SmartETF

Tracking Mean Reversion After Bad Months

Our research concludes that you are on the right track but your focus is too linear. Mean reversion over the long-term is an academic boon for getting a Nobel Laureate designation but it does not translate into a workable application in the real world. For example, MVO demonstrates domestic equities have returned 10% over 80 years. Therefore, you should get a 10% return on average. In the real world, the domestic equity market is down over the past 1, 3, and 10 years; yes 10 years. Granted it worked in the 80’s & 90’s, but not the 60’s & 70’s, and definitely not this era. It’s like a broken clock that is right twice a day; it is devoid of market cycles.

Short-term MVO is very interesting and much more meaningful. The question is, and will always be, what time frame is best for analyzing the time series of data (aka, time parameter estimation). I think you are off track when you try to curve fit your data by selecting a particular number of months. Markets don’t move in a linear pattern like monthly. You will have much greater success by rebalancing when markets move by a defined level of volatility or price (or both). Take volatility as an example, last February the market hit an extreme level of volatility (and price drop); buying at the level would have been very profitable. It is these extreme moves (up & down) that create the fat-tails of distributions and are reflected in the extreme technical patterns like Relative Strength. A more scientific approach is to go with a Noble winning approach from 2002 (in effect tossing the MPT model from 1959) and incorporate Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) which examines the clustering of data; basically, a scientific approach to short-term mean-variance. The analogy is MVO works like the Farmer’s Almanac for predicting weather; whereas GARCH acts like the Doppler Radar. Alternatively, you can use price and volatility movement to create a poor man’s GARCH model to track short term mean-variance. Cheers -

What Is Diversification Worth?

Good try but you have an archaic application to asset allocation. Asset allocation relies on four basic attributes: Risk, Return, Dependency (Correlation), and Data Management. These four attributes are managed in a 3 step process: the first step, called a ‘Univariate Model’, measures the risk & return of an asset, the second step, or ‘Bivariate Model’ measures the dependency between two securities, and the third step ranks the bivariate model in what is called a ‘Multivariate Model’ to create the efficient frontier. Your model contains four critical flaws:
First you use the most simplistic measure of dependency to diversify a portfolio with the use of correlation. Correlation assumes a fixed relationship between two securities over the sampled time period and is purely academic. Correlation increases dramatically during extreme events, in fact during any volatile market. If you want a lesson in correlation look to the merry band of MPT disciples at Long-Term Capital Management for a classic case study, or look at Merriweather’s current performance! As the adage goes ‘the only thing that goes up in a down market is correlation’. Trash the static correlation model and move to a dynamic correlation model like Copula Dependency.
Second, you measure risk using standard deviation (σ). Standard deviation, semi-variance and Value-at-Risk are all hyper-flawed because they all rely on normal distributions. Do you really think a 5σ event will only occur every 7000 years or an 87’ magnitude crash will only happy once in every three lifetimes of the universe? Enlighten yourself to the world of Stable Distributions using logarithmic, not arithmetic distributions. You will find 5σ events really occur every 3-4 years. I recommend you convert to Expected Shortfall as you new method of risk measurement.
Third, how can you forecast using any of the methods you suggest? Running a simulation model using Black-Litterman (an Arbitrage Pricing Theory model) or the other solutions are simply band-aids on the old MVO model; the only difference is you are trying to tilt the results to more of a bullish or bearish state. This doesn’t solve the problem it just makes it less damaging. Why not take a scientific physics approach and use a data management tool like GARCH (that won the Noble Prize in 2002) instead of relying on Markowitz and his methodology from 1959? You do know you have faster processors and electronic data exchanges and advanced math models; why not upgrade after 40 years?
Since this article is ostensibly an advertisement for Quantext, I feel its fair game to point out the inherent flaws in your model as well as other suggested models using old mathematical applications and theories. I’m happy to unconditionally prove the superiority of newer models and their specific attributes and will cite the works of Benoit Mandelbrot and Extreme Value Theory as a comparative solution. Set yourself free from averaging thinking!

Relative Returns By Equity Asset Class

Thank you for sharing; always nice to see performance from a multiple time-frame perspective!

Fundamentally Weighted ETFs: Mixed Performance in '07

I think it is time to see through the veil of what a cap-weighted index really is……a glorified momentum index. WAIT! That is comment is sacrilegious! Defend yourself!
Okay, one only needs to look at the sector mix of an index to see the change in market weight caused by the momentum effect. As an example, In December of 2002 the E-Trade Russell 2000 Index Fund composition was approximately 70% small-cap value/ 30% small–cap growth. Three years later (December 2006) the index was approximately 20% small-cap value/ 80% small–cap growth. Imagine trying to beat the small-cap index as a small-cap value manager during those three years!

Let’s take it a step further; pretend you were a small-cap growth manager during this booming three year run. Your track record looks good as you capitalized on this momentum and you soundly beat the small-cap index. On the wings of good fortune you get hired by the institutions and investors. Then the enviable happens, the sector rotates back to small-cap value (and/or some other asset class) and your performance drops and you fall out of favor.

In this example its evident indexing small-cap stocks using a cap-weighted approach capitalizes on the change in momentum while fundamental indexing would have given a more accurate description of how the small-cap securities actually performed.

I don’t have enough data points to judge weather fundamental indexing is better or worse than cap-weighting indexing but I do believe the momentum effect may favor cap-weighting, albeit with more volatility. So the trade-off of risk-adjusted returns is open for debate. What is clear to me is that cap-weighting is nothing more than a momentum strategy masked in the guise of a passive strategy. I’m sure if this were a chat log I’d burn in flames! I applaud Rob Arnott’s work on fundamental indexing and appreciate anyone challenging the norms of convention wisdom.