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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.

Tests of Strategic Allocations Based on Risk Metrics

Risk-focused asset allocation strategies derive from evidence that forecasting asset return volatility is easier than forecasting average return. Is there a best risk-focused strategy? In his September 2012 paper entitled “A Small Survey of Quantitative Models that Discard Estimation of Expected Returns for Portfolio Construction”, Stefano Colucci compares asset allocation strategies that rely on forecasted asset risk metrics but not on forecasted average returns. Specifically, he compares future gross annualized return-risk ratios, Ulcer indexes, one-month maximum drawdowns and average monthly portfolio turnovers for the following asset allocation strategies:

  1. Minimum Variance (least volatile, or left-most, efficient portfolio per Modern Portfolio Theory).
  2. Minimum Expected Shortfall with weightings estimated by Monte Carlo simulation.
  3. Equal Risk Contribution (each asset weighted by the inverse of its forecasted maximum expected shortfall).
  4. Maximum Diversification (related to expected shortfall with weightings again estimated by numerical simulation).
  5. Risk Parity (each asset weighted by the inverse of its portfolio volatility contribution).
  6. Equal Weighting (requiring neither average return nor volatility forecasts) as a benchmark.

He reforms portfolios every 20 trading days (approximately monthly) and estimates future risk metrics based on a rolling historical window of 500 trading days (approximately two years). Using daily returns over recent periods for stock and bond indexes and individual stocks segregated into several asset selection universes, he finds that: Keep Reading

Mean-Variance Optimizations Versus Equal Weight

Does mean-variance optimization reliably beat simple equal weighting? In his August 2012 paper entitled “The Efficiency of Mean-Variance Optimization with In-depth Covariance Matrix Estimation and Portfolio Rebalancing”, Joonas Hämäläinen tests how many of 96 different mean-variance optimization implementations based on daily data outperform simple equal weighting after accounting for trading frictions. He considers three methods of determining weights for minimum variance portfolios. For each method, he considers three historical intervals for estimating optimal portfolio weights (20, 60 and 250 trading days). He considers three fixed-interval (5, 20 and 60 trading days) and one threshold-based rebalancing rules. His benchmark strategy is equal weight, rebalanced weekly (EW). He tests strategy combinations on four sets of asset returns in euros constructed from 23 MSCI country indexes: 11 European Monetary Union markets during June 2002 through May 2006 (EMU1) and during June 2006 through May 2010 (EMU2); and, 12 big emerging markets during June 2002 through May 2006 (BEM1) and during June 2006 through May 2010 (BEM2). He assumes constant trading frictions of 0.2% (0.4%) of traded value for EMU (BEM) data sets. He focuses on annualized net Sharpe ratio (with risk-free rate zero) and portfolio turnover as critical evaluation metrics. Using daily country total return index levels during June 2001 through May 2010, with out-of-sample tests commencing June 2002, he finds that: Keep Reading

Mean-Variance Investing Basics

How and how well does mean-variance investing work? In his August 2012 draft book chapter entitled “Mean‐Variance Investing”, Andrew Ang compares outcomes for complex asset allocation strategies based on forecasted return statistics to those for very simple strategies such as equal weighting. He illustrates with a horse race among allocation strategies applied to four asset classes (U.S. government bonds, U.S. corporate bonds, U.S. stocks and international stocks), with portfolios reformed monthly based on return statistics estimated from five-year lagged rolling intervals and shorting constrained to no more than -100% for each asset. Using mathematical derivations and monthly return data for the example asset classes during 1973 through 2011, and contemporaneous one-month Treasury bill yields as the risk-free rate, he concludes that: Keep Reading

Fundamentals of Portfolio Weights and Rebalancing

What are the fundamental considerations for portfolio weights and rebalancing rules over the long run? In the July 2012 version of his book excerpt entitled “Dynamic Portfolio Choice”, Andrew Ang elaborates these considerations as derived from two precepts: (1) periodic or conditional rebalancing of the components of a diversified portfolio is foundational to long-term investing; and, (2) target weights for portfolio components can vary for each rebalancing interval as investment opportunities change and investor liabilities, income and risk tolerance evolve. Using mostly theory and some simple example portfolios composed of U.S. stocks and Treasuries during 1926-1940 and 1990-2011, he concludes that: Keep Reading

Mean-Variance Optimization Versus Equal Weight

Is equal weighting of diversified portfolio assets good enough, or are mean-variance optimized allocation strategies constructed from asset return and variance forecasts worth the complexities of implementation? In the June 2012 draft of their paper entitled “Market Volatility, Optimal Portfolios and Naive Asset Allocations”, Massimiliano Caporin and Loriana Pelizzon investigate the conditions under which mean-variance optimized portfolios outperform an equal-weight portfolio. They consider four optimized allocation strategies (mean-variance, and three variations of global minimum variance with no shorting). They apply these strategies to five sets of equity assets diversified across different U.S. stock anomalies according to: (1) industry; (2) size/value; (3) size/short-term reversal; (4) size/momentum; and, (5) size/long-term reversal. They consider four methods for forecasting returns and volatilities for these assets (lagged rolling values, regression on explanatory variables and two technical autoregressions that detect mean reversion), all based on a 60-month or 120-month rolling historical window. They use Sharpe ratio to compare portfolio performances. Using monthly data for the five selected sets of equity assets from Kenneth French’s library spanning April 1953 through December 2010 (693 months), they find that: Keep Reading

