Standard Deviation, a Poor Measure of Risk

As actuaries and/or risk managers we've been professionally brought up with some deep-rooted assumptions about what 'risk' is....

Difference between Science and Religion
One of my favorite statements is that there is no fundamental difference between a religion (believe) or science. Both depend on a number of axioms, the basic assumptions. Assumptions, we 'believe' or 'take for granted' on basis of our intuition and/or personal experience. Only by means of those axioms we're able to 'prove' other theorems in our system or model.

So what we have to conclude is that what we prove in our our statistical models, is as strong as the foundation (assumptions) on which our models are based.

Main problem is that the assumptions in our models are so trivial and often so frequently implicitly used, that we don't realize their impact. We've developed a blind spot.......


Risk Axioms
With regard to 'risk' I'll just discuss two of the most dangerous (risky ;-) ) assumptions on which most of our investment risk models are build:

1. Risk = Standard Deviation (SD)
2. Mean Reversion
   The theory that a given value will continue to return to an average value over time, despite fluctuations above and below the average value.

Explication

Risk is a much wider concept than just 'standard deviation'.
First of all there's an 'impact difference' between a downside risk and an upside risk. In general, what we perceive as risk is more in terms of downside risk. But yet..., we keep measuring and concluding  about risk on basis of 'standard deviation'.

Why SD Fails as a measure of risk
To illustrate the failure of Standard deviation (SD) as a measure of risk, take a look at the next example in which we compare the performance of two different asset classes, AC-I and AC-II, with the next characteristics:

• AC-I and AC-II have the same average (compound) return of 2.5% per year
• AC-I has a Standard Deviation of  13,9% and AC-II a SD of 27%
• AC-I has a maximum deviation of minus 40.0% and AC-II of 76.3%

By definition AC-II is more risky than AC-I.....

However.., a two year old child will point out AC-I as far more risky than AC-II. First, downside deviations are  more risky than upside deviations and secondly, the 'incremental downside risk' of AC-II can be 'managed' much more effective than the 'crash downside risk' of AC-I.

Conclusion
The times of modeling risk on basis of Standard Deviation are over. We need more sophisticated models that describe and measure risk multidimensional and with respect to downside risk and not upward potential.

Let's conclude with a final question to test your 'stock crash insight'.

What was the worst performance of the S&P 500 and in which year?

Click on 'answer' to find out!

ANSWER

Read more about the S&P 500 performance on: S&P 500 Five Worst One Year Performances (in %)


Related Links
- Actuary-Info: Equity Returns and Mean Reversion (2010)
- Risk is more than standard deviation (2005)
- Our Monetary Blind Spot
- Black Ducks Comic Strips