The exact definition of Risk has been debated for decades. While a lot of literature considers volatility to be the total measure of risk, David Dreman did not agree with this. In my view though, risk is the uncertainty associated with the expected outcome of any variable. This uncertainty can be both in positive direction or negative.
The Chinese have a symbol for risk, of which the first part signifies danger, while the second part signifies opportunity. I agree with this principle that although we should be careful about risk, higher or excess return too is dependent upon the amount of risk taken. It is an established fact in modern portfolio theory that higher the risk, more the return (Damodaran).
However, excessive risk taking should be avoided and how risk averse a person is should depend on his risk appetite and willingness. So it becomes very important to first determine the risk threshold of an investor before taking on risk.
Measurement of risk has also been widely debated. I think that standard deviation or volatility is a good measure of total risk associated with a variable. It may be a very crude term and researchers have been working on a more sophisticated measure, but I think till date, volatility remains the most appropriate risk measure, irrespective of the nature of the risk (Damodaran).
Risk can be broadly classified into credit risk, market risk, operational risk and other risks. New risk measures have been developed in recent times, such as value at risk (VaR), Beta etc., on which most of the modern portfolio theories and practical investment measures are based. While there are limitations to each of these measures, they give a very good idea about the uncertainty associated with the expected value of a variable, which is the basic definition of risk.
References
Damodaran, A. Models of Risk and Return. NYU Stern. Retrieved from http://people.stern.nyu.edu/adamodar/pdfiles/ovhds/ch3.pdf.
