Strategic Allocation

A subscriber asked for an extended test of a very simple momentum strategy that each month holds Vanguard 500 Index Fund Investor Shares (VFINX) or Vanguard Long-Term Treasury Fund Investor Shares VUSTX according to which of these funds has the highest total return over the last three months. To investigate, based on the way mutual funds report prices, we calculate past 3-month total returns using dividend-adjusted prices for month-ends and strategy returns using dividend adjusted prices for first days of the following month. We assume zero fund switching costs and no restrictions on monthly fund switching. We use buying and holding VFINX as a benchmark. Using the specified fund price series and monthly 3-month U.S. Treasury bill (T-bill) yield from the end of May 1986 (limited by VUSTX) through the beginning of March 2021, we find that: Keep Reading

Investors seeking low-cost, automated, tax-efficient and potentially alpha-generating solutions increasingly follow model portfolios of exchange-traded funds (ETF). Is there a top-down way to characterize those models? In their November 2020 paper entitled “Using Data Science to Identify ETF Model Followers”, Ananth Madhavan and Aleksander Sobczyk apply machine learning methods and cluster analysis to identify all models using at least three iShares ETFs based on monthly holdings data. Using monthly data on positions and accounts holding those positions across all iShares ETFs (370 at the end of the sample period) during January 2013 through June 2020, they find that:

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Can diversification across economic states improve portfolio performance? In their November 2020 paper entitled “Investing Through a Macro Factor Lens”, Harald Lohre, Robert Hixon, Jay Raol, Alexander Swade, Hua Tao and Scott Wolle study interactions between three economic “factors” (growth, defensive/U.S. Treasuries and inflation) and portfolio building blocks (asset classes and conventional factor portfolios). Their proxies for economic factors are: broad equity market for growth; U.S. Treasuries for defensive; and, spread between inflation-linked bonds and U.S. Treasuries for inflation. To diversify across economic states, they calculate historical performance of each portfolio building block during each of four economic regimes: (1) rising growth and rising inflation; (2) rising growth and falling inflation; (3) falling growth and rising inflation; and, (4) falling growth and falling inflation. They then look at benefits of adding defensive and inflation economic factor overlays to a classis 60%/40% global equities/bonds portfolio. Using monthly economic factor data and asset class/conventional factor portfolio returns during February 2001 through May 2020, they find that: Keep Reading

A subscriber asked for a performance comparison between 50% Simple Asset Class ETF Value Strategy (SACEVS) Best Value-50% Simple Asset Class ETF Momentum Strategy (SACEMS) equal-weighted top two (EW Top 2), rebalanced monthly (SACEVS-SACEMS 50-50), and the following monthly rebalanced allocations to three exchange-traded funds (3-ETF):

• 30% Vanguard Total Stock Market Index Fund (VTI).
• 30% Vanguard Total International Stock Index Fund (VXUS).
• 40% Vanguard Total Bond Market Index Fund (BND).

Using monthly returns for SACEVS-SACEMS 50-50 and month-end dividend-adjusted prices for VTI, VXUS and BND during January 2011 (limited by inception of VXUS) through January 2021, we find that: Keep Reading

Can investors use leveraged exchange-traded funds (ETF) as building blocks for long-term portfolios? In his January 2021 presentation package entitled “One Year Later. Leveraged ETFs in Portfolio Construction and Portfolio Protection”, Mikhail Smirnov updates multi-year performance of a monthly rebalanced partially 3X-leveraged portfolio consisting of:

• 40% ProShares UltraPro QQQ (TQQQ)
• 20% Direxion Daily 20+ Year Treasury Bull 3X Shares (TMF)
• 40% iShares 20+ Year Treasury Bond ETF (TLT)

The last three years are out-of-sample with respect to specification of this portfolio. He also looks at a more conservative portfolio of 20% TQQQ and 80% TLT, rebalanced monthly. Using pre-inception simulated and actual monthly total returns for these ETFs during January 1, 2005 through January 15, 2021, he finds that: Keep Reading

