Market-Based Risk Measures for Banks
The purpose of market-based risk measures is to take advantage of the information on e.g. the investors' expectations for the future contained in bond and share prices. This information may supplement the accounts-based analysis of the banks in the chapter on the financial sector. Market-based risk measures are founded on a number of assumptions as to the efficiency of the financial markets and as to whether the assets are sufficiently liquid for the price development to reflect information about the level of risk. In addition, market-based indicators are influenced by general trends in the financial markets.
When market-based analyses are used to assess the banks' risks, it is important to consider the specific regulation applying to banks. This chapter introduces a share-based risk measure, distance to insolvency, that takes into account the significance of the capital-adequacy regulation of banks. The distance to insolvency for the Nordic banking groups shows a strengthening during 2003, as a result of the generally calmer financial markets after the end of the war in Iraq, among other factors.
Market-based analyses
The price development of financial assets issued by banks may provide information on how financial markets assess risk in banks. This information may be summarised in market-based risk measures, supplementing accounts-based analyses.[1] Market-based indicators have a number of advantages in that they may be forward-looking, they reflect the expectations of a wide range of investors, and data is available with a high frequency. However, the use of market-based indicators assumes a liquid market for financial assets issued by the banks, which is only the case for the largest Danish banks. Furthermore, the prices are influenced by factors that are not specific to the individual bank, but result from a general trend in e.g. the stock market. Finally, shares or bonds issued by a bank may be priced on the basis of other considerations than expected return and risk.
The most frequently used market-based risk measures are founded on bond or share prices. Furthermore, the price of hedging credit risk on assets issued by banks, i.e. the price of credit default swaps (CDS),[2] may be used. CDS are not frequently used in Denmark.
Bond-based risk measures
The large banking institutions issue bonds as supplementary financing to e.g. deposits. Contrary to depositors, bank-bond investors are not protected by deposit insurance. Bonds may be issued as subordinate debt that may be included in a bank's capital base within certain limits. The credit spread on bonds issued as subordinate debt, i.e. the difference between the yield demanded by investors if they are to invest in the bank's bonds and a risk-free yield such as the government-bond yield, is an indicator of how the investors assess the risk for the bank in question.
Chart 41 illustrates the credit spread for euro-denominated bonds issued by the Nordic groups, category A, relative to a benchmark euro government bond since January 2002. The groups' issues in euro were chosen to eliminate the effect of exchange-rate fluctuations. Furthermore, these issues are large and relatively liquid.
In 2003, the credit spread declined for all Nordic groups as a result of the general development in the financial markets. An analysis performed by the ECB shows that bond-based risk measures are robust indicators until six months before the bank experiences problems, e.g. a downrating.[3]
Bond-based indicators have certain weaknesses as risk measures for banks. Since maturity, etc. may vary considerably, bonds issued by the banks are not homogenous and thus difficult to compare. When credit spread is used as a forward-looking risk measure, bonds should furthermore be traded regularly.
Share-based risk measures
Equity owners, i.e. shareholders, rank last among the creditors in the event of default and thus bear the greatest credit risk. The ECB's analysis shows that share-based risk measures are robust indicators 1½-½ year prior to a bank encountering problems.
In the following three types of share-based risk measures are considered: share-price gap, distance to default, and distance to insolvency. The advantage of share-based risk measures is that a share is by definition a stake in the company's equity capital. Share-based risk measures thus avoid the comparability problems of bond-based measures. The limited liability of the shareholders means that they cannot lose more than the capital invested while the gain is in principle unlimited. This asymmetric return profile means that the shareholders have an option-like properties, i.e. a share can be seen as an option on the company's assets.[4]
Like bond-based measures, share-based measures are subject to the requirement that the shares must be liquid and thus frequently traded. This is only the case for the shares of the major Danish banks.
Chart 42 shows that the pattern of share prices varies relatively strongly between the banks in the period under review, 2000-04. This does not necessarily mean considerable variations in performance between the Danish banks in the period, but rather that the shares of the medium-sized banks in particular were influenced by expectations of acquisitions, etc. The assumptions for application of share-based risk measures are thus presumably only met for the major Danish banks.
| Development in share prices for danish banking institutions, 2000-04 |
Chart 42
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| Source: Bloomberg. | |
The difference between the development in the banks' share prices and the development in the leading share index, the share price gap, provides a measure of how the banks perform in relation to the country's stock-exchange-listed companies in general.[5] A positive gap indicates that the bank share outperforms the general stock market and a negative gap indicates the opposite.
