Aggregate Financial Stability Index

• AFSI is a composite macro-financial indicator that aggregates diverse sectoral sub-indices and latent risk measures to quantify system-level stability.
• It integrates data from real, fiscal, financial, and external sectors using both equal and weighted approaches to balance methodological trade-offs.
• AFSI serves as a policy-facing tool by offering descriptive surveillance and early-warning signals to inform systemic risk management.

Aggregate Financial Stability Index (AFSI) denotes a synthetic, system-level measure intended to summarize the stability, resilience, or fragility of a financial system across multiple sectors, markets, or transmission channels. In its most explicit form, it is a composite macro-financial indicator built from sectoral sub-indices; in related literatures, closely aligned constructs appear as aggregate financial stress indices, systemic vulnerability measures, network fragility indicators, and modular sub-indices designed to enter a broader stability dashboard (Ahamed et al., 27 Jul 2025, Varga et al., 2024). This suggests that AFSI is best understood as a family of aggregation frameworks rather than a single canonical formula.

1. Conceptual domain and relation to adjacent measures

AFSI sits at the intersection of several partially overlapping concepts. One strand defines financial stress as the realised level of risk in the financial system, with classic manifestations including flight to quality, flight to liquidity, rising uncertainty, and greater information asymmetry (Varga et al., 2024). Another strand defines systemic risk as the risk of widespread financial instability that impairs financial-system functioning with severe macroeconomic consequences, and operationalizes it through vulnerabilities of interconnected segments rather than through a single observed market variable (Mezei et al., 2014). A third strand defines global stability inversely, through a vulnerability index such as

$$\xi\left(\mathcal{K},G,\gamma,\Phi,\Upsilon\right),$$

where lower values imply higher global stability under a specified contagion scenario (DasGupta et al., 2012).

These formulations are not identical. Some indices measure stability directly, some measure stress, and some measure fragility or vulnerability and then infer stability as an inverse or complement. The expert-aggregation framework based on a Fuzzy Cognitive Map (FCM), for example, yields an overall systemic risk score that can be transformed into a stability score by inversion, such as $1-SR$ when the risk score is normalized to $[0,1]$ (Mezei et al., 2014). In practice, AFSI is therefore not a uniquely signed object; its interpretation depends on whether the underlying construction is stability-oriented or risk-oriented.

The literature also differs on scope. The Bangladesh paper defines AFSI as a comprehensive indicator of the stability and resilience of the financial system built from macro-financial sectors (Ahamed et al., 27 Jul 2025). The UK non-stationary factor model is narrower in observable inputs—mainly market-based daily indicators—but broader in dynamics because it is designed to capture persistent latent stress states and vulnerability buildup (Varga et al., 2024). This suggests that AFSI can be either a broad composite across institutional domains or a latent state extracted from a narrower but high-frequency information set.

2. Composite sectoral construction

The most explicit AFSI in the supplied literature is the Bangladesh framework, which covers 2016–2024 and uses 19 indicators across four sectors: Real Sector (RS), Financial and Monetary Sector (MS), Fiscal Sector (FS), and External Sector (ES) (Ahamed et al., 27 Jul 2025).

Sector	Count	Indicators
Real Sector	5	GDP Growth Rate, Agricultural Production, Quantum Index of Industrial Production, Inflation, Domestic Credit to GDP Ratio
Financial and Monetary Sector	6	Domestic Credit Growth, Performing Loan Ratio, Capital to Risk-Weighted Assets Ratio, Return on Assets, Capital Market Return, Call Money Rate
Fiscal Sector	3	Fiscal Balance to GDP, Government Debt to GDP, Tax Revenue to GDP
External Sector	5	External Debt to GDP, Reserve to External Debt Ratio, Current Account Balance to GDP, Real Effective Exchange Rate, Net International Investment Position as % of GDP

The construction begins by converting the raw figures into percentage form and then normalizing each indicator using the standardized-score transformation

$\frac{x-\bar{x}}{\sigma}.$

Sectoral sub-indices are then formed from the standardized indicators belonging to each sector, and the aggregate AFSI is reported as

$$AFSI_t = 0.15\,RS_t + 0.15\,FS_t + 0.30\,ES_t + 0.40\,MS_t.$$

The paper also states that the weight of each indicator is equal, giving the example $1/19$, while simultaneously reporting the sector-weighted aggregate formula above (Ahamed et al., 27 Jul 2025).

