Portfolio Optimization and Analytics Results

For each optimization’s anniversary date on Aug. 1, we would select two sample periods for the historical data. The first sample period was the previous one year; the second sample period was the previous 10-year period. The baseline risk, return and correlation values are calculated for every asset as the average of these two periods. We believe these two periods merge a positive predictive momentum signal arising from the one-year data with the stock’s performance over at least one full market cycle in the long sample. We tested staggered multiple optimization intervals and found no material effect. We applied the sampling procedure uniformly over all sectors and years.

Figure 8 shows what happens as real-world portfolios from macroaxis.com are graphed using the actual risk and return values obtained: The positive association of risk and return is no longer apparent. The ex-ante relationship vanishes ex-post.

Fundamentally, risk and return are not two separate things, but the same. Risk is simply negative returns (Figure 9).

This foundational tenet is always obvious to investors in retrospect. Nevertheless, there are widespread errors in risk estimation, definition, and application across the entire industry. Risk cannot be known in advance; it must be estimated. In a risk-based weighting scheme, any such estimation faces the impossible task of measuring the known unknowns and the unknown unknowns. One may liken risk measurement to holding a tape measure around a black hole without succumbing to the event horizon.

There may be some salvage value in risk minimization, certainly from diversification, but also from simple avoidance of the riskiest elements of the market. The most volatile decile of the Russell 1000 constituents underperformed the full index in the subsequent year by 8.52 percent for the period 1972 to 2012 (Ghayur, 2013).

One of the traditional methods of portfolio optimization and construction is mean-variance optimization (MVO), which was pioneered by Harry Markowitz in the 1950s (Markowitz, 1952). Markowitz and the variations he has spawned have had significant application in our industry, but they have only recently gained traction as index construction methodologies.

MVO’s focus on volatility fails to exploit an asymmetric diversification/return relationship (Damschroder, 2009). Furthermore, diversification is shown to have greater stability in a crisis (Damschroder, 2009).

In aggregate, the Diversification Weighted 500 outperformed the S&P 500 index by 427 basis points per year (Figures 10 and 11). The Diversification Weighted strategy is reported net of fees, estimated at 90 bps, and net of an estimated 20 bps trading cost.

Diversification looks to have had its worst relative year in 1998, despite putting up a 17.7 percent return. In calendar year 2008, DW was 80 bps under the S&P 500 Index despite having a few percent better drawdown through the crisis. While over the entire crisis the DW strategy did better, it also had a worse losing month, losing 3.43 percent more than the S&P 500 in October 2008.

The full-sample upside- and downside-capture statistics for the DW 500 are:
Up Capture: 105 percent Down Capture: 87 percent

A few weighting approaches were excluded from the risk table in Figure 13, as the maximum drawdown statistic requires comparable histories for accurate comparison, and risk stats for any product having not lived through the crisis of 2008 seem trite.

To the chagrin of efficient market theorists, the diversification Weighted strategies in most cases produce higher returns while lowering the portfolio variance. This hypothesizes massive market inefficiency, perhaps induced by the trillions of dollars attached to capitalization-weighted approaches.

Diversification goes both ways. Most investors intuit the benefit of defensive diversification, but diversification can play offense, too. The defensive ability of diversification to protect capital is a function of the noncorrelation and is available to all investors in any strategy. Diversification as a proactive strategy is comparable to a rebalancing bonus. The sum of the defensive and offensive performance capabilities of diversification is what we call the “Diversification Alpha.”

The alpha is made possible by exploiting diversification, volatility and some sort of trading activity, such as rebalancing, but it can be other activity such as reconstitution or reoptimization. This trilogy of portfolio variables combines the idiosyncratic asset volatilities to produce alpha.

Portfolio managers get the defensive contribution of diversification whether or not they try to. The driver is the amount of correlation exploited. In Diversification Returns and Asset Contributions, Fama and Booth (1992) coined the term “diversification returns,” which represents an additive portfolio return attributed to diversification. Booth and Fama approximated this as half the variance reduction in the portfolio given by diversification. The weighted average asset variance would be the portfolio variance if the correlations were all 1. For the most recent Diversification Weighted 500, the weighted average asset variance is 9.35, corresponding to a standard deviation of 30.57 percent. The portfolio variance is 3.41 percent, corresponding to a standard deviation of 11.64 percent.

