The convenience yield of a commodity is the benefit that arises from physical access. In conjunction with storage costs, it wields great influence on the slope of the futures curve. On its own, a high convenience yield translates into backwardated futures curves and positive carry. Different sections of the commodity curve contain different implied convenience yields. A new paper proposes a measure of convenience yield risk, based on the difference in volatility of convenience yields implied by the front and subsequent section of the curve. Panel regression for 27 commodities and nearly 60 years suggests that the convenience yield risk signal positively predicts commodity returns, similar to the predictive power of dividend growth volatility for equity returns. A convenience yield risk-based trading signal seems to have added significant investor value.

The below post is based on a summary of quotes from the paper and some related sources.

This post ties in with this site’s summary of implicit subsidies.

## Convenience yield basics

“The convenience yield [is] the __benefit that accrues to the holder of the physical commodity__.”

“Commodity processors, such as oil refineries, metallurgical plants, and food manufacturers, require physical availability of raw materials to sustain their business activity. To avoid a costly disruption of the production process, they may be forced to purchase a commodity at a spot price much higher than the corresponding futures price…The theory of storage…introduces the concept of convenience yield…__to explain the observed discrepancy between spot and futures prices__ and thus the shape of the commodity term structure.” [Bollinger and Kind]

“Holding physical inventories carries benefits of flexibility for industrial consumers. The __value of such inventories increases when scarcities arise__. As a consequence, convenience yields help predict future demand and price changes.” [Macrosynergy]

“Given its prominence, it is therefore not surprising that several studies analyze its information content [documenting] a significant cross-sectional relationship between the convenience yield and future commodity returns [and] that __the ‘carry’, which is related to the convenience yield, predicts commodity returns in the time series and cross-section__.”

“We [can compute] daily implied convenience yield using the cost-of-carry relationship. For the ith and jth nearby futures contracts [the below equation applies]:

- f
_{t}^{i}and f_{t}^{i}are the logarithmic prices of the jth and ith nearby futures contracts on day t (with j > i), respectively. - r
_{t}^{ij}is the annualized risk-free rate on day t for the period starting at i and ending at j. - cy
_{t}^{ij}is the annualized convenience yield on day t referring to the period between the expiration dates of the ith and jth futures contracts. - m
_{t}^{i}and m_{t}^{j}are the days to expiry of the above contracts.”

“We then compute the convenience yield by rearranging [the above] equation. Our methodology is deliberately non-parametric as opposed to approaches which model convenience yield as a continuous-time stochastic process. Apart from avoiding restrictive assumptions, our approach has the benefit of __allowing us to back out the convenience yield for any pair of contract maturities__.”

“We obtain daily futures price…for 27 commodities. The dataset comes from Bloomberg and covers the period from July 7, 1959, to December 31, 2018. This dataset includes a broad range of liquid commodity futures markets which can be grouped into 6 sectors: energy, grains, livestock, metals, oilseeds, and softs. The table [below] shows the commodities included in our analysis, together with information on the exchange where each commodity futures trades, its expiry schedule, and contract size. Following the standard practice, __we construct continuous futures price series by rolling over each contract at the end of the month preceding the month prior to the delivery month__. By taking this step, we aim to alleviate concerns about stale prices occurring in the final month before the end of trading of the futures contracts.”

“Descriptive statistics for the nearest convenience yield i.e., the one computed from the first and second nearby futures contracts, are presented in [the table above]. __The first-order autocorrelation coefficients [AR(1)] indicate that the convenience yield is persistent__. We document substantial variation in the first two moments of the convenience yields across commodities. For instance, the mean (standard deviation) of the convenience yield of natural gas is equal to 10.45% (173.35%), while the corresponding figure for gold is 0.53% (1.47%). This __cross-sectional variation in the convenience yield is strongly influenced by seasonal demand and supply patterns__. For example, the seasonal variation in the convenience yield of natural gas and heating oil is mainly driven by the heating demand during cold months. Similarly, the seasonality in the convenience yield of agricultural commodities, such as corn or soybeans, relates to the annual harvest cycle…As one would expect, we obtain the strongest evidence of seasonality in the convenience yield of commodities in the energy, agricultural and livestock sectors, and the weakest in metals.”