That dual statement is methodologically important. Factually, the paper uses a normalized-score approach, sectoral sub-indices, and a fixed aggregate weighting rule. At the same time, it presents an internal tension between “equal weighting” at the indicator level and the reported sector weights. The paper further uses directional markers $W_a$ and $W_d$ to distinguish variables whose increases are favorable versus unfavorable for stability, although the notation is not fully explained in the text (Ahamed et al., 27 Jul 2025).

Substantively, this architecture makes AFSI a transparent, policy-facing composite. Its content is broad rather than purely financial-market-based: loan quality, capital adequacy, inflation, fiscal balance, reserves, external debt, and capital-market performance all enter the same aggregate score. This type of design is the clearest example of AFSI as a macro-financial dashboard compressed into a single number.

3. Latent-factor and expert-aggregation approaches

A second architecture treats AFSI not as a hand-built weighted average but as a latent state extracted from many indicators. The UK framework starts from the dynamic factor representation

$X_t = L f_t + \varepsilon_t,$

with factor dynamics

$\Phi(B) f_t = d + \Theta(B) u_t,$

and allows some common factors to be non-stationary, with roots on or outside the unit circle (Varga et al., 2024). In this formulation, non-stationary factors capture the persistent “location” of stress in the system, while stationary factors capture common fluctuations or volatility. The paper’s empirical result is that the extracted statistical factors are smoother and more persistent than market-specific factors, and that all five selected statistical factors are non-stationary in the UK application (Varga et al., 2024).

Methodologically, this matters because many financial-stability applications want persistence to be treated as signal rather than nuisance. The UK paper explicitly argues that forcing stationarity can remove low-frequency information and leave a factor that mainly reflects common volatility rather than slow-moving vulnerability buildup (Varga et al., 2024). In AFSI terms, this is a direct argument for latent indices with persistent components when the objective is macroprudential surveillance.

A third architecture uses expert knowledge and network-aware aggregation. The systemic-risk aggregation paper decomposes the system hierarchically into interconnected segments, models the system as an FCM, and aggregates node vulnerabilities with the Choquet integral rather than a simple weighted average (Mezei et al., 2014). The discrete Choquet integral is written as

$1-SR$0

and, in the 2-additive form used for systemic-risk interaction,

$1-SR$1

The point of this construction is that the aggregate should reflect not only the level of vulnerabilities but also their interrelations (Mezei et al., 2014).

These two architectures—latent non-stationary factors and expert-weighted nonlinear aggregation—address different weaknesses of simple composites. The factor approach handles persistence and co-movement statistically; the FCM/Choquet approach handles tacit supervisory knowledge and interaction explicitly. A plausible implication is that AFSI methodology divides naturally into data-driven latent extraction and structure-aware aggregation rather than a single universal recipe.

4. Network, concentration, and contagion modules

Several papers contribute operational modules that can enter an AFSI even when they do not themselves produce a complete index.

One such module is the Concentration Risk Indicator (CRI),

$1-SR$2

a volatility-weighted, inverse-market-share-weighted concentration measure based on squared portfolio weights (Kashyap, 2024). The paper explicitly states that the CRI can become an indicator of financial stability at regional, national, or international aggregation levels and is best understood as a concentration-risk module for a broader AFSI rather than as a full stability architecture (Kashyap, 2024).

A second module comes from cross-border portfolio investment networks. The paper on global portfolio networks uses the algebraic connectivity of the equity securities network, $1-SR$3, as a measure of structural robustness, and the edge density of the long-term debt securities network at the percolation threshold, $1-SR$4, as a measure of interdependence. The debt-network threshold is reported as

$1-SR$5

and the edge density is

$1-SR$6

The main claim is that low $1-SR$7 indicates fragility because the network becomes easier to fragment, while rising $1-SR$8 is associated with derivative proliferation and potentially dangerous levels of market interdependence (Joseph et al., 2013).

