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"Monetary Review – 4th Quarter 2002"

Sensitivity Analysis of Denmark's International Investment Position

Thomas Bie, Statistics, and Frank Øland Hansen, Economics

Introduction

Denmark's net international investment position, or net external debt, is the difference between Danish residents' assets and liabilities vis-à-vis abroad, stated at market value. The net external debt fell from 42 per cent of annual GDP in 1990 to 17 per cent in mid-2002. This is primarily due to the fact that since 1990 Denmark has had a current-account surplus every year except 1998.

Both external assets and liabilities have more than doubled since 1990, however. At the same time the composition of the net external debt has changed to include more net liabilities as bonds and net assets as shares. Consequently, the fluctuations on the international financial markets have gained greater importance to the development in the net external debt.

Statistical elucidation of the international investment position has improved greatly in recent years. Danmarks Nationalbank has begun to publish quarterly statements of Denmark's international investment position to complement the annual statements issued so far. The statements are prepared on a very detailed basis with breakdowns of Danish residents' foreign assets and liabilities by sectors, financial instruments, country of counterpart and currency of issue, which makes it possible to undertake equivalent detailed analyses.

In the following, this data basis is applied to distribute the development in the net external debt in the 2nd quarter of 2002 by the period's transactions, and by market price and currency gains/losses. The new information on the composition of assets and liabilities is also used to analyse the sensitivity of the net external debt to fluctuations in currency rates and in share and bond prices. The effect of hedging is not taken into account, however, since sufficient data is unavailable. The method of analysis is Value-at-Risk (VaR), which with a given probability states an upper limit for the expected fluctuation in a given period. The VaR analysis shows that with a probability of 95 per cent value adjustments will not increase the net external debt by more than approx-imately kr. 50 billion within one quarter.

Development in the net external debt

Due to the increase in both assets and liabilities, portfolio value adjustments have acquired greater significance to the overall development in the net external debt. In the short term the effect of value adjustments often eclipses the current-account surplus, cf. Chart 1. However, value adjustments of assets and liabilities tend to be equalised over time, so that the balance of payments is decisive to the long-term development in the net external debt.

The strong fluctuations in the international financial markets in recent years are reflected in fluctuations around the trend, which is determined by the current-account balance, cf. Chart 2. The external debt has thus increased since 1999 in spite of the current-account surplus, primarily as a result of strongly receding share prices since the beginning of 2000.

Breakdown of the development in the net external debt

The detailed data basis for calculation of the net external debt, cf. Box 1, makes it possible to break down the development from the start to the end of the period, taking into account the development in both exchange rates and stock-market prices:

Portfolio, end º portfolio, start +
net transactions + exchange-rate adjustments + market-price adjustments

The total value adjustments are determined on the basis of information about the portfolios at the start and end of the period, as well as the net transactions during the period. Then the total value adjustments are broken down into exchange-rate adjustments and market-price adjustments. The exchange-rate adjustments are calculated on the basis of the development in the most important currencies.^[1] The statement of the international investment position includes hedging as derivatives, e.g. forward contracts under loans, deposits, etc. The degree of detail for derivatives does not permit a breakdown of the total value adjustment for loans, deposits, etc. by exchange-rate and market-price effect.

Denmark's net external debt increased from kr. 224 billion to kr. 234 billion in the 2nd quarter of 2002. This is primarily related to the fact that the quarter's current-account surplus of kr. 7 billion was more than offset by the price development in the financial and currency markets, cf. Table 1. The development in exchange rates reduced the net external debt by kr. 8 billion, while the development in stock-market prices increased the net external debt by kr. 25 billion.

The decrease in international share prices in the 2nd quarter of 2002 meant that the foreign portfolio shares held by Danish residents lost kr. 55 billion in value. To this should be added an exchange-rate loss on foreign portfolio shares of kr. 22 billion, primarily reflecting a decline by more than 12 per cent in the value of the US dollar vis-à-vis the krone.

Likewise, the falling Danish share prices have meant that Danish port-folio shares held by non-residents have lost kr. 24 billion in value, which reduces Denmark's net external debt. It may seem illogical that falling Danish share prices contribute to reducing the net external debt. However, the lower market value results in losses to both residents and non-residents. The loss to residents reduces domestic assets, while the loss to non-residents reduces their outstanding claims and thereby the net external debt. An extreme case was observed in 1998-1999 when non-residents' ownership of the rapidly rising Nokia share was reflected in an increase in Finland's net external debt. Correspondingly, a decrease in the market value of this one paper is the major single reason that Finland's net external debt was reduced by 75 per cent from 2001 to mid-2002.

