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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.

SACEMS vs. Luck

How lucky would a asset class picker with no skill have to be to match the performance of the Simple Asset Class Momentum Strategy (SACEMS), which each month picks winners from the following set of exchange-traded funds (ETF) based on total returns over a specified lookback 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)

To investigate, we run 1,000 trials of a “strategy” that each month allocates funds to one, the equally weighted two or the equally weighted three of these nine assets picked at random. We focus on gross compound annual growth rate (CAGR) and gross maximum drawdown (MaxDD) as key performance statistics. Using monthly total (dividend-adjusted) returns and for the specified assets during February 2006 (limited by DBC) through October 2017, we find that:

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Return Forecasts Good Enough for Mean-variance Optimization?

Are there stock return forecasts good enough to make mean-variance optimization work as a stock portfolio allocation strategy? In their October 2017 paper entitled “Mean-Variance Optimization Using Forward-Looking Return Estimates”, Patrick Bielstein and Matthias Hanauer test whether firm implied cost of capital (ICC) based on analyst earnings forecasts is effective as a stock return forecast for mean-variance portfolio optimization. They derive ICC annually for each stock as the internal rate of return (discount rate) implied by a valuation model that equates forecasted cash flows, derived from analyst earnings forecasts, to market valuation. To refine ICC estimates, they correct predictable analyst forecast errors (slow reactions to news) by including a standardized, rescaled momentum variable based on return from 12 months ago to one month ago (ICCadj). They then employ ICCadj to specify annual (each June 30) mean-variance optimized (maximum Sharpe ratio) long-only stock allocations (with maximum weight 5%) based on stock return covariances calculated from returns over the last 60 months. For benchmarks, they consider the value-weighted market portfolio (VW), the equal-weighted market portfolio (EW), the minimum variance portfolio (MVP) and a maximum Sharpe ratio portfolio based on 5-year moving average actual returns (HIST). They focus on U.S. stocks, which have relatively broad analyst coverage. They test robustness of findings with data from selected international developed markets, different return variable specifications, different subperiods and impact of transaction costs. Using monthly data for the 1,000 U.S. common stocks with the biggest prior-month market capitalizations since June 1985 and the 250 biggest stocks in each of Europe, UK and Japan since 1990, all through June 2015, they find that:

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Multi-class, Multi-factor Investing

What is the best way to tackle multi-class, multi-factor investing? In their August 2017 paper entitled “Investing in a Multi-Asset Multi-Factor World”, Alexandar Cherkezov, Harald Lohre, Sergey Protchenko and Jay Raol investigate the use of factor investing across multiple asset classes. They define several factors for each of four asset classes, as follows:

  1. Equities (individual stocks for developed and emerging markets) – value, momentum, quality and low volatility.
  2. Currencies (forwards for developed and emerging markets) – carry, value, momentum and quality.
  3. Commodities (24 futures series) – carry, term (duration) and momentum.
  4. Interest rates (10-year swaps for developed and emerging markets) – carry, value, momentum and quality.

To integrate the portfolio with high diversification, they employ diversified risk parity by each month: (1) identifying uncorrelated clusters of risk across asset classes and factors based on a rolling 60-month or expanding (inception-to-date) lookback window; and, (2) setting long-only allocations such that each uncorrelated risk cluster contributes equally to overall portfolio risk. For comparison, they also consider equal weight, minimum variance and equal risk contribution (equal contribution to portfolio risk by each individual factor) allocation approaches. Using data needed to form factor portfolios and measure factor returns in U.S. dollars across asset classes from the end of January 2001 through the end of December 2016, they find that:

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Trend-following Managed Futures to Make Retirement Safer?

Should retirement portfolios include an allocation to managed futures? In his October 2017 paper entitled “Using Trend-Following Managed Futures to Increase Expected Withdrawal Rates”, Andrew Miller compares seven 30-year retirement scenarios via backtests and modified backtests. Specifically, he compares maximum annual real withdrawal rates as a percentage of initial assets that do not exhaust any 30-year retirement portfolios starting each year during 1926-2012 (SAFEMAX). The seven scenarios, all rebalanced annually, are:

