*Asset valuation and risk management are fundamental precepts of finance. But while asset valuation seems to be well understood by most investment enthusiasts, risk and risk management appear to be poorly understood by many investment enthusiasts. Before undertaking successful risk management, a solid understanding of risk itself is necessary.*

The following is a brief primer on risk in economics and finance.

The following is a brief primer on risk in economics and finance.

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In economics, including the subfield finance, there are at a minimum four aspects of risk that are central to understanding and using risk management techniques.

1) The definition of risk in economics

2) Specific risks

3) Measures of risk

4) The two components of risk

**1) Definition of risk**

Before defining risk we need to define the related term uncertainty.

*Uncertainty simply means that we are not certain what will happen in the future.*

or

*Uncertainty means more than one outcome is possible.*

The standard definition of risk in economics is straightforward.

*Risk is uncertainty that affects people’s welfare, i.e. risk is uncertainty that is nontrivial.*

Here is another way of expressing the definition of risk in economics.

*A risky situation is a nontrivial situation where more than one outcome is possible.*

Sometimes, particularly when discussing financial asset risk, we divide the uncertainty (risk) of the returns into two parts. The upside uncertainty is called opportunity or upside opportunity, and the downside uncertainty is called risk or downside risk.

Nearly 100 years ago economist Frank Knight formalized a distinction between risk and uncertainty. Knight’s method of separating risk and uncertainty is rarely used today. But when it is used, the terms are called “Knightian risk” and “Knightian uncertainty”.

Finally, the definition of risk in economics is neither a specific risk, nor is it a measure of risk.

**2) Specific risks**

There are many ways to classify risks but often in economics households are classified as being exposed to five major risk categories.

- Sickness, disability, and death

- Unemployment risk

- Consumer durable asset risk (damage to home, car, etc.)

- Liability risk

- Financial asset risk

When considering investments we are usually most concerned about financial asset risks. There are a multitude of specific financial asset risks. Consider the specific risks of investing in corporate bonds. At a minimum there is interest rate risk, inflation risk, credit risk, and reinvestment risk. The bond investor is exposed to all four of these risks. While each of these specific risks meets the definition of risk, none of them are the definition of risk, and none of them measure risk.

**3) Measures of risk**

There are many measures of risk when considering financial asset risk. Some common measures of financial asset risk are standard deviation (often called volatility), duration, beta, option pricing and option implied volatility, swap prices, and interest rate spreads to name just a few. Annual standard deviation (volatility) is the most common measure of asset return risk. Measures of risk always involve calculating a numerical value or set of values. The definition of risk has no numerical value(s) involved, and neither do specific risks.

Examples from other fields should clear up any confusion between risk measurement and specific risks and the definition of risk.

A Geiger counter measures levels of radioactivity. But Geiger counter readings are not the definition of radioactivity and they are not a specific risk of being exposed to high levels of radioactivity.

A blood pressure monitor measures blood pressure levels. But blood pressure readings are not the definition of blood pressure, nor are they a specific risk associated with abnormal blood pressure.

**4) The two components of risk**

Any risk has two elements, which are sometimes called the two components of risk.

i) the probability of the risk occurring

ii) the magnitude of the risk

Since neither component of risk is more important than the other, risk is the product of the two components of risk.

Risk = (Probability of risk) x (Magnitude of risk)

These two components of risk are not a definition of risk, but they are elements of every risk and we should prefer risk measures that take both risk components into account when assessing risk. This is one reason why standard deviation is a favored measure of financial asset return risk.

For example, we can calculate the annual standard deviation of the return from a portfolio. To calculate the risk of the portfolio for a single year we simply need, in addition to the standard deviation, the portfolio’s mean return, and the distribution of the return. We are then able to calculate both the probability and magnitude of the portfolio’s risk. For instance, if we estimate that the average portfolio return is 8% and the standard deviation is 10%, and the distribution of the return is normal, then there is about a 65% probability that the return will be between -2% and 18% next year. And there is about a 95% probability the return will be between -12% and 28% next year.

If there are no deposits or withdrawals from the portfolio then the standard deviation after (t) years is simply the square root of (t) times the annual standard deviation.

(t)^0.5 x (annual standard deviation).

In that case a similar analysis of risk to the annual analysis above can be performed.

If there are deposits or withdrawals affecting the portfolio the analysis becomes more difficult and simulation methods such as Monte Carlo are typically used, but standard deviation remains the key measure of risk in such simulation methods.

BobK