# Stranded fossil-fuel assets translate to major losses for investors in advanced economies

### Global energy demand

To generate global oil and gas demand and price time series for each scenario, we use the IAM E3ME-FTT-GENIE^{13,14} framework based on observed technology evolution dynamics and behaviour measured in economic and technology time series. It covers global macroeconomic dynamics (E3ME), S-shaped energy technological change dynamics (FTT)^{15,16,17}, fossil-fuel and renewable-energy markets^{41,42}, and the carbon cycle and climate system (GENIE)^{18}. We project economic change, energy demand, energy prices and regional energy production. Global energy demand is only weakly dependent upon the choice of IAM (Supplementary Note 10 and Supplementary Figs. 10–13).

The E3ME-FTT-GENIE integrated framework is described in Supplementary Note 1. The full set of equations underpinning the framework is given and explained in Mercure et al.^{13}. Assumptions for all scenarios are described in Supplementary Note 2.

### Energy supply

The allocation of oil and gas production, revenues and income is estimated by integrating data from the Rystad Ucube^{43} dataset in the form of break-even cost distributions at the asset level into E3ME-FTT-GENIE’s energy market model. The Rystad dataset documents 43,439 oil and gas existing and potential production sites worldwide covering most of the current global production and existing reserves and resources. It provides each site’s break-even oil and gas prices, reserves, resources and production rates. We use this information with the exception of Rystad’s projected rates of asset production and depletion^{44}. Instead, our projections are based on E3ME-FTT-GENIE’s energy market model, derived from a dynamic fossil-fuel resource-depletion model^{13} that does not rely on Rystad assumptions.

The energy market model assumes that each site has a likelihood of being in a producing mode that is functionally dependent on the difference between the prevailing marginal cost of production and its own breakeven cost. The marginal cost is determined by searching, iteratively with the whole of E3ME, for the value at which the supply matches the E3ME demand, which is itself dependent on energy carrier prices. Dynamic changes in marginal costs are interpreted as driving dynamic changes in energy commodity prices.

The Rystad dataset includes information about each asset’s location (country of production), the owners of the asset (among 3,113 fossil-fuel companies) and the country of the owners’ headquarters. For each asset, annual levels of oil and gas production, revenue and income are estimated per scenario and aggregated at country of production or firm headquarters country. We estimate stranded assets by comparing expected discounted profit streams under a realignment from a baseline to policy scenario at a high level of disaggregation (asset-level). Then, by aggregating the losses at the firm and country level, we can study the loss propagation from the asset level to the fossil-fuel companies, and from the country of production to the headquarters countries (see detail in section Asset-specific and aggregated stranding).

The regional production levels are based on production to reserve ratios, which are exogenous parameters representing producer decisions. Initial values are obtained from the data to reproduce current regional production according to the reserve and resources database. Future changes in production to reserve ratios for each region are determined according to chosen rules for the quota and sell-off scenarios. Changes are only imposed on production to reserve ratios of OPEC countries, to either achieve a production quota that is proportional to global output (quota scenario, thereby reducing production to reserve ratios accordingly), or to attempt to maintain constant absolute production while global demand is peaking and declining (sell-off scenario, thereby increasing production to reserve ratios). While oil and gas output in OPEC are thus altered by these parameter changes representing producer decisions, this change affects the allocation of production globally so as to match global demand.

Renewables are limited through resource costs by technical potentials determined in earlier work^{41}.

We supplement the Rystad assets with additional oil and gas resources data used in earlier versions of E3ME that are based on national geological surveys and tapped as Rystad reserves decline in the future. This hardly affects our 15 yr horizon but where such resources are tapped, the asset is split among companies active in the asset’s country in 2019 according to their 2019 share in national reserves. We apply the same method of ownership allocation to Open Acreage assets in Rystad.

