The limit on tracking error for the Petroleum Fund

1. Background

We refer to a letter of 21 April 1999 from the Ministry of Finance on the limit on tracking error for the Petroleum Fund. Norges Bank has been asked to evaluate this measure of risk. The Ministry is interested in hearing about experience of this risk measure generally, and how Norges Bank's systems are handling it. An evaluation is also desired of how high the limit for tracking error should be set in the future.

The tracking error limit determines how far investments in the Petroleum Fund can deviate from the benchmark portfolio. Whereas the Ministry of Finance decides on the benchmark portfolio and the limit for deviations, Norges Bank is responsible for the actual deviations from this portfolio. This assures a clear sharing of responsibilities between the Ministry and the Bank in the management of the Petroleum Fund.

In the National Budget for 1998, two arguments were used for deviating from the benchmark portfolio. These related to cost-effective management and active management, respectively. It was also pointed out that during a period with large net transfers to the Petroleum Fund and changes in the asset mix, it may also be necessary to have a somewhat greater tolerance for deviations from the benchmark portfolio, and thus a higher limit for tracking error. Consequently the Ministry set the limit on tracking error at 1.5 percentage points. This limit was consistent with Norges Bank's recommendation.

In a letter of 21 April 1999, the Ministry of Finance points out that the accumulation of the equity portion of the Fund was completed at the end of May 1998, and that preliminary estimates indicate that allocations to the Fund will be lower than previously assumed. The Fund thus appears to be entering a period during which the portfolio will grow more slowly and undergo less changes. According to the Ministry, this may mean that the limit on tracking error need not be as high as it has been previously.

In this submission a closer examination is made of the issues taken up by the Ministry of Finance.

Experience to date is discussed, and an evaluation made of the future need for tracking error in the management of the Petroleum Fund. Norges Bank concludes by recommending that the current limit on tracking error be maintained.

At present Norges Bank is reviewing the frequency of rebalancing and transfers to the Fund, and the arrangement with the Petroleum Buffer Portfolio. This work may result in proposals for changes that influence the need for a tracking error for the Petroleum Fund. The evaluation in this submission is therefore based on the assumption that the current system with quarterly rebalancing and transfers is continued.

2. Calculation of expected tracking error

In a letter of 19 December 1997, the Ministry of Finance set the limit for tracking error at an annualised 1.5 percentage points, and specified that this was to apply at all times. The framework was defined as the expected (ex ante) tracking error resulting from application of the analytical tools in the BARRA models. BARRA is the risk management system used to calculate the market risk for the Petroleum Fund.

Norges Bank Investment Management collects daily data on holdings and prices for all subportfolios. Figures for expected tracking error were calculated daily in 1998, but since 1999 aggregate figures have only been calculated every Friday, and also on the last day of each month. This is because it is extremely resource-consuming to make daily calculations of tracking error for the whole Fund. With the level of relative market risk in question, less frequent calculations have in practice not reduced the effectiveness of monitoring to ensure that the limit is constantly complied with. In the contracts with external managers, a cap is placed on tracking error, and managers are monitored constantly. Tracking error is calculated daily for the internally managed portfolios.

A knowledge of variation and covariation in the return on all assets in a portfolio is a prerequisite for calculating tracking error. This information is expressed in the form of a covariance matrix. This matrix therefore has to be estimated, and this is done in BARRA on the basis of observed time series. With more than 2000 different securities in the portfolio, the covariance matrix will be so large that in practice it cannot be handled without restrictions being imposed on it. This problem is solved in BARRA by assuming that movements in asset prices are driven by a limited number of underlying risk factors.

