Is there a best way to select and weight asset classes for long-term diversification benefits? These blog entries address this strategic allocation question.
One concern about simple momentum strategies is data snooping bias impounded in selection of the lookback interval(s) used to measure asset momentum. To circumvent this concern, we consider the following argument:
The CBOE Volatility Index (VIX) broadly indicates the level of financial markets distress and thereby the tendency of investors to act complacently (when VIX is low) or to act in panic (when VIX is high).
Complacency translates to resistance in changing market outlook (long memory and lookback intervals), while panic translates to rapid changes of mind (short memory and short lookback intervals).
The inverse of VIX is therefore indicative of the actual aggregate current lookback interval affecting investor actions.
We test this argument by:
Setting a range for VIX using monthly historical closes from January 1990 through December 2006, before the sample period used for most tests of the Simple Asset Class ETF Momentum Strategy (SACEMS).
Applying buffer factors to the bottom (0.9) and top (1.1) of this actual inverse VIX range to recognize that it could break above or below the historical range in the future.
Segmenting the buffer-extended inverse VIX range into 12 equal increments and mapping these increments by rounding into momentum lookback intervals of 1 month (lowest segment) to 12 months (highest segment).
Applying this same method to future end-of-month inverse VIX levels to select the SACEMS lookback interval for the next month.
We test the top one (Top 1), the equal-weighted top two (EW Top 2) and the equal-weighted top three (EW Top 3) SACEMS portfolios. We focus on compound annual growth rate (CAGR), maximum drawdown based on monthly measurements, annual returns and Sharpe ratio as key performance statistics. To calculate excess annual returns for the Sharpe ratio, we use average monthly yield on 3-month Treasury bills during a year as the risk-free rate for that year. Benchmarks are these same statistics for tracked (baseline) SACEMS. Using monthly levels of VIX since inception in January 1990 and monthly dividend-adjusted prices of SACEMS assets since February 2006 (initial availability of a commodities ETF), all through April 2026, we find that:Keep Reading
Portfolio construction agents each independently employ Step 2 and 3 outputs to proposed a portfolio based on an assigned method (such as equal weight, inverse volatility, mean-variance optimization or risk parity), including:
A researcher agent to propose novel portfolio construction methods.
An adversarial agent to uncover unconventional allocation ideas.
Multiple agents review all proposed portfolios and vote on them.
A chief investment officer agent scores, selects and combines surviving proposed portfolios using an ensemble of seven combination methods. This agent then summarizes a final recommendation/reasoning/dissenting views.
They include a meta-agent that compares forecasted and realized returns and rewrites agent scripts to improve future performance. They specify each agent in this system via a description, a set of scripts, a collection of skills and a structured output. An Investment Policy Statement (specifying asset class universe, objective, tracking error) constrains the AI agents. Overall, this system compresses days or weeks of human work into minutes. Based on prior research and experience with LLM-based AI agents, they observe that:Keep Reading
Much prior research indicates that most stock anomalies fail to deliver due to data snooping in their discovery, post-publication market adaptation and, especially, implementation costs. In their March 2026 paper entitled “Reviving Anomalies”, Heiner Beckmeyer, Florian Berg, Timo Wiedemann and Jonas Wortmann describe and test a framework to address the poor performance of simple long-short portfolios by double-sorting based first on anomaly rules and then on expected next-month net returns of anomaly stocks. They employ machine learning return forecasts based on 153 firm/stock characteristics to compute expected returns. They quantify expected trading frictions with impact of trading scaled by fund size (micro, small, medium and large). Using data for the 153 firm/stock characteristics and return data for a broad sample of U.S. stocks during January 2004 to December 2023, they find that:Keep Reading
Homes typically represent a substantial fraction of investor wealth, often leveraged via mortgages. Are there reliable relationships between U.S. home prices and the U.S. stock market? For example, does a rising stock market stimulate home prices? Do homes diversify stocks? To investigate, we consider the following inputs:
Monthly levels of the non-seasonally adjusted S&P/Case-Shiller U.S. National Home Price Index (Home Price Index) during January 1987 through December 2025, with release lag about three months.
