Norges Bank

Submission

Rebalancing regime for the Government Petroleum Fund

The following letter was submitted to the Ministry of Finance on 22 August 2001

1. Introduction

In a discussion of a rebalancing regime for the Petroleum Fund, it is important to distinguish between the strategic benchmark and the actual benchmark. The strategic benchmark for the Petroleum Fund is defined by the weightings set by the Ministry of Finance for the regions (Europe/North America/Asia-Oceania equal to 50/30/20) and the asset classes (equities/fixed-income instruments equal to 40/60). These weightings are referred to as strategic weightings. The actual benchmark, against which management performance is measured, is based on the strategic weightings. However, during the period between two rebalancing operations, the weightings in the actual benchmark are influenced by the relative price changes of the various asset classes/regions. This means, for example, that if equity prices advance sharply in a period, the equity portion in the actual benchmark will be higher than 40 per cent. Rebalancing brings the weightings in the actual benchmark back to the strategic weightings. With the exception of deviations due to active management, management of the Petroleum Fund follows the actual benchmark. This means that when the weightings in the actual benchmark are changed (rebalancing), the same changes will normally be made in the Petroleum Fund. Hence, rebalancing entails transaction costs linked to necessary buying and selling. This gives rise to a dilemma: if rebalancing takes place too seldom, the portfolio will drift away from the strategic weightings, while frequent rebalancing will lead to high transaction costs. A rebalancing strategy must therefore be devised that weighs up these two considerations.

Under the existing regime for the Petroleum Fund, the Fund and the actual benchmark are rebalanced at the end of each quarter so that the share of the different asset classes are returned to the share in the strategic benchmark. This rebalancing takes place at the same time that capital is transferred to the Fund, which has made it possible to rebalance relatively frequently without substantial transaction costs. This is because the capital transferred has been used to buy asset classes where the exposure is to be increased. However, there are two reasons why transaction costs will become an increasingly important consideration over the next years. First, capital transfers as a share of the Fund's overall value will decline. This means that a larger share of rebalancing will involve financing securities purchases by corresponding sales of securities. Second, the Fund's benchmark will also include non-government-guaranteed bonds, which are less liquid than today's securities in the Fund. The transaction costs linked to non-government-guaranteed bonds are higher. As a result of these changes, the Fund's rebalancing regime should be reassessed. If the rebalancing frequency is changed, it would also be appropriate to reconsider the frequency of capital transfers to the Fund.

The Ministry of Finance has announced that the Fund's equity share will be reassessed in the National Budget for 2002. The implementation of a new rebalancing regime for the Fund should be considered in conjunction with such possible changes in the Fund's investment strategy.

2. Choice of rebalancing regime

The choice of rebalancing regime for the Petroleum Fund will influence the evolution of the Fund's benchmark over time. The benchmark shall safeguard two important considerations.

One is that the benchmark shall reflect the strategic choices underlying the investment strategy adopted. These choices shall reflect the owner's trade-off between expected return and risk. Hence, it is important that the rebalancing regime chosen prevents the weightings in the actual benchmark from deviating excessively from the weightings in the strategic benchmark.

The other consideration is that the benchmark shall serve as a basis for evaluating active management. The benchmark should thus represent an objective and transparent basis of comparison. This is best achieved if rebalancing is calendar-based or rule-based (conditional). Furthermore, it is important that it is the owner that defines the principles underlying changes in the benchmark, and that these are unequivocal and easy to control.

Managers use the benchmark as a basis for actual investments. This means that changes in the benchmark normally lead to changes in the actual portfolio. Consequently, frequent changes in the benchmark may lead to substantial changes in the actual portfolio.It is therefore important that the benchmark is constructed to avoid excessive transaction costs. In addition to the transaction costs, frequent rebalancing may also be associated with indirect costs since rebalancing also involves operational resources in investment management.

It is common to distinguish between two rebalancing regimes.

The first regime is calendar-based. This regime seems to be the most widely used by large funds, which then choose monthly, quarterly or annual rebalancing. Under a calendar-based regime, the rebalancing day is by definition known in advance. Rebalancing can be planned and carried out as a matter of routine, which is perceived as being an advantage. A disadvantage of the regime is that rebalancing is carried out irrespective of need (the degree of deviation from the weightings in the strategic benchmark).