BARRA consists among other things of various subsidiary models for equities and bonds, respectively, and an aggregate model. When the expected tracking error for the whole Petroleum Fund is measured, this aggregate model is used. However, it is dependent on information from the subsidiary models. The aggregate model combines the individual covariance matrices from the subsidiary models into an aggregate covariance matrix. This matrix is calculated on the basis of time series for returns. For fixed income instruments and equities, the monthly returns over the last decade are used, while for foreign exchange, daily observations over the past two years are used. Common to the different time series is that greater emphasis is placed on new than on old observations. This means that changes in the magnitude of fluctuations in the foreign exchange market are reflected more rapidly in the estimate for tracking error than fluctuations in the equity and fixed income markets. If highly unusual market conditions occur, the changes in the risk outlook will not be picked up quickly enough by the estimated covariance matrix. This means, for example, that in a period when the stock market features a high degree of either volatility or stability, it will take time before the new risk level is reflected in the risk estimate. If the aim is to predict risk over a relatively short time horizon, the estimate in such cases will be inaccurate.

In general, it can be said that BARRA risk models for global equity and fixed-income markets are expected to function better for diversified portfolios than for individual securities. This is partly because market conditions and structure may vary across local markets.

The Ministry of Finance now allows portions of the Petroleum Fund to be invested in fixed-income instruments issued by private companies, and in emerging equity markets. Norges Bank has not yet started such investments. BARRA risk models lend themselves primarily to analysis of market risk. When one invests in corporate bonds, credit risk plays an important part. BARRA provides a slightly simplified treatment of credit risk. Since the Petroleum Fund has so far only invested in fixed-income instruments with a very high credit rating, this has not been a problem, however. Before the Fund begins investing in instruments with a lower credit rating than hitherto, it is necessary to study whether we have a tool accurate enough to measure how credit risk contributes to the Fund's overall tracking error.

Experience shows that time series for returns in emerging equity markets show a statistically less normal distribution than similar series from developed markets. This may mean that estimates for absolute volatility and tracking error that include emerging equity markets provide less accurate information about the outcome set of future returns.

As mentioned previously, BARRA's model for estimating tracking error uses a covariance matrix based on historical time series for monthly returns in the various markets. The covariance matrix therefore remains unchanged for a period of a month, until new return figures are available. When the covariance matrix undergoes monthly updating, the tracking error of the Petroleum Fund will change, even if both benchmark portfolio and actual portfolio remain unchanged. In a submission of 16 February 1998 to the Ministry, Norges Bank assumes that an overrun of the limit as a result of updating of the covariance matrix is not regarded as a breach of the Ministry of Finance's guidelines. The Ministry confirms this interpretation in its letter of 26 February 1998, on the condition that the portfolio is adjusted immediately to bring expected tracking error under the permissible limit. Norges Bank has not had any experience to indicate that the effect on tracking error when the covariance matrix is updated from one month to the next is significant in relation to the tracking error level. Simulations carried out by Norges Bank indicate that the effect is seldom more than a few basis points when the tracking error is of the order of 100 basis points.

3. Active compared with passive management

One important question for an investor is whether the portfolio should be managed actively or passively (ie according to an indexing strategy). The answer depends partly on how efficient the markets are. Market efficiency means that prices reflect so much of all available information that it is not possible over time for a manager who is trying to identify under- or overpriced assets to increase returns more than it costs to obtain the extra information.

Adherents of the hypothesis of market efficiency maintain that active management is very largely wasted, and cannot justify the increased costs. This seems to indicate that management should follow a passive strategy whereby a well diversified index portfolio is established, without any attempt to find over- or undervalued assets. Advocates of active management believe that markets are not completely efficient, and that it is possible to achieve an extra return by trading "incorrectly priced" individual assets, or by predicting broad market movements (market timing).

There is a trend among investors internationally to choose a combination of passive and active strategy. This means that a large portion of the portfolio is managed passively according to index mandates (passive core), while a smaller portion is managed according to active mandates with a fairly high tracking error limit. The theory is that expected excess return can be created for lower management costs if risk-taking is concentrated on a small portion of the portfolio. Moreover, the use of specialised mandates provides better opportunities for utilising the competitive advantage of the individual manager. The proportion of portfolios that are indexed is increasing. It is difficult to say whether this means a general decrease in active management, since the remaining portion may be being managed actively at a higher risk. Few investors choose pure index strategies.

