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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.

Adjust the SACEMS Lookback Interval?

The Simple Asset Class ETF Momentum Strategy (SACEMS) each month picks winners based on total return over a specified ranking (lookback) interval from the following eight asset class exchange-traded funds (ETF), plus cash:

PowerShares DB Commodity Index Tracking (DBC)
iShares MSCI Emerging Markets Index (EEM)
iShares MSCI EAFE Index (EFA)
SPDR Gold Shares (GLD)
iShares Russell 2000 Index (IWM)
SPDR S&P 500 (SPY)
iShares Barclays 20+ Year Treasury Bond (TLT)
Vanguard REIT ETF (VNQ)
3-month Treasury bills (Cash)

This set of ETFs offers: (1) opportunities to capture momentum across global developed and emerging equity markets, large and small U.S. equities, bonds and commodities; (2) gold and cash as safe havens; (3) histories long enough for backtesting across multiple market environments; and, (4) simplicity of computation and recognition of the trade-off between number of ETFs and trading frictions. As historical data accumulate, we can estimate an increasingly robust optimal lookback interval. Should we change the baseline lookback interval at this point? To investigate, we revisit relevant analyses and conduct further robustness tests, with focus on the equal-weighted (EW) Top 3 SACEMS portfolio. Using monthly dividend-adjusted closing prices for asset class proxies and the yield for Cash during February 2006 (when all ETFs are first available) through December 2018, we find that: Keep Reading

Combining Fundamental Analysis and Portfolio Optimization

Can stock return forecasts from fundamental analysis make conventional mean-variance stock portfolio optimization work? In their December 2018 paper entitled “Optimized Fundamental Portfolios”, Matthew Lyle and Teri Yohn construct a portfolio that combines fundamentals-based stock return forecasts and mean-variance optimization and then compare results with portfolios from each employed separately. To suppress implementation costs, they focus on long-only portfolios reformed quarterly. Their fundamentals return forecasting model uses cross-sectionally normalized versions of book-to-market ratio, return on equity, change in net operating assets divided by book value and change in financial assets divided by book value. They update fundamental variables quarterly at the end of the reporting month. They generate stock return forecasts via a complicated multivariate regression of cross-sectionally normalized versions of the variables based on five years of rolling historical data. They then form a portfolio of the tenth (decile) of stocks with the highest expected returns, either value-weighted or equal-weighted. They consider several portfolio optimization methods, including minimum variance (requiring no return forecasts); mean-variance optimization with target expected return; and, Sharpe ratio maximization. Their combined approach employs fundamental stock return forecasts as inputs to those portfolio optimization methods that require returns. They use data from 1991-1995 to generate initial model inputs and 1996-2015 for out-of-sample testing. Using end-of-month data for a broad but groomed sample of U.S. common stocks with at least three years of historical data during January 1991 through December 2015, they find that:

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Robustness of SACEMS Based on Sharpe Ratio

Subscribers have asked whether risk-adjusted returns might work better than raw returns for ranking Simple Asset Class ETF Momentum Strategy (SACEMS) assets. In fact, “Alternative Momentum Metrics for SACEMS?” supports belief that Sharpe ratio beats raw returns. Is this finding strong enough to justify changing the strategy, which each month selects the best performers over a specified lookback interval from among the following eight asset class exchange-traded funds (ETF), plus cash:

PowerShares DB Commodity Index Tracking (DBC)
iShares MSCI Emerging Markets Index (EEM)
iShares MSCI EAFE Index (EFA)
SPDR Gold Shares (GLD)
iShares Russell 2000 Index (IWM)
SPDR S&P 500 (SPY)
iShares Barclays 20+ Year Treasury Bond (TLT)
Vanguard REIT ETF (VNQ)
3-month Treasury bills (Cash)

To investigate, we update the basic comparison and conduct three robustness tests:

  1. Does Sharpe ratio beat raw returns consistently across Top 1, equally weighted (EW) Top 2, EW Top 3 and EW Top 4 portfolios, and the 50%-50% SACEMS EW Top 3-Simple Asset Class ETF Value Strategy (SACEVS) Best Value portfolio?
  2. Does Sharpe ratio beat raw returns consistently across different lookback intervals?
  3. For multi-asset portfolios, does weighting by Sharp ratio rank beat equal weighting? In other words, do future returns behave systematically across ranks?