A European subscriber asked about the effect of the dollar-euro exchange rate on the Simple Asset Class ETF Value Strategy (SACEVS) and the Simple Asset Class ETF Momentum Strategy (SACEMS). To investigate, we each month adjust the gross returns for these strategies for the change in the dollar-euro exchange rate that month. We consider all strategy variations: Best Value and Weighted for SACEVS; and, Top 1, equally weighted (EW) Top 2 and EW Top 3 for SACEVS. We focus on SACEVS Best Value and SACEMS EW Top 3. We consider effects on four gross performance metrics: average monthly return; standard deviation of monthly returns; compound annual growth rate (CAGR); and, maximum drawdown (MaxDD). Using monthly returns for the strategies and monthly changes in the dollar-euro exchange rate since August 2002 for SACEVS and since July 2006 for SACEMS, both through December 2020, we find that: Keep Reading

Is it possible to achieve an attractive return with very low risk from a small universe of exchange-traded funds (ETF)? In the January 2021 revision of his paper entitled “Lazy Momentum with Growth-Trend Timing: Resilient Asset Allocation (RAA)”, Wouter Keller constructs and tests the Resilient Asset Allocation (RAA) strategy as a more aggressive version of the Lethargic Asset Allocation (LAA) strategy. LAA switches between risky (equal-weighted  QQQ, IWD, IEF and GLD) and defensive (equal-weighted IWD, GLD, SHY and IEF) portfolios based on trend in the U.S. unemployment rate (bullish when above and bearish when below its 12-month simple moving average). RAA alters LAA in three ways:

1. Changes the risky portfolio to an All Weather-like portfolio, with five equal-weighted assets (QQQ, IWN, IEF, TLT, GLD) instead of four and only two equal-weighted assets (IEF and TLT) as a risk-off portfolio.
2. Adds “canary” crash protection from the Defensive Asset Allocation strategy for signaling the market trend with a fast filter (bearish when either or both of VWO or BND turn bad).
3. Slows the unemployment rate trend signal, simply comparing recent unemployment rate with that of a year ago.

RAA is in the defensive portfolio only when both the canary and unemployment rate trend signals are bearish. Using a combination of modeled and (as available) actual monthly price data for the specified ETFs during December 1970 through November 2020, he finds that: Keep Reading

“Simple Asset Class ETF Value Strategy” (SACEVS) finds that investors may be able to exploit relative valuation of the term risk premium, the credit (default) risk premium and the equity risk premium via exchange-traded funds (ETF). However, the backtesting period is limited by available histories for ETFs and for series used to estimate risk premiums. To construct a longer test, we make the following substitutions for potential holdings (selected for length of available samples):

• Monthly average 3-Month Treasury Bill (T-bill) Secondary Market Rate instead of monthly average 3-Month T-bill Constant Maturity Rate as the risk-free rate and return on Cash.
• Vanguard GNMA Investor Shares (VFIIX) instead of  iShares 20+ Year Treasury Bond (TLT).
• Vanguard Long-Term Investment Grade Investor Shares (VWESX) instead of iShares iBoxx $ Investment Grade Corporate Bond (LQD).
• Vanguard 500 Index Fund Investor Shares (VFINX) instead of SPDR S&P 500 (SPY).

To enable estimation of risk premiums over a longer history, we also substitute:

• Monthly average Moody’s Seasoned Baa Corporate Bond Yields rather than day before end-of-month Baa yields for calculation of the credit risk premium. This substitution ignores a one-day delay in release of daily data.
• Robert Shiller’s S&P Composite Index monthly average levels instead of S&P 500 Index monthly closes. This substitution ignores any delay in posting of Shiller data (but new data are available elsewhere in real time).
• Robert Shiller’s monthly S&P Composite Index (GAAP, or as-reported) earnings instead of S&P Dow Jones S&P 500 operating earnings. We lag the Shiller earnings by four months to ensure real-time availability. In other words, the earnings yield for a month is the S&P Composite Index level for that month divided by index annual GAAP earnings as of four months ago. GAAP earnings are generally lower than operating earnings (see “Stock Market Valuation Ratio Trends”).
• Robert Shiller’s monthly average Long Interest Rates instead of monthly average yields on 10-year Constant Maturity U.S. Treasury notes. This substitution ignores any delay in posting of Shiller data (but new data are again available elsewhere with little delay).

