4.4 Decomposition of Index Returns
5.1.1 Risk and Return Profile
When it comes to financial investing the first two regarded measurements are risk and return. When an investor puts his money into an asset he is interested in the profit he will earn, i.e. the expected return of the investment, and the entered risk, e.g. measured by the volatility of the expected return. Recall, in Section 3 we identified the two drivers of commodity futures prices to be the spot price respectively the expectation of the future spot price and a risk premium respectively a risk premium on inventories called convenience yield. Because our investment focus is long term orientated and commodities are traded with futures having a maturity we have to roll over the investment by and by. As we have seen in Section 4.4 the calculable excess return representing the pure commodity return can be divided into the spot return, i.e. a return that is generated by the value change of a commodity, and the roll return, i.e. a return that is generated by the change of risk premiums. At the end of the day expected future returns are based on the experiences of the past. Therefore, this section shall give an empirical overview of the risk and return profile of historical commodity returns.
For it, we identified a small peer group including respectively a single commodity from each commodity group as of Figure 2.1, a sub index representing each com- modity group and the two market dominating broad indices, the DJ-AIGCI and the GSCI.
To examine the value development of the different commodity indices we use the annualized sample mean for a small peer group.107 Continuous returns are time ad-
ditive108 and so annualized values are reached by linear scaling of the sample mean
by the average number of observations per year. Table 5.1 shows the results for the return components109 of the different commodity indices of our small peer group.
107To be precise: Let {r
1, . . . , rT} be a discrete random sample of returns as of Definition C.2 at times t ∈ {1, . . . , T }. The sample mean is defined as:
¯ r = 1 T T X t=1 rt (5.1) 108See Equation (C.5).
109The single return components were separated as described in Section 4.4. Excess and spot return series are published by the index issuers and the roll returns were calculated as of Theorem 4.1.
Excess Return Spot Return Roll Return Gasoline 33.6% 29.3% 4.3% Natural Gas -16.0% 26.5% -42.5% Nickel 35.5% 32.1% 3.4% Zinc 11.9% 20.5% -8.6% Gold 9.4% 14.2% -4.8% Corn -25.7% 1.7% -27.4% Lean Hogs -13.5% 6.6% -20.1% Sugar 7.5% 9.4% -1.9% Energy Index 25.5% 29.7% -4.3% Industrial Metals Index 17.7% 20.1% -2.4% Precious Metals Index 10.3% 14.5% -4.2% Agricultural Index -14.9% 3.3% -18.2% DJ-AIGCI 12.0% 19.9% -7.9% GSCI 15.3% 22.0% -6.7% Table 5.1: Return Components of different Commodity Indices (1998-2006)
Over the 8 year period starting in August 1998 all commodities have produced on average a positive spot return. But because commodity investments include rolling futures positions forward we need to take the roll returns into consideration. All group and broad indices including more than one participant produced on average negative roll returns. Implicating, most commodities have been in contango. Hi- lary Till, co-founder of Premia Capital Management LLC, has investigated into the source of steady commodity returns. In [Till 2000] she identified commodities with statistically significant returns as these, whose underlying commodity have difficult storage situations. For these commodities, either storage is impossible, prohibitively expensive, or producers decide, it is much cheaper to leave the commodity in the ground than to store it. Her findings are in line with earlier research by [Kolb 1996] who examined 45 commodity futures contracts between 1982 and 2004. Both men- tion soybean meal, live cattle, live hogs, crude oil, gasoline and copper to be difficult to store and to have significant positive returns. Storage can act as a buffer. If too little of a commodity is produced, one can draw on storage and price does not need to ration demand. But for commodities with a difficult storage situation, ”... price has to do a lot (or all) of the work of equilibrating supply and demand ...”.110 [Kolb 1996] showed that the average geometric excess return of the difficult to store commodities was 3.5% over the period of 1982 to 2004. In contrast, the average geometric excess return of the not difficult to store commodities was -4.3% over the same period.
Morgan Stanley investigated into the relationship between excess returns and the time a commodity spent in contango respectively in backwardation. In the presenta- tion [Nash Shrayer 2004] they show findings regarding the existence of a weak linear relationship between the average annualized return produced by a commodity and the time it spend in backwardation. They examined 18 commodities over the period 1983 to 2004 and identified heating oil, live cattle, copper, crude oil and gasoline as commodities with positive return and positive time the commodity spend on average in backwardation.