A related network-centric literature generalizes this idea from a small number of network statistics to a large candidate set: mean correlation, eigen-entropy, edge count, edge density, average weighted degree, clustering, modularity, communication efficiency, clique number, and edge-based curvature measures such as Ollivier-Ricci, Forman-Ricci, Menger-Ricci, and Haantjes-Ricci (Samal et al., 2021). In the reported crisis signatures, fragile periods are characterized by more connected, less modular, more homogeneous networks, shorter paths, larger cliques, higher OR/MR/HR curvature, and lower FR curvature (Samal et al., 2021). This provides a broad menu of structural fragility components for an AFSI.

A simpler co-movement version of the same logic uses rolling cross-correlations and principal components. The paper on contagion across financial sectors treats rising pairwise cross-correlation and rising dominance of the first principal component as direct indicators of falling aggregate stability. In its four-sector PCA, the first fractional eigenvalue $1-SR$9 is around $[0,1]$0 to $[0,1]$1 before crisis and rises above $[0,1]$2, even above $[0,1]$3, during the crisis window (Choudhari et al., 2021). This gives a low-data co-movement module suitable for a market-based AFSI.

Two further contagion modules extend beyond financial-market topology. The supply-chain paper defines a firm-level Financial Systemic Risk Index,

$[0,1]$4

which measures the share of total banking equity put at risk by failure of firm $[0,1]$5 after accounting for supply-chain contagion (Tabachová et al., 2023). The interbank-credit paper, by contrast, does not define a single scalar index, but it makes reserve mismatch, interbank borrowing dependence, and central bank assistance central to systemic stability through variables such as reserve need

$[0,1]$6

and central bank support $[0,1]$7 (Biondi et al., 2017). In both cases, the implication is that an AFSI can be expanded by adding real-economy contagion and liquidity-coordination modules that standard market-stress indices omit.

5. Tail, narrative, and high-frequency extensions

An AFSI can also be extended in the tail-risk, text, and high-frequency directions.

The block-tail fragility paper defines the fragility index of a partitioned system as

$[0,1]$8

where $[0,1]$9 counts the number of blocks containing at least one exceedance above threshold $\frac{x-\bar{x}}{\sigma}.$0 (Ferreira et al., 2011). Under multivariate extreme-value assumptions, the paper derives

$\frac{x-\bar{x}}{\sigma}.$1

Higher values imply that, conditional on at least one block being hit by a tail event, more blocks are likely to be hit as well (Ferreira et al., 2011). This is directly useful when an AFSI is intended to monitor cross-sector or cross-region crisis breadth rather than ordinary co-movement.

The text-analysis paper adds a forward-looking narrative pillar through Relative Sentiment Shift (RSS),

$\frac{x-\bar{x}}{\sigma}.$2

built from Reuters text using Directed Algorithmic Text Analysis (Ormerod et al., 2015). The paper’s central AFSI-relevant claim is that RSS improves one-quarter-ahead U.S. GDP forecasts and Granger-causes both the Cleveland and St. Louis financial stress indices, which makes it a plausible leading component for a broader stability-monitoring framework (Ormerod et al., 2015).

A more purely market-based high-frequency alternative is the information-theoretic $\frac{x-\bar{x}}{\sigma}.$3 index,

$\frac{x-\bar{x}}{\sigma}.$4

computed from weighted visibility graphs of return series (Gonçalves et al., 2017). The paper treats sustained values of $\frac{x-\bar{x}}{\sigma}.$5 as a warning that a crisis may be underway, and interprets a rapid return toward $\frac{x-\bar{x}}{\sigma}.$6 as resilience (Gonçalves et al., 2017). This is not a full AFSI, but it is a compact high-frequency instability component.

Taken together, these approaches indicate that AFSI need not be confined to balance-sheet, macro, or market-level composites. It can also incorporate tail clustering, narrative sentiment, and graph-based turbulence as distinct but complementary dimensions.

6. Empirical applications and interpretive use

Empirically, the Bangladesh AFSI reports that overall financial stability deteriorated in FY2024, despite modest improvements in the real and fiscal sectors, because the Financial and Monetary Sector Index deteriorated sharply and the External Sector Index remained weak. The main cited stress points are rising non-performing loans, declining CRAR, declining ROA, negative capital-market returns, a spike in the call money rate, shrinking foreign-exchange reserves, rising external debt, and a worsening current account position (Ahamed et al., 27 Jul 2025). This is the clearest example of AFSI used as a policy-facing macro-financial scorecard.

