Strategic Allocation

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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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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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

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:

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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

A subscriber asked about a strategy that rotates among equity sectors according to the Leading Economic Index (LEI), published monthly by the Conference Board (see “Leading Economic Index and the Stock Market”). To assess LEI usefulness for sector rotation, 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 consider two LEI-based variables: (1) monthly change in LEI; and, (2) 3-month average change in LEI (average of current value, revised value for prior month and twice-revised value for two months ago) 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 LEI variable. The first test looks for linear relationships, and the second test looks for non-linear relationships. Monthly measurements employ closes on LEI release dates, generally after the market open about three weeks after ends of calendar months reported. Using monthly changes in LEI from archived Conference Board press releases and contemporaneous dividend-adjusted daily levels of the above sector ETFs and of SPDR S&P 500 (SPY) from mid-July 2002 (limited by LEI press releases) through mid-November 2021 (233 monthly LEI observations), we find that: Keep Reading

Do quarterly allocation updates for the Best Value and Weighted versions of the “Simple Asset Class ETF Value Strategy” (SACEVS) work as well as monthly updates? These strategies allocate funds to the following asset class exchange-traded funds (ETF) according to valuations of term, credit and equity risk premiums, or to cash if no premiums are undervalued:

3-month Treasury bills (Cash)
iShares 20+ Year Treasury Bond (TLT)
iShares iBoxx $ Investment Grade Corporate Bond (LQD)
SPDR S&P 500 (SPY)

Changing from monthly to quarterly allocation updates does not sacrifice information about lagged quarterly S&P 500 Index earnings, but it does sacrifice currency of term and credit premiums. To assess alternatives, we compare cumulative performances and the following key metrics for quarterly and monthly allocation updates: gross compound annual growth rate (CAGR), gross maximum drawdown (MaxDD), annual gross returns and volatilities and annual gross Sharpe ratios. Using monthly dividend-adjusted closes for the above ETFs during September 2002 (earliest alignment of months and quarters) through September 2021, we find that:

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A subscriber asked about performance of Simple Asset Class ETF Momentum Strategy (SACEMS) hedge portfolios, which each month buy the asset class exchange-traded funds (ETF) in the SACEMS universe with the highest past returns and sell (short) those with the lowest. To investigate, we look at three hedge portfolios:

• Top 1 – Bottom 1: long the ETF with the highest past return and short the ETF with the lowest.
• EW Top 2 – EW Bottom 2: long the equal-weighted (EW) two ETFs with the highest past returns and short the two with the lowest.
• EW Top 3 – EW Bottom 3: long the equal-weighted three ETFs with the highest past returns and short the three with the lowest. 

For each portfolio, monthly rebalancing sets the long and short sides to equal dollar amounts. We consider monthly gross portfolio  performance statistics (ignoring any rebalancing and shorting frictions), gross compound annual growth rate (CAGR), maximum drawdown (MaxDD) and gross annual Sharpe ratio. To calculate annual excess 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. SACEMS Top 1, EW Top 2 and EW Top 3 SACEMS long-only portfolios serve as benchmarks. Using monthly gross returns for SACEMS ETFs (and cash) by rank during July 2006 through October 2021, we find that:

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Does adding a position take-profit (stop-gain) rule improve the performance of the “Simple Asset Class ETF Momentum Strategy” (SACEMS) by harvesting some upside volatility? SACEMS each months picks winners from among the a set of eight asset class exchange-traded fund (ETF) proxies plus cash based on past returns over a specified interval. To investigate the value of stop-gains, we augment SACEMS with a simple rule that: (1) exits to Cash from any current winner ETF when its intra-month return rises above a specified threshold; and, (2) re-sets positions per winners at the end of the month. We focus on gross compound annual growth rate (CAGR) and gross maximum drawdown (MaxDD) 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 and intra-month maximum returns for the specified assets during February 2006 through September 2021, we find that: Keep Reading

Does adding a position stop-loss rule improve the performance of the “Simple Asset Class ETF Momentum Strategy” (SACEMS) by avoiding some downside volatility? SACEMS each months picks winners from among the a set of eight asset class exchange-traded fund (ETF) proxies plus cash based on past returns over a specified interval. To investigate the value of stop-losses, we augment SACEMS with a simple rule that: (1) exits to Cash from any current winner ETF when its intra-month return falls below a specified threshold; and, (2) re-sets positions per winners at the end of the month. We focus on gross compound annual growth rate (CAGR) and gross maximum drawdown (MaxDD) 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 and intra-month drawdowns for the specified assets during February 2006 through September 2021, we find that: Keep Reading