Figure 5.1 shows the percentage time a commodity spend in backwardation plotted against the annualized mean of its excess return as of Table 5.1. Indeed, we can also identify a linear relationship between this two components.
Figure 5.1: Relationship between Backwardation and annualized Return
More recently, [Till Feldman 2006] extended the framework originated in the work of [Nash Shrayer 2004]. They found that the power of backwardation to explain commodity futures return is indeed valid, but requires the investor to have a very long investment horizon when relying on this indicator. Specifically, they examined soybean, corn and wheat futures over the period of 1950 to 2004. They found that a contracts average level of backwardation only explains 25% of the variation in futures returns over one year time frames, 42% of variation over two year time frames, 63% of variation over five year time frames and robust 77% of variation over eight year time frames.
All these research aims to answer the question whether commodities offer a signifi- cant risk premium or not. This depends on how futures prices deviate from expected future spot prices or equivalent on how high their convenience yield is. This is very different from equities. Since the main reason to buy stocks is investment, for stocks
it is plausible that prices are set such that the expected return exceeds the inter- est rate and is higher for more risky stocks. For commodity futures to offer a risk premium, we need hedging demand to pull futures prices away from the respective expected future spot price. For the identified difficult to store commodities there is plausible tendency for hedgers to be predominantly on the sell side. As a result, the expected futures return is more likely to be positive than negative.
In general, no uniform conclusion about significant excess returns can be made. But we came to the conviction that commodity’s risk premium vary over time de- pendent on the current and expected supply and demand situation. Moreover, the price of commodities and therewith the realized returns move through cycles over time caused by commodity’s consumption good facility. In periods of scarcity and high hedging demand with high risk premiums new supply will enter the market yielding, according to experience, into over supply periods with falling prices, low or negative risk premiums and negative industry growth with falling supply. New demand thrusts are firstly buffered by inventories to a certain degree but yielding again, according to experience, in a new period of scarcity and the circle starts anew.
The current price surge came in line with high price movements over short periods, such as recently seen in crude oil and copper markets, for instance. Therefore, commodities are often thought to be extremely volatile. Indeed, in response to weather related events, supply shocks, e.g. caused by news about existing reserves, and speculative trading some commodity prices may exhibit large swings over short periods. First research regarding this phenomena goes back to the theory of storage. Following [Kaldor 1939] volatility is inversly related to the level of inventories. When there are little or no inventories to buffer supply and demand disequilibriums, prices may rise dramatically. As a consequence, rising prices and rising volatility come in line and both are negatively correlated to the level of inventory.
Today, there exists a vast amount of literature what investigates the volatility of com- modity futures. A statistical study performed by [Fama French 1987] on a number of commodity futures including metals, wood and animals shows that the variance of prices increases adversely to inventory levels. [German Nguyen 2002] investigated worldwide soybean inventories over a 10 year period and showed that volatility can be written as an exact inverse function of inventory. Regarding energy markets, the property is the same and widely discussed in actuality: whenever there is a down- ward adjustment of the estimated oil reserves in the US or another region, oil prices and their volatility increase sharply.
To investigate the variability of different commodity indices we calculate the an- nualized sample standard deviation, the minimum and the maximum of daily log returns separately for the respective excess return (ER), spot return (SP) and roll return (RR). The annualized sample standard deviation, denoted by ¯σ, is calculated as the root of the the annualized sample variance111 and gives an absolute measure of the variability of returns to either the negative or positive side of the mean. In Table 5.2 we represent our findings for the small peer group already known from Table 5.1.
The first observation is that spot volatility explains the main part of excess return volatility. The dispersion of roll returns are generally quite small in comparison to spot volatility. To understand this we have to recover that the spot price of a commodity is approximated by the price of the first nearby futures contract. The roll return is made by rolling the investment from the first into the second month futures contract and therefore, the difference between these two prices relative to the price of the first nearby futures contract, e.g. the spot price. This difference depends of the shape of the forward curve. As we have already seen in Section 5.1.1, the shape of the forward curve is an expression of the current and expected supply and demand equilibrium. The rolling periods of our sample are monthly and therewith short term orientated. Caused by the small time difference between the first and the second nearby futures contract, sudden extreme events will effect both prices and rolling over the investment will create only small roll returns. The described phenomena can be seen in the copper example of the previous section. Going back to Table 4.5 we see a huge sudden spot price surge during March and April from 5,440 US dollar per contract to 7,118 US dollar per contract. But the price of the second month contract was influenced in the same way. From Table 4.6 we take a small roll return of 0.3% in this month. This observation goes in line with the Samuelson effect well known and often analyzed in commodity related research, e.g. [Samuelson 1965] and [Anderson Danthine 1983]. The Samuelson effect is called the property of commodity price volatility to decrease with increasing maturity. It
111To be more precise: Let {r1, . . . , rT} be a discrete random sample of returns as of Definition C.2 at times t ∈ {1, . . . , T } and ¯r be the sample mean as in Equation (5.1). The sample variance is defined as: ¯ σ2= 1 T − 1 T X t=1 (rt− ¯r)2 (5.2) Annualized values are calculated by scaling linear with the average number of observations per year because continuous returns are time additive. The square root of the sample variance:
¯ σ =
√ ¯
σ2 (5.3)
Return Std. Deviation Minimum Maximum ER 38.2% -12.8% 11.2% Gasoline SP 38.3% -12.8% 11.2% RR 5.4% -2.5 1.9 ER 55.0% -16.7% 18.8% Natural Gas SP 55.5% -16.7% 18.8% RR 7.3% -7.7% 2.0% ER 36.0% -18.3% 13.6% Nickel SP 35.5% -18.2% 12.4% RR 4.9% -4.7% 10.8% ER 23.3% -8.9% 8.9% Zinc SP 23.1% -9.0% 8.9% RR 2.0% -2.1% 4.1% ER 16.4% -7.6% 8.8% Gold SP 16.3% -7.6% 8.8% RR 1.1% -1.4% 1.4% ER 22.2% -5.3% 6.5% Corn SP 22.7% -5.3% 6.5% RR 4.3% -3.3% 3.0% ER 27.5% -7.4% 6.9% Lean Hogs SP 30.4% -12.2% 11.8% RR 11.3% -5.4% 7.9% ER 32.9% -9.3% 8.4% Sugar SP 33.3% -9.3% 8.4% RR 4.5% -2.5% 2.5% ER 33.3% -14.4% 8.0% Energy Index SP 33.3% -14.4% 8.0% RR 3.5% -3.7% 2.8% ER 19.5% -9.0% 7.6% Industrial Metals Index SP 19.1% -9.1% 7.6% RR 2.5% -2.3% 4.4% ER 16.3% -8.3% 8.5% Precious Metals Index SP 16.3% -8.2% 8.5% RR 1.2% -1.5% 1.5% ER 17.0% -10.5% 8.6% Agricultural Index SP 17.4% -12.5% 9.8% RR 4.3% -2.9% 5.0% ER 15.0% -4.3% 4.8% DJ-AIGCI SP 15.2% -4.3% 4.8% RR 1.9% -2.1% 0.8% ER 22.7% -9.2% 6.5% GSCI SP 22.7% -4.3% 4.8% RR 2.2% -2.3% 1.6%
Table 5.2: Volatility Components of different Commodity Indices (1998-2006)
is explained by the fact that the arrival of news (e.g. on inventories) will have an immediate impact on short-term futures prices, while long-term contract prices tend to remain unchanged since production adjustments are likely to take place before the contracts come to delivery at maturity.
The second observation is regarding the dispersion of the different commodities. They differ not only among each other, but also among each commodity group as the sub indices tell. Moreover, the annualized standard deviations range from as much as 55.0% for natural gas to as low as 16.4% for gold. Therefore, general statements about the ”high volatility” implicating high risks for investors cannot be supported. [Kat Oomen 2006] examined the development of commodity return
volatility during different periods of the business cycle over a period of 1965 to 2005 and conclude, that changes in the dispersion level can be observed. Especially oil’s and oil product’s prices react differently in different business cycle periods. During recessions they tend to be high volatile and at the beginning of an expansion phase their variability tend to decrease. Moreover, they report that most commodities including i.e. oil and oil products, silver, platinum, copper, soybeans, cocoa and corn tend to be more volatile when the forward curve is in backwardation. This is not surprising when interpreting backwardation as an indication of scarcity that usually is followed by price surges and as described above this is positively related to volatility increases.112
Third, sub indices exhibit in general smaller standard deviations as their partici- pants. This might be an indication for diversification effects and our guess is under- lined by the small standard deviation of the broad indices.