# Diagnosing the Asset Allocation Engine

Posted by Syntrinsic Investment Counsel on 02/02/10 in History, Markets, Risk

In *Zen and the Art of Motorcycle Maintenance* (nostalgia trip anyone?), author/philosopher, Robert Pirsig, postulates that if one is to rely on a motorcycle to move through life, then one should understand how a motorcycle works and better yet, be able to care for that vehicle. Developing such an understanding of the mechanics behind the movement would, theoretically, make riding the cycle that much more meaningful.

This, of course, brings us to asset allocation modeling.

We here at Syntrinsic have been spending entirely too much of our free time trying to take apart asset allocation theory piece by piece, examining each aspect, cleaning them if you will, and ultimately, trying to better understand how to reassemble them in a manner that makes common sense going forward.

Take standard deviation for instance. The whole premise of using standard deviation as a predictive component is based on the presumption that returns are earned in a normal distribution around a mean. Essentially, we are trying to ascertain whether return distributions are indeed “normal” for the most liquid and efficient of investable markets. To this end, we have calculated the standard deviation and mean of the annual returns of the S&P 500 from 1956 to 2009, then also for all of the rolling fifteen-year periods in that time frame, with a particular emphasis on the two most recent 15 year periods.

S&P 500 | 1956 – 2009 | 1980 – 1994 | 1995 – 2009 |
---|---|---|---|

Mean (Average Return) | 11.09% | 15.18% | 10.37% |

Standard Deviation | 17.35% | 12.55% | 21.17% |

Low Expected Range (2.5%) | -23.60% | -9.93% | -31.97% |

High Expected Range (97.5%) | 45.78% | 40.28% | 52.72% |

When we plot the annual distributions from 1956-2009 (see chart below), one can see the number of occurrences of each annual return during that 54 year period. The green represents those years when returns occurred within one standard deviation, the red within two, and the black (1974, 2008) are outside the expected range.

**Chart I: Range of S&P 500 Annual Returns, 1956 -2009
**

The chart reveals a distribution that is “normal” in the statistical sense, but is far removed from the pretty bell curves often used in academic literature (and investment sales presentations). We would argue that it is better to think of US equity returns as a “flat-normal” distribution, with the “flat” in front to emphasize the nature of the distribution.

Before we leave off this week, let’s consider the two 15 year periods in the table above. Could you construct a more divergent profile for the same investable market? Earn 15% per year with moderate volatility, and then earn 10% per year with volatility almost doubled. Below, see the distribution of annual returns for 1980- 1994, a time when the mean was 15.18%. All of the returns fall within the predicted high-low range; yet it is hard to see the “normalcy” of the distribution.

**Chart II: Range of S&P 500 Annual Returns, 1980-1994
**

Contrast this with the table below of the period from 1995-2009, when the mean was 10.37% and the standard deviation was at 21.17%, well above the 17.35% average since 1956 and almost double the 12.55% of the previous 15 years. Yes, there is a bit of a curve off to the right, but that is a very long tail to the left. The distribution is essentially flat, not normal. Using the term “normal” is really unfair when the 95% likelihood range of returns is over 84% from low to high. That’s not very helpful from a planning standpoint—and this is all about planning.

**Chart III: Range of S&P 500 Annual Returns, 1995-2009
**

So what have we learned? The asset allocation motorcycle is a mess. No matter how flashy the packaging, how crisp the presentation materials, how well-pressed the suit, nor how slick the hairstyle, the inner workings of asset allocation modeling as we know it are based on mechanics that need a massive overhaul.

And that’s okay so long as we know it and make decisions accordingly. Perhaps together, we can rebuild the asset allocation engine.