The share price gap for the Nordic groups, category A, since 1990 is shown in Chart 43. The significant differences at the beginning of the 1990s are attributable to the effect of the banking crisis in the other Nordic countries. Furthermore, a major correction appears around 2000. In the long term, the course of bank shares will only in special cases deviate from the general stock-market trends resulting from real-economic development. Share-price-gap fluctuations reflect short-term trends as well as any economic shocks that affect banks differently from other companies.
The banking crisis in the other Nordic countries resulted in significant fluctuations in the share-price gap while only a few small banks in Denmark were affected.
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Box 20
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A number of central banks, including the ECB, use market-based indicators when analysing financial stability. With share-based indicators it is possible to weigh together the patterns for banks across the member states in order to get a picture of the general soundness of the EU banking sector.1 Sveriges Riksbank has analysed the Swedish banking crisis in the early 1990s using market-based indicators.2 It finds that the bond-based risk measures are less suitable indicators since the credit spread on the banks' bonds in the period seems to reflect the general level of interest rates and the macroeconomic climate rather than circumstances specific to individual banks. The share-based measures are better at indicating problems at an early stage, inter alia as a result of the high liquidity of the shares in the largest Swedish banks. Sveriges Riksbank's results show that a share-based measure captures the problems in the Swedish banking sector several years before the banks asked for support from the Swedish government. In addition, the measure is found to distinguish between banks that were subsequently liquidated and banks that survived the crisis. The Bank of England applies all three types of market-based risk measures: credit spreads, share-based risk measures and credit default swaps. For the large British banks, the liquidity in the underlying securities is sufficient for all three measures to be applicable as indicators. |
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| 1 See ECB, Financial Stability Review, 2003. 2 Persson, Mattias and Martin Blåvarg, 2003. The use of market indicators in financial stability analysis, Penning- och valutapolitik 2/2003, Sveriges Riksbank. |
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Share-based risk measures
Distance to default
Distance to default measures the probability that the market value of the assets becomes lower than the value of the debt. Especially for banks, it is difficult to determine the "true" value of the assets that mainly comprise loans of which only the bank itself has information. The value of the assets is therefore determined on the basis of the liabilities. The value of the bank's debt appears from the bank's accounts and the value of the equity capital can be calculated from the share price, cf. Box 21. Chart 44 shows the calculated distance to default for the Nordic groups.
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Box 21
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Share prices are used to determine the unknown market value of the assets. The return profile on shares is asymmetrical since the capital invested constitutes the lower limit on losses while there is no ceiling on gains. In theory this means that when the value of the equity approaches zero, and the shareholders have thus lost nearly all of the capital invested, the shareholders have an incentive to induce the company to make risky investments. If the investments pay off, the shareholders receive part of the gain, but if the investments do not pay off, the shareholders lose only the capital invested. A share can thus be seen as a call option on the assets of a company.1 Under certain stringent conditions, share prices can be determined using the Black and Scholes2 model for pricing of options. The price of this "option" is equal to the share price, and using the share price and its volatility it is thus possible to "reverse" the Black and Scholes model and determine the market value and volatility of the assets. This is illustrated in the Chart below. The Chart shows the relationship between the market value of the assets and the value of the option, i.e. the share price. The Chart illustrates how the share price, Pt, and the related risk, measured as the standard deviation, sE, stated on the Y axis of the diagram, are converted into a market value for the assets, Vt, and the related risk, sv, stated on the X axis. As the graph shows, the value of the option, i.e. the share, lies above the 45-degree line. In addition, it is more than zero although the value of the assets is lower than the value of the debt. The reason is the option-like properties of a share. There is still a chance that the market value of the assets may increase sufficiently for the share to have a positive value at the time when the debt matures. The Black and Scholes model is based on a number of assumptions about the statistic properties of share prices. In practice these are hardly ever met in full. Moreover, the model's results are sensitive to the way in which volatility, etc. is calculated. The results should therefore be interpreted with caution. |
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| Relationship between option price and the value of the underlying asset | |
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| 1 Merton, R, An analytical derivation of the cost of loan guarantees and deposit insurance: An application of modern option pricing theory, Journal of Banking and Finance 1, 1977. 2 Black and Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy 3, 1973. |
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| Distance to default for the nordic groups, 1999-2003 |
Chart 44
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| Note: The distance-to-default risk measure includes the banks' equity capital as a buffer. | |
| Source: Own calculations. | |
Distance to insolvency
The distance to default assumes that the bank's total equity capital can be used as a buffer. The distance-to-insolvency risk measure is based on the amount of losses on assets a bank can sustain without falling below the statutory capital-adequacy requirement. Banks must have a solvency ratio of at least 8 per cent and a core capital ratio of at least 50 per cent of the regulatory capital. If the capital base falls below the capital-adequacy requirement, the bank risks losing its licence to operate as a bank. The share of the capital in excess of the statutory requirement – together with current earnings – thus make up the bank's buffer against losses and thus ensure the bank's ongoing independent operation. The difference between the buffers of the two measures is illustrated in Chart 45.