The UK non-stationary factor model validates an aggregate stress/vulnerability measure in a different way. It finds 5 factors with cumulative explained variance 0.920, reports that all five statistical factors are non-stationary, and shows that the 5-factor model performs best among factor models at 3- and 6-month horizons in forecasting downside GDP risk, while the 1-factor model is marginally better at 1 month and SovCISS performs better at 12 months (Varga et al., 2024). The empirical lesson is that AFSI-like measures can be evaluated by macroprudential usefulness, not only by visual crisis dating.

The cross-border network paper provides a structural early-warning application. The algebraic connectivity of the E-PIN drops sharply in 2005 and reaches an all-time low in 2007, before the global financial crisis, while the LD-PIN edge density tracks and partly leads several OTC derivative series, most notably CDS with a 6-month lead in the preferred specification (Joseph et al., 2013). This supports the use of network topology as an early-warning layer in an AFSI.

The supply-chain contagion paper validates a different dimension: losses transmitted from the real economy into bank capital. It finds that supply-chain contagion amplifies bank-level EL, VaR, and ES by factors of 4.3, 4.5, and 3.2, respectively, and amplifies the corresponding system-wide measures by 4.9, 9.7, and 7.8 (Tabachová et al., 2023). This is strong evidence that an AFSI restricted to direct financial exposures can materially understate systemic risk.

The text-analysis paper provides predictive validation from a narrative channel. RSS raises adjusted $\frac{x-\bar{x}}{\sigma}.$7 in one-quarter-ahead GDP forecasting from 0.159 to 0.219, and Granger-causes both CFSI and STLFSI, with the strongest result for STLFSI at $\frac{x-\bar{x}}{\sigma}.$8 (Ormerod et al., 2015). The concentration-risk paper, finally, shows that diversified crypto portfolios can beat BTC in terms of risk, return, and CRI, illustrating how a concentration-vulnerability module can complement traditional risk-return reporting (Kashyap, 2024).

These applications show that AFSI-style constructs are used in at least three ways: as descriptive surveillance tools, as early-warning devices, and as stress-propagation diagnostics.

7. Limitations, ambiguities, and unresolved design questions

The literature does not support a single settled AFSI design. The Bangladesh framework provides an explicit aggregate index, but it contains a methodological inconsistency between the claim of equal weighting across indicators and the reported sector weights $\frac{x-\bar{x}}{\sigma}.$9 (Ahamed et al., 27 Jul 2025). The UK factor paper finds that aggregation after extraction matters substantially and explicitly notes that simple arithmetic averaging of factors degraded performance (Varga et al., 2024). The implication is that weighting and post-extraction aggregation remain open design problems.

Threshold calibration is also incomplete. The CRI paper does not propose formal CRI threshold bands or supervisory cutoffs (Kashyap, 2024). The Bangladesh paper provides no red-amber-green interpretation regime for AFSI levels (Ahamed et al., 27 Jul 2025). The expert-aggregation framework provides a coherent aggregation operator, but cross-country comparability depends on scale anchoring, elicitation discipline, and confidence weighting of expert inputs (Mezei et al., 2014). Network-contagion approaches, meanwhile, are scenario-conditioned and can depend heavily on modeling assumptions, exposure data quality, and the choice of shock mechanism (DasGupta et al., 2012, Tabachová et al., 2023).

Coverage is another persistent issue. Market-based and network-based measures are often high-frequency and informative, but they are not full structural dashboards. The UK factor index is built mainly from market indicators, not from banking balance sheets, credit growth, housing, or leverage (Varga et al., 2024). CRI captures concentration risk, not leverage, liquidity, solvency, or contagion (Kashyap, 2024). Supply-chain contagion models add a major omitted channel, but still simplify or omit interbank contagion, fire sales, sovereign-bank feedback, and policy response (Tabachová et al., 2023). Some individual indicators also have context-dependent signs: the DRC framework treats private credit to GDP mainly as a financial-depth proxy but also recognizes that excessive credit growth can signal instability risk (Pinshi, 2017).

A plausible implication is that serious AFSI deployment requires three layers of discipline beyond indicator selection itself: explicit sign conventions, empirical calibration of thresholds and reference ranges, and a modular architecture that separates resilience, stress, interdependence, tail fragility, and contagion channels instead of forcing them into a single undifferentiated number.