Analysis of Bank Equity Prices
The equity prices of the Nordic financial groups, category A, have been rising in recent years, while equity-price volatility has been declining. This can be interpreted as market expectations of a diminished risk of solvency problems for the groups. Historical data show, however, that market-based risk measures (e.g. distance to insolvency) can change significantly in a short space of time.
The equity prices of the Nordic groups exhibit relatively high mutual correlation, which may be due to exposure to common factors. Thus shocks affecting one group would probably affect other groups as well.
EQUITY-PRICE DEVELOPMENT
The positive equity-price development in the Nordic groups, category A, since early 2003, cf. Chart 42 and the chapter on the financial markets, may reflect market expectations of higher returns and lower risks facing the groups. The overall earnings of the groups actually rose to a very high level in 2004, cf. the chapter on the financial sector.
| EQUITY PRICES FOR THE NORDIC GROUPS, 1999-2004 |
Chart 42
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| Source: Bloomberg. | |
In this chapter, equity-price data are used to estimate two equity market-based risk measures for banks (distance to insolvency and economic capital) and to analyse the comovement between the banks' equity prices and possible exposure to common factors.
DISTANCE TO INSOLVENCY – NEW VERSION
Financial Stability 2004 introduced "distance to insolvency" – a market-based risk measure specifically tailored to banks, which are subject to statutory capital-adequacy requirements. Distance to insolvency is compiled on the basis of accounting and equity-price data in an option price model, cf. Box 11. The distance to insolvency illustrates the market's assessment of the probability that the bank will be able to comply with the statutory capital-adequacy requirement. The distance to insolvency measures the changes (in number of standard deviations) in the market value of the assets that can be accommodated within the bank's buffer.
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Box 11
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Distance to insolvency was defined in Financial Stability 2004 as "the number of standard deviations on the assets' market value which the bank's buffer can absorb". The current market value and volatility of the assets are not known, but are estimated on the basis of accounting and equity-price data in an option price model in which the share capital is seen as a call option on the company's assets less liabilities. The resulting estimates of the market value and volatility of a company's assets may be compared with a critical value that would cause problems for the company, cf. the Chart. A frequently used risk measure for non-financial companies is distance-to-default, which measures the difference between the estimated market value of the assets and the interest-bearing liabilities (the critical value), scaled by the standard deviation of the assets' market value (in the Chart the relationship between |AC| and the standard deviation). The distance to default may (with an assumed probability distribution of the fluctuations of the assets' market value) be expressed as an estimated probability of default (P|0C| in the Chart). Unlike non-financial companies, banks are under an obligation to meet statutory capital requirements, which are therefore included with the liabilities in the critical value for distance to insolvency (|AB| in the Chart). The distance to insolvency or the market's assessment of the excess capital relative to the capital requirement may (subject to the same reservation) also be expressed as an estimated probability of solvency or capital-adequacy problems (P|0B| in the Chart). |
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| DIFFERENCE BETWEEN DISTANCE TO INSOLVENCY AND DISTANCE TO DEFAULT | |
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In order to better utilise information in the equity market on investor expectations of the future, the distance-to-insolvency model has been modified in several respects relative to Financial Stability 2004 as follows:
- Accounting data are interpolated between the quarterly accounting dates to compile weekly estimates of debt, capital requirements and the market value of assets.
- Equity-price volatility is measured using a more sensitive GARCH model[1], which better captures the changing nature of volatility. Financial Stability 2004 used the 50-week standard deviation of changes in equity prices, which was a more backward-looking measure.
The result is weekly estimates of the distance to insolvency, cf. Chart 43. The distance to insolvency has increased significantly for the Nordic groups in category A since the autumn of 2002 as a result of higher equity prices, decreasing volatility and enhanced profits. The weekly distance-to-insolvency figures also show, however, that the market assessment of the banks' situation may change rapidly, as was the case in September 2001 and in the autumn of 2002.
| DISTANCE TO INSOLVENCY FOR THE NORDIC GROUPS, 2000-04 |
Chart 43
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Distance to insolvency may be seen as a value-at-risk measure, with a distance to insolvency of 3 corresponding to a market assessment of a mere 0.13 per cent probability that losses will exceed the buffer.
