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Author:Balduzzi, Pierluigi 

Working Paper
Minimum-variance kernels, economic risk premia, and tests of multi-beta models
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).
AUTHORS: Balduzzi, Pierluigi; Robotti, Cesare
DATE: 2001

Working Paper
Mimicking portfolios, economic risk premia, and tests of multi-beta models
This paper considers two alternative formulations of the linear factor model (LFM) with nontraded factors. The first formulation is the traditional LFM, where the estimation of risk premia and alphas is performed by means of a cross-sectional regression of average returns on betas. The second formulation (LFM*) replaces the factors with their projections on the span of excess returns. This formulation requires only time-series regressions for the estimation of risk premia and alphas. We compare the theoretical properties of the two approaches and study the small-sample properties of estimates and test statistics. Our results show that when estimating risk premia and testing multi-beta models, the LFM* formulation should be considered in addition to, or even instead of, the more traditional LFM formulation.
AUTHORS: Balduzzi, Pierluigi; Robotti, Cesare
DATE: 2005

Working Paper
Asset-pricing models and economic risk premia: a decomposition
The risk premia assigned to economic (nontraded) risk factors can be decomposed into three parts: (i) the risk premia on maximum-correlation portfolios mimicking the factors; (ii) (minus) the covariance between the nontraded components of the candidate pricing kernel of a given model and the factors; and (iii) (minus) the mispricing assigned by the candidate pricing kernel to the maximum-correlation mimicking portfolios. The first component is the same across asset-pricing models and is typically estimated with little (absolute) bias and high precision. The second component, on the other hand, is essentially arbitrary and can be estimated with large (absolute) biases and low precisions by multi-beta models with nontraded factors. This second component is also sensitive to the criterion minimized in estimation. The third component is estimated reasonably well, both for models with traded and nontraded factors. We conclude that the economic risk premia assigned by multi-beta models with nontraded factors can be very unreliable. Conversely, the risk premia on maximum-correlation portfolios provide more reliable indications of whether a nontraded risk factor is priced. These results hold for both the constant and the time-varying components of the factor risk premia.
AUTHORS: Balduzzi, Pierluigi; Robotti, Cesare
DATE: 2005

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