Annual median sales prices for existing homes during 1963 through 2025, as assembled by Claude (with guidance).
Using these sources, monthly levels of the S&P 500 Index (SP500) and yields on 3-month and 1-year U.S. Treasury bills (T-bills) for Sharpe ratio calculations during January 1963 through February 2026, we findthat:
Have retirement target date funds (TDF) from the principal offerors exhibited asset allocation wisdom over the past 20 years? In his February 2026 paper entitled “The Asset Allocation Wisdom of Wall Street”, Harry Mamaysky classifies TDFs into risk buckets and constructs portfolios that replicate these buckets using low-cost exchange traded funds (ETF). Specifically, he replicates eight risk buckets from S&P 500 Index and U.S. Treasury ETFs with equity weights 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 0.95 and compares TDFs to matching replicants. Using returns for all TDFs (mutual funds) from 14 offerors with target dates from 2005 through 2070, encompassing over $1 trillion in assets, he finds that:Keep Reading
Subscribers asked whether substituting Invesco QQQ Trust (QQQ) for SPDR S&P 500 (SPY) in the Simple Asset Class ETF Value Strategy (SACEVS) and the Simple Asset Class ETF Momentum Strategy (SACEMS) improves outcomes. To investigate, we substitute monthly QQQ dividend-adjusted returns for SPY dividend-adjusted returns in the two model strategies. We then compare the modified performance with the original baseline performance, including: gross compound annual growth rates (CAGR) at various horizons, average gross annual returns, standard deviations of gross annual returns, gross annual Sharpe ratios and maximum drawdowns (MaxDD) based on monthly measurements. In Sharpe ratio calculations, we employ the average monthly yield on 3-month U.S. Treasury bills during a year as the risk-free rate for that year. Using the specified methodology and data to generate SACEVS monthly returns starting August 2002 and SACEMS monthly returns starting July 2006, all through February 2026, we find that:
A subscriber asked whether more granularity in international equity choices for the “Simple Asset Class ETF Momentum Strategy” (SACEMS) would improve performance. To investigate, we augment/replace international developed and emerging equity market exchange-traded funds (ETF) such that the universe of assets becomes:
We compare original (SACEMS Base) and modified (SACEMS Granular), each month picking winners from their respective sets of ETFs based on total returns over a fixed lookback interval. We focus on gross compound annual growth rate (CAGR), maximum drawdown (MaxDD) and gross annual Sharpe ratio (average annual excess return divided by standard deviation of annual excess returns, using average monthly T-bill yield during a year to calculate excess returns) as key performance statistics for the Top 1, equally weighted (EW) Top 2 and EW Top 3 portfolios of monthly winners. Using monthly total (dividend-adjusted) returns for the specified assets during February 2006 through February 2026, we find that:Keep Reading
A subscriber requested a test of Ray Dalio‘s All Weather (AW) portfolio with different rebalancing frequencies, allocated to exchange-traded funds (ETF) as asset class proxies as follows:
30% – Vanguard Total Stock Market (VTI)
40% – iShares 20+ Year Treasury (TLT)
15% – iShares 7-10 Year Treasury (IEF)
7.5% – SPDR Gold Shares (GLD)
7.5% – Invesco DB Commodity Tracking (DBC)
To investigate, we test:
AW portfolios rebalanced monthly (AW-1), quarterly (AW-3), semiannually at the ends of June and December (AW-6) or annually at the end of December (AW-12).
As a benchmark, a 60%-40% VTI-TLT portfolio rebalanced annually (60/40-12).
We consider the following gross performance metrics, all based on monthly measurements: average monthly return, standard deviation of monthly returns, compound annual growth rate (CAGR), maximum drawdown (MaxDD) and Sharpe ratio (with the 3-month Treasury bill yield as the risk-free rate). We also compare number of rebalance actions for each portfolio. Using monthly dividend-adjusted returns for the specified assets during February 2006 (limited by DBC) through January 2026, we find that:Keep Reading
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