The distance to insolvency views the market value of and risk on the assets, calculated as described in Box 21, in relation to the bank's buffer in the form of excess capital and current earnings stated at book value[6]. The distance to insolvency thus illustrates the market's assessment of the probability that the bank observes the capital requirement. The distance to insolvency is measured as the number of standard deviations on the assets' market value which the bank's buffer can absorb.
The distance to insolvency illustrates the bank's ability to resist losses and thus comprises only some of the factors which may affect a bank's ability to continue operating independently. In reality banks take account of many other risk factors and provisions which are important in terms of continued independent operations. Examples include banks' financial risks and liquidity risks. The choice of share-based risk measure is therefore based on the circumstances which the stock market is expected to react to.
Distance to insolvency for Nordic groups
The development in the Nordic groups' estimated distance to insolvency is illustrated in Chart 46.
If the model's underlying assumptions hold true, the distance to insolvency can be seen as a Value-at-Risk measure where a distance to insolvency of 3 corresponds to a probability of only 0.13 per cent that losses will exceed the buffer. There has been a tendency for the distance to insolvency to decline since the end of 2001. The reason is the increased stock-market volatility since 11 September 2001. All other things being equal, greater volatility will increase the probability that the market value of the assets falls below the debt. The increase in the latter part of the period is a result of the reduced uncertainty in the stock markets after the end of the war in Iraq. The course of the distance to insolvency seems to reflect negative expectations of the banks after 11 September 2001, but more positive expectations after the end of the war in Iraq. The dispersion between the institutions' distance to insolvency seems to have increased, particularly since 2001. To the extent that the banks' distances to insolvency develop along the same lines, this will reflect the general market development, while relative shifts in the banks' distances to insolvency indicate the relative assessments of the banks.
The development in distance to insolvency is determined by the buffer and the volatility in share prices. The buffers of the Nordic groups are illustrated in Chart 47, while the development in volatility is shown in Chart 48.
| Buffers for nordic groups, 1999-2003 |
Chart 47
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| Source: Annual reports. | |
Volatility in share prices for the Nordic groups increased concurrently with the war in Iraq, but has now returned to the pre-war level. However, the dispersion between the groups seems to have increased.
A comparison of the distance to insolvency for the Nordic groups, Chart 46, with the distance to default, Chart 44, shows that the distance to insolvency is generally a little lower than the distance to default. This reflects the fact that the distance-to-default measure includes the entire equity capital as a buffer.
[1] See also financial stability reports from the European Central Bank (ECB), the Bank of England, Sveriges Riksbank, etc.
[2] In a credit default swap (CDS) on e.g. bonds issued by a bank the seller of the CDS accepts to compensate the buyer of the CDS in case the bank defaults on the bond. In return for assuming the credit risk on the bank, the seller receives a stipulated premium from the buyer of the CDS. The premium reflects the seller's perceived credit risk on the bank in question, i.e. the probability that the bank goes into liquidation during the term of the CDS as perceived by the seller. See Suzanne Hyldahl, Credit Derivatives – Possible Implications for Financial Stability, Danmarks Nationalbank, Monetary Review, 4th Quarter 2001.
[3] See Groop, Reint, Jukka Vesala and Giuseppe Vulpes, Equity and bond market signals as leading indicators of bank fragility, the European Central Bank, Working Paper, No. 150, June 2002.
[4] Merton, R, An analytical derivation of the cost of loan guarantees and deposit insurance: An application of modern option pricing theory, Journal of Banking and Finance 1, 1977.
[5] However, the leading share index should be adjusted for the bank shares included in the index. This is not the case in the analysis below.
[6] As a consequence of the normal-distribution assumption in the Black and Scholes model, a distance to insolvency of e.g. three standard deviations is equal to a probability of only 0.13 per cent that the bank will not meet the capital-adequacy requirement. A large distance to insolvency is thus an indication that the market finds it relatively unlikely that losses on assets will lead to solvency problems.