To calculate Sharpe ratios, we each month for each asset subtract the risk-free rate (Cash yield) from raw monthly total returns to generate monthly total excess returns over a specified lookback interval. We then calculate Sharpe ratio as average monthly excess return divided by standard deviation of monthly excess returns over the lookback interval. We set Sharpe ratio for Cash at zero (though it is actually zero divided by zero). Using monthly dividend-adjusted closing prices for asset class proxies and the yield for Cash during February 2006 (when all ETFs are first available) through December 2018, we find that: Keep Reading

Does Active Stock Factor Timing/Tilting Work?

Does active stock factor exposure management boost overall portfolio performance? In their November 2018 paper entitled “Optimal Timing and Tilting of Equity Factors”, Hubert Dichtl, Wolfgang Drobetz, Harald Lohre, Carsten Rother and Patrick Vosskamp explore benefits for global stock portfolios of two types of active factor allocation:

  1. Factor timing – exploit factor premium time series predictability based on economic indicators and factor-specific technical indicators.
  2. Factor tilting – exploit cross-sectional (relative) attractiveness of factor premiums.

They consider 20 factors spanning value, momentum, quality and size. For each factor each month, they reform a hedge portfolio that is long (short) the equal-weighted fifth, or quintile, of stocks with the highest (lowest) expected returns for that factor. For implementation of factor timing, they consider: 14 economic indicators standardized by subtracting respective past averages and dividing by standard deviations; and, 16 technical indicators related to time series momentum, moving averages and volatilities. They suppress redundancy and noise in these indicators via principal component analysis separately for economic and technical groups, focusing on the first principal component of each group. They translate any predictive power embedded in principal components into optimal factor portfolio weights using augmented mean-variance optimization. For implementation of factor tilting, they overweight (underweight) factors that are relatively attractive (unattractive) based on valuations of factor top and bottom quintile stocks, top-bottom quintile factor variable spreads, prior-month factor returns (momentum) and volatilities of past monthly factor returns. Their benchmark portfolio is the equal-weighted combination of all factor hedge portfolios. For all portfolios, they assume: monthly portfolio reformation costs of 0.75% (1.15%) of turnover value for the long (short) side; and, annual 0.96% cost for an equity swap to ensure a balanced portfolio of factor portfolios. For monthly factor timing and tilting portfolios only, they assume an additional cost of 0.20% of associated turnover. Using monthly data for a broad sample of global stocks from major equity indexes and for specified economic indicators during January 1997 through December 2016 (4,500 stocks at the beginning and 5,000 stocks at the end), they find that: Keep Reading

SACEVS with SMA Filter

Does  applying a simple moving average (SMA) filter improve performance of the “Simple Asset Class ETF Value Strategy” (SACEVS), which seeks diversification across the following three asset class exchange-traded funds (ETF) plus cash according to the relative valuations of term, credit and equity risk premiums?

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

Since many technical traders use a 10-month SMA (SMA10), we test effectiveness of requiring that each of the ETFs pass an SMA10 filter by comparing performances for three scenarios:

  1. BaselineSACEVS as currently tracked.
  2. With SMA10 Filter – Run Baseline SACEVS and then apply SMA10 filters to dividend-adjusted prices of ETF allocations. If an allocated ETF is above (below) its SMA10, hold the allocation as specified (Cash). This rule is inapplicable to any Cash allocation.
  3. With Half SMA10 Filter – Same as scenario 2, but, if an allocated ETF is above (below) its SMA10, hold the allocation as specified (half the specified allocation and half cash at the T-bill yield).