When evaluing active management, it is usual to compare the performance (after costs) with that achieved by pursuing a pure indexing strategy. In principle it will also be desirable to take account of the risk associated with the various investment strategies. This is because a distinction is normally made between risk that is priced by the market (which is the source of risk premiums) and risk that is not priced by the market. However there is still dissension in the professional literature and among managers as to which risk is priced and how large the risk premiums are. This means that it is difficult to distinguish between results from active management that are due to the market rewarding the taking of risk, and results attributable to the skill of the manager. Nor can one say that the manager should not take a priced risk. It will be to the client's advantage for the manager to use his or her scope for manoeuvre to take a priced risk if it contributes to a better ratio between performance and risk on the total portfolio. In principle, active management may just as easily result in lower as in higher total risk. Irrespective of the evaluation method chosen, it is important to remember that it will inevitably take time before one can conclude with reasonable certainty that a given positive average performance is not due to random variation.

A number of empirical studies have been carried out to determine whether there are advantages to active management as opposed to passive indexing strategies. The results show that it is difficult to achieve a risk-adjusted excess return after costs. First, active managers do more poorly on average than market indices. This is not particularly surprising, since active managers as a group must be expected to follow the indices closely, while at the same time they have higher costs than passive managers. Second, there are few active managers who achieve consistently good results over time. One objection to these conclusions is that there are methodological weaknesses associated with the majority of the surveys. Another is that the majority of the studies are from the US. The US market is larger and better developed than the European and Asian markets, and there is stronger competition between participants. It is therefore uncertain how far results from the US can be applied to other markets. A third weakness is that the empirical data are mainly from mutual funds. We have limited access to data on historical returns for other investors. This means, for example, that not much is known about the results of organisations that systematically choose between good and bad managers, as Norges Bank does for the Petroleum Fund.

One reason for choosing active management may be that it is costly and requires skill to collect and process information, and that different agencies will therefore possess different information. As in other commercial activities, it is required that the use of resources and expertise be rewarded by a superior performance. Under the circumstances, it is impossible to conceive of prices reflecting all available information, because then there would be no-one with grounds for collecting and processing relevant information. The reward to those who perform such work best and most efficiently will be a higher return than those who do poorer work.

The decision of how much active management to use should depend on both the opportunities for achieving an informational edge, and on investors' risk tolerance. As a rule, large investors will have greater opportunities than small investors, because large investors can distribute the information costs over a larger portfolio, and are in a better position to build up or purchase the expertise required for good, efficient collection and processing of information. However, there may also be disadvantages associated with size, because there is a risk that large transactions will influence market prices more strongly in an unfavourable direction than small transactions.

The main elements of Norges Bank's strategy to achieve an excess return through active management are presented in Norges Bank's annual report for 1999 on the management of the Petroleum Fund, in the form of a feature article headed "Strategy for achieving the best possible performance". Two general arguments can be given for engaging in active management. First, the benchmark index only represents a limited selection of the Fund's investment universe. It may be possible to enhance performance by investing in assets other than those included in the index. Second, there may be market inefficiency that can be exploited. For example, a large proportion of index management may create inefficiency through price movements resulting from the addition to and removal of enterprises from the indices. IPOs provide another example. When an equity is included in the index just after a public issue, it may be a particularly good opportunity to buy the equity at a lower price than the one at which it will enter the index.

4. Other managers

It may be of interest to compare the limit on tracking error in the Petroleum Fund with similar limits or targets used by other management organisations. At the outset, efforts should be made to identify investors that are as comparable as possible with the Petroleum Fund. Criteria that may be relevant for purposes of comparison are size, asset composition, the purpose of the Fund, time horizon, risk tolerance and organisational factors. However, it may be difficult to say anything definite about some of these criteria. On the basis of a discretionary review of these factors, we have contacted some pension and government funds. We have also had a dialogue with a couple of consulting companies.

