Understanding and managing risk is a critical part of being a successful investor. But what is risk? We would look at it from two different angles:

#### risk as uncertainty

Many academics and the more quantitatively-oriented investors view risk as volatility of returns, often expressed by measures such as the the standard deviation of returns.

This approach to measuring risk has certain advantages: with a relatively modest amount of return history one can make some statistical inferences about risk. In addition, a full range of statistical procedures can be used to make predictions about risk.

This approach also has certain disadvantages. For example, the measurement of risk depends in part on the measurement intervals. For the same stock, risk measured using daily returns often looks very different than risk measured using monthly returns. Also, statistical risk measurements usually are backwards looking; but the investor typically cares about the risk embedded in future returns.

Using the standard deviation of returns can lead to some big surprises. A common practice is to calculate the standard deviation of past returns and assume that the standard of deviation of future returns will be similar. Often this works but sometimes it doesn’t in a really bad way, with the future being far more volatile than the past would suggest.

A final problem with variance or standard deviation is that upside volatility is considered as undesirable as downside volatility. Actual investors may care only about downside volatility.

#### risk as losing money

Some professional investors and a large share of the public define risk as the possibility of losing money. This sounds simple, but in practice it is can be difficult to incorporate into the management of a portfolio.

For example, how does one reasonably estimate the potential for losing money if stocks have gone up for several years in a row? Lacking data that is both recent and meaningful, the risk assessment becomes almost entirely subjective.

Another problem is whether the losses will be temporary in nature or more permanent. If losses are likely temporary, then should they be disregarded? How does one decide whether a loss will be temporary?

What do you think?