### Company ownership

The company financial and ownership data are from Bureau van Dijk’s ORBIS database. They were downloaded in January 2020, typically reporting financial data from 2019 and, where not yet available, from 2018. It is neither feasible nor desirable to download the entire database: 300 million companies, with the download interface allowing about 100,000 companies per download (the exact number depends on the number of variables selected) and most companies small with missing financial and ownership data, and therefore separate from an ownership network. Instead, the download protocol relies on downloading first important (large) companies and then using a snowballing method to capture other companies that are reported as owners of these large companies but were not downloaded. In the first step, data for every company labelled ‘large’ or ‘very large’ were downloaded, as well as the 1,759 companies that were matched with Rystad oil and gas companies. Large and very large companies include all companies that have one of operating revenue >US$13 million, total assets >US$26 million, employees >149 or a stock market listing. Subsequently, via the snowballing method, all companies were downloaded that were listed as shareholders but were not yet downloaded. This iterative procedure was performed six times. Ultimately, the download resulted in 1,772,899 companies (including subsidiaries and their parents) connected by 3,196,429 equity ownership links, with a residual 12,876 unidentified owners. Most ownership links connect companies; however, per country there is one node for individuals and a handful of other summary nodes reflecting partially missing information (for example, unknown investors that are known to be pension funds), thereby summarizing a much larger number of nodes into one for every country. A concordance of types of companies, shareholders and types of financial firms with ORBIS indicators is provided in Supplementary Table 2. Further discussion of limitations of the data is provided in Supplementary Note 5.

Matching Rystad with ORBIS data was done manually due to widely varying spelling conventions. Many companies in Rystad were abbreviated, for example, NNPC, which is the Nigerian National Petroleum Corporation in ORBIS. In total, 1,759 Rystad companies could be matched unambiguously, accounting for 93.4% of the total discounted profit loss calculated in Rystad for the medium realignment.

Equity links occasionally summed to more than 100% of company ownership, most likely because the ORBIS dataset does not relate to a specific snapshot in time. When this happened, ownership fractions were scaled proportionately to sum to 100%. When ownership links summed to less than 100% ownership, the residual ownership would remain in the company as ultimate corporate shareholder (stage 3) and assigned on a country-by-country basis to an ‘unknown’ owner node in stage 4 or a ‘government’ node if the company is a state-owned company.

### Imputation of missing company data

Roughly 1.3 million of the 1.77 million companies in the network have some missing balance-sheet data. For the network analysis, for all companies we need to know the equity *E* to determine insolvencies and the total assets *A* to derive leverage. We estimate missing data from statistical models that are built from the 460,000 companies that have all data for equity *E*, total assets *A*, revenue *R*, number of employees *W* and size *S*.

Equity and total assets are the best predictors of each other (correlation of log-transformed variables, 0.90). Therefore, if only one of these data is missing for a company, we estimate it from the other. If neither is present, we use revenue *R* to estimate assets *A* (correlation of log-transformed variables, 0.71) and use the estimated *A* to estimate equity *E*. If none of these data are present, we estimate *A* (and then *E*) from the number of employees *W* (correlation of log-transformed variables, 0.45). Linear regressions of natural log-transformed variables are used for these estimates, that is

$$\ln \;v_1 = a + b\;\ln \;v_2$$

(1)

where *v*_{1} is the dependent variable, *v*_{2} is the predictor, and *a* and *b* are fitting constants. We apply these regressions stochastically to avoid artificially reducing the variance of the equity distribution, calculating the mean prediction from the regression relationship, and then adjusting the estimate by drawing randomly from the residual standard error. When applying the regressions, we enforce the inequality *A* ≥ *E*, by simply applying *E* = min(*A*,*E*). The regression coefficients and standard errors are tabulated in Supplementary Table 3.

All of these four data are missing for ∼340,000 companies, and for these we estimate total assets using the categorical variable size *S* (large, medium, small, very large). For these companies, we do not use regression, but instead draw *A* randomly from a normal distribution of the log-transformed data which depends upon size. Randomly drawn assets less than $100,000 are assigned a value of $100,000. We then estimate equity from the regression against *A* (Supplementary Table 4), again enforcing the inequality *A* ≥ *E* by applying *E* = min(*A*,*E*).

The imputation code is available at ref. ^{45}.

### Asset-specific and aggregated stranding

We define an asset, indexed by *k* in *1*,…, *K*, as the present value of a sequence of a share of profits from a particular oil or gas field, accruing to an oil or gas company that owns that share including via service- and revenue-sharing contracts^{46}. There are 43,439 unique oil and gas fields with non-zero reserves, and these are partitioned into *K* = 69,990 ownership shares and hence assets. Oil and gas fields have a production profile at each time *t* (measured in years) for scenarios *a*, *b*. Revenue at asset *k* at time *t* in scenario *a* is defined as the price of oil or gas, *p*_{t,a}, multiplied by the output, *q*_{k,t,a}, from the oil or gas field accruing to the owner of *k*. Profits are estimated in the same way, by subtracting asset-level costs, *c*_{k}(*q*_{k,t,a}), which are a function of the quantity produced, from revenue. Thus, we calculate the net present value (NPV) of asset-level profit losses, which we call asset stranding, *A*_{k} (a positive number is a profit loss and so stranding is positive), that occurs by an expectations realignment, from baseline, *a*, to policy scenario, *b*, as

