
We tend to think of risk in predominantly negative terms, as something to be avoided or as a threat that we hope won't materialize. In the investment world, however, risk is inseparable from performance and, rather than being desirable or undesirable, is simply necessary. Understanding risk is one of the most important parts of a financial education. This section will examine ways in which we measure and manage risk in making investment decisions.
Tutorial: Managing Risk And Diversification
Risk  Good, Bad and Necessary
A common definition for investment risk is "deviation from an expected outcome." We can express this deviation in absolute terms or relative to something else like a market benchmark. Deviation can be positive or negative, and it relates to the idea of "no pain, no gain"  to achieve higher returns in the long run, you have to accept more shortterm volatility. How much volatility depends on your risk tolerance  an expression of the capacity to assume volatility based on specific financial circumstances and the propensity to do so, taking into account your psychological comfort with uncertainty and the possibility of incurring large shortterm losses. (To learn more, read Determining Risk And The Risk Pyramid and Personalizing Risk Tolerance.)
Absolute Measures of Risk
One of the most commonly used absolute risk metrics is standard deviation, a statistical measure of dispersion around a central tendency. For example, during a 15year period from August 1, 1992 to July 31, 2007, the average annualized total return of the S&P 500 Stock Index was 10.7%. This number tells you what happened for the whole period, but it doesn't say what happened along the way.
The average standard deviation of the S&P 500 for that same period was 13.5%. Statistical theory tells us that in normal distributions (the familiar bellshaped curve) any given outcome should fall within one standard deviation of the mean about 67% of the time and within two standard deviations about 95% of the time. Thus, an S&P 500 investor could expect the return at any given point during this time to be 10.7% +/ 13.5% just under 70% of the time and +/ 27.0% for 95% of the time. (For more insight, read The Uses And Limits Of Volatility.)
Risk and Psychology
While standard deviation information may be helpful, it does not fully address an investor's risk concerns. The field of behavioral finance has contributed an important element to the risk equation, demonstrating asymmetry between how people view gains and losses. In the language of prospect theory, an area of behavioral finance introduced by Amos Tversky and Daniel Kahneman in 1979, investors exhibit loss aversion  they put more weight on the pain associated with a loss than the good feeling associated with a gain. (For more on this, read Behavioral Finance: Prospect Theory.)
Thus, what investors really want to know is not just how much an asset deviates from its expected outcome, but how bad things look way down on the lefthand tail of the distribution curve. Value at risk (VAR) attempts to provide an answer to this question. The idea behind VAR is to quantify how bad a loss on an investment could be with a given level of confidence over a defined period of time. For example, the following statement would be an example of VAR: "With about a 95% level of confidence, the most you stand to lose on this $1,000 investment over a twoyear time horizon is $200." The confidence level is a probability statement based on the statistical characteristics of the investment and the shape of its distribution curve. (To learn more, read Introduction to Value At Risk  Part 1 and Part 2.)
Of course, even a measure like VAR doesn't guarantee that things won't be worse. Spectacular debacles like that of hedge fund Long Term Capital Management (LTCM) in 1998 remind us that socalled "outlier events" may occur. After all, 95% confidence allows that 5% of the time results may be much worse than what VAR calculates. In the case of LTCM, the outlier event was the Russian government's default on its outstanding sovereign debt obligations, an event that caused the hedge fund's performance to be much worse than its expected value at risk. (To learn about LTCM and other similar events, read Massive Hedge Fund Failures and Pocket Change Or Prison: The Galleon Hedge Fund Scandal.)
Another risk measure oriented to behavioral tendencies is drawdown, which refers to any period during which an asset's return is negative relative to a previous high mark. In measuring drawdown, we attempt to address three things: the magnitude of each negative period (how bad), the duration of each (how long) and the frequency (how many times).
In short, risk is inseparable from return. Every investment involves some degree of risk, which can be very close to zero in the case of a U.S. Treasury security or very high for something such as concentrated exposure to Sri Lankan equities or real estate in
In the remainder of this section, we'll talk about a few investment products companies can use to manage some of the financial risks they face. (To learn more about the risks companies face, read Identifying And Managing Business Risks and The Evolution of Enterprise Risk Management.)
Options Basics

Investing
Value at Risk (VaR)
Value at risk, often referred to as VaR, measures the amount of potential loss that could happen in an investment or a portfolio of investments over a given time period. 
Trading
How To Convert Value At Risk To Different Time Periods
Volatility is not the only way to measure risk. Learn about the "new science of risk management". 
Investing
An Introduction To Value at Risk (VAR)
Volatility is not the only way to measure risk. Learn about the "new science of risk management". 
Managing Wealth
Standard Deviation
Learn about how standard deviation is applied to the annual rate of return of an investment to measure the its volatility. 
Investing
How Investment Risk Is Quantified
FInancial advisors and wealth management firms use a variety of tools based in Modern portfolio theory to quantify investment risk. 
Investing
A Simplified Approach To Calculating Volatility
Though most investors use standard deviation to determine volatility, there's an easier and more accurate way of doing it. 
Personal Finance
Backtesting ValueatRisk (VaR): The Basics
Learn how to test your VaR model for accuracy. 
Investing
Quantitative Analysis Of Hedge Funds
Hedge fund analysis requires more than just the metrics used to analyze mutual funds. 
Investing
5 Ways To Measure Mutual Fund Risk
These statistical measurements highlight how to mitigate risk and increase rewards. 
Trading
Trading With Gaussian Models Of Statistics
The entire study of statistics originated from Gauss and allowed us to understand markets, prices and probabilities, among other applications.