EQUITY-MARKET ASSESSMENT OF ECONOMIC CAPITAL
The distance-to-insolvency model can be used to estimate the equity market's assessment of the individual bank's need for economic capital. It should be underlined that the measurement of economic capital in itself is subject to considerable uncertainty. What is calculated here is the capital that a bank needs to be able – with a probability of 99.9 per cent – to absorb fluctuations in the market's assessment of the value of the assets within the capital. This corresponds to a distance to default of about three standard deviations (assuming that changes to the market value of assets follow a normal distribution).
These estimates of the equity market's assessment of the Nordic groups' need for economic capital can be expressed as a ratio of the risk-weighted assets and compared with the actual solvency ratios of the banks, cf. Chart 44.
| SOLVENCY RATIO AND ESTIMATED NEED FOR ECONOMIC CAPITAL, 2004 |
Chart 44
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| Note: The need for economic capital is an estimate of the market's assessment of the need for economic capital as a ratio of risk-weighted assets. The rating is specified in the order: Moodys/Standard&Poor's/Fitch. | |
| Source: Own calculations. | |
For several of the banks, the estimated need for economic capital has been lower than the supervisory requirement of 8 per cent and lower than the groups' actual solvency ratios. The model calculations suggest that, in the market's assessment, several of the banks have scope to reduce their capital adequacy. However, this result reflects to a large degree the general equity-market development, and Charts 43 and 44 show that market-based risk measures can change sharply and quickly, and that they are sensitive to the assumptions made. This points to the need for caution against balancing too close to the capital requirement.
COMOVEMENT IN EQUITY PRICES
In Financial Stability, the Nordic groups in category A are used as the benchmark peer group for the two largest banks in Denmark, Danske Bank and Nordea Danmark. The relevance thereof depends on whether the earnings and risk profiles of the Nordic groups have more in common with each other than with other possible peer groups, e.g. other domestic banks, other non-Nordic internationally active banks or Nordic insurance companies. The extent to which the financial condition of the banks is driven by common factors may be clarified by analysing key financial indicators. An alternative approach, used e.g. in the Bank of England Financial Stability Review[2], is to analyse the comovement of asset prices, for indications of market expectations of the impact of common factors.
Below, weekly equity-price changes[3] (measured in euro) are assessed for the following categories:
- the six Nordic financial groups in category A, with Kaupthing Bank (which has acquired FIH[4]) as a possible addition,
- the six largest (by market capitalisation) banks in category B,
- the six largest euro-area banks,
- the five largest Nordic insurance companies,
- the broadest equity-market indices for Denmark, Sweden, Norway and the euro area (as indicators for common macro factors for each currency area).
Correlation analysis of equity-price changes
The correlation matrix for equity-price changes is shown in Table 10 in a colour-coded "heatmap", i.e. the higher the correlation between the changes in two companies' equity prices, the darker the colour. The correlations are shown for two time periods: 1999-2004 in the upper right-hand side (north-east) and 2003-04 in the lower left-hand side (south-west) of the matrix.
| CORRELATION MATRIX FOR WEEKLY EQUITY-PRICE FLUCTUATIONS FOR 1999-2004 AND FOR 2003-04 |
Table 10
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Among the Nordic groups, there is a particularly high correlation between the four Swedish groups. Danske Bank and Norwegian DnB NOR's correlations with the rest of the category are somewhat lower, but Danske Bank's correlations were higher in 2003-04 than in the period 1999-2004 as a whole. The last two years have also seen higher correlations than previously between the Nordic groups and the major euro-area banks. During both periods, Kaupthing had a very low correlation with the other Nordic groups.
