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Mean-Variance Asset Allocation for Individual Investors

Posted in Individual Investing, Strategic Allocation

Can individual investors practically implement mean-variance optimization in a multi-asset class context? In their April 2016 paper entitled “Asset Allocation: A Recommendation for Resolving the Collision between Theory and Practice”, Larry Prather, James McCown and Ron Shaw describe how individual investors can construct and maintain a low-cost optimal (maximum Sharpe ratio) multi-class portfolio via the Excel Solver function. They consider four criteria in selecting asset class proxies: (1) market capitalization-weighted coverage of a wide variety of investable assets; (2) small initial investment; (3) low annual expenses; and, (4) versions that investors can short. Based on these criteria, they select five Vanguard index mutual funds and three precious metals:

  • Vanguard Total Stock Market Index Fund Investor Shares (VTSMX), capturing the U.S. equity market.
  • Vanguard Total International Stock Index Fund Investor Shares (VGTSX), representing 98% of the capitalization of non-U.S. equity markets.
  • Vanguard Emerging Markets Stock Index Fund Investor Shares (VEIEX), supplementing VGTSX to better capture emerging market equities.
  • Vanguard Total Bond Market Index Fund Investor Shares (VBMFX), providing broad exposure to U.S. investment grade bonds.
  • Vanguard REIT Index Fund Investor Shares (VGSIX), providing broad exposure to U.S. Real Estate Investment Trusts (REIT).
  • Spot gold, platinum and palladium, offering safe haven and currency exchange rate protection.

These mutual funds and metals have exchange-traded fund (ETF) analogs, supporting optimization with short selling. They assume a constant risk-free rate of 3%. Using daily mutual fund returns and spot metals prices during September 1998 through June 2015, they find that:

  • Annualized returns from daily data are:
    • 9.1%, 7.5% and 13.1% for U.S., foreign and emerging equity markets, respectively.
    • 4.9% for bonds.
    • 14.1% for REITs.
    • 8.7%, 6.7% and 5.2% for gold, platinum and palladium, respectively.
  • Annualized risk measured as variance (square of standard deviation) from daily data are:
    • 4.2%, 4.2% and 5.3% for U.S., foreign and emerging equity markets, respectively.
    • 0.2% for bonds.
    • 8.7% for REITS.
    • 3.3%, 5.5% and 11.4% for gold, platinum and palladium, respectively.
  • Daily return correlations:
    • Among equities classes and REITs are positive and relatively high.
    • Between bonds and equities/REITs are modestly negative.
    • Between equities/REITs and metals are near zero.
    • Among metals are modestly to moderately positive.
  • For long-only optimization (mutual fund solution) over the sample period, optimal allocations to risky assets are about: 76% bonds, 8% gold, 7% emerging markets equities, 4% U.S. equities, 4% REITs and 1% platinum, generating annualized return 6.3% and Sharpe ratio 0.74. Specifying higher annualized return requires suboptimal portfolios (lower Sharpe ratios). Specifically:
    • Requiring an 8% annualized return drives U.S. equities and platinum out of the portfolio and generates annualized Sharpe ratio 0.66.
    • Requiring 12% annualized return further drives the bonds out of the portfolio and generates annualized Sharpe ratio 0.52.
    • Depending on level of risk aversion, asset allocations are 25%-57% to emerging markets equities, 0%-38% to bonds, 12%-33% to REITs and 10%-24% gold. These ranges are dramatically different from conventional wisdom.
  • For long-short optimization (ETF solution) over the sample period, optimal allocations include all eight asset classes, six long and two short. Resulting annualized return is 6.9%, with Sharpe ratio 0.79. Again, requiring higher return means lower Sharpe ratio, but Sharpe ratio deterioration is much less pronounced than for long-only.
  • The larger any separate allocation to cash, the lower the return and risk for all portfolios. For investors with the highest and lowest levels of risk aversion, cash allocations alter risky portfolio allocations.

In summary, evidence indicates that optimal multi-asset portfolio allocations differ greatly from conventional wisdom.

Cautions regarding findings include:

  • As noted in the paper, sample period returns, volatilities and correlations for the selected assets may not be good forecasts of future statistics. 
  • The analysis is in-sample. An investor would not know the inputs required to calculate optimal allocations until the end of the sample period. The authors do not present any out-of-sample tests.
  • The risk-free rate is arguably not constant.
  • Results ignore trading frictions for spot metals and ETFs, and shorting costs for long-short optimization. Any such costs would reduce returns and thereby affect optimal allocations.
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