As with ETFs, we consider two alternatives for exploiting premium undervaluation: Best Value, which picks the most undervalued premium; and, Weighted, which weights all undervalued premiums according to degree of undervaluation. Based on the assets considered, the principal benchmark is a monthly rebalanced portfolio of 60% VFINX and 40% VFIIX. Using monthly risk premium calculation data during March 1934 through November 2020 (limited by availability of T-bill data), and monthly dividend-adjusted closing prices for the three asset class mutual funds during June 1980 through November 2020 (40+ years, limited by VFIIX), we find that:

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Is there a better way than the Fed model to measure relative attractiveness of equities and bonds. In his October 2020 paper entitled “Towards a Better Fed Model”, Raymond Micaletti examines seven Fed Model alternatives, each comparing a 10-year forward annualized estimate of equity returns to the yield of 10-year constant maturity U.S. Treasury notes (T-note). The seven estimates of future equity returns are based on autocorrelation-corrected quarterly regressions using 10 years of past quarterly data for one of: (1) Aggregate Investor Allocation to Equities (AIAE); (2) Cyclically-Adjusted Price-to-Earnings Ratio (CAPE); (3) Tobin’s Q (QRATIO); (4) Market Capitalization-to-Nominal GDP (MC/GDP); (5) Market Capitalization-to-Adjusted Gross Value Added (MC/AGVANF); (6) Market Capitalization-to-Household and Non-Profit Total Assets (MC/HHNPTA); and, (7) Household and Non-Profit Equity Allocation-to-Nominal GDP (HHNPEQ/GDP). He calculates AIAE as total market value of equities divided by the sum of total market value of equities and total par value of bonds, approximated by adding the liabilities of five categories of borrowers. He then tests for each alternative a tactical asset allocation (TAA) strategy that each month weights equities and bonds based on a modified z-score of the forecasted 10-year equity risk premium (equity return minus T-note yield) computed by subtracting the median and dividing by the standard deviation of actual monthly premiums over the past 10 years. If modified z-score is greater than 1 (less than -1), the strategy is 100% in equities (0% in equities). In between those thresholds, weights are based on linear interpolation. Using quarterly data from the Archival Federal Reserve Economic Database (ALFRED) and Robert Shiller’s data library and daily U.S. equity market returns and U.S. Treasury bond/note roll-adjusted futures returns as available from the end of the fourth quarter of 1951 through the end of the third quarter of 2020, he finds that: Keep Reading

Target-date funds (TDFs) are popular fund-of-funds retirement investments that offer asset class diversification and periodic rebalancing aimed at a specific retirement year. TDFs typically charge layers of fees (fund-of-funds fee plus fees of underlying funds). Can investors do better themselves? In their October 2020 paper entitled “Off Target: On the Underperformance of Target-Date Funds”, David Brown and Shaun Davies assess feasibility and costs of emulating TDFs with low-cost exchange-traded funds (ETF) based on publicly disclosed TDF initial portfolio allocations and dynamic adjustments (glide paths). They identify TDFs as those mutual funds with one of 2005, 2010, 2015, 2020, 2025, 2030, 2035, 2040, 2045, 2050, 2055 or 2060 in their names. They replicate TDFs by matching each of their holdings to the one of 50 Vanguard ETFs (as available when they reach $50 million in assets) with the highest full-sample monthly correlation of returns. Using monthly returns, holdings and expense ratios for TDFs and the funds they hold and monthly returns for the 50 Vanguard ETFs during January 2006 through December 2017, they find that:

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