Another important source of value adjustments is non-residents' holdings of Danish bonds. In the 2nd quarter of 2002 the market value declined, in spite of net purchases and rising stock-market prices. This was due to an exchange-rate adjustment of kr. 18 billion as a result of non-residents owning Danish bonds issued in US dollars for kr. 136 billion in the 2nd quarter of 2002.

Sensitivity of the net external debt to exchange rates and share prices

The isolated financial consequences of fluctuating exchange rates and stock-market prices can be assessed using the detailed statement of the international investment position. Here the effects of currency fluctuations and the development in the stock markets are examined. The calculations do not include the effect of derivatives, for which detailed information is not available, and consequently the analysis does not provide a full picture. Since derivatives are used more to hedge exposures than to incur risks, the calculations can be seen as high-end estimates.

Table 2 Breakdown by currency, end of 2nd quarter 2002

Danish residents hold more assets in euro than in any other currency, cf. Table 2. The assets in euro exceed the liabilities by almost kr. 500 billion, so that exchange-rate fluctuations vis-à-vis the euro would result in large losses or gains. In practice the Danish fixed-exchange-rate policy entails that fluctuations are very small, and value adjustments due to the rate of the euro have been insignificant. Danish residents also hold considerable assets and liabilities in US dollars, but since they are on more or less the same scale the net exposure is modest. If the rate of the dollar falls by 10 per cent, Denmark's net external debt will increase by less than kr. 2 billion. The largest net exposures are in pounds sterling and Swedish kronor, both of which fluctuate a good deal vis-à-vis the Danish krone. A 10-per-cent decline in one of these currencies would result in a loss of kr. 9 billion or kr. 7 billion respectively. The remaining foreign-exchange exposure is relatively modest, and fluctuations in individual exchange rates will not lead to major value adjustments of the overall net external debt. 

The Danish holdings of foreign shares have increased significantly since the early 1990s, cf. Chart 3. Especially insurance and pension companies, investment associations, etc. and social security funds have invested large proportions of their assets in foreign stock-exchange-listedportfolio shares. For pension companies this development reflects the fact that the share ceiling has been raised several times, from 25 per cent in 1990 to a maximum of 70 per cent at present.

After the falling share prices in 2001 and the first half of 2002 the market value of Danish residents' foreign portfolio shares was kr. 342 billion at the end of the 2nd quarter of 2002. Almost a third was in US shares, cf. Chart 4.

A drop by 10 per cent in the US stock market would thus result in a direct Danish wealth loss of almost kr. 11 billion. Since there tends to be considerable co-variation in the development on the international stock markets, simultaneous losses will often be suffered in other stock markets. Danish shares also tend to shadow the fluctuations abroad, which reduces the total value adjustment of the net external debt, regardless of the size of the losses incurred by individual investors.

Value-at-Risk

To gain a full overview of how fluctuations in the financial markets affect the net external debt, the probability of fluctuations in the factors affecting the net external debt should be taken into account.

Value-at-Risk (VaR), a tool used in financing theory, is an expression of the risk connected to a given portfolio. With a chosen probability, VaR states the greatest loss to be expected in a future period under normal market conditions. For portfolio managers VaR is a useful management tool which e.g. takes into account the co-variation in the price development of the assets. Danmarks Nationalbank thus applies VaR in connection with overall portfolio decisions and the ongoing monitoring of Danmarks Nationalbank's market risk.^[2] VaR can also be applied to ana-lyses of the net external debt. Since the latter is a compilation of all residents' assets and liabilities vis-à-vis abroad, the calculation of VaR for the net external debt solely serves analytical purposes. A VaR analysis of the net external debt can be used to estimate the size of a "normal" fluctuation in the net external debt as a result of value adjustment.

The VaR estimate depends on the chosen time horizon for which the risk is assessed, since a longer time horizon results in a higher VaR. For the calculation of VaR for the net external debt a time horizon of three months has been selected, to match the statistical statements. In addition, the estimate depends on a number of technical assumptions, including whether it is based on daily, monthly or quarterly observations, and the estimation period applied for the risk factors used. The distribution and co-variation of the risk factors are here estimated on the basis of daily observations for the period from January 2001 to September 2002. In the calculation the selected risk factors are fluctuations in key currencies, share indices, 10-year government bonds and 3-month money-market instruments, cf. Box 2. The use of aggregate risk factors reflects the level of detail in the statement of the international investment position, which is a simplification in relation to basing the calculations on information about the individual securities.

Box 2 Calculation of Value-at-Risk for the net external debt

With a time horizon of 3 months and a probability of 95 per cent, VaR for the net external debt can be calculated at kr. 54 billion at the end of the 2nd quarter of 2002. In other words, with a probability of 95 per cent value adjustments are not likely to increase the debt by more than kr. 54 billion in the subsequent quarter.