The other regime is conditional (rule-based) rebalancing. Here, a rule is defined, which states that the portfolio shall be rebalanced when a certain change occurs, for example, when the weightings in the actual benchmark move outside a specified interval around the weightings in the strategic benchmark. Since the strategy for the Petroleum Fund is linked to the selected weightings for equities, fixed income instruments and three regions, it may be natural to rebalance the actual benchmark should one (or several) of the asset classes move outside the interval. Asset classes refer here to equities and bonds in Europe, North America and Asia-Oceania (six classes).1One advantage of a conditional regime is that rebalancing is only undertaken if the deviations from the strategic benchmark reach a certain limit, which could reduce the rebalancing frequency and thereby the transaction costs. It may also be an advantage if market participants, e.g. brokers, do not know the exact date of rebalancing of the Petroleum Fund. This may make it easier to achieve cost-effective rebalancing. However, a conditional rebalancing regime can be more complex than a calendar-based regime. In order to ensure that the conditional regime is sufficiently transparent, it is important that the rules are formulated precisely.

We have looked at several theoretical and empirical studies of various rebalancing regimes. These studies provide no clear indication of which rebalancing regime one should choose. The only certainty is that frequent rebalancing increases the cumulative transaction costs. How the portfolio's return and risk is influenced by the rebalancing regime depends on the period studied, the markets considered and the underlying pricing processes for the various assets. In particular, the degree of autocorrelation2 of the return is of importance. Some studies suggest that international equity returns are characterised by a negative autocorrelation over time (mean reversion), but that cycles are long and last several years. However, it is doubtful whether any particular rebalancing regime can be designed to consistently exploit these fluctuations for return enhancement.

3. Relationship between transfers and rebalancing

Today both rebalancing and transfers to the Petroleum Fund normally take place at the end of each quarter. 3 The capital that is to be transferred to the Petroleum Fund is accumulated over a three-month period in a buffer portfolio, which is part of the foreign exchange reserves. Exposures in the buffer portfolio are determined by the Petroleum Fund's rebalancing requirements. This means that the buffer portfolio contains an excess weighting of the asset classes whose exposure is to be increased in connection with the rebalancing of the Fund's actual benchmark. At the end of each quarter when the buffer portfolio is transferred to the Petroleum Fund, the composition of the Fund is automatically brought closer to the strategic benchmark. This reduces the need for rebalancing the Fund.

As the Fund grows and new asset classes are included (non-government-guaranteed bonds), the costs of the existing rebalancing regime will increase. The frequency of transfers to the Fund and the frequency of rebalancing the Fund's actual benchmark should therefore be reassessed.

In choosing the frequency of transfers to the Fund, two considerations must be weighed against each other. On the one hand, frequent transfers will make it difficult to take advantage of the transfers to the Fund in connection with the Fund's rebalancing. On the other hand, capital that is to be transferred to the Petroleum Fund should not accumulate outside the Fund (in the Petroleum Fund's buffer portfolio) over longer periods. Norges Bank would recommend that transfers be made monthly under the new rebalancing regime. An advantage of monthly transfers over quarterly transfers is smaller market transactions, and thereby reduced likelihood of adverse market impacts.

The transfers to the Petroleum Fund are expected to be substantial in the coming years. It is appropriate to use these transfers in connection with the rebalancing of the Fund. However, Norges Bank would not recommend that full rebalancing coincide with the end-month transfers to the Fund. Such a regime would result in large transaction costs and use of operational management resources. However, it is still possible to use the monthly transfers to influence the need for future rebalancing. This can be accomplished by defining a transfer portfolio that is composed in such a way that when it is combined with the Petroleum Fund's actual benchmark, the weightings in the new benchmark will to the largest extent possible return to the weightings in the strategic benchmark. At the beginning of each month, the weightings in the actual benchmark will be set equal to the weightings arrived at by combining the transfer portfolio and the actual benchmark at the end of the previous month. The weightings in the new benchmark will not necessarily be brought all the way back to the strategic weightings. Only in the months where the transfers are very large and/or the deviations from the strategic weightings are small will the weightings be fully returned to the strategic weightings. As a rule, however, monthly rebalancing will return the weightings close to, but not entirely back to the strategic weightings. Monthly rebalancing can therefore be characterised as partial rebalancing. Such a regime requires unequivocal rules that describe an optimal transfer portfolio. Norges Bank will submit a separate letter with recommendations regarding such rules.