The six banks in category B had low correlations both with one another and with other possible comparators. Whether this is attributable to technical factors (e.g. less liquid share prices) or whether these banks are not driven by the same factors as the Nordic groups, the correlation analysis provides no reason for changing the breakdown between categories A and B.
The major euro area banks exhibit more noticeable correlation with one another than the Nordic financial groups even though cross-border banking activities between their home countries have been less prevalent than between the Nordic countries. The high correlations may reflect exposures to other common factors, e.g. global financial-market factors, domestic economies with a common currency, interest rates (and increasingly) interest margins as well as credit risk on loans to large companies that are easier to trade and diversify.
Among the Nordic insurance companies, Skandia, which has ventured into bancassurance, has the most noticeable correlations with others. There are no indications to suggest that the Danish insurance companies are particularly exposed to any common factors that might be driving the banks in categories A and B.
The correlations with the broad equity-market indices[5] may be interpreted as macroeconomic sensitivity and are generally seen as high – and highest for the euro area banks and a few of the Swedish banks.
The comovement of equity prices may change over time, reflecting whether exposure to common factors has increased or decreased. The correlations between the Nordic groups are of particular interest to financial stability in Denmark. Chart 45 shows the average correlations for each year between 1999 and 2004 for weekly equity-price changes between all groups in category A, between the Swedish groups in cate-gory A, and between Danske Bank and each of the other groups in category A.
| AVERAGE CORRELATIONS BETWEEN EQUITY-PRICE CHANGES, 1999-2004 |
Chart 45
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| Note: Average correlations between weekly equity-price changes for all groups in category A, between the Swedish groups, and for Danske Bank vis-à-vis the other groups in category A. | |
| Source: Bloomberg and own calculations. | |
The high correlation between the Swedish groups has been evident for each of the last four years, while Danske Bank's correlation with the rest of the groups in category A has varied from year to year. The analyses below focus on data covering the period 2003-04.
Cluster analysis of equity-price changes
Cluster analysis, described in Box 12, attempts to determine the natural grouping of data for equity-price changes by, without any predetermined structure, "letting data do the talking". Chart 46 shows the clustering process as a dendrogram, in which the horizontal axis represents the distance between the groups at each clustering point.
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Box 12
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Cluster analysis attempts to identify quantitatively a natural grouping of data. The agglomerative hierarchical cluster process applied here (there are other types of cluster analysis) starts by considering the 25 financial companies as 25 separate groups, each containing one company. The difference2 between the weekly equity-price changes of each group is calculated and the closest pair are clustered into one new group. This process is repeated until all companies are clustered together into one group comprising 25 companies. The clustering process and the Euclidian distance for each clustering step can be illustrated graphically in a dendrogram, cf. Chart 46. The largest number of groups that are statistically significant3 can be seen as natural groupings. A minimum spanning tree is an open-chain graph in which N variables (in this case banks) are linked to N-1 (i.e. the minimum number of) relations. The connections are selected from a ranked list of all bivariate correlations. The process selects the connections with the highest correlations but deselects those connections that would "close" the chain by connecting variables that are already linked indirectly. For a given correlation matrix (of N specified variables for a given time period), the resulting minimum spanning tree thus provides a unique network of the most relevant correlation connections for each variable. |
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| 1 For a more in-depth description, see Hawkesby, Marsh and Stevens, Comovements in the prices of securities issued by large complex financial institutions, Bank of England, working paper no. 256, 2005. 2 Intuitively, the difference can be seen as a decreasing function of the correlation coefficient. Formally, it is the Euclidian distance between two points. In the cluster analysis, the points (each group) are defined by vectors with N variables (in this case; each weekly equity-price fluctuation) between which the Euclidian distance is measured in an N-dimensional space. 3 T test for the statistical significance of fusion values at a level of 5 per cent. |
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| CLUSTER ANALYSIS DENDROGRAM FOR EQUITY-PRICE CHANGES, 2003-04 |
Chart 46
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| Note: Cluster analysis based on squared Euclidean distance between untransformed weekly percentage changes in equity prices measured in euro. | |
The cluster analysis based on equity-price changes results in the following (mathematically) natural groupings:
- the Danish and Swedish groups in category A (shown in blue),
- the Norwegian institutions (DnB NOR and Store Brand) (yellow),
- the major internationally active banks in the euro area (red),
- the Danish insurance companies (green),
- the major Danish banks in category B (brown),
- the two remaining companies (Kaupthing and Skandia) remain independent clusters.
