RISK AND VOLATILITY: ECONOMETRIC MODELS
AND FINANCIAL PRACTICE
Nobel Lecture, December 8, 20031
by
Robert F. Engle III
New York University, Department of Finance (Salomon Centre), 44 West
Fourth Street, New York, NY 10012-1126, USA.
INTRODUCTION
The advantage of knowing about risks is that we can change our behavior to
avoid them. Of course, it is easily observed that to avoid all risks would be im-
possible; it might entail no flying, no driving, no walking, eating and drinking
only healthy foods and never being touched by sunshine. Even a bath could
be dangerous. I could not receive this prize if I sought to avoid all risks. There
are some risks we choose to take because the benefits from taking them ex-
ceed the possible costs. Optimal behavior takes risks that are worthwhile. This
is the central paradigm of finance; we must take risks to achieve rewards but
not all risks are equally rewarded. Both the risks and the rewards are in the fu-
ture, so it is the expectation of loss that is balanced against the expectation of
reward. Thus we optimize our behavior, and in particular our portfolio, to
maximize rewards and minimize risks.
This simple concept has a long history in economics and in Nobel cita-
tions. Markowitz (1952) and Tobin (1958) associated risk with the variance in
the value of a portfolio. From the avoidance of risk they derived optimizing
portfolio and banking behavior. Sharpe (1964) developed the implications
when all investors follow the same objectives with the same information. This
theory is called the Capital Asset Pricing Model or CAPM, and shows that
there is a natural relation between expected returns and variance. These con-
tributions were recognized by Nobel prizes in 1981 and 1990.
Black and Scholes (1972) and Merton (1973) developed a model to evalu-
ate the pricing of options. While the theory is based on option replication ar-
guments through dynamic trading strategies, it is also consistent with the
CAPM. Put options give the owner the right to sell an asset at a particular
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