The composition of the monthly transfers to the Fund will be as similar as possible to the composition of the transfer portfolio. This ensures that the changes in the Fund correspond to the changes in the benchmark. Normally, it will not be necessary to carry out Fund transactions in connection with the monthly, partial rebalancing.

With the current estimate for the transfers to the Fund over the next years, our calculations show that these are not expected to be adequate to bring the weightings in the actual benchmark back to the weightings in the strategic benchmark at the end of each month. This means that a gradual discrepancy between the weightings in the actual benchmark and the strategic weightings may arise over time. In addition to the partial rebalancing that the optimal transfers represent, a supplementary rebalancing rule should be devised to limit the discrepancy between the weightings in the actual and the strategic benchmark. This is discussed below.

4. An evaluation of different rebalancing regimes

Norges Bank has assessed two alternatives to the current regime of quarterly, full rebalancing. Both alternatives are based on monthly, optimal transfers. One alternative is annual (calendar-based) rebalancing. The other alternative is conditional rebalancing when the weightings of one (or more) of the six asset classes in the actual benchmark deviate substantially from the weightings in the strategic benchmark.

A key question regarding the conditional regime is how substantial a deviation from the strategic benchmark is to be allowed before full rebalancing is triggered. If there is a broad band around the strategic weightings, rebalancing will be infrequent and as a consequence, transaction costs will be low. However, a broad band may mean that the weightings in the actual benchmark deviate substantially from the strategic weightings for longer periods. If one allows substantial deviations, the question of how to implement rebalancing operations once they are triggered will also arise. Since the rebalancing operations may then require considerable transactions in the Fund, an alternative may be to only partially rebalance back to the strategic weightings. According to Norges Bank's assessment, an appropriate trade-off between the different considerations would be to set the band limits to +/- 3 percentage points around the strategic weightings for the six asset classes in the Fund's benchmark. Such band limits will make it possible to relatively quickly bring the weightings in the Fund's actual benchmark back to the strategic weightings when rebalancing is triggered. The proposed band limits will be consistent with the intervals within which the equity and regional shares must lie (+/- 10 percentage points).

Under the conditional regime, we have assumed that the assessment about whether rebalancing shall be implemented is made immediately after the actual benchmark has been adjusted for the optimal transfer portfolio. To avoid rebalancing due to a short-term increase in market volatility, a requirement could be that the actual benchmark shall only be fully rebalanced if one or more of its weightings are outside the band limits over two consecutive months. If the conditions for rebalancing are met, rebalancing begins one month later. Those responsible for operational implementation would then have time to plan the rebalancing. The size of the rebalancing, which depends on the Fund's size and the deviations from the strategic benchmark, will determine how quickly the weightings in the actual benchmark can be realigned to the strategic weightings.

Using a stochastic portfolio model, we have simulated future developments of the Petroleum Fund under the two alternative rebalancing regimes as well as under the current regime with quarterly transfers and full rebalancing. The model is based on an assumption that prices of equities and fixed income instruments as well as exchange rates follow correlated geometric Brownian motion (GBM). GBM is a fairly common model used for price processes for financial assets because these processes are easy to simulate when there are several asset classes. One disadvantage of GBM may be that these price processes do not allow autocorrelation of the return (like e.g. mean reversion) and that they may underestimate the frequency of large changes in returns (e.g. sudden and sharp declines in the financial markets). The lack of mean reversion may in isolation lead to an over-estimation of future rebalancing transactions, transaction costs and number of rebalancing operations in a conditional rebalancing regime. On the other hand, the imperfect description of substantial changes in the returns may in isolation lead to an underestimation of these parameters.

We have assumed that expected nominal annual returns on bonds and equities will be 5 per cent and 8 per cent respectively, regardless of region. These are the same estimates used in our letter to the Ministry of Finance on 15 March 2001 ("An analysis of the Government Petroleum Fund's equity portion").4 We have assumed that expected future exchange rates are the same as current exchange rates. The volatility of the asset classes (including the exchange rates) and mutual correlations have been set at historic values over a period of 15 years from January 1986 to May 2001.