$$A_{k,a,b} = \mathop {\sum }\limits_{t = t_0}^{t_0 + T} \left[ {\left( {p_{t,a}q_{k,t,a} – c_k(q_{k,t,a})} \right) – \left( {p_{t,b}q_{k,t,b} – c_k(q_{k,t,b})} \right)} \right]\left( \frac{1}{1 + r} \right)^{t – t_0}$$

(2)

where *r* is the discount rate, which we set to 6%, *t*_{0} = 2022 is the time of change of expectations and *T* = 14 years the horizon over which we assume companies to include future expected profits in their balance sheet.

These stranded assets are then aggregated. Thus, we calculate the NPV of asset losses, *σ*, from expectations realignment for some group, *G*, of assets, from baseline *a* to policy scenario *b* as

$${\upsigma}_{G,a,b} = \mathop {\sum}\limits_{k \in {{{\mathrm{G}}}}} {{{{\mathrm{A}}}}_{k,a,b}}$$

(3)

where *G* can be defined by company ownership and/or geography, up to *G* = {1,…, *K*} for global asset stranding. To arrive at the loss distribution in stage 1, we partition the set of stranded assets according to their geographic location. To move to further stages, we first partition stranded assets according to their fossil-fuel company ownership. In particular, if the *i*th fossil-fuel company owns the set of assets *C*_{i}, we define the stranded assets of company *i* as

$${\upsigma}_{i,a,b} = \mathop {\sum}\limits_{k \in C_i} {A_{k,a,b}}$$

(4)

This distribution of stranded assets across fossil-fuel companies serves as the input for the propagation of ownership risk in our network model.

### Network propagation

Stranded assets reduce the value of some assets to zero. When these assets are owned by another entity, the loss propagates to them. We call this propagation a ‘shock’. We have built a network model to propagate the stranded asset shock through to ultimate owners. Our study is focused explicitly on the ownership of fossil-fuel assets and so we consider only the direct effects on equity, neglecting distress to the debt network and the potential for fire sales^{47}.

We have a network comprising *N* = 1,772,899 companies connected by 3,196,429 equity ownership links. Each link connects an owned company *i* with one of its owners *j*, and is defined by the fraction of equity *f*_{ij} of company *i* owned by company *j*. The initial shocks from equation (4), which are \(s_i^0 = \sigma _{i,a,b}\) for *i* = 1,…, *N*, are distributed across the 1,759 fossil-fuel companies within the network (yielding the loss distribution at stage 2 and propagated through the ownership tree, to get to stage 3).

At each iteration *l* we work through the owners and their respective ownership links in turn and transmit any shock *s*_{i} in owned company *i* to its owners, determined by either *f*_{ij}, the fractional holding of company *i* by company *j* or \(f_{ij}^m\), the fraction of company *i* owned by the managed funds of company *j*. Thus the iteration step for owner *j* can be expressed as

$$s_j^{l + 1} = s_j^l + \mathop {\sum }\limits_i f_{ij}\left( {s_i^l – s_i^{l – 1}} \right)\;{{{\mathrm{for}}}}\;{{{\mathrm{all}}}}\;{{j}}$$

(5)

$$m_j^{l + 1} = m_j^l + \mathop {\sum }\limits_i f_{ij}^m\left( {s_i^l – s_i^{l – 1}} \right)\;{{{\mathrm{for}}}}\;{{{\mathrm{all}}}}\;{{j}}$$

(6)

where *m*_{j} is the shock to managed funds, which are not propagated further. Note that \(s_j^l\) is the total shock experienced at company *j* accumulated up to iteration *l* but only the shock increase at the previous iteration is propagated onwards along the ownership chain at each iteration.