We focus on compound annual growth rates (CAGR) and maximum drawdowns (MaxDD) of SACEVS Best Value, SACEVS Weighted and the 60%-40% SPY-TLT benchmark (60-40) portfolios. Using required SACEVS monthly historical data and monthly dividend-adjusted closing prices for the above asset class proxies and the yield for Cash over the period July 2002 (the earliest all ETFs are available) through November 2018, we find that: Keep Reading

Managing Asset Class Exposures with Leveraged ETFs

Are there advantages to using leveraged exchange-traded funds (ETF) to implement conventional asset class exposures? In their October 2018 paper entitled “A Portfolio of Leveraged Exchange Traded Funds”, William Trainor, Indudeep Chhachhi and Chris Brown investigate performance of diversified portfolios of 2X or 3X leveraged ETFs that limit exposures to those typically achieved with 1X ETFs. Specifically, when using 2X (3X) funds, allocations are only one half (one third) those for corresponding 1X ETFs. While this approach allows large allocations to a safe asset, it also exposes the portfolio to the higher expense ratios, internal financing costs, leverage decays and rebalancing frequencies of leveraged ETFs. The authors two strategic allocations:

  1. Actual ETFs during 2010-2017 (see the first table below) – 1X portfolio allocations are 30% U.S. large caps, 10% U.S. midcaps, 10% U.S. small caps, 10% non-U.S. developed market stocks, 10% emerging market stocks, 5% real estate investment trusts (REIT), 5% >20-year U.S. Treasuries, 5% 7-year to 10-year U.S. Treasuries and 15% aggregate corporate bonds. “Savings” from holding leveraged ETFs goes to the aggregate bond ETF, for which there are no leveraged counterparts. Rebalancing occurs whenever equities combined deviate from the specified overall levels by more than 10%.
  2. Simulated ETFs during 1946-2017 – 1X portfolio allocations are 50% S&P 500, 10% U.S. midcaps, 10% U.S. smallcaps, 15% >20-year U.S. Treasuries, 15% 7-year to 10-year U.S. Treasuries. An equal-weighted ladder of 1-year, 2-year, 5-year and 7-year U.S. Treasuries. “Savings” from holding leveraged ETFs goes to an equal-weighted ladder of 1-year, 2-year, 5-year, and 7-year treasury bonds.  Rebalancing occurs whenever equities combined deviate from the specified overall level by more than 10%.

Using daily returns for specified ETFs since 2010 and data required to simulate specified ETFs since 1946, all through December 2017, they find that: Keep Reading

Unbiased Performance of Endowment Investments

Do non-profit endowments beat the market with their investments? In their November 2018 paper entitled “Investment Returns and Distribution Policies of Non-Profit Endowment Funds”, Sandeep Dahiya and David Yermack estimate investment returns and distribution rates for a broad and unbiased (not self-reported or self-selected) sample of U.S. non-profit endowment funds. Using annual IRS Form 990 filings for 28,696 organizations and annual total returns for a capitalization-weighted U.S. Stock market index and a U.S. Treasuries index during 2009-2016, they find that:

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SACEMS with SMA Filter

A subscriber asked whether applying a simple moving average (SMA) filter to “Simple Asset Class ETF Momentum Strategy” (SACEMS) winners improves strategy performance. SACEMS each months picks winners from among the following asset class exchange-traded fund (ETF) proxies based on past returns over a specified interval:

PowerShares DB Commodity Index Tracking (DBC)
iShares MSCI Emerging Markets Index (EEM)
iShares MSCI EAFE Index (EFA)
SPDR Gold Shares (GLD)
iShares Russell 2000 Index (IWM)
SPDR S&P 500 (SPY)
iShares Barclays 20+ Year Treasury Bond (TLT)
Vanguard REIT ETF (VNQ)
3-month Treasury bills (Cash)

Since many technical traders use a 10-month SMA (SMA10), we test effectiveness of requiring that each winner pass an SMA10 filter by comparing performances for three scenarios:

  1. Baseline – SACEMS as presented at “Momentum Strategy”.
  2. With SMA10 Filter – Run Baseline SACEMS and then apply SMA10 filters to dividend-adjusted prices of winners. If a winner is above (below) its SMA10, hold the winner (Cash). This rule is inapplicable to Cash as a winner.
  3. With Half SMA10 Filter – Same as scenario 2, but, if a winner is above (below) its SMA10, hold the winner (half the winner and half cash at the T-bill yield).