Our investigations reveal that most funds look at the relationship between the active return achieved and the magnitude of the fluctuations shown by this return (ie the relative risk). Otherwise, there does not appear to be any common point of focus. Some funds operate with target zones in their use of relative risk. However, very few institutions appear to control the deviation of the fund as a whole from the benchmark portfolio according to a formal tracking error limit. It is therefore difficult to compare the level of tracking error used by the Petroleum Fund with the level used by other institutions. Our impression is nevertheless that the maximum limit for relative risk in the Petroleum Fund is somewhat lower than the average actual risk of other managers.

In order to form a picture of the Petroleum Fund's overall risk profile compared with that of other funds, it is also necessary to compare absolute risk. This is determined by choice of investment universe and benchmark portfolio. Some funds include unlisted equities and real property, and have a higher equity portion and a different geographical distribution from the Petroleum Fund. However, we have no reliable grounds for stating that the Petroleum Fund has higher or lower absolute risk than other funds.

5. Management of the Petroleum Fund in 1998 and 1999

The new guidelines from the Ministry of Finance and the new organisation of the management in Norges Bank were introduced in January 1998. Charts 1 and 2 show expected tracking error in the Petroleum Fund for the years 1998 and 1999 respectively (attached). We see that the highest levels were achieved during the increasing of the equity portion of the Fund in spring 1998. This was attributable to the fact that equities were purchased a few days before the equity portion of the benchmark portfolio was increased. Having the freedom to make the major equity purchases at times other than month-ends made it possible to achieve low transaction costs, partly because it was easier to utilise crossing opportunities.

Since then, the expected tracking error for the Petroleum Fund has been less than 40 basis points, except during the first half of October 1998, when it was between 50 and 80 basis points, and 30 November 1998, when it was measured at 98 basis points. From the beginning of July 1998 to the end of 1999, the average expected tracking error has been about 25 basis points.

The right to deviate from the benchmark portfolio was thus not fully utilised during this period. This can be attributed to active management requiring an organisation that it takes time to build up. The aim over time is to utilise a larger portion of the risk quota, providing that this proves to yield an excess return.

Tracking error measures deviation from the benchmark portfolio. In the National Budget for 1998, the Ministry of Finance mentioned two grounds for allowing deviations from the benchmark portfolio. The one is cost-effective management. The other is active management. Cost-effective management consists of three elements: indexing, rebalancing of the benchmark portfolio, and transfers to the Fund. These components are discussed in more detail below, in the light of experience so far with the Petroleum Fund.

5.1 Cost-effective management

If not coordinated, the accumulation of the Petroleum Buffer Portfolio and the need for rebalancing of the Petroleum Fund may lead to transactions which entail unnecessary transaction costs for the two portfolios. The combined transaction costs will be lower if assets that are overweighted in the Fund itself can be underweighted when the Petroleum Buffer Portfolio is accumulated, and vice versa. The most advantageous approach will be for the Petroleum Buffer Portfolio to be accumulated in such a way that at the time of transfer it covers as much as possible of the Petroleum Fund's rebalancing needs. As a means of avoiding unnecessary transaction costs, Norges Bank has applied limits to the management of the Petroleum Buffer Portfolio that are somewhat broader than those applying to the Petroleum Fund. This applies to distribution by asset class, and by currency and market. Moreover, no benchmark portfolio or limit on tracking error has been defined for the Petroleum Buffer Portfolio. With the Buffer Portfolio arrangement in place, there is therefore less need to constantly use tracking error in relation to the Petroleum Fund in order to achieve cost-effective transactions in connection with allocations to the Fund.

In a letter of 21 April 1999, the Ministry of Finance points out that the accumulation of the equity portion of the Fund was completed at the end of May 1998, and that preliminary estimates indicate that allocations to the Fund will be lower than previously assumed. In the opinion of the Ministry, this may mean that the tracking error can be set at a lower level. In practice, however, there may be an inverse relationship between the size of the amount transferred, and the need for tracking error. Since the composition of the Buffer Portfolio can be adjusted according to rebalancing needs, the tracking error needed for a given rebalancing requirement will be larger if there are no transfers than if there are large transfers. This is because when there are no transfers, rebalancing must be covered exclusively by transactions within the Fund itself. This process can take time.

