Astute financial advisors are always searching for better ways to measure how much risk makes sense for a client. Some swear by a particular risk questionnaire; others rely on detailed interviews and intuition.

Either way, most methods focus on the probability of risk and less, if at all, on the extent of that risk, says Richard Fullmer, senior portfolio strategist with Seattle-based Russell Investment Group in a paper entitled Mismeasurement of Risk in Financial Planning. The result, he says, is that many older investors end up with portfolios that are far too aggressive.

For many years, advisors used deterministic models to calculate whether a portfolio might last a lifetime. By plugging in a desired rate of return and a projected rate of inflation, they could model how long a portfolio would last. But it is difficult to know what rates of return or inflation are reasonable to assume. And even if markets do deliver the assumed return, the plan could still fail if the returns are realized unevenly over time.

Monte Carlo simulations were a big improvement. These run a portfolio through many potential market results and then spit out a “success rate” showing the percentage of scenarios in which there is any money left upon the death of the client.

But defining risk as “the probability that the plan may fail” is only half the story, Fullmer’s paper says; risk is really the probability of an event occurring and the magnitude of its impact when it does occur. An event with a high probability and a low magnitude may have the same exposure to risk as an event with low probability and high magnitude.

Most retirement calculators capture only the shortfall — the difference between the desired income/estate preservation and the ability of a portfolio to provide these things. In other words: shortfall risk equals probability of shortfall.

A better risk measure, however, in Fullmer’s view, would be: shortfall risk equals the probability of a shortfall times its magnitude. This is how insurers work, agreeing to accept certain risks in exchange for a premium payment.

How much is the risk transfer worth? The answer, Fullmer says, is a function of the frequency by which claims may occur (the probability) and the potential size of those claims (the magnitude).

Consider a more prosaic example: say a speeding ticket is $100 when the driver’s speed is less than 15 kilometres per hour over the speed limit and $1,000 when it is more than 15 km/h over the limit. Now, say you are driving on a road where the posted speed limit is 50 km/h. “Clearly, the risk to you of driving 67 km/h on this road is much greater than the risk of driving 63 km/h,” the paper says. “This is true even if the probability of getting caught is the same.”

Thus, the paper concludes, when measuring risk as the probability of failure, the subsequent asset-allocation decision will typically err on the side of being too aggressive. This is a direct result of ignoring the magnitude of failure. If all risks (spending shortfalls or traffic fines) are treated the same, regardless of magnitude, then aggressive actions (higher equity allocations, higher speeds) will not appear as risky as they would if the overall impact was also considered.

As a result, some risk models may give certain clients a false sense of security — a potentially dangerous result, given recent dramatic market swings. IE