Use of appropriate risk measures is crucial when assessing capital and solvency requirements and when pricing risk transfer opportunities, among many other business needs. When risk measures are not well understood, opportunities to optimize the allocation of risks are too often missed. It is therefore of fundamental importance that business decisions are based on the most robust measures of risk available. This article aims to promote awareness of the advantages and limitations associated with common risk measures. In addition, some lesser-known techniques for measuring financial risks are also examined.

## Value at Risk

The financial industry began researching new methods for measuring exposure to downside risks in the late 1980s, following the infamous Black Monday stock market crash. It was then that value at risk (VaR) became popular as a risk measure. VaR is a single value from a loss distribution, often with an associated probability of exceedance.

The insurance industry later adopted the widespread use of VaR as a measure of catastrophe risk. During the early years of its use, VaR was often confused with probable maximum loss (PML); however, it is not the maximal or most probable extreme loss. Rather, VaR_{p} indicates the *minimum* loss that is likely to be met or *exceeded* in a given year for a given level, *p*, of probability. In mathematical terms, if we define a random variable, X, as the annual loss, VaR is the loss, *π*_{p}, that has a corresponding annual exceedance probability of *p*.

* VaR*_{p}(X) = π_{p}

P(X ≥ π_{p}) = p

The use of a single value to represent an entire risk profile may be a tempting option for decision-makers—especially for regulators and rating agencies, which require intuitive measures that can be easily adopted when comparing risk profiles across many peer companies. However, VaR cannot tell the full story of a company's exposure to financial risks.

Figure 2 shows a plot of simulated hurricane losses for two companies (Company A from the previous exhibit and a peer Company B). Can you tell which company is riskier based on the VaR_{0.4%} level alone? The answer, of course, is no. Comparing the two companies based on a single point value fails to demonstrate that each company varies in exposure to risks at different exceedance probabilities. For example, Company A's risk profile indicates that it may be at risk to larger and more frequent losses than Company B below the VaR_{0.4%} level. On the other hand, Company B is riskier than Company A toward the tail of the risk profile, meaning that Company B may experience more significant losses than Company A, should a less likely but more extreme disaster occur. This information is not apparent based on the VaR_{0.4%} level alone.

VaR can exhibit large variations after even minor adjustments to the underlying exposure data or to model assumptions. VaR also fails to capture the severity of extreme loss-causing events in the tail of the loss distribution, beyond the probability with which it is associated. This clearly becomes problematic for stakeholders who aim to hedge tail risks, especially for making catastrophe reinsurance purchasing decisions or for assessing capital-based requirements. Not surprisingly, VaR has become an outdated measure for catastrophe risks.