In Figure 16, each of the line-graphs represents the relative performance of the diversification-weighted sector and composite indexes with regard to their cap-weighted counterparts. Only the industrial sector underperformed. Curiously, the diversification-weighted technology sector showed material underperformance during the late 1990s. When a market-leading sector or industry arises, we have seen the worst available correlations come from that leading sector. As a result, unless otherwise neutralized by stronger expected performance, it is the diversification process’s natural tendency to underweight the market leader segment.

Figure 17 includes a stacked chart to help illustrate the consistency of the incremental performance for each sector over time.

The sector allocation also reveals an interesting and intuitive dynamic: Whenever the market heats up, asset correlations tend to come in, leaving the investor with relatively fewer diversification sources. Telecom and utilities are the largest active weights of the Diversification Weighted strategy over the whole period.

The DW 500 shows an R2 of.80 for a single-factor market risk and an R2 of.83 for a five-factor model. It had statistically insignificant factor exposures to size, momentum, and the risk-free rate. The value factor gave a positive exposure, with a coefficient of.23. For the analysis period, value paid investors 2.09 percent annually, which boosted the returns to the DW 500 by 49 basis points. We expect this is an artifact of the focus on diversification.
Value companies by their nature have a greater proportion of idiosyncratic performance when compared to growth, which often shares homogenizing factors such as cyclicality (data is from the Ken French website (French, 2014)).

Diversification Weighting carries with it a theme of sustainability not found in any other weighting scheme except fundamental weighting. A weighting scheme is an allocation scheme, and an allocation scheme inherently matches providers of capital (investors) with demanders of capital (companies). Diversification lives in the crevice of finance. Any two mega-cap companies are globally interwoven into the mesh that buoys the correlation of the two and decreases their diversification potential. Value companies have a greater proportion of idiosyncratic risk and thus tend to enjoy lower correlations compared with growth companies. Imagine a world where capital formation is free of the massive head winds of regulation and scale, afforded to a few thousand public companies that can shoulder such overhead. The correlation of entrepreneurs, ideas, and execution provides an infinite pool of diversification sources, and we hope that diversification optimization drives capital in the most beneficial way.

The Diversification Weighted 500 demonstrates material and consistent outperformance against other weighting approaches and within the sectors sleeves that we consolidated into the composite.

We explain a framework for diversification measurement and optimization. Diversification Optimization builds on this framework, and the results contrast favorably versus other weighting approaches. We quantify the Diversification Return at 2.97 percent, and we introduce the Diversification Alpha. Total alpha for the strategy is 652 bps annually for over 18 years. We further introduce the ability to stack the Diversification Alpha at the security, sector and asset class level.

The flexibility and efficacy of Diversification Optimization, combined with the demonstrated consistency, attractive risk metrics and total return, presents a strong case for the institutional application of Diversification Weighting as an overlay weighting strategy, product-sleeve, core-satellite model or index.

This portfolio is hypothetical. This is a historical simulation of the portfolio performance an investor would have obtained had you invested in the same selections at the beginning of the simulation. This report provides information on how the portfolio holdings would have changed and would have performed for a certain period.
We have strived to reduce or eliminate potential biases in the process to provide the most accurate assessment of the performance prospects of the strategy. Because Portfolio ThinkTank offers a significant However, it may not be possible for any historical simulation to completely ensure it is free of all biases.
Please see The Gold Standard for Portfolio Backteting and The Seven Deadly Sins Of Portfolio Backtesting for a more complete understanding of biases and risks when backtesting portfolio strategies.
Backtested strategies also run the risk of cherry picking. Cherry Picking is when the author of the backtest has created many variations and is presenting one of the variations that is more favorable. This research was not produced in whole or in part by cherry picking.
This simulation is based on an account with tax exempt or tax deferred growth. Taxable accounts will have to pay the appropriate taxes for dividends, interest and capital gains, which will decrease the performance depicted.
This simulation is not based on actual trading accounts or account composites which may or may not exist for this strategy and may be materially different including worse than the performance illustrated above. Past performance is not necessarily indicative of future performance. Performance results including risk, return and diversification measures are not guaranteed to persist in the future.