We apply these shocks to a company’s balance sheet. We reduce the asset side by the amount of the shock, and to keep the sheet balanced, we reduce the liability side by subtracting an equal amount of equity. If the shock *s*_{j} felt by any company exceeds its equity, that company is considered technically insolvent, and any excess shock is not transmitted to the owners of the company. The excess shocks are accumulated to totals for the country and sector of the technically insolvent company (or as a domestic creditor liability in stage 4). Fund managers’ balance sheets are not affected by a shock to their managed funds. We continue looping until convergence, defined to be when the total transmitted shock during an iteration, \(\mathop {\sum }\limits_j \left( {s_j^l – s_j^{l – 1}} \right)\), is less than US$100,000. At convergence, we discontinue the propagation algorithm, and then sum the shocks in all companies to derive the aggregated shock at stage 3.

To derive the accounting summary (which integrates shocks and allocates them by country and sector at stages 3 and 4), we conservatively assume that the complete chain of ownership is consolidated into the ultimate corporate owner, so that no shock is ever counted twice, that is, it is not counted for companies in intermediate steps of the ownership chain. To do so we weight the shock in each company by the fraction of its equity that is not owned by another company in the network. For example, if company A is 30% owned by no other company (either because of lack of ownership data or because it is owned by ultimate owners such as individuals), 30% of the shock to that company will be recorded in the company itself as the ultimate corporate owner, while 70% of the shock will be recorded in the ownership chain. The globally integrated weighted shock is thus calculated as

$$S = \mathop {\sum }\limits_{i = 1}^{N} \left( {1 – F_i} \right)s_i + m_i$$

(7)

where \(F_i = \mathop {\sum }\limits_{j = 1}^{N} f_{ij}\) is the fraction of each company that is owned by other companies in the network, noting that this definition means *S* is identically equal to the input shock \(\mathop {\sum }\limits_{i = 1}^{N} \sigma _i^0\). By summing over subsets of companies, we arrive at the loss distribution at stage 3.

Finally, to allocate losses from ultimate corporate to ultimate owners (Stage 4) we pass on the shock in ultimate corporate owners to governments, shareholders (both via equity and fund ownership), creditors where losses exceed equity on balance sheets, and, where no ultimate owner is given for equity losses, to an ‘unknown’ ultimate owner.

The following should be noted with respect to the data. First, in the raw downloaded network data there were ∼100 ownership loops of two or more companies through which companies own each other (most simply when company A owns company B which owns company A). These are unrealistic data errors which may, for instance, arise from the fact that ORBIS data do not relate to a precise snapshot in time. We searched for these ‘bad links’ by applying a uniform shock to every node in the network and iterating forwards. Ownership loops do not converge but instead amplify a shock to infinity. Using this approach, we identified 391 connections within circular loops, and we bypass these connections during the shock propagation. All other loops converge according to a geometric series with a common ratio below 1.

Second, two alternative sets of imputed data were tested to check the robustness of our results with respect to uncertainty about company equity size driven by stochastic imputation of missing data (see above). The only effect of the size of a company’s equity in the propagation algorithm is to determine whether or not a company is shocked hard enough to make it technically insolvent (at which point the shock stops propagating and is accounted for as a shock to unknown creditors rather than to the company’s owners, see also Supplementary Note 4). The shocks to unknown creditors in the default network agreed to within 5% between two alternative imputed networks (US$402 billion and US$417 billion). These two imputed datasets generated 1,479 and 1,448 insolvencies, respectively, and 1,303 of the insolvent companies were common to both analyses. These comparisons suggest that imputation uncertainties are modest at the highly aggregated level of results we provide, although clearly caution is demanded when interpreting outputs at the company level. Each company is associated with a flag that identifies whether its data have been imputed to aid such interpretation.

Third, to discuss how stock-market-listed companies and financial companies are affected in the main text section ‘Risk of loss amplification in financial markets’, we make one modification to the assumption of complete consolidation of the ownership chain into the ultimate parent company. Specifically, in Fig. 4, we do not integrate weighted shocks (equation (7)), but instead integrate them as the unweighted sum \(\mathop {\sum }\limits_{i = 1}^{N} s_i\). Since stock market indices record listed companies, regardless of where they are located in our order of propagation, this method allows us to calculate the impact of our realignments on the stock market. Similarly, since potentially all financial companies in an ownership chain are affected by the loss, this provides an upper bound to the effect on the financial system. Since some financial companies in the ownership chain may be subsidiaries of others, however, without an independent balance sheet, this complete disaggregation of companies can be seen as an upper bound of the effect on the financial system, while the complete aggregation into an ultimate corporate owner can be seen a lower bound.

The network code is available at ref. ^{45}.