Objective research to aid investing decisions

Value Investing Strategy (Strategy Overview)

Allocations for June 2024 (Final)

Momentum Investing Strategy (Strategy Overview)

Allocations for June 2024 (Final)
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Strategic Allocation

Is there a best way to select and weight asset classes for long-term diversification benefits? These blog entries address this strategic allocation question.

Review of Dual Momentum with Just Three Assets

A subscriber suggested review of “Accelerating Dual Momentum [ADM] Investing”, which allocates all funds to U.S. stocks, international (ex-U.S.) small-capitalization stocks or long-term U.S. Treasury bonds, as follows:

  1. Each month, calculate for each of the two equity assets the sum of its 1-month, 3-month and 6-month past returns.
  2. If both sums are negative, buy U.S. Treasury bonds.
  3. If both sums are not negative, buy the equity asset with the higher sum.

To investigate, we apply these rules to three exchange-traded funds (ETF):

  • SPDR S&P 500 (SPY) to represent U.S. stocks.
  • iShares MSCI EAFE Small-Cap ETF (SCZ) to represent international small stocks.
  • iShares 20+ Year Treasury Bond (TLT) to represent long-term U.S. Treasury bonds.

Using end-of-month dividend-adjusted prices of these ETFs during December 2007 (limited by SCZ) through April 2022, we find that: Keep Reading

SACEVS with SMA Filter

The “Simple Asset Class ETF Value Strategy” (SACEVS) allocates across 3-month Treasury bills (Cash, or T-bill), iShares 20+ Year Treasury Bond (TLT), iShares iBoxx $ Investment Grade Corporate Bond (LQD) and SPDR S&P 500 (SPY) according to the relative valuations of term, credit and equity risk premiums. Does applying a simple moving average (SMA) filter to SACEVS allocations improve its performance? Since many technical traders use a 10-month SMA (SMA10), we apply SMA10 filters to dividend-adjusted prices of TLT, LQD and SPY allocations. If an allocated asset is above (below) its SMA10, we allocate as specified (to Cash). This rule does not apply to any Cash allocation. We focus on gross compound annual growth rates (CAGR), maximum drawdowns (MaxDD) and annual Sharpe ratios (using average monthly T-bill yield during a year as the risk-free rate for that year) of SACEVS Best Value and SACEVS Weighted portfolios. We compare to baseline SACEVS as currently tracked and to the SMA rule applied to a 60%-40% monthly rebalanced SPY-TLT benchmark portfolio (60-40). Finally, we test sensitivity of main findings to varying the SMA lookback interval. Using SACEVS historical data, monthly dividend-adjusted closing prices for the asset class proxies and yield for Cash during July 2002 (the earliest all funds are available) through March 2022, we find that:

Keep Reading

SACEMS with Momentum Breadth Protection Update

“SACEMS with Momentum Breadth Crash Protection” evaluates in depth the potential of a simple momentum breadth rule to improve performance of the Simple Asset Class ETF Momentum Strategy (SACEMS). This rule forces the model to all cash when fewer than some threshold of the non-cash SACEMS assets have positive returns over a specified lookback interval. Do major findings of that evaluation still hold? To update, we repeat some of the analyses with the minor changes since made to SACEMS plus recent data. We focus on compound annual growth rates (CAGR) and maximum drawdowns (MaxDD) for the Top 1, equal-weighted (EW) Top 2 and EW Top 3 SACEMS portfolios. We look at all possible momentum breadth thresholds for the baseline SACEMS lookback interval. We then consider lookback intervals ranging from one to 12 months for a specific momentum breadth threshold. Using monthly dividend-adjusted closing prices for SACEMS assets and the T-bill yield during February 2006 through February 2022, we find that:

Keep Reading


A subscriber proposed adding Utilities Select Sector SPDR Fund (XLU) to the Simple Asset Class ETF Momentum Strategy (SACEMS) asset universe based on the relatively low correlation of XLU with the broad U.S. stock market. To investigate, we:

  • Expand the SACEMS asset universe to include XLU.
  • Generate performance data for this expanded universe for the SACEMS Top 1, equal-weighted (EW) Top 2 and EW Top 3 portfolios.
  • Compare results to those for baseline SACEMS portfolios.

