Strategic Allocation

How much performance improvement comes from rebalancing a stocks-bonds portfolio, and what specific rebalancing approach works best? In their August 2014 paper entitled “Testing Rebalancing Strategies for Stock-Bond Portfolios Across Different Asset Allocations”, Hubert Dichtl, Wolfgang Drobetz and Martin Wambach investigate the net performance implications of different rebalancing approaches and different rebalancing frequencies on portfolios of stocks and government bonds with different weights and in different markets. With buy-and-hold as a benchmark, they consider three types of rebalancing rules: (1) strict periodic rebalancing to target weights; (2) threshold rebalancing, meaning periodic rebalancing to target weights if out-of-balance by 3% or more; and, (3) range rebalancing, meaning periodic rebalancing to plus (minus) 3% of target weights if above (below) target weights by more than 3%. They consider annual, quarterly and monthly rebalancing frequencies. They use 30 years of broad U.S., UK and German stock market, bond market and risk-free returns to construct simulations with 10-year investment horizons. Their simulation approach preserves most of the asset class time series characteristics, including stocks-bonds correlations. They assume round-trip rebalancing frictions of 0.15% (0.10% for stocks and 0.05% for bonds). Using monthly returns for country stock and bonds markets and risk-free yields during January 1982 through December 2011 to generate 100,000 simulated 10-year return paths, they find that: Keep Reading

“Sticky Winner Asset Class ETF Momentum Strategy” tests whether limiting the trading of the “Simple Asset Class ETF Momentum Strategy” by holding onto the winner until it drops out of the top three boosts performance of the latter by reducing trading and thereby suppressing trading frictions. A subscriber proposed a more precise approach to limit trading: continue holding a past winner until it loses to a new winner by a significant margin. To investigate whether this approach (Buffered Winner) works, we compare it to the original strategy (Winner), which allocates all funds at the end of each month to the asset class exchange-traded fund (ETF) or cash with the highest total return over the last five months, as applied to the following nine assets:

PowerShares DB Commodity Index Tracking (DBC)
iShares MSCI Emerging Markets Index (EEM)
iShares MSCI EAFE Index (EFA)
SPDR Gold Shares (GLD)
iShares Russell 1000 Index (IWB)
iShares Russell 2000 Index (IWM)
SPDR Dow Jones REIT (RWR)
iShares Barclays 20+ Year Treasury Bond (TLT)
3-month Treasury bills (Cash)

Using monthly adjusted closing prices for the asset class proxies and the yield for Cash over the period July 2002 (or inception if not available then) through June 2014 (144 months), we find that: Keep Reading

Is there a practical way to apply momentum investing in a Modern Portfolio Theory (MPT) framework? In his June 2014 paper entitled “Momentum, Markowitz, and Smart Beta”, Wouter Keller constructs a long-only, unleveraged Modern Asset Allocation (MAA) model in three steps

1. Make MPT tactical by using short historical intervals to predict future asset returns (rate of return, or absolute momentum), return volatilities (based on daily returns) and return correlations (based on daily returns), assuming that measured behaviors will materially persist the next month. Assign zero weight to assets with negative returns over the historical measurement interval.
2. Simplify correlation calculations by relating daily historical returns for each asset to those for a single market return (the average return of all assets weighted equally) rather than to returns for all other assets separately.
3. Dampen errors in rapidly changing asset return, volatility and correlation predictions by “shrinking” them toward their respective averages across all assets in the universe, and dampen the predicted market volatility by “shrinking” it toward zero.

He reforms the MAA portfolio monthly at the first close. His baseline historical interval for estimation of all variables is four months (84 trading days). His baseline shrinkage factor for all variables is 50%. His principal benchmark is the equally weighted (EW) “market” of all assets, rebalanced monthly. He assumes one-way trading friction of 0.1%. He considers a range of portfolio performance metrics: annualized return, annual volatility, maximum drawdown, turnover, Sharpe ratio, Omega ratio and Calmar ratio. Using daily dividend-adjusted prices for assets allocated to three universes (10 exchange-traded funds [ETF], 35 ETFs and 104 U.S. stocks/bonds) during December 1997 through December 2013, he finds that: Keep Reading