Since rebalancing needs are determined by market movements, they are very difficult to predict in practice. If the market is volatile at the end of a quarter, anticipated rebalancing needs may change within a short space of time. In principle, this means that it is only possible so see what Buffer Portfolio composition will be optimal on the transfer date. With a view to limiting transaction costs for the foreign exchange reserves, restrictions have been placed on the sale of securities in the Buffer Portfolio (once they have been purchased). Close alignment with the new benchmark portfolio is contingent on access to updated information on the composition of the portfolio, and prices, which in practice are not available until the following day. Rebalancing of the actual portfolio on the same day as the rebalancing of the benchmark portfolio must therefore be based on market values from the previous day, and corrections must be made the following day, when correct market values applying at the time of rebalancing are available. On the whole, predictions have been accurate, and the most recent rebalancings have therefore not led to any appreciable increases in expected tracking error.

In autumn 1998, however, there was price volatility in the equity market. On 30 September 1998, the share of equities in the benchmark portfolio was down to 34.8%, rising to 43.2% on 30 November 1998. On the rebalancing dates 30 September and 30 November, tracking errors were 50 basis points and 98 basis points respectively, measured against the old benchmark portfolio after the addition of new assets from the Buffer Portfolio. In the days preceding rebalancing, the tracking error was between 20 and 30 basis points. The need for such large risk quotas for rebalancing was largely a result of the market volatility prior to these two dates. On the last day of quarters with transfers, there may be a particular need for tracking error because the Fund is then still considered in relation to the old benchmark portfolio, whereas assets added to the Fund that day are aligned to the new benchmark portfolio.

By measuring the Petroleum Fund's total deviation from the new benchmark portfolio, before and after transfers of new capital, we can estimate how much the transfers have contributed to rebalancing the actual portfolio. We find that, on average, the transfers have contributed to eliminating half of the deviations. The degree to which the deviations are reduced varies from 80% at most to zero when there has been no transfer. This indicates that in some quarters rebalancing needs are largely taken care of through allocations to the Petroleum Fund, while in other quarters adjustments must to a substantial degree take place within the Fund.

5.2 Active management

The degree of active management has been limited while the management organisation has been built up. At the end of 1999, there was still only a moderate degree of active management, measured by means of tracking error. In the equity portfolio, about NOK 25 billion of a total of NOK 94 billion was managed with active mandates, with a relative market risk that was more than 500 basis points tracking error for some of the mandates. Nevertheless, overall risk-taking in the active mandates was only about 200 basis points, because of the low correlation between the active subportfolios. The equity portfolio's contribution to tracking error was even more modest, because of the small active portion and low correlation between the active subportfolios and the index portfolios. Aggregate relative market risk in the equity portfolio was less than 50 basis points.

At the end of 1999, active management in the fixed-income portfolio was limited to strategies conducted by internal managers. Total relative market risk in the fixed-income portfolio was only 12 basis points.

In 1998 and 1999 the Petroleum Fund outperformed the benchmark portfolio by 0.23 and 1.11 percentage points respectively. The results in 1999 are very good compared to what can be expected for the level revealed by measurements of expected tracking error through the year.

All seven active equity mandates showed an excess return in 1999, and this excess return was fairly consistently positive throughout the year. The most important explanation for the excess return is the managers' choice of individual equities. Through 1999 there were unusually large differences in return within individual sectors, between companies that performed well and others that performed poorly. This effect was particularly marked in the technology sector. The Petroleum Fund's active equity managers demonstrated great skill in selecting the companies that would do well, in both the technology and other sectors.

