Relative Entropy and Minimum-Variance Pricing Kernel in Asset Pricing Model Evaluation

Abstract

Recent literature shows that many testing procedures used to evaluate asset pricing models result in spurious rejection probabilities. Model misspecification, the strong factor structure of test assets, or skewed test statistics largely explain this. In this paper we use the relative entropy of pricing kernels to provide an alternative framework for testing asset pricing models. Building on the fact that the law of one price guarantees the existence of a valid pricing kernel, we study the relationship between the mean-variance efficiency of a model’s factor-mimicking portfolio, as measured by the cross-sectional generalized least squares (GLS) R 2 statistic, and the relative entropy of the pricing kernel, as determined by the Kullback–Leibler divergence. In this regard, we suggest an entropy-based decomposition that accurately captures the divergence between the factor-mimicking portfolio and the minimum-variance pricing kernel resulting from the Hansen-Jagannathan bound. Our results show that, although GLS R 2 statistics and relative entropy are strongly correlated, the relative entropy approach allows us to explicitly decompose the explanatory power of the model into two components, namely, the relative entropy of the pricing kernel and that corresponding to its correlation with asset returns. This makes the relative entropy a versatile tool for designing robust tests in asset pricing.

The Gibbons, Ross, and Shanken Test for Portfolio Efficiency: A Note Based on Its Trigonometric Properties

“…Ryan et al [12], utilizing the GRS-test, look at the average value of absolute intercepts, α i = 0 to test whether the regression intercepts are jointly equal to zero, with the idea being that the intercept is indistinguishable from zero if an asset pricing model completely captures the expected returns (in which case the portfolio is efficient). Suarez and Alonso-Conde [13] looked at an entropy-based decomposition that captures the divergence between the factor-mimicking portfolio and the minimum-variance pricing kernel as distinct from quadratic test statistics, such as the GRS-test (determined as a function of pricing errors). Solórzano-Taborga et al [14], utilize the GRS test for identifying restrictions (they termed 'efficiency factor') to test the null of asset pricing errors equaling zero.…”

Sustainable Construction and Financing—Asset-Backed Securitization of Expressway’s Usufruct with Redeemable Rights

“…If the face value of the bond is CNY 100, and the interest was paid once a year, letting the maturity date of the bond be N and the coupon rate be CR, the yield to maturity r t in year t could be determined according to the interest rate term structure of the bond with the same credit rating. Then the bond coupon rate CR could be obtained by Formula (5).…”

“…Sheraz et al [4] believed that in many cases, no arbitrage risk measurement was difficult to be realized through using numerical method, and the minimum entropy method provided a new idea for the determination of risk neutral measurement. Based on HJ pricing kernel, Rojo-Suárez and Alonso Conde [5] divided the core of asset pricing into two parts, the relative entropy of the pricing kernel and the relative entropy related to asset pricing. Liao et al [6] calculated the yield volatility of each sub-market of Chinese bond market through an auto-regressive model, and further got the volatility spillover effect between each sub-market of bonds.…”