Forget the Umbrella, Build an Ark
The recent market volatility has likely led to many plan sponsors looking for guidance on how to respond to another decline in the financial position of their defined benefit (DB) plan. While an umbrella can provide shelter in the rain, should DB plan sponsors be thinking about building an ark for future pension storms?
This article reviews research by renowned mathematician, Benoit Mandelbrot, who borrowed stories from the book of Genesis to help explain two of his research findings – the “Joseph Effect” and the “Noah Effect”. The ark saved Noah during the Great Flood, but to what extent can the insights of Mandelbrot’s Noah Effect assist DB plan sponsors?
Joseph Effect: Price moves have momentum and continue in one direction for a period of time before changing direction.
Noah Effect: Price discontinuity results in market crashes.
“Noah” is costly: Joseph Effects rule the market most of the time, but Noah Effects can be the most costly.
Dynamic risk management: Markets will crash. A dynamic approach to managing asset mix may have better odds of limiting the impact of a market crash.
Working together: Dynamic risk management is an area where consultants and investment managers can work together to reduce risk for
The Joseph Effect is named after Joseph’s interpretation of the Pharaoh’s dream of seven fat cows and seven gaunt ones to mean that there would be seven prosperous years followed by seven lean ones. For markets, the trend relates to the movement in returns where they continue in one direction for a period of time before changing direction.
On the other hand, the “Noah Effect” describes discontinuity — after the story of the Great Flood. The flood came and went – catastrophic and transient. Noah survived, as he had prepared against the coming flood by building an ark strong enough to withstand it. Mandelbrot found that market crashes are similar — when something changes, it can change abruptly. For example, a stock priced at $30 a share can quickly fall to $5 without first being priced at $25 or $20, if something significant triggers its collapse.
A Joseph Effect occurs when markets are evolving gradually and continuously, but a Noah Effect is about cataclysms. One example of a Noah Effect is the week of September 11 2001, when stock exchanges around the world closed and dropped significantly on re-opening. Another example is the market declines during the global financial crisis of 2008, which saw the collapse of large financial institutions in reaction to liquidity shortfalls.
Joseph Effects rule the market most of the time, so they are what many financial models reflect. But Noah Effects can put a sudden end to best-made plans.
Under statistical modelling, market returns are often assumed to follow a standard bell curve. Yet, comparing the expected range of monthly returns for the Canadian and US equity markets (represented by the S&P/TSX Composite and S&P 500 index local returns) suggests that Noah Effects are more regular than what many investors expect.
Our analysis compared actual monthly returns for the 40-year period to June 30, 2011. Returns were segmented into “return bins” that represented 1, 2, and 3 standard deviations from the average monthly return. The same analysis was modelled assuming a bell curve distribution based on the historical average return and volatility.
The chart below shows the net percentage difference in the frequencies of the actual and expected observations for each of the return bins (i.e., 1, 2 and 3 standard deviation occurrences). In other words, had the number of actual occurrences been the same as expected, the net percentage is zero. If the number of occurrences were double what had been expected, the net percentage is 100%. A positive percentage implies there were more occurrences than expected, while a negative percentage implies there were fewer occurrences than expected.
The chart highlights the historical tail risk, where large negative returns occurred more frequently than expected. The bell curve of the actual results was also negatively skewed with less frequent than expected positive return occurrences.
Effective risk management
A traditional approach to risk management is to develop a fixed long-term asset mix and to set rebalancing parameters (e.g., +/- 5%) around the major asset classes. When markets are trending, this approach is effective most of the time.
However, traditional risk management approaches tend not to be as effective during periods of significant market stress. As our analysis indicates significant negative market movements happen more often than expected, suggesting plan sponsors should consider risk management approaches that adequately protect against this tail-end risk.
Adopting a more dynamic approach to managing asset mix (and the interaction with liabilities) should improve a plan’s ability to limit the impact of significant market corrections. In other words, it may be appropriate to develop an asset mix approach that better reflects the risk of Noah Effects.
It is for these reasons that many consulting firms are proactively promoting dynamic risk management to plan sponsors. There are variations in their approaches, but they have two common themes:
The catalyst for a dynamic asset mix change typically reflects a change in the funded position of a DB plan and leads to an increase in matching assets as the funded position improves.
Working together, consultants and investment managers can assist DB plan sponsors in the development and implementation of a dynamic risk management approach. The consultant helps develop the strategy for the risk management approach, while the investment manager has “hands-on” experience to facilitate the timing and implementation of the asset mix changes.
For further discussion on how dynamic asset allocation may assist your plan, please contact:
The author acknowledges Mike Faulkner, CEO of P-Solve in the UK, who discussed some of Mandelbrot’s research at a recent P-Solve conference in London.