Joint Normality Test for the Returns on the Futures and Spot

Sheng-Syan Chen, Cheng Few Lee and Keshab Shrestha

Chapter 33 in Handbook of Investment Analysis, Portfolio Management, and Financial Derivatives:In 4 Volumes, 2024, pp 1129-1158 from World Scientific Publishing Co. Pte. Ltd.

Abstract: It is well known that the optimal hedge ratios derived based on the mean-variance approach, the expected utility-maximizing approach, the mean extended-Gini approach, and the generalized semivariance approach will all converge to the minimum-variance hedge ratio if the futures price follows a pure martingale process and if the spot and futures returns are jointly normal. In this chapter, we perform empirical tests to see if the pure martingale and joint normality hypotheses hold using 25 different futures contracts and five different hedging horizons. Our results indicate that the pure martingale hypothesis holds for all commodities and all hedging horizons except for three stock index futures contracts. As for joint normality, we propose two new tests based on the generalized method of moments, which allow for calculating multivariate test statistics that take account of the contemporaneous correlation across spot and futures returns. Our findings show that the joint normality hypothesis generally does not hold except for a few contracts and relatively long hedging horizons.

Keywords: Financial Accounting; Financial Auditing; Mutual Funds; Hedge Funds; Asset Pricing; Options; Portfolio Analysis; Risk Management; Investment Analysis; Momentum Analysis; Behavior Analysis; Futures; Index Futures; CDCs; Financial Econometrics; Statistics; Financial Derivatives; Financial Accounting (search for similar items in EconPapers)
JEL-codes: G1 G11 G12 G3 M41 M42 (search for similar items in EconPapers)
Date: 2024
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