.g., measures like Value at Risk), but these measures capture
only part of the story. Any complete risk-management system must address
two other important factors—prices and preferences. Together with
probabilities, these compose the three P’s of “Total Risk Management.” This
article describes how the three P’s interact to determine sensible risk profiles
for corporations and for individuals—guidelines for how much risk to bear
and how much to hedge. By synthesizing existing research in economics,
psychology, and decision sciences and through an ambitious research agenda
to extend this synthesis into other disciplines, a complete and systematic

approach to rational decision making in an uncertain world is within reach.

lthough rational decision making in the
face of uncertainty is by no means a new
aspect of the human condition,

1

recent
events have helped to renew and deepen
interest in risk management. Two forces in particular
have shaped this trend: advances in financial tech-
nology (models for pricing derivative instruments
and computationally efficient means for implement-
ing them) and an ever-increasing demand for new
and exotic financial engineering products (perhaps
because of increased market volatility or simply
because of the growing complexity of the global
financial system). These forces, coupled with such
recent calamities as those of Orange County, Gibson
Greetings, Metallgesellschaft, Procter & Gamble,
and Barings Securities, provide more than sufficient
motivation for a thriving risk-management industry.
Current risk-management practices focus
almost exclusively on the

statistical

aspects of risk.
For example, one of the most popular risk-
management tools, Value at Risk (VAR), is
described in J.P. Morgan’s RiskMetrics system doc-
umentation in the following way:

Value at Risk is an estimate, with a predefined
confidence interval, of how much one can lose
from holding a position over a set horizon.
Potential horizons may be one day for typical
trading activities or a month or longer for port-
folio management. The methods described in
our documentation use historical returns to
forecast volatilities and correlations that are
then used to estimate the market risk. These
statistics can be applied across a set of asset
classes covering products used by financial
institutions, corporations, and institutional
investors. (Morgan Guaranty Trust Company,
1995, p. 2)

Although measures like VAR play an impor-
tant role in quantifying risk exposure, they
address only one piece of the risk-management
puzzle—probabilities. Probabilities are an indis-
pensable input into the risk-management process,
but they do not determine how much risk a
corporation should bear and how much should be
hedged. In this article, I argue that any complete
risk-management protocol—what might be called
“Total Risk Management” (TRM),

2

to borrow a
phrase from the quality control literature—must
include two other pieces: prices and preferences.
Together with probabilities, these three P’s form
the basis of a systematic approach to rational
decision making in an uncertain world. All three
P’s are central to TRM: prices in considering how
much one must pay for hedging various risks;
probabilities for assessing the likelihood of those
risks; and preferences for deciding how much risk
to bear and how much to hedge.
Despite being a trendy catchphrase, TRM has
deep intellectual roots in economics, statistics, and
mathematics and is based on research that can be
traced back to the very foundations of probability
theory (Ramsey 1926), statistical inference (Savage
1954), and game theory (von Neumann and Mor-
ganstern 1944). Of course, the term “risk manage-
ment” never appears in that literature, but the
issues that these early pioneers grappled with are
precisely those that concern us today. Indeed, I

Andrew W. Lo is Harris & Harris Group Professor at
the Massachusetts Institute of Technology’s Sloan
School of Management.
A

Financial Analysts Journal

14



Association for Investment Management and Research

hope to show much can be gained by synthesizing
and extending the various disparate strands of
research that have grown out of these seminal
works: Current risk-management practices have so
far drawn on only one such strand.

The Three P’s

To understand the interactions among prices, prob-
abilities, and preferences, consider the most funda-
mental principle of economics, namely, the law of
supply and demand. This law states that the market
price of any commodity and the quantity traded are
determined by the intersection of supply and
demand curves, where the demand curve represents
the schedule of quantities desired by consumers at
various prices and the supply curve represents the
schedule of quantities producers are willing to sup-
ply at various prices. The intersection of these two
curves is the price–quantity pair that satisfies both
consumers and producers; any other price–quantity
combination may serve one group’s interests but not
the other’s.
Even in such an elementary description of a
market, the three P’s are present. The demand
curve is the aggregation of individual consumers’
demands, each derived from optimizing an indi-
vidual’s preferences, subject to a budget constraint
that depends on prices and other factors (e.g.,
income, savings requirements, and borrowing
costs). Similarly, the supply curve is the aggrega-
tion of individual producers’ outputs, each derived
from optimizing an entrepreneur’s production
function, subject to a resource constraint that also
depends on prices and other factors (e.g., costs of
materials, wages, and trade credit). And probabili-
ties affect both consumers and producers as they
formulate their consumption and production plans
over time and in the face of uncertainty—uncertain
income, uncertain costs, and uncertain business
conditions.
Formal models of asset prices and financial
markets, such as those of Merton (1973b), Lucas
(1978), Breeden (1979), and Cox, Ingersoll, and Ross
(1985), show precisely how the three P’s simulta-
neously determine an “equilibrium” in which
demand equals supply across all markets in an
uncertain world where individuals and corpora-
tions act rationally to optimize their own welfare.
Typically, these models imply that a security’s price
is equal to the present value of all future cash flows
to which the security’s owner is entitled. Two
aspects make this calculation unusually challeng-
ing: Future cash flows are uncertain, and so are
discount rates. Although pricing equations that
account for both aspects are often daunting,

3

their
intuition is straightforward and follows from the
dividend discount formula: Today’s price must
equal the expected sum of all future dividends mul-
tiplied by discount factors that act as “exchange
rates” between dollars today and dollars at future
dates. If prices do not satisfy this condition, then
there must be a misallocation of resources between
today and some future date. This situation would be
tantamount to two commodities selling for different
prices in two countries after exchange rates have
been taken into account.
What determines the exchange rate? For indi-
viduals, it is influenced by their preferences (the
ratio of marginal utilities of consumption, to be
precise), and it is determined in an equilibrium by
the aggregation of all the preferences of individuals
in the market through the equalization of supply
and demand.
These models show that equilibrium is a pow-
erful concept that provides a kind of adding-up
constraint for the three P’s: In an equilibrium, any
two P’s automatically determine the third. For
example, given an equilibrium in which preferences
and probabilities are specified, prices are deter-
mined exactly (this is the central focus of the asset-
pricing literature in economics). Alternatively,
given an equilibrium in which prices and probabil-
ities are specified, preferences can be inferred
exactly (see, for example, Bick 1990, He and Leland
1993, Aït-Sahalia and Lo 1998b, and Jackwerth
1998). And given prices and preferences, probabili-
ties can be extracted (see, for example, Rubinstein
1994 and Jackwerth and Rubinstein 1996).
This functional relationship suggests that the
three P’s are inextricably linked, and even though
current risk-management practices tend to focus on
only one or two of them, all three P’s are always
present and their interactions must be considered
carefully. In the sections to follow, I consider each
of the three P’s in turn and describe how each is
related to the other two. Although all three P’s are
crucial for any TRM system, I will argue that pref-
erences may be the most fundamental, the least
understood, and therefore, the most pressing chal-
lenge for current risk-management research.

Prices

One of the great successes of modern economics is
the subfield known as asset



pricing,

4

and within
asset pricing, surely the crowning achievement in
the past half-century is the development of precise
mathematical models for pricing and hedging deriv-
ative securities. The speed with which the ideas of
Black and Scholes (1973) and Merton (1973a) were
embraced, both in academia and in industry, is