  1. Historical Returns 50-50: uses actual annual returns for a 50% allocation to large-capitalization U.S. stocks and a 50% allocation to intermediate-term U.S. Treasuries.
  2. Historical Returns 50-40-10: same as Scenario 1, except shifts 10% of the Treasuries allocation to a trend-following managed futures strategy that is long and short 67 stocks, bonds, currencies and commodities futures series based on equally weighted 1-month, 3-month and 12-month past returns with a 10% annual volatility target.
  3. Lower Historical Returns 50-50: same as Scenario 1, but reduces monthly returns for stocks and Treasuries by 0.19%, reflecting end-of-2016 valuations.
  4. Lower Historical Returns 50-40-10: same as Scenario 2, but reduces monthly returns for stocks, Treasuries and managed futures by 0.19%.
  5. Lower Managed Futures Sharpe Ratio 50-40-10: same as Scenario 2, but reduces the Sharpe ratio for managed futures from an historical level to 0.5.
  6. Lower Historical Returns/Lower Managed Futures Sharpe Ratio 50-40-10: same as Scenario 4, but reduces Sharpe ratio for managed futures to 0.5.
  7. Historical Returns 50-50 with Trend Following for Stocks: same as Scenario 1, but each month puts the stocks allocation into stocks (30-day U.S. Treasury bills) when the return on stocks is positive (negative) over the prior 12 months.

He ignores all trading frictions, fees and taxes. Using monthly asset class returns as specified and monthly inflation data during January 1926 through December 2012, he finds that: Keep Reading

Effects of Execution Delay on SACEVS

How does execution delay affect the performance of the Best Value and Weighted versions of the “Simple Asset Class ETF Value Strategy” (SACEVS)? These strategies each month 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)

To investigate, we compare 21 variations of each strategy with execution days ranging from end-of-month (EOM) per the baseline strategy to 20 trading days after EOM (EOM+20). For example, an EOM+5 variation computes allocations baed on EOM but delays execution until the close five trading days after EOM. We focus on gross compound annual growth rate (CAGR) and gross maximum drawdown (MaxDD) as key performance statistics. Using daily dividend-adjusted closes for the above ETFs from late July 2002 through mid-September 2017, we find that:

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Slow Down or Speed Up SACEMS with Volatility?

A subscriber, noting an article on slowing down intrinsic (absolute or time series) momentum for SPDR S&P 500 (SPY) when its return volatility is relatively high, suggested doing the same for the Simple Asset Class ETF Momentum Strategy (SACEMS). The hypothesis is that this dynamic lookback interval approach avoids undesirable whipsaws when asset returns are volatile. SACEMS each month picks winners from the following set of exchange-traded funds (ETF) based on total returns over a fixed lookback 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)

To investigate the suggested dynamic lookback interval, we each month:

  1. Calculate the average of the standard deviations of daily returns over the last 60 trading days for the individual risky assets (all except Cash).
  2. Calculate the average of these end-of-month averages over the past 12 months.
  3. Divide the current month average standard deviation by the 12-month average of averages to get a lookback interval factor.
  4. Multiply the baseline fixed lookback interval by the current lookback interval factor.
  5. Round the result to the nearest whole number of months as the current dynamic lookback interval.

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 daily and monthly total (dividend-adjusted) returns for the specified assets during February 2006 (limited by DBC) through August 2017, we find that: Keep Reading

Trend Following to Boost Retirement Income

Does simple asset price trend following based on 10-month simple moving average (SMA10) reliably boost the performance of retirement portfolios? In their July 2017 paper entitled “Can Sustainable Withdrawal Rates Be Enhanced by Trend Following?”, Andrew Clare, James Seaton, Peter Smith and Steve Thomas compare effects of asset class diversification and trend following on safe withdrawal rates from UK retirement portfolios. They consider 60-40 UK stocks-bonds, 30-70 UK stocks-bonds and equally weighted UK stocks, global stocks, bonds, commodities and UK real estate (EW Multi-asset). They further consider risk parity (RP) multi-asset (each class weighted by the inverse of its prior-year volatility) and 100% global stocks (equally weighted across five regions). They focus on a 20-year retirement period (but also consider 30-year), assume annual withdrawals the first day of each year and ignore taxes and rebalancing frictions. They use both in-sequence historical asset returns and Monte Carlo simulations (random draws with replacement from the historical annual returns of each portfolio). They apply trend following separately to each asset by holding the asset (cash) when asset price is above (below) its SMA10. Their key portfolio performance metric is Perfect Withdrawal Rate (PWR), the constant real (inflation-adjusted) withdrawal rate as a percentage of initial portfolio value that exactly exhausts the portfolio at the end of the retirement period. Using monthly total returns in pounds sterling for the selected asset classes and values of the UK consumer price index during 1970 through 2015, they find that: Keep Reading