Such company-specific factors must of necessity be poorly represented in risk modelling, and experience in 1999 may indicate that this contributed to the BARRA model underestimating market risk. At the same time, the correlation pattern between sectors changed in 1999, particularly between technology and the other sectors. This will not be fully reflected in the BARRA model until the new pattern has been in place for a while, and this change thus constituted a further reason for market risk being underestimated in 1999.

In interpreting expected tracking error, it must also be taken into account that return is a stochastic variable with fatter tails in the probability distribution than the normal distribution usually used as a frame of reference. The fatness of the tails may vary over time, and in 1999 the spread in the outcome set was unusually large, so that interpretations of expected tracking error based on a statistically normal distribution were further out than usual.

The version of the BARRA model used in 1998 and 1999 is now being replaced. In the new version, which according to plan will be introduced in the second quarter of 2000, measurements of expected tracking error will be based to a greater extent on specific regional models. These models capture the risk factors specific to an individual region better than the current global model. Through 1999, the regional models showed a higher level for expected tracking error than was actually reported for the Petroleum Fund on the basis of the global model. In future there is reason to expect that the new version of BARRA will provide a more accurate prediction of actual market risk.

However, there will always be sources of error in model-based measurement of market risk. All models have to be based on historical patterns of variation and covariation, and will only gradually be able to incorporate changes in these patterns. In consequence, measurements of expected tracking error can never be interpreted as providing full coverage of the market risk one faces.

6. Evaluation of the need for tracking error in the time ahead

6.1 Cost-effective management

As discussed above, there has normally only been a limited need for deviations in connection with rebalancing, with the exception of autumn 1998, when the tracking error was between 50 and 60 basis points, at a time when there was little active management. Allowance must be made in the future, too, for the possibility that market volatility may lead to substantial deviations in the days around the updating of the benchmark portfolio. The need for deviations is increased if the supply of new capital for the Fund is reduced, as a share of the total market value of the Fund. It is difficult to quantify the maximum deviation that may arise as a result of rebalancing.

Experience indicates that rebalancing may be an important source of tracking error for the Petroleum Fund, but that allocations made at the same time as rebalancing have the effect of reducing the need for tracking error. In the years ahead, there is reason to believe that even if there are substantial transfers of new capital, they will constitute a steadily smaller share of the Fund's total market value. Situations in which there is not full adjustment to the new benchmark portfolio will therefore arise more often. If, in addition, the market is volatile around the rebalancing date, it may be necessary to make substantial use of the Fund's risk framework. The management of the Fund must be organised so that it does not exceed the maximum risk limit even in extreme circumstances. This means that tracking error must normally be substantially lower than the upper limit imposed.

It must therefore be assumed that in some cases 50-60 basis points tracking error will be necessary for rebalancing. This is additional to the day-to-day index management, which is assumed to require 10-20 basis points.

6.2 Active management

When the risk limit is reviewed, the most important question is how much active management there should be. Active management of both equity and fixed income portfolios is being gradually extended. The Petroleum Fund currently has five external equity managers with a total of seven mandates for active management. At the same time, internal active management has commenced. There is slightly more internal active management on the fixed income side, and three external mandates were allocated in the first quarter of 2000. During the year it is also intended allocating external mandates for global tactical asset allocation.

As pointed out in the Petroleum Fund's quarterly reports, monitoring of active management is more demanding than monitoring of indexing strategies. Consequently, the building up of active management has taken place over time, to ensure that the necessary monitoring routines are put in place and function.

Another, equally important reason for proceeding by degrees is that the amount of active management should depend on experience acquired along the way. Although our experience of active management has been highly positive so far, this does not necessarily mean that all types of active management will be profitable. If we find in the course of time that certain active strategies cost more than they yield in terms of gross excess return, the use of these strategies will be discontinued. On the other hand, the use of strategies that do result in net profitability will be gradually increased. Such factors will have to be assessed continuously. The amount of active management and make up of the active management portfolios will never be fixed for too long a time ahead. Norges Bank invests considerable resources in choosing systematically between good and poor external managers.