Using inputs during February 2006 (inception of DBC as a proxy for commodities) through February 2022, we find that: Keep Reading

Asset Class Momentum Faster During Bear Markets?

A subscriber asked whether the optimal momentum ranking (lookback) interval for the “Simple Asset Class ETF Momentum Strategy” (SACEMS) shrinks during bear markets for U.S. stocks. To investigate, we compare SACEMS monthly performance statistics when the S&P 500 Index at the previous monthly close is above (bull market) or below (bear market) its 10-month simple moving average. We consider Top 1, equal-weighted (EW) Top 2 and EW Top 3 portfolios of monthly winners for the baseline SACEMS lookback interval. We focus on monthly return, monthly volatility and compound annual growth rate (CAGR) as key performance metrics. In a robustness test for the EW Top 2 and EW Top 3 portfolios, we consider lookback intervals ranging from one to 12 months. Using monthly total (dividend-adjusted) returns for SACEMS assets since February 2006 and monthly S&P 500 Index level since September 2005, all through January 2022, we find that:

Keep Reading

Best Weighting Scheme for a Stock Portfolio?

What is the overall best way to weight stock portfolios? In their February 2022 paper entitled “Weighting for the Right One: Weighting Scheme Design for Systematic Equity Portfolios”, Wei Dai, Namiko Saito and Gigi Wang compare eight stock portfolio weighting schemes frequently used in systematic strategies, five that ignore prices and three that do not, as follows:

  • Weighting schemes that ignore prices are:
    1. Equal weighting – assign all stocks the same dollar weight.
    2. Rank weighting – separately rank all stocks from large to small, growth to value and low to high profitability, and then re-rank and weight based on averages of individual ranks.
    3. Z-score weighting: separately calculate z-scores (number of standard deviations from average) for each firm’s market capitalization, relative price and profitability, transform the z-scores into a value between 0 and 1, and weight in proportion to the product of the three standardized z-scores.
    4. Inverse volatility weighting: weight each stock in proportion to the inverse of its daily return volatility over the last 60 trading days.
    5. Fundamental weighting: weight each stock in proportion to the sum of book equity, sales and cash flow per share during its latest fiscal year.
  • Weighting schemes that incorporate prices are:
    1. Rank x mcap: weight each stock in proportion to the product of its rank weighting (as defined above) and its market capitalization.
    2. Z-score x mcap: weight each stock in proportion to the product of its standardized z-scores (as defined above) and its market capitalization.
    3. Integrated core: separately sort all firms by market capitalization, relative price and profitability into groups with similar characteristics; within each group, weight firms in proportion to their market capitalizations; and, further weight each group in proportion to its aggregate market capitalization times a multiplier capturing its overall size, value and profitability premiums as modified for interactions among them.

They rebalance each portfolio semiannually. They consider stock universes with and without microcaps (bottom 4% of market capitalizations). Their approach focuses on the importance of accounting for current market prices that reflect the latest news and market expectations. Using data as described for all U.S. common stocks (excluding REITs, tracking stocks and investment companies) during July 1974 through December 2019, they find that:

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Federal Reserve Holdings and the U.S. Stock Market

Using quarterly data in their April 2013 paper entitled “Analyzing Federal Reserve Asset Purchases: From Whom Does the Fed Buy?” Seth Carpenter, Selva Demiralp, Jane Ihrig and Elizabeth Klee find that some categories of investors appear to sell U.S. Treasuries to the Federal Reserve and rebalance toward riskier assets (corporate bonds, commercial paper, and municipal debt). Are stocks, proxied by for SPDR S&P 500 (SPY), a part of this process? To investigate, we relate weekly, monthly and quarterly U.S. stock market returns to changes in the Federal Reserve’s System Open Market Account (SOMA) holdings, comprised of U.S. Treasury bills, U.S. Treasury notes and bonds, U.S. Treasury Inflation-Protected Securities (TIP) and Mortgage-Backed Securities (MBS). The Federal Reserve reports these holdings as of Wednesday, typically with a 1-day lag. Using weekly (Thursday close) dividend-adjusted prices for SPY and weekly total SOMA holdings during early July 2003 through January 2022, we find that:

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Expanded/Modified SACEMS Asset Universe?