We focus on compound annual growth rates (CAGR) and maximum drawdowns (MaxDD) of SACEMS Top 1, equally weighted (EW) Top 2 and EW Top 3 portfolios. Using monthly dividend-adjusted closing prices for the asset class proxies and the yield for Cash over the period February 2006 (the earliest all ETFs are available) through November 2018, we find that: Keep Reading

U.S. Equity Turn-of-the-Month as a Diversifying Portfolio

Is the U.S. equity turn-of-the-month (TOTM) effect exploitable as a diversifier of other assets? In their October 2018 paper entitled “A Seasonality Factor in Asset Allocation”, Frank McGroarty, Emmanouil Platanakis, Athanasios Sakkas and Andrew Urquhart test U.S. asset allocation strategies that include a TOTM portfolio as an asset. The TOTM portfolio buys each stock at the open on the last trading day of each month and sells at the close on the third trading day of the following month, earning zero return the rest of the time. They consider four asset universes with and without the TOTM portfolio:

  1. A conventional stocks-bonds mix.
  2. The equity market portfolio.
  3. The equity market portfolio, a small size portfolio and a value portfolio.
  4. The equity market portfolio, a small size portfolio, a value portfolio and a momentum winners portfolio.

They consider six sophisticated asset allocation methods:

  1. Mean-variance optimization.
  2. Optimization with higher moments and Constant Relative Risk Aversion.
  3. Bayes-Stein shrinkage of estimated returns.
  4. Bayesian diffuse-prior.
  5. Black-Litterman.
  6. A combination of allocation methods.

They consider three risk aversion settings and either a 60-month or a 120-month lookback interval for input parameter measurement. To assess exploitability, they set trading frictions at 0.50% of traded value for equities and 0.17% for bonds. Using monthly data as specified above during July 1961 through December 2015, they find that:

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Retirement Withdrawal Modeling with Actuarial Longevity and Stock Market Mean Reversion

How does use of actuarial estimates of retiree longevity and empirical mean reversion of stock market returns affect estimated retirement portfolio success rates? In the October 2018 revision of his paper entitled “Joint Effect of Random Years of Longevity and Mean Reversion in Equity Returns on the Safe Withdrawal Rate in Retirement”, Donald Rosenthal presents a model of safe inflation-adjusted retirement portfolio withdrawal rates that addresses: (1) uncertainty about the number of years of retirement (rather than the commonly assumed 30 years); and, (2) mean reversion in annual U.S. stock market returns (rather than a random walk). He estimates retirement longevity as a random input based on the Social Security Administration’s 2015 Actuarial Life Table. He estimates stock market real returns and measures their mean reversion using S&P 500 Index inflation-adjusted total annual returns during 1926 through 2017. He models real bond returns using 10-year U.S. Treasury note (T-note) total annual returns during 1928 through 2017. He applies Monte Carlo simulations (3,000 trials for each scenario) to assess retirement portfolio performance by:

  • Assuming an initial retirement portfolio either 100% invested in stocks or 60%/40% in stocks/T-notes (rebalanced at each year-end).
  • Debiting the portfolio each year-end by a fixed, inflation-adjusted percentage of the initial amount.
  • Calculating percentage of simulation trials for which the portfolio is not exhausted before death (success) and average portfolio terminal balance for successful trials.

He considers two benchmarks: (1) no stock market mean reversion (random walk) and fixed 30-year retirement; and, (2) no stock market mean reversion and actuarial estimate of retirement duration. He also runs sensitivity tests to see how changes in assumptions affect success rate. Using the specified data, he finds that:

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