Commodity carry as a trading signal – part 1

Commodity futures carry is the annualized return that would arise if all prices remained unchanged. It reflects storage and funding costs, supply and demand imbalances, convenience yield, and hedging pressure. Convenience and hedging can give rise to an implicit subsidy, i.e., a non-standard risk premium, and make commodity carry a valid basis for a trading signal. An empirical analysis of carry for the front futures in 23 markets shows vast differences in size and volatility, with storage costs being a key differentiator. Also, carry is, on average, not strongly correlated across commodities, making it a more diversified signal contributor. To align carry measures more closely with expected premia, one can adjust for inflation, seasonal fluctuations, return volatility, and carry volatility. Most adjusted carry metrics display highly significant predictive power for returns.

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Finding (latent) trading factors

Financial markets are looking at a growing and broadening range of correlated time series for the operation of trading strategies. This increases the importance of latent factor models, i.e., methods that condense high-dimensional datasets into a low-dimensional group of factors that retain most of their underlying relevant information. There are two principal approaches to finding such factors. The first uses domain knowledge to pick factor proxies up front. The second treats all factors as latent and applies statistical methods, such as principal components, to a comprehensive set of correlated variables. A new paper proposes to combine domain knowledge and statistical methods using penalized reduced-rank regression. The approach promises improved accuracy and robustness.

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Equity convexity and gamma strategies

Equity convexity means that a stock outperforms in times of large upward or downward movements of the broad market: its elasticity to the market return is curved upward. Gamma is a measure of that convexity. All else equal, positive gamma is attractive, as a stock would outperform in market rallies and diversify in market stress. However, gamma is not observable, changeable, and needs to be estimated. Only a subset of stocks displays statistically significant gamma. Empirical analysis suggests that convex stocks can mostly be found in the materials, telecom, industrials, and energy sectors. High past volatility and price-to-book ratios have also been indicative of high gamma. Macroeconomic drivers that trigger gamma performance have been interest rates and oil prices. Systematic long-convexity strategies that seek to time convexity exposure have reportedly produced significant investor value.

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How to estimate factor exposure, risk premia, and discount factors

The basic idea behind factor models is that a large range of assets’ returns can be explained by exposure to a small range of factors. Returns reflect factor risk premia and price responses to unexpected changes in the factors. The theoretical basis is arbitrage pricing theory, which suggests that securities are susceptible to multiple systemic risks. The statistical toolkit to estimate factor models has grown in recent years. Factors and exposures can be estimated through various types of regressions, principal components analysis, and deep learning, particularly in form of autoencoders. Factor risk premia can be estimated through two-pass regressions and factor mimicking portfolios. Stochastic discount factors and loadings can be estimated with the generalized method of moments, principal components analysis, double machine learning, and deep learning. Discount factor loadings are particularly useful for checking if a new proposed factor does add any investment value.

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Fundamental value strategies

Value opportunities arise when market prices deviate from contracts’ present values of all associated entitlements or obligations. However, this theoretical concept is difficult and expensive to apply. Instead, simple valuation ratios, such as real interest rates or equity earnings yields with varying enhancements, have remained popular. Moreover, value strategies can take a long time to pay off and positive returns may be concentrated on episodes of “critical transitions”.
Historically, it has been easier to predict relative value between similar contracts rather than absolute value. Also, simple valuation ratios become more meaningful when combined with related economic indicators. Thus, long-term bond yields are plausibly related to inflation expectations and the correlation of bond prices with economic cycles and market trends. Equity earnings yields can be enhanced by economic trends and market information. And effective exchange rates become a more meaningful metric when combined with inflation differentials and measures of competitiveness of a currency area.

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Risk premia in energy futures markets

Energy futures markets allow transferring risk from producers or consumers to financial investors. According to the hedging pressure hypothesis, net shorts of industrial producers and consumers bias futures prices towards the low side. According to the theory of storage, inventory and supply shortages bias spot and front futures’ prices to the high side relative to back futures. Under both popular hypotheses, “backwardated” futures curves are – all other influence being neutral– indicative of premia paid to longs in back futures. A new paper finds sizeable hedging pressure premia. Long-short positions across a range of energy futures based on hedging pressure and term structure factors seem to have produced significant returns. A promising approach is to integrate various factors into a single long-short portfolio across the spectrum of energy futures.

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Machine learning for portfolio diversification

Dimension reduction methods of machine learning are suited for detecting latent factors of a broad set of asset prices. These factors can then be used to improve estimates of the covariance structure of price changes and – by extension – to improve the construction of a well-diversified minimum variance portfolio. Methods for dimension reduction include sparse principal components analysis, sparse partial least squares, and autoencoders. Both static and dynamic factor models can be built. Hyperparameters tuning can proceed in rolling training and validation samples. Empirical analysis suggests that that machine learning adds value to factor-based asset allocation in the equity market. Investors with moderate or conservative risk preferences would realize significant utility gains.

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Accounting data as investment factors

Corporate balance sheet data are important building blocks of quantitative-fundamental (“quantamental”) investment factors. However, accounting terms are easily misunderstood and confused with economic concepts. Accounting is as much driven by assessment of risk as it is by economic value. For example, earnings are recognized only when receipt of cash is highly certain. Investment spending is recognized as such only when there is a high probability of related payoffs. Acknowledging links to risk and the double-entry system, accounting data can be combined into factors that capture the information that they jointly convey. For example, earnings yields become a more meaningful indicator when also considering return on equity and expended investment ratios.

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Markets’ neglect of macro news

Empirical evidence suggests that investors pay less attention to macroeconomic news when market sentiment is positive. Market responses to economic data surprises have historically been muted in high sentiment periods. Behavioral research supports the idea that investors prefer heuristic decision-making and neglect fundamental information in bullish markets, but pay more attention in turbulent times. This allows prices to diverge temporarily from fundamentals and undermines the conventional risk-return trade-off when sentiment is high. Low-risk portfolios tend to outperform subsequently. The sentiment bias also means that fundamental predictors of market prices work better in low-sentiment periods than in high-sentiment periods.

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Factor timing

Factors beyond aggregate market risk are sources of alternative risk premia. Factor timing addresses the question when to receive and when to pay such risk premia. A new method for predicting the performance of cross-sectional equity return factors proposes to focus only on the dominant principal components of a wide array of factors. This dimension reduction seems to be critical for robust estimation. Forecasts of the dominant principal components can serve as the basis of portfolio construction. Empirical evidence suggests that predictability is significant and that market-neutral factor timing is highly valuable for portfolio construction, over and above directional market timing. Factor timing is related to macroeconomic conditions, particularly at business cycle frequency.

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