Theoretical studies show that the greater (lower) upside asymmetry is associated with lower (higher) expected returns. Wu, Zhu, and Chen (2020) examined return asymmetry in the Chinese stock market with a new distribution-based asymmetry measure (IE) of Jiang et al. (2020) that uses the difference between upside and downside return probabilities to capture the degree of asymmetry. Consistent with the theory, they have found that the average value-weighted return spread between the highest and lowest IE decile is -0.81% per month. This novel study builds upon the previous research and expands an asymmetric measure IE to the new asset class. The paper examines various long-short commodity portfolios and studies the best-performing portfolio in detail. Overall, almost all studied portfolios exhibit statistically significant and economically large returns. Besides, the correlation analysis has shown that the asymmetry-based portfolios are related to the skewness effect, but these two anomalies are distinct. Accordingly, including the asymmetry effect into the portfolio provides an investor an additional benefit different from the skewness effect. Naturally, going long on the commodities with the lowest IE and shorting those with the highest IE results in a profitable trading strategy. A strategy that takes a long position in the bottom seven commodities with the lowest IE in the previous month and shorts the top seven commodities with the highest IE achieved a 4.36% annual return with a corresponding Sharpe ratio of 0.58. Additionally, it can serve as a hedge to the stock portfolio because of its negative correlation with the stock market.
A new measure IE that asymmetric strategy relies on uses the difference between upside and downside return probabilities to capture the degree of asymmetry. The greater the measure, the greater the upside potential of the asset return. Typical risk-averse investors prefer extreme gains and avoid extreme losses. Consequently, they bid up the prices of assets with a high chance of extreme gains and pay a lower price for assets with a high likelihood of extreme losses. As a result, the high (low) IE assets become overvalued (undervalued), and their subsequent returns are lower (higher). Therefore, the asymmetric strategy goes short on the most overvalued commodities with the highest IE and long on the most undervalued commodities with the lowest IE. Besides, the correlation analysis between the proposed strategy and the corresponding skewness portfolio indicates a low positive correlation with a correlation coefficient of 0.46. Even though the skewness and asymmetry effects are related, the correlation is not that high, and both effects form distinct trading strategies.
Table 1, Portfolio 7, Annualized return
Table 1, Portfolio 7, Annualized volatility
22 commodity futures, namely: soybean oil, corn, cocoa, cotton, feeder cattle, gold, copper, heating oil, coffee, live cattle, lean hogs, natural gas, oats, orange juice, palladium, platinum, soybean, sugar, silver, soybean meal, wheat, and crude oil
Table 1, Portfolio 7, Maximal drawdown
The investment universe consists of 22 commodity futures, namely: soybean oil, corn, cocoa, cotton, feeder cattle, gold, copper, heating oil, coffee, live cattle, lean hogs, natural gas, oats, orange juice, palladium, platinum, soybean, sugar, silver, soybean meal, wheat, and crude oil. Firstly, at the beginning of each month, construct the asymmetry measure (IE) for each commodity based on the latest 260 daily returns using the following formula (the formula originally consists of theoretical density and integrals, however the solution is simple when empirical distribution is utilized): IE = (number of trading days when the daily return is greater than the average plus two standard deviations) – (number of trading days when the daily return is smaller than the average minus two standard deviations). Then rank the commodities according to their IE. Buy the bottom seven commodities with the lowest IE in the previous month and sell the top seven commodities with the highest IE in the previous month. Weigh the portfolio equally and rebalance monthly.
Yes - When the monthly S&P 500 return was negative the average monthly
S&P 500 return was -3.50%. However, the average monthly return of the IE Portfolio 7 was 0.50%. Based on regression of the Portfolio 7 returns on the S&P 500 returns, there is a negative slope coefficient of β = -0.04 (t-stat = -1.53). The correlation between Portfolio 7 and S&P 500 returns varies over time with an average correlation coefficient of ρ = -0.08 (tstat = -1.53). Figure 4 shows that the negative relationship becomes more significant during stock market declines like in the early 2000s, 2007, and 2020.
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