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Risk Management Across Assets and Over Time

| | Posted in: Strategic Allocation

Do both asset-level and portfolio-level risk management techniques enhance portfolio performance? In the October 2015 version of his paper entitled “Optimal Dynamic Portfolio Risk Management”, Valeriy Zakamulin investigates risk management across assets (relative weighting of risky assets) and risk management over time (timing the market via positions in the risk-free rate/leverage). For risk management across risky assets, he consider equal weighting, risk parity (based on asset volatility forecasts) and minimum variance (based on asset volatility and correlation, or covariance, forecasts). He employs an Exponentially Weighted Moving Average (EWMA) for forecasting volatilities and covariances as needed. For risk management over time, he uses portfolio-level variance targeting, applying leverage to risky assets when expected variance is low and shifting capital to the risk-free asset when expected variance is high. He focuses on Sharpe ratio as a performance metric. He ignores costs of portfolio adjustments and leverage. Using daily returns for market capitalization-weighted groupings of U.S. common stocks formed via size-value, size-momentum, size-long reversal and industry sorts (as risky assets) and daily 90-day U.S. Treasury bill yields (as the risk-free rate) from the data library of Kenneth French during January 1972 through December 2014, he finds that:

  • Portfolios reformed frequently (daily) based on risk parity or minimum variance mostly outperform equal weight on a gross basis (see the chart below). Minimum variance is generally optimal.
    • Because forecast accuracy deteriorates with forecast horizon, the more frequent the forecast updates the better the performance.
    • Multivariate GARCH and EWMA covariance forecasts have 50% smaller errors than conventional rolling window forecasts. 
  • Portfolios with frequently updated risk management both across assets and over time outperform portfolios with risk management only across assets (again, see the chart below).

The following chart, constructed from data in the paper, compares average gross Sharpe ratios for several risk management approaches applied daily across the four sets of factor and industry stock groupings specified above. An equal weight investor assumes neither returns, return volatilities nor return correlations are predictable. A risk parity investor assumes neither returns nor return correlations are predictable. A minimum variance investor assumes only returns are unpredictable.

The blue columns compare average gross Sharpe ratios for equal weight, risk parity and minimum variance approaches applied at a daily frequency separately to the four sets of factor and industry stock groupings with no market timing. Results indicate that risk parity works a little better than equal weight, and that minimum variance works better than the other two approaches.

The red columns compare average gross Sharpe ratios after adding market timing based on portfolio-level variance targeting (using leverage or shifting funds to the risk-free asset, as indicated) to asset-level risk management. Results indicate that market timing modestly improves equal weight and risk parity asset weighting and substantially improves minimum variance weighting.


In summary, evidence based on gross performance indicates that U.S. equity investors should apply risk management at both the asset level (relative weights of risky assets) and at the portfolio level (market timing, via an allocation to a risk-free asset or leverage).

Cautions regarding findings include:

  • As noted in the paper, reported Sharpe ratios are gross, not net. Costs of daily portfolio adjustments, and leverage when indicated, would reduce all Sharpe ratios. Since portfolio turnover and leverage requirements likely differ across risk management approaches, net findings may differ from gross findings.
  • Moreover, analyses employ ideal factor/industry groupings as assets, not tradable funds. Costs of translating these portfolios into funds (if feasible) would reduce all returns and Sharpe ratios.
  • Even though testing is out-of-sample, applying multiple approaches to the same data sets introduces snooping bias, such that the best approach likely overstates expectations.
  • As noted in the paper, the complex risk management approaches considered do not convincingly outperform equal weight for industry portfolios, undermining belief that these approaches work consistently across different kinds of assets.
  • The risk management methods tested are beyond the reach of many investors, who would bear fees when delegating such management.
  • Daily data acquisition and processing as described is likely not feasible over the early part of the sample period. Early availability of such capabilities may have changed asset price behavior.
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