## Estimating convenience yield risk

“We propose a measure of convenience yield risk…For each commodity market, __we compute the convenience yield implied by (i) the first and second nearby futures contracts as well as (ii) the second and third nearby futures contracts__…We denote these quantities the first and second convenience yield estimates, respectively. At the end of each month__, we use all daily data pertaining to the month to compute the monthly volatility__ of each of the two convenience yield series. Finally, __we obtain the convenience yield risk signal as the trailing 12-month average of the difference between the volatility of the first and second convenience yield series__…Intuitively, we take the difference between the two volatility estimates in order to remove any asset-specific effect [and] we average the difference in the volatility estimates over a 12-month trailing window in order to alleviate concerns about measurement errors.”

“We then define the convenience yield risk [cyr_{t}] as follows:

Here σ^{1,2}_{cy,t-i} and σ^{2,3}_{cy,t-i} are the volatilities [standard deviations] of the first and second nearest convenience yields of month t – i. “

Several factors motivate our computation of the convenience yield risk. First, by computing the monthly volatility of the convenience yield, we capture the monthly time variation in the convenience yield. Second, __we compute the difference between the monthly volatility of the first two convenience yield series…to remove any market-specific effect__. Third, we use a 12-month measurement period to (i) address the issue of seasonality in both the level and volatility of the convenience yield series and (ii) alleviate concerns about measurement errors.

## Predictive power

“We estimate a panel regression of commodity returns on the lagged convenience yield risk signal…The results from the above predictive regressions are presented in [the table below]…We find that the __convenience yield risk signal positively predicts commodity returns__ as evidenced by the significant t-statistic.”

“We augment our baseline panel regression with time- and commodity-fixed effects and reach similar conclusions. We also control for the impact of other prominent commodity signals documented in the literature and reach the same conclusion: the convenience yield risk is a significant predictor of commodity futures returns.”

“This finding mirrors [equity research] that documents that the volatility of the dividend growth rate positively forecasts stock market returns.”

## Application in trading strategies

“We examine the economic value of the predictive power of convenience yield risk. To this end, we develop and implement a simple trading strategy. At the end of each month, __we sort all commodities by their convenience yield risk signal. We then open long and short positions in the commodities with the signal higher and lower than the median signal__, respectively.”

“The strategy generates a positive and significant annualized average return of 6.93% (t-stat.=3.24) and an annualized Sharpe ratio of 0.46.”

“We estimate spanning regressions of the convenience yield risk strategy returns on a set of commodity risk factors recently proposed in the literature. We find that the average risk-adjusted return of the convenience yield risk strategy (average 4.6%, t-statistic 2.09) is positive, highly significant, and comparable to the unadjusted average return (average 6.93% and t-statistic 3.24). Collectively, __the empirical evidence suggests that the returns of the convenience yield risk strategy are un-spanned by the existing commodity market strategies__.”

“We perform several checks to assess the robustness of our findings. We show that our results are robust to the addition of more nearby futures contracts when computing the convenience yield risk signal. Furthermore, we show that the convenience yield risk strategy remains profitable when the assets are rank-, rather than equal-, weighted in the portfolios. We also repeat our analysis focusing on the top and bottom tertile portfolios and obtain similar results. We analyze the impact of a decision delay of 1-month between the computation of the signal and the implementation of the trading strategy. Overall, we find that the decision delay does not materially affect our results. Furthermore, we show that the convenience yield risk strategy is profitable across various periods, including the high and low volatility regimes.”

“Finally, we establish that the convenience yield risk strategy returns remain profitable after accounting for transaction costs.”