Extended Simple Momentum Strategy Test of TSP Funds/Proxies

A subscriber asked about extending “Simple Momentum Strategy Applied to TSP Funds” back in time to 1988. That test employs the following five funds, all available to U.S. federal government employees via the Thrift Savings Plan (TSP) as of January 2001:

G Fund: Government Securities Investment Fund (G)
F Fund: Fixed Income Index Investment Fund (F)
C Fund: Common Stock Index Investment Fund (C)
S Fund: Small Cap Stock Index Investment Fund (S)
I Fund: International Stock Index Investment Fund (I)

S Fund and I Fund data limit the combined sample period. To extend the test back to first availability of G Fund, F Fund and C Fund data in February 1988, we use Vanguard Small Cap Index Investors Fund (NAESX) as a proxy for the S Fund and Vanguard International Value Investors Fund (VTRIX) as a proxy for the I Fund prior to 2001. We first perform a sensitivity test of fund ranking (lookback) intervals ranging from one to 12 months on the following monthly reformed portfolios: the winner fund (Top 1); an equally weighting of the top two funds (EW top 2); an equally weighting of the Top 3 funds (EW Top 3); and, an equal weighting of all five funds (EW All). We then perform detailed tests using a representative lookback interval. Using monthly returns for the five TSP funds as available during February 1988 through June 2017 (351 months) and monthly returns for NAESX and VTRIX during February 1988 through December 2000, we find that:

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Optimal Rebalancing Frequency/Months?

Is there a preferred frequency and are there preferred months for rebalancing conventional asset class portfolio holdings? To investigate we consider annual, semiannual and quarterly rebalancing of a simple portfolio targeting a 60-40 stocks-bonds mix. We consider all possible combinations of calendar month ends as rebalancing points. We ignore rebalancing (and dividend-reinvestment) frictions and tax implications, thereby giving an advantage to frequent rebalancing. We focus on compound annual growth rate (CAGR) as the critical portfolio performance metric. Using dividend-adjusted monthly closes for SPDR S&P 500 (SPY) to represent stocks and Vanguard Total Bond Market Index (VBMFX) to represent bonds over the period January 1993 (SPY inception) through June 2017 (about 24 years), we find that: Keep Reading

Conservative Breadth Rule for Asset Class Momentum Crash Protection

Does an asset class breadth rule work better than a class-by-class exclusion rule for momentum strategy crash protection? In their July 2017 paper entitled “Breadth Momentum and Vigilant Asset Allocation (VAA): Winning More by Losing Less”, Wouter Keller and Jan Keuning introduce VAA as a dual momentum asset class strategy aiming at returns above 10% with drawdowns less than -20% deep. They specify momentum as the average of annualized total returns over the past 1, 3, 6 and 12 months. This specification gives greater weight to short lookback intervals than a simple average of past returns over these intervals. Specifically, they:

  1. Each month rank asset class proxies based on momentum.
  2. Each month select a “cash” holding as the one of short-term U.S. Treasury, intermediate-term U.S. Treasury and investment grade corporate bond funds with the highest momentum. 
  3. Set (via backtest) a breadth protection threshold (B). When the number of asset class proxies with negative momentum (b) is equal to or greater than B, the allocation to “cash” is 100%. When b is less than B, the base allocation to “cash” is b/B.
  4. Set (via backtest) the number of top-performing asset class proxies to hold (T) in equal weights. When the base allocation to “cash” is less than 100% (so when b<B), allocate the balance to the top (1-b/B)T asset class proxies with highest momentum (irrespective of sign).
  5. Mitigate portfolio rebalancing intensity (when B and T are different) by rounding fractions b/B to multiples of 1/T.

They construct four test universes from: a short sample of 17 (mostly simulated) exchange traded fund (ETF)-like global asset class proxies spanning December 1969 through December 2016; and, a long sample of 21 index-like U.S. asset classes spanning December 1925 through December 2016. After reserving the first year for initial momentum calculations, they segment each sample into halves for in-sample optimization of B and T and out-of-sample testing. For all cases, they apply 0.1% one-way trading frictions for portfolio changes. Their key portfolio performance metrics are compound annual growth rate (CAGR), maximum drawdown (MaxDD) and a composite of the two. Using monthly returns for the selected ETF-like and index-like assets over respective sample periods, they find that:

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