We have used Norwegian krone (NOK) as the reference currency in the simulations. The initial value of the Petroleum Fund has been set at NOK 650bn, which is the assumed value towards year-end 2001. In the simulations, we have used existing estimates for transfers to the Fund in the period 2002-2006. We have chosen to focus on an investment horizon of five years. The transaction costs in connection with the rebalancing operations have been set at 6 and 25 basis points (bp) for bonds and shares respectively, regardless of region.5 Since costs are deducted from the value of the Fund on an ongoing basis, the returns reported are net returns.6 As a result, the simulations provide expected values for the development of the Petroleum Fund over the five-year period 2002-2006.

Table 1 shows features of the Fund under the alternative rebalancing regimes. The table shows that there is only a marginal difference in return and risk (in the form of volatility, probable range of outcomes for portfolio values at the end of the period, and the probability of negative returns over a five-year period) with the three regimes. The regimes vary considerably with regard to expected value of rebalancing transactions and the associated transaction costs. Both alternatives to the current regime will reduce the expected frequency of rebalancing, the cumulative value of rebalancing transactions and transaction costs. Chart 1 shows expected transaction costs in NOK billions for the current regime and the two alternatives. The chart shows that the conditional regime involves the lowest transaction costs.

The individual rebalancing transaction value will be larger under both alternative regimes than under the current regime. Relative to the Fund's current value, it will increase from 2.2 per cent under the current regime to 4.2 per cent with annual rebalancing and 9.6 per cent under the conditional regime. This may increase the risk of a negative effect on market prices at the time of rebalancing.7 In order to avoid this, one should allow the Fund to be rebalanced gradually back to the strategic weightings. Chart 2 shows the expected value of rebalancing transactions in NOK billions. Although the transactions may appear to be substantial under the conditional regime, one must remember that full rebalancing occurs very infrequently under this regime (less than one rebalancing operation over a five-year period is expected).

Table 1 shows that the expected (average) equity portion is only marginally higher under the alternative regimes than in the current regime. Under the alternative regimes, however, the Petroleum Fund's portfolio weightings may drift further away from the strategic weightings than under the current regime. Chart 3 shows the most probable range of outcomes for the equity portion under the different regimes.8The chart shows that with both annual and conditional rebalancing, we cannot exclude the possibility that the equity portion may deviate from the strategic weighting (which is 40 per cent) by 4-5 percentage points in some periods.

The conditional rebalancing regime has two advantages compared with the annual rebalancing regime. First, the portfolio is only rebalanced when deviations from the strategic benchmark reach the maximum limits allowed by the owner. As a result, full rebalancing occurs less frequently and transaction costs are lower. Second, market participants will be less likely to foresee the exact time of rebalancing of the Petroleum Fund. This may make it easier to rebalance the portfolio in a cost-effective manner.

5. Recommendation

Under the current rebalancing regime, the weightings in the actual benchmark are realigned with the strategic weightings every quarter. So far, the quarterly transfers to the Fund have been so substantial that it has only been necessary to sell a limited number of assets in the Petroleum Fund when the Fund has been rebalanced in accordance with the actual benchmark. If the Petroleum Fund increases in size, one can imagine situations in the future when such a rebalancing regime will result in relatively large transaction costs. Therefore, Norges Bank recommends changing over to a conditional rebalancing regime. Such a regime involves three changes in relation to the current regime.

First, there will be monthly transfers to the Petroleum Fund. Second, there will be partial rebalancing in connection with the monthly transfers. This will be accomplished by defining a transfer portfolio that is composed in such a way that when it is combined with the Petroleum Fund's actual benchmark, the weightings in the new benchmark will to the largest extent possible be brought back to the weightings in the strategic benchmark. Third, the partial rebalancing each month should be supplemented by a rule for conditional full rebalancing. The condition for full rebalancing should be that one (or more) of the six asset classes in the actual benchmark exceeds a specified limit for deviation from the weightings in the strategic benchmark over two consecutive months. The weightings are measured immediately after the actual benchmark has been adjusted for the optimal transfer portfolio. The limits are set at +/- 3 percentage points. If this condition is satisfied, the actual benchmark will be fully rebalanced. How quickly the portfolio is fully rebalanced depends on the extent of transactions involved.

The advantage of the new rebalancing regime is that the transaction costs will be considerably lower than with quarterly, full rebalancing. The combination of monthly, partial rebalancing and conditional, full rebalancing will also mean that the deviations from the strategic benchmark are expected to be limited. Under the new regime, capital that is to be transferred to the Fund will no longer need to be accumulated outside the Fund for long periods. A conditional rebalancing regime may, however, be more complex than a calendar-based