The tracking error limit must also be evaluated in the light of the expected growth of the Fund. In Norges Bank's submission of 22 August 1997, it was pointed out that in due course the Fund will invest substantial amounts in the international financial markets, and that experience has shown that it can be difficult to engage in active management with large sums. The Bank consequently recommended that a large portion of the Petroleum Fund should be managed according to a long-term strategy that involves only small deviations from the benchmark portfolio.

Norges Bank's plans will bring the scope of active management of both the equity and the fixed income portfolio up to a level where a larger portion of the current risk limit of 1.5 percentage points will be utilised. Constant full utilisation of the risk framework cannot be planned, because there must be some leeway for rebalancing.

6.3 Changes in strategy

In a letter of 21 April 1999, the Ministry of Finance mentions that the rate of change in the Fund strategy is one factor suggesting that the tracking error limit need not be as high as it is at present. The Ministry points out that the accumulation of the equity portion of the Fund was completed at the end of May 1998. Any need to changes in strategy will be associated primarily with changes in the benchmark portfolio, and will therefore occur quite rarely. In the event of substantial changes in the benchmark portfolio, there may be a need for flexibility in adapting the Fund to the new strategy so that adaptation can take place in a cost-effective manner. In the first half of 1998, it was thus cost-effective for the Fund to be slightly in advance of the increase in the equity portion of the benchmark portfolio. This may imply a need for tracking error during a transition period. In the view of Norges Bank, it will not be advisable to make allowance for possible future changes in the benchmark portfolio when the tracking error limit is stipulated, since such changes will not take place particularly often. When the Ministry changes the benchmark portfolio, the need for a transition period with special adjustments should be considered separately. If the situation warrants it, the tracking error limit could be made higher in the transitional phase, as Norges Bank has done with the foreign exchange reserves.

7. Overall evaluation and conclusion

The need for tracking error depends on two factors: cost-effective management and active management.

The most important aspect of cost-effective management is rebalancing of the benchmark portfolio. Given the current programme for rebalancing and transfers of capital, there will continue to be a need in the future for tracking error, to ensure cost-effective transactions in connection with rebalancing. In some situations this need may be substantial.

The work of establishing active management has not yet come so far that much experience has been acquired of utilising the limit implicit in Norges Bank's recommendation in its letter of 22 August 1997. The active management results achieved so far have been very favourable. The bank's active management plans imply that the risk framework will be utilised to a greater extent in the time ahead.

Following a comprehensive evaluation, Norges Bank recommends that the tracking error limit remain unchanged. We have argued above that a portion of the overall risk quota must be retained for the quarterly rebalancing. This means that, on average, the use of risk will lie appreciably below the upper limit.

Yours sincerely

Svein Gjedrem

Harald Bøhn

Notes:

1) For a more general description of the concepts of risk measure and tracking error, see the feature article "Tracking error as a measure of market risk".

2) The management of the Petroleum Fund provides an illustration. For many months in 1999 the absolute volatility of the Fund's return was lower than that of the benchmark portfolio.

3) To determine portfolio risk, it is not sufficient to measure the variation in return on the individual asset classes. It is also necessary to know the degree of covariation in the return on the various asset classes.

4) Crossing means that instead of taking place over the Stock Exchange, trading takes place directly between managers.

5) This is discussed in detail in a feature article in Norges Bank's annual report for 1999 on the management of the Petroleum Fund. "Can index performance be achieved through index management?" As a result of transaction costs, the return achieved is lower than the index return if a manager always trades securities in accordance with the benchmark index. The article discusses strategies to minimise costs and strategies that enhance the performance achieved by indexing (enhanced indexing).

6) Fat tails mean that the probability of extremely large (positive or negative) returns is larger than the normal distribution would indicate.

7) In a submission of 16 February 1998 to the Ministry of Finance, Norges Bank stated that BARRA's Total Plan Risk model would be used to measure expected tracking error for the total fund against the limit stipulated by the Ministry. The change involves replacing Total Plan Risk with the Orion product.