Does using after-tax, rather than pre-tax, returns make a big difference in allocating assets based on mean-variance optimization? In their June 2014 paper entitled “What Would Yale Do If It Were Taxable?” Patrick Geddes, Lisa Goldberg and Stephen Bianchi illustrate a three-step approach for adapting the Yale Endowment for investors obligated to pay U.S. taxes:

1. Reverse engineer Yale Endowment allocations by applying covariances of matched benchmark indexes to derive implied pre-tax asset class returns.
2. Apply assumptions about taxes to convert the pre-tax returns to after-tax returns.
3. Apply mean-variance optimization to after-tax returns to calculate optimal allocations based on after-tax returns.

The asset classes addressed are: absolute return (hedge funds), equity (U.S. and global combined), bonds, natural resources, real estate, private equity and cash. For estimating tax impacts, the authors assume: returns from bonds and cash are ordinary income; there are distinct tax obligations for returns from active, passive (index fund) and tax loss-advantaged equity; hedge fund returns are tax-wise similar to active equity; 30% of appreciation from natural resources and private equity are realized each year as long-term gains; and, 30% of appreciation from real estate are realized each year as ordinary income. They ignore any effects of portfolio liquidation. Using Yale Endowment allocations and U.S. tax rules as of  the end of 2013, along with benchmark index covariances during December 1998 through June 2013, they find that:

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Risk parity asset strategies generally make large allocations to low-volatility assets such as bonds, which tend to fall in value when interest rates rise. Is risk parity a safe strategy when rates rise? In their June 2014 research note entitled “Risk-Parity Strategies at a Crossroads, or, Who’s Afraid of Rising Yields?”, Fabian Dori, Manuel Krieger, Urs Schubiger and Daniel Torgler examine how the rising interest rate environment of the U.S. in the 1970s affects risk parity performance. They also examine how inflation and economic growth affect risk parity performance. They use the yield on the 10-year U.S. Treasury note (T-note) as a proxy for the interest rate. Their risk parity model uses 40-day past volatility for risk weighting and allows leverage to target an annualized portfolio volatility (7.5%, per Fabian Dori). They consider two benchmark portfolios: conservative, allocating 60% to bonds, 30% to stocks and 10% to commodities; and, aggressive, allocating 40% to bonds, 40% to stocks and 20% to commodities. They rebalance all portfolios daily, including estimated transaction costs. They compare six-month returns of risk parity and benchmark portfolios across ranked fifths (quintiles) of contemporaneous six-month changes in interest rates, inflation and Gross Domestic Product (GDP) growth rate. Using daily levels of a generic 10-year T-note, the S&P 500 Index and the Goldman Sachs Commodity Index during January 1970 through June 1996 and actual daily futures prices for 2-year, 5-year and 10-year T-notes, the S&P 500 Index, the NASDAQ 100 Index and the DJ UBS Commodity Index during July 1996 through April 2014, along with contemporaneous interest rate, inflation and GDP data, they find that: Keep Reading

The “Simple Asset Class ETF Momentum Strategy” each month allocates all funds to the one of the following eight asset class exchange-traded funds (ETF), or cash, with the highest total return over the past five months:

PowerShares DB Commodity Index Tracking (DBC)
iShares MSCI Emerging Markets Index (EEM)
iShares MSCI EAFE Index (EFA)
SPDR Gold Shares (GLD)
iShares Russell 1000 Index (IWB)
iShares Russell 2000 Index (IWM)
SPDR Dow Jones REIT (RWR)
iShares Barclays 20+ Year Treasury Bond (TLT)
3-month Treasury bills (Cash)

“Simple Asset Class ETF Momentum Strategy Robustness/Sensitivity Tests” shows that, among uniform ranking intervals, five months is optimal. Citing the optimality of a three-month ranking interval in “Simple Debt Class Mutual Fund Momentum Strategy”, a subscriber inquired whether using a three-month ranking interval just for TLT might improve Simple Asset Class ETF Momentum Strategy performance. To investigate more generally, we compute net terminal values for 108 variations of the strategy by letting the ranking interval for each asset range from one to 12 months, while holding the ranking interval for all other assets at five months. In order to compare ranking intervals of different lengths, we use the average total return per month for ranking. For example, the average monthly total return for a five-month ranking interval is the five-month total return divided by five. Using monthly dividend-adjusted closes for the asset class proxies and the yield for Cash during July 2002 (or inception if not available then) through May 2014 (141 months), we find that:

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A subscriber suggested an alternative to the “Simple Asset Class ETF Momentum Strategy” that weights asset class ETFs according to five-month past return ranking (such as 35-25-20-10-4-3-2-1) rather than allocating all funds to the winner. Do the diversification benefits of this alternative outweigh the loss of momentum purity? To investigate, we return to 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 1000 Index (IWB)
iShares Russell 2000 Index (IWM)
SPDR Dow Jones REIT (RWR)
iShares Barclays 20+ Year Treasury Bond (TLT)
3-month Treasury bills (Cash)

As one benchmark, we allocate all funds at the end of each month to the asset class ETF or cash with the highest total return over the past five months (5-1). As another benchmark, we maintain an equal-weighted (EW), monthly rebalanced portfolio of all nine asset classes. As alternatives, we test two momentum rank-weighted (RW), linearly-scaled combinations of all nine classes, one steep across ranks and one shallow. We also test EW combinations of the Top 5, Top 4, Top 3 and Top 2 momentum ranks. Using monthly 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 May 2014 (100 months), we find that: Keep Reading

We have updated the detail at “Momentum Strategy” to incorporate the historical data changes described in “Simple Asset Class ETF Momentum Strategy Data Changes”. The principal effects are to decrease the performance of the Top 1 portfolio and increase the performance of the Top 2 portfolio.

Over the coming week, we will accordingly update much of the supporting research listed at “Momentum Strategy”.

Does the relative performance of 10-year U.S. Treasuries and 30-year U.S. Treasuries offer a useful risk-on/risk-off regime change signal? In their February 2014 paper entitled “An Intermarket Approach to Tactical Risk Rotation Using the Signaling Power of Treasuries to Generate Alpha and Enhance Asset Allocation” (the National Association of Active Investment Managers’ 2014 Wagner Award third place winner), Michael Gayed and Charles Bilello examine whether the relationship between the monthly total returns of the 10-year and 30-year Treasuries usefully indicate when to hold (or tilt toward) Treasuries versus stocks. They reason that informed investors migrate toward intermediate-term (long-term) Treasuries when they anticipate strong (weak) economic conditions. Therefore, the relative strength of 10-year and 30-year Treasuries signals when to take an aggressive or defensive investment posture. Using monthly total returns for 10-year and 30-year Treasuries and for the broad U.S. stock market during April 1977 through December 2013, they find that: Keep Reading

What factors make asset class diversification work? To investigate empirically, we consider the following mix of exchange-traded funds (ETF) as asset class proxies (the same used in “Simple Asset Class ETF Momentum Strategy”):

PowerShares DB Commodity Index Tracking (DBC)
iShares MSCI Emerging Markets Index (EEM)
iShares MSCI EAFE Index (EFA)
SPDR Gold Shares (GLD)
iShares Russell 1000 Index (IWB)
iShares Russell 2000 Index (IWM)
SPDR Dow Jones REIT (RWR)
iShares Barclays 20+ Year Treasury Bond (TLT)
3-month Treasury bills (Cash)

We calculate the monthly gross return-risk ratio (average monthly return divided by standard deviation of monthly returns) for an equally weighted, monthly rebalanced portfolio of all nine asset class proxies. We then recalculate the return-risk ratio nine times, each time excluding one of the assets, and relate the resulting return-risk ratios to three characteristics of the respectively excluded assets: (1) average monthly return; (2) standard deviation of monthly returns; and, (3) average (pairwise) cross-correlation of monthly returns with the other eight assets. The objective is to determine whether any of these three characteristics explain asset contribution to diversification benefit.  We ignore trading frictions associated with monthly rebalancing, which would be similar for all combinations. Using dividend-adjusted monthly returns for the above nine asset class proxies during September 2006 (so that monthly returns for all assets are available in equal-weight calculations) through April 2014 (92 monthly returns), we find that: Keep Reading