Had the optimum number of groups been smaller, the next cluster would have been between the Norwegian institutions and the natural grouping of Danish and Swedish groups in category A. Kaupthing, on the other hand, does not seem to belong in the natural grouping of category A groups, in line with Kaupthing's low correlation with these groups in Table 10.
The cluster analysis results shown in Chart 46 will to some extent reflect correlations with common factors, i.e. the high correlations with equity-market indices in Table 10. Adjusted for the portion of equity-price fluctuations that can be explained by the broad equity-market indices[6], the cluster analysis shows a slightly different result, i.e. that the gap between the Nordic groups and most of the euro area banks narrows, while the separation between the groups in category A and the banks in category B remains.
Minimum spanning trees
The "heatmap" correlation matrix in Table 10 emphasised equity-price correlations above certain absolute threshold values. A minimum spanning distils the correlation matrix of equity-price changes into one unique connected network with the lowest possible number of connections with the highest possible correlation coefficients. The method is described in more detail in Box 12, and the results are illustrated in Chart 47. The analytical categories of the banks are colour-coded and the line thickness indicates the strength of bivariate equity-price correlations.
| MINIMUM SPANNING TREE OF EQUITY-PRICE FLUCTUATIONS, 2003-04 |
Chart 47
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Several interesting observations can be drawn from the minimum spanning tree of equity-price correlations:
- the groups in category A, the banks in category B and most of the euro area banks have the closest correlation connections within their own categories (although the absolute correlations among the banks in category B are lower),
- the banks in category B are connected to the rest of the network through groups in category A,
- most Nordic insurance companies are connected to the network through euro area banks rather than through categories A or B,
- the absolutely weakest correlation connection in the network is to Kaupthing bank. The weakest correlation connections in the network after that are to the Danish insurance companies and the banks in category B.
Analysis of the banks' equity prices using the analytical tools described in this chapter – correlation analysis, cluster analysis and the minimum spanning tree – may, in combination with analysis of accounting figures and other data, help to test on an ongoing basis the relevance for Financial Stability of the analytical groupings used. The analysis confirms the relevance of the grouping into categories A and B, and at present there seem to be no compelling grounds for extending these categories – either geographically (e.g. to include other internationally active banks operating in Denmark) or sectorally (e.g. to include insurance companies).
Several of the Nordic groups in category A seem to have a high exposure to common factors. Thus shocks causing problems for one of the Nordic groups (however unlikely this may be) would probably weaken other groups in the same category as well.
[1] In the GARCH (generalised autoregressive conditional heteroscedasticity) model, the equity price is estimated as an autoregressive process (i.e. a function of its own former values) together with a conditional variance for the stochastic error term (the conditional heteroscedasticity).Output is an econometric estimate of equity-price volatility.
[2] Marsh, Stevens and Hawkesby, Large complex financial institutions: common influences on asset price behaviour?, Bank of England, Financial Stability Review, December 2003.
[3] Weekly intervals are preferred in order to obtain a sufficient number of observations for a relevant time period also avoids the noise and holiday problems associated with day-to-day data. Equity prices are measured as percentage changes in order to avoid spurious correlation between random-walk processes.
[4] The acquisition is described in the box on structural development in the chapter on the financial sector.
[5] Broad equity-market indices reduce the weight of each share in the index, but do not fully eliminate it. The correlation coefficients of major Danish and Norwegian companies with the Copenhagen and Oslo equity markets in particular should therefore be interpreted with caution.
[6] By using the residuals from a regression of equity-price changes as a function of changes in the broad equity-market indices.