# Complete Guide To Corporate Finance

## Risk Management And Options - Introduction To Risk Management

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.

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 15-year 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 bell-shaped 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

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

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 left-hand 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 two-year 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

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 so-called "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

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).

Argentina . Risk is quantifiable both in absolute and in relative terms. A solid understanding of risk in its different forms can help investors to better understand the opportunities, trade-offs and costs involved with different investment approaches.

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

**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 short-term 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 short-term 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 15-year 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 bell-shaped 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 left-hand 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 two-year 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 so-called "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*.)