Hedging Stock Portfolios with VIX Futures Index Products

Are popular exchange-traded products (ETP) such as VXX (iPath S&P 500 VIX Short Term Futures) and VXZ (iPath S&P 500 VIX Mid-Term Futures), designed to track specific S&P 500 VIX futures constant maturity index series, good hedges for stock portfolios? In their June 2012 paper entitled “Are VIX Futures ETPs Effective Hedges?”, Geng Deng, Craig McCann and Olivia Wang investigate whether these ETPs effectively hedge basic U.S. stock portfolios or exchange-traded funds (ETF) that leverage U.S. stock market indexes. Because the ETPs are only very recently available, they use the one-month (SPVXSP) and five-month (SPVXMP) S&P 500 VIX futures constant maturity indexes as proxies for them. They examine the hedging effectiveness of these indexes for five stock portfolios: 100% SPDR S&P 500 (SPY); 100% Vanguard Total Stock Market Index Fund (VTSMX); 80% VTSMX and 20% Vanguard Total Bond Market Index Fund (VBMFX); 60% VTSMX and 40% VBMFX; and, 40% VTSMX and 60% VBMFX. They also examine the hedging effectiveness of these indexes for three 2x-leveraged exchange-traded funds (ETF): ProShares Ultra S&P500 (SSO); ProShares Ultra QQQ (QLD); and, ProShares Ultra Dow30 (DDM). They compute optimal hedge ratios using consecutive (non-overlapping) 26-week lagged regressions of weekly total returns of each portfolio/ETF versus weekly returns of the hedging instrument. Using weekly data for all portfolio funds and VIX futures indexes since December 2005, and for leveraged ETFs since late July 2006, all through mid-April 2012, they find that: Keep Reading

Worst Case Asset Allocation

Is planning for the worst case paramount in asset class allocation? In their May 2012 paper entitled “Minimax: Portfolio Choice Based on Pessimistic Decision Making”, Steffen Schaarschmidt and Peter Schanbacher examine the worst case scenario as a basis for portfolio optimization (Minimax strategy). Specifically, each year they run Monte Carlo simulations based on the last 250 trading days of returns to model all possible return scenarios for all possible long-only portfolio allocations. They then choose for the next year the portfolio allocation with the largest return for the worst case scenario. Using daily returns for the S&P 500 Index, Barclays Aggregate Bond Index, a Real Estate Investment Trust (REIT) index and the S&P GSCI Index, and the contemporaneous yield on 90-day Treasury bills as the risk-free rate, during 1990 through 2010, they find that: Keep Reading

Persistent Usefulness of Emerging Markets in Equity Diversification

How does consideration of return distribution tails (not just linear correlations) affect assessment of global equity diversification benefits? In their May 2012 paper entitled “Is the Potential for International Diversification Disappearing? A Dynamic Copula Approach”, Peter Christoffersen, Vihang Errunza, Kris Jacobs and Hugues Langlois examine the evolution of equity market diversification benefits based on a methodology that accommodates non-linearity in the relationship between return streams. They focus on differences between developed and emerging markets. Using weekly returns in U.S. dollar for 16 developed markets during January 1973 through mid-June 2009, 13 emerging markets during late January 1989 through July 2008 and 17 emerging markets during July 1995 through mid-June 2009, they find that: Keep Reading

Correlation Timing of Sector Allocations

Can reacting to short-term changes in asset return correlations improve efficient portfolio allocation? In their May 2012 paper entitled “The Role of Correlation Dynamics in Sector Allocation”, Elena Kalotychou, Sotiris Staikouras and Zhao Gang investigate the economic value of correlation timing in mean-variance optimal sector allocations. They test the usefulness of several correlation forecast methods by constructing dynamic, one-step-ahead (day, week or month) mean-variance optimal portfolios comprised of ten sectors in the Japanese, UK or U.S. equity markets (energy, basic materials, industrials, consumer goods, health care, consumer services, telecommunication, utilities, financials and technology). They use a static portfolio based on total-sample correlations as a benchmark. They use an initial subperiod (July 1996 through May 2005) to generate initial correlation forecasts and a later subperiod (Jun 2005 through May 2007) to implement recursive forecasts. They estimate sector index trading frictions for daily (monthly) portfolio rebalancing as approximately 0.07% (0.09%) for U.S., 0.30% (0.32%) for Japanese and 0.50% (0.52%) for UK sector indexes. Using daily prices for the ten sector indexes for each of the Nikkei 225, FTSE-All and S&P 500 during July 1996 through May 2007, along with corresponding interbank and U.S. Treasury bill yields as risk-free rates, they find that: Keep Reading

Overview of Equity Return Predictors

What is the big picture on stock return predictors? In their May 2012 paper entitled “The Supraview of Return Predictive Signals”, Jeremiah Green, John Hand and Frank Zhang examine aggregate characteristics of 333 signals for which formal research indicates power to predict stock returns. They categorize each signal as accounting-based (from firm financial statements, such as accruals), finance-based (directly or indirectly from stock prices, such as return momentum) or other-based (such as stock buybacks). They standardize across studies via annualization by multiplying daily, weekly, monthly and quarterly returns by 250, 52, 12 and 4, respectively. They compile equal-weighted returns and value-weighted returns separately. They focus on Sharpe ratio as a widely used metric for comparing investment performance. Using a database of predictive signals as published in top-tier U.S. accounting, finance and practitioner journals and as disseminated in academic working papers via the Social Science Research Network (SSRN) during 1970 through 2010, they conclude that: Keep Reading

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