With the current risk scenario, price fluctuations for portfolio shares are the major source of value adjustments. If all other risk factors are disregarded, VaR can be calculated at kr. 51 billion on the basis of share-price risk, cf. Table 3. It can therefore be expected that the developments in the international share market in each quarter have a greater impact on the net external debt than the current account. Bond prices fluctuate far less than share prices, but due to the large portfolios, particularly on the liabilities side, bond prices are also a major source of value adjustment.

Table 3 Value-at-risk for Denmark's net external debt, end of 2nd quarter 2002

The sum of the contributions to VaR from the individual risk factors exceeds the portfolio's total VaR. The reason is that the risk factors do not always pull in the same direction, and thereby do not always result in losses/gains at the same time. This diversification gain is significant and can be calculated at kr. 31 billion for VaR at 95 per cent. In connection with the compilation of the net external debt the diversification gain reflects the fact that the risk on the net external debt as value adjustments is exaggerated if single factors are viewed in isolation.

The value adjustments of the net external debt amounted to kr. -11 billion in the 1st quarter of 2002 and kr. -17 billion in the 2nd quarter of 2002. Compared with the calculated VaR of kr. 54 billion the realised value adjustments were modest. This was due to moderate price changes in the 1st quarter, while large net losses on portfolio shares in the 2nd quarter were partly offset by gains on e.g. direct investments. On the other hand, the net loss on portfolio shares of kr. 53 billion in the 2nd quarter of 2002, as a result of a decline in all international share indices, is higher than the calculated VaR with a probability of 95 per cent for portfolio-share-price risk. For portfolio shares, value adjustments on this scale can be expected to occur a few times in a decade.

Total value adjustments exceeding the calculated VaR for the overall net external debt are also observed from time to time. For instance, positive value adjustments, primarily resulting from increasing foreign share prices, reduced the external debt by kr. 114 billion in 1999. For comparison, the previously calculated VaR based on daily observations projected to a time horizon of one year was kr. 108 billion.

We have used daily observations over a relatively short period to reflect the current risk scenario. When daily observations are used to calculate VaR with a time horizon of one quarter, it is assumed that the development tomorrow is independent of the development today. This is a theoretical assumption, which in some situations is unrealistic. For instance, the krone stays close to its central rate vis-à-vis the euro, so that fluctuations are equalised over time. If the risk scenario is determined on the basis of observations with a frequency corresponding to the time horizon for which the uncertainty is to be assessed, in this case quarterly observations, this problem is avoided. If quarterly observations are used, a longer estimation period is also required in order to have a sufficient number of observations.

A longer historical period may be used to determine a VaR which is less influenced by the recent unrest on e.g. the stock market. This would give a less true picture of the current market risk, but may be used to assess value adjustments in relation to a more average market risk. If quarterly observations for the period 1st quarter 1995 – 2nd quarter 2002 are used, we find that with a probability of 95 per cent value adjustments will not increase the debt by more than kr. 41 billion. As was expected, the more average market risk is lower than the current market risk, but the altered calculation basis does not significantly change the picture of the expected fluctuations in the net external debt. It is primarily the share-price risk that is lower if a longer estimation period is used. The negative value adjustments of the net external debt seen in the last few quarters are not unusual either in relation to the lower average market risk.

There is no point in calculating VaR for the net external debt by sector. To calculate the total risk of the individual sectors, the exposure to other residents must be included, and all types of hedging taken into account. The external-debt statements do include statements of financial derivatives, but firstly they only include the market value vis-à-vis non-residents, and secondly the statistics are not sufficiently detailed to be used as a basis for a sector analysis.

It is therefore only possible to make qualitative statements about the sectors contributing to the net external debt VaR. Share-price risk nat-urally relates to the sectors which own foreign shares, mainly insurance and pensions, as well as investment associations. Non-residents also bear a risk in relation to Danish shares. Interest-rate risk is primarily attributable to government and mortgage-credit bonds. Exchange-rate risk is not attributable to particular sectors, as residents to a large extent hedge and take on exchange-rate risks via Danish banks, which in turn hedge their exposures abroad.

Conclusion

The statement of Denmark's international investment position is now made on a more detailed basis than before. The more detailed information will gradually be presented in the coming quarterly statements of the international investment position.

In this article the detailed data basis is used to break down the net external debt and its development over a given period of time. Value-at-Risk is used to illustrate how fluctuations in share prices, exchange rates and interest together can influence the net external debt. In the longer term the effects of the upward and downward fluctuations in the net external debt will offset each other, but the VaR analysis based on historical data shows that quarterly fluctuations in the net external debt of approximately kr. 50 billion as a result of developments in the financial markets may be expected from time to time.

Footnotes

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Version 1.0 December 2002 Nationalbanken.
Published by Danmarks Nationalbank December 2002, http://www.nationalbanken.dk/