Commodity diversification looks weakest when this paper's connectedness measure surges, from a 14.12% average to above 50% in 2008 across five markets. The crisis peaks deserve attention. The transmitter rankings do not deserve a trade: their net balances fall below two percentage points, and we found no confidence bands for any of them.
How Ertuğrul, Polat, Yürük and Akgül measure the links
Energy enters other sectors through production and transport costs; gold draws the crisis bid. The economic story is familiar. Commodity financialization since the early-2000s should make index money bind these sectors more closely, especially during a panic. Sector diversification within a commodity book would then offer least protection when it is most needed.
The authors use five S&P GSCI sector indices from Refinitiv: Energy, Agriculture, Industrial Metals, Precious Metals, Livestock. Daily log returns span 10 January 1983 to 26 June 2024. Following Adekoya et al. (2022), they split each return series in two. Positive returns enter a series that is zero on down days; the negative series reverses that treatment. They estimate each of the three systems (overall, positive, negative) with a TVP-VAR(1), whose coefficients change through time. BIC selects the lag.
A 20-step generalized forecast error variance decomposition supplies the connectedness measures. It measures how much of each sector's forecast error variance comes from shocks in the other four. The total connectedness index (TCI) averages these cross-sector shares; a sector's net balance subtracts what it receives from what it sends.
Average TCI reaches 14.12% overall, 12.45% for positive returns and 14.67% for negative returns. The authors report peaks above 50% during the GFC and above 35% during COVID-19. Energy and both metals emerge as net transmitters; livestock is the net receiver. BDS tests, which check for nonlinear dependence, reject linearity at 1% for all five series. The paper also presents a quantile VAR using a 200-day rolling window, though its results appear only as heatmaps.
A 2.2 points advantage for negative-return connectedness
Negative shocks should connect markets more than positive shocks, according to the paper's second hypothesis. Average negative-return TCI exceeds positive-return TCI by 2.22 points, at 14.67% against 12.45%. For adjusted cTCI, the gap is 2.78 points, or 18.34% against 15.56%. The ordering supports the hypothesis. The difference is small.
The crisis claim goes further: the paper attributes the most pronounced TCI spikes to negative shocks. Yet the reported peaks, above 50% and above 35%, have no series attached, and the paper supplies no peak values by sign. Readers must judge the negative-versus-positive difference at those peaks from Fig. 2. We also did not find a formal asymmetry test. Because each split series takes a zero on every day with the opposite sign, the systems are estimated on different data.
What does livestock's isolation mean?
Livestock receives several incompatible descriptions. The paper calls it "the most insulated from shocks, receiving 92.72% of return shocks". In the conclusion it becomes "the most isolated sector", while the discussion says its structure "makes it resilient to intermarket fluctuations". The conclusion also says it absorbs 91.19% of negative shocks, "making it highly vulnerable to a market downturn," and describes it as "the least affected sector" in that same sentence. The negative-shock paragraph, meanwhile, identifies livestock as a net transmitter. The authors retain all these readings.
The decomposition table puts 92.72% on the diagonal: livestock's own shocks explain that share of its forecast error variance. The other four sectors account for just 7.28%. The paper labels that cross-sector share TO and describes it as shocks transmitted; the labelling discussion below explains why it measures shocks received. Livestock's net balance is negative, at -1.25 overall and -1.61 for negative returns. Both are small beside the 92.72% own share.
The raw data tell a similar story. Livestock records the lowest daily variance, 0.853, and the lowest excess kurtosis, 1.664. Its Kendall correlations range from 0.025 with precious metals to 0.068 with agriculture.
For a trader, livestock looks like the sector here that largely moves on its own.
Net spillovers stay below two points in every sector
The abstract describes energy, industrial metals and precious metals as "strong net transmitters of both positive and negative shocks". Their overall net balances are +0.72 for industrial metals, +0.65 for energy and +0.29 for precious metals. Precious metals reaches only +0.06 under negative returns; industrial metals reaches +0.08 under positive returns. Energy has the largest transmitter balance anywhere in Table 3: +0.96 under negative returns, alongside +0.76 under positive returns. Even the largest falls below one point. Without bands, we cannot distinguish any of these estimates from zero.
The authors' results text is more restrained. It describes energy and industrial metals as only slightly more likely to transmit than receive, and energy's net connectedness as relatively balanced. Why does the abstract promote these same figures to "strong"?
Industrial metals does have the most activity. Cross links in each direction run to roughly 18 to 19 points, and its connection with precious metals is the system's strongest pair (7.8% and 7.83%, Kendall 0.180). That finding stands. A busy node can nevertheless send and receive nearly equal amounts; +0.72 is close to balance.
The table's labels create a separate problem. Its TO column contains each row's off-diagonal sum, while the NET row subtracts the TO entry from the FROM entry. In the usual Diebold-Yilmaz orientation, rows measure what a sector receives. On that reading, NET is correct and the labels are reversed.
The paper's construction supports this reading. Each row in Table 3 sums to 100 (energy: 84.99, 3.99, 5.51, 3.99, 1.52). Eq. (12) uses those row terms to construct connectedness from others, so the row sums are FROM. The prose instead describes off-diagonal entries as "the shocks from the i th component to the j th component," contradicting the orientation implied by its own NET row. It also says industrial metals is "passing on 18.31%" of its shocks. The NET row's arithmetic makes 18.31% received and 19.03% sent.
At least twice, the prose departs from the table again. The negative-shock paragraph calls livestock a net transmitter despite its NET of -1.61. The discussion describes agriculture as transmitting positive shocks and receiving negative ones. Table 3 gives the opposite ordering, -0.30 and +0.09. Rankings built on such thin net balances are fragile.
Keep the commodity TCI as a regime monitor
The useful contrast is between average connectedness of 14.12% and the crisis peaks. Across the five sectors, own shocks explain about 86% of forecast error variance on average. That share ranges from 81.69% for industrial metals to 92.72% for livestock. Reported TCI crossed 50% in 2008 and 35% in 2020. Rising TCI can warn a risk manager that diversification across commodity sectors is weakening, without requiring a causal account of which sector set the move off.
The authors advise investors to adjust diversification as conditions change. We did not find a portfolio, hedging or out-of-sample test anywhere in the paper. Adekoya et al. (2022), their methodological template, includes "investment strategies" in its title. This paper ends with connectedness.
We could not replicate it. Our data do not establish coverage of these five S&P GSCI sector histories, and we have no livestock futures with which to reconstruct the fifth sector. Our history also begins well after January 1983.
Bootstrap bands excluding zero for energy's +0.96 net under negative returns would change our view of the rankings. Until someone reports them, those rankings describe one point estimate per sector.