A subscriber suggested expanding and modifying the asset universe for the Simple Asset Class ETF Momentum Strategy (SACEMS) to consist of the following exchange-traded funds (ETF):

  • SPDR Portfolio S&P 500 Growth (SPYG)
  • SPDR Portfolio S&P 500 Value (SPYV)
  • iShares Russell 2000 Growth (IWO)
  • iShares Russell 2000 Value (IWN)
  • Invesco QQQ Trust (QQQ)
  • iShares MSCI EAFE Index (EFA)
  • iShares MSCI Emerging Markets Index (EEM)
  • iShares Barclays 20+ Year Treasury Bond (TLT)
  • iShares Core U.S. Aggregate Bond (AGG)
  • iShares U.S. Real Estate ETF (IYR)
  • SPDR Gold Shares (GLD)
  • Invesco DB Commodity Index Tracking (DBC)
  • 3-month Treasury bills (Cash)

To investigate attractiveness of this alternative, we first look at compound annual growth rates (CAGR) and maximum drawdowns (MaxDD) for the expanded universe across SACEMS momentum measurement (lookback) intervals ranging from 1 to 12 months to identify effective lookback intervals. We then compare annual performance statistics of the Top 1, equal-weighted (EW) Top 2, EW Top 3 and EW Top 4 portfolios for the expanded and baseline asset universes with the SACEMS baseline lookback interval. Using monthly dividend-adjusted returns for the expanded asset universe during February 2006 (limited by DBC) through December 2021 and monthly returns for baseline SACEMS over the same period, we find that: Keep Reading

Substitute VIG for SPY in SACEVS and SACEMS?

A subscriber asked whether substituting the less volatile Vanguard Dividend Appreciation Index Fund (VIG) for SPDR S&P 500 (SPY) in the Simple Asset Class ETF Value Strategy (SACEVS) and the Simple Asset Class ETF Momentum Strategy (SACEMS) would improve outcomes. To investigate, we substitute monthly VIG dividend-adjusted returns for SPY dividend-adjusted returns in the two model strategies. Because VIG is not available for the entire sample periods used in the tracked models, we splice VIG returns into the SPY position starting with inception of the former in May 2006. We then compare the spliced performance with the original baseline performance, including: gross compound annual growth rates (CAGR), gross annual returns, average gross annual returns, standard deviations of gross annual returns, gross annual Sharpe ratios and maximum drawdowns (MaxDD). 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 December 2021, we find that:

Keep Reading

Interest Rate Changes Exploitable for Sector Rotation?

A subscriber asked about a strategy that rotates among equity sectors according to changes in interests rate as set by Federal Reserve Bank monetary policy. To investigate, we consider the following nine sector Standard & Poor’s Depository Receipts (SPDR) exchange-traded funds (ETF):

Materials Select Sector SPDR (XLB)
Energy Select Sector SPDR (XLE)
Financial Select Sector SPDR (XLF)
Industrial Select Sector SPDR (XLI)
Technology Select Sector SPDR (XLK)
Consumer Staples Select Sector SPDR (XLP)
Utilities Select Sector SPDR (XLU)
Health Care Select Sector SPDR (XLV)
Consumer Discretionary Select SPDR (XLY)

We use monthly effective federal funds rate (EFFR) as the interest rate. We consider two EFFR-based variables: (1) monthly change in EFFR; and, (2) 3-month slope of EFFR for signal smoothing. For each variable and each sector ETF, we consider two tests: (1) correlation of the variable with ETF return each of the next three months; and, (2) average next-month ETF returns across ranked fifths (quintiles) of the EFFR variable. The first test looks for linear relationships, and the second test looks for non-linear relationships. Measurements are at month ends, with a 1-day delay for ETF return calculations to ensure availability of EFFR data. Using monthly levels of EFFR since September 1998 and dividend-adjusted monthly levels of the above sector ETFs and of SPDR S&P 500 (SPY) since December 1998 (limited by sector ETFs), all through November 2021, we find that: Keep Reading

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