Financial Risk

Overview

The primary tradeoff that occurs when choosing to hold a given set of assets is the expected return versus the inherent risk. What this means exactly is hard to pin down. In particular, what risk means exactly, and how can it be measured is not an easy topic.

Choice and Risk

The primary definition of risk comes from microeconomics and the theory of choice. In that context, risk is simply uncertainty.

This definition does not typically match most people's intuitions, largely because it implies there is risk in situations for which there are no possible losses, only gains.

In addition, the definition of risk as uncertainty does not indicate how risk is to measured. A large part of the theory of financial risk focuses on this issue of measurement. (see below)

Measuring Risk

The standard definition of risk as uncertainty typically leads one to adopt any of a number of statistical dispersion measures (such as variance or standard deviation) as the measure of risk. Other measures of risk are used to focus more on the possibility of losses, rather than the uncertainty of gains.

• Return Standard Deviation : uses the standard measure of the variance or standard deviation of a random variable as the measure of risk.
• Value at Risk : is a measure of risk that measures the dollar amount of loss that is possible at a certain statistical threshold. It is equivalent to the variance in some cases. It is also more useful for certain types of portfolios, particularly leveraged portfolios.

Risk and Returns

Within the context of portifolio theory, risk takes on a new dimension. While it is generally still viewed as uncertainty, the ability to choose a portfolio of assets leads to the possibility of diversification.

Standard economic theory hypothesizes a relationship between the risk and the return of a given asset. (see for example, efficient market hypothesis) However, the ability to diversify creates complexity, beacuse it is possible to reduce the risk of portfolio, while not changing the expected return.

The Capital Asset Pricing Theory was one of the first frameworks that elaborated a theory for the relationship between risk and return incorporating the effects of diversification.

Additional Topics

• Risk Attribution is the process of attributing the risk into the sum of factors that affect the portfolio. This information is often used in order to gauge whether the bets that a manager has made actually paid off they way they were anticipated.
• Axioms of Risk : provides a set of axioms for constructing a rational risk measure.