This paper tests whether the traditional futures hedge ratio (h_T) and the carry cost rate futures hedge ratio (h_c) vary in accordance with the Sercu and Wu (2000) and Leistikow et al. (2019) “h_c” theory. It does so, both within and across high and low spot asset carry cost rate (c) regimes. The high and low c regimes are specified by asset across time and across currency denominations. The findings are consistent with the theory. Within and across c regimes, h_T is inefficient and h_c is biased. Across c regimes, h_c’s Bias Adjustment Multiplier (BAM) does not vary significantly. Even though h_c’s bias-adjusted variant’s BAM is restricted to old data that is from a different c regime, the hedging performance of h_c and its bias-adjusted variant (=h_c × BAM), are superior to that for h_T. Variation in c may account for the h_T variation noted in the literature and variation in c should be incorporated into ex ante hedge ratios.

Many investors see little opportunity for active portfolio managers to exploit relative returns in environments with high return correlation. Contrary to what current-day Chicken Littles believe, the authors empirically find a positive relation between the S&P 500’s average constituent stock relative-return volatility and its average between-constituent return correlation. Moreover, the S&P 500’s index-return variance, average between-constituent return correlation, average constituent relative-return variance, and average constituent residual-return variance are all positively related to a statistically significant degree. The authors also provide a theoretical foundation for these empirical findings.

This study shows that a “rational,” capital asset pricing model (CAPM) type of positive relationship between short-horizon expected arithmetic return and risk can lead to a negative long-horizon relationship between compound annual return and risk (whether risk is measured by volatility or beta). This result follows from the stochastic portfolio theory relationship that a stock’s growth rate is less than its expected arithmetic return by approximately one-half its variance of return. The negative long-horizon relationships between return mean and volatility/beta often have been noted and characterized as the low-volatility and low-beta anomalies. Thus, these characterizations may be problematic.