Minimum-Variance Kernels, Economic Risk Premia, and Tests of Multi-beta Models

Pierluigi Balduzzi and Cesare Robotti
Working Paper 2001-24
November 2001

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This paper uses minimum-variance (MV) admissible kernels to estimate risk premia associated with economic risk variables and to test multi-beta models. Estimating risk premia using MV kernels is appealing because it avoids the need to 1) identify all relevant sources of risk and 2) assume a linear factor model for asset returns. Testing multi-beta models in terms of restricted MV kernels has the advantage that 1) the candidate kernel has the smallest volatility and 2) test statistics are easy to interpret in terms of Sharpe ratios. The authors find that several economic variables command significant risk premia and that the signs of the premia mostly correspond to the effect that these variables have on the risk-return trade-off, consistent with the implications of the intertemporal capital asset pricing model (I-CAPM). They also find that the MV kernel implied by the I-CAPM, while formally rejected by the data, consistently outperforms a pricing kernel based on the size and book-to-market factors of Fama and French (1993).

JEL classification: G12

Key words: minimum-variance kernels, intertemporal capital asset pricing model, economic risk premia

The authors thank Eric Jacquier, Luanne Isherwood, and seminar participants at Boston College, the 1999 Meetings of the Society for Computational Economics, the 2000 Meetings of the European Finance Association, and the 2000 Meetings of the Financial Management Association for useful comments. The authors also acknowledge financial support from Boston College research grants. The views expressed here are the authors’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors’ responsibility.

Please address questions regarding content to Pierluigi Balduzzi, associate professor of finance, Wallace E. Carroll School of Management, Boston College, 140 Commonwealth Avenue, Chestnut Hill, Massachusetts 02467-3808, 617-552-3976, 617-552-0431 (fax),, or Cesare Robotti, financial economist, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, Georgia 30309-4470, 404-498-8543, 404-498-8810 (fax),