Roll Returns

As we have seen in the previous section roll returns are a major reason why in- vestors couldn’t participate wholly on the commodity price surge of the last years. Figure 5.9 shows the negative performance of the DJ-AIGCI roll return in larger scale than in Figure 5.7. In this large scale the rolling periods can better be seen and we clearly observe that roll returns follow a jump process caused by their sea- sonal occurrence monthly.

Negative roll returns come in line with a time when the majority of the underlying commodities are in contango and positive roll returns occur when the majority of the underlying commodities are in backwardation. Figure 5.9 shows that longer periods of backwardation are followed by longer periods of contango and that the negative returns in contango periods are higher than the positive returns in backwardation periods. This explains the wavelike downwards move of the performance line. At the moment discussions are coming up that speculate about a synthetic created contango caused by a similar rolling procedure of the major commodity indices. To investigate this problem we show in Figure 5.10 the percent of time the DJ-AIGCI

123_{Because the minimum return of -9.17% occurred as a stand alone outlier at the inception of the} DJ-AIGCI, we cut of the value for better observability of the general return development. 124_{For a detailed discussion of the VaR see [Zagst 2002].}

Figure 5.9: Performance of DJ-AIGCI Roll Returns

spent in contango versus the time it spend in backwardation. Indeed, there is a small trend that the time of contango is increasing. But this is not a phenomena created during the last years it seems to be a steady process of 4% growth over a five year period.

Figure 5.10: Time the DJ-AIGCI spent in Contango or in Backwardation

Matt Schwab, a managing director in the investor coverage group at AIG Financial Products, mentioned in an interview, the people who are involved in the creation and maintenance of the DJ-AIGCI are aware of the fact that commodities spent histor- ically more time in contango than in backwardation. Moreover, ”when institutions ask me if passive flows are causing the contango and hurting index performance, we highlight the fact that at the end of 2005, passive money was just 3% of the size of the overall over-the-counter commodity derivatives market.”125 _{In contrast to} 125_{See [Risknet 2006].}

Deutsche Bank who changed their rolling procedure into a dynamic optimum yield one, many investors are not interested in these kind of trading strategy. John Bryn- jolfsson, head of the Pimco Real Return Commodity Strategy Fund126 stated in an interview: ”Aside from missing the liquidity that is present in the front-end month, having an index that can make or lose money by extending to different calendars is a relatively speculative process that certainly should not be part of a passive index definition strategy.”127

Because roll returns are zero during the non rolling periods and this is the main time during a month, the zero return is the dominant one as shown in the left diagram of Figure 5.11.

Figure 5.11: Distribution Change

We plotted on the left side a histogram128 of the real roll returns and on the right side we plotted the pure roll returns, i.e. the roll return that actually occurred dur- ing the rolling periods. Of the original 3902 daily observations, only 908 data points are left taking only the pure roll returns into consideration. This has the advantage that we can separately analyze the contango and the backwardation times of the market, i.e. how are positive and negative roll returns distributed. As the right diagram in Figure 5.11 clearly shows negative returns occurred historically more of- ten than positive ones, i.e. the bars on the negative side of the diagram are higher than the bars on the positive side. But high irregular outliers can be found more

126_{Recall, the fund was introduced in Section 4.3 and is by far the biggest commodity mutual fund} on the market. It tracks the DJ-AIGCI.

127_{See [Risknet 2006].}

often on the positive side of the distribution, i.e. the distribution has a long right tail.

Finally, Table 5.6 shows the key statistics for both, the actual and the pure roll returns.

Roll Return Pure Roll Return Annualized arithmetic mean -2.85% -2.85% Total value gain -35.85% -35.85% Annualized standard deviation 1.71% 1.68% Minimum (daily) -0.58% -0.58% Maximum (daily) 2.16% 2.16% Mean (daily) -0.01% -0.05% Median (daily) 0.00% -0.04% 99% VaR -0.41% -0.48% 95% VaR -0.18% -0.40% Table 5.6: Key Statistics of DJ-AIGCI Roll Return

It can clearly be seen that mean and median are negative in pure roll returns what additionally underlies the statement that commodities where historically more of- ten in contango than in backwardation. Because the data population decreased, the VaR values have more explanatory power and are not biased to zero.

In the following section we will switch between the actual and the real pure returns depending on the analysis. It makes no sense to investigate in Section 5.2.3 the distribution of the actual roll returns because as it can be seen in the left diagram of Figure 5.11 the distribution is too much biased to zero. But on the other hand, it makes no sense to analyze pure roll returns in Section 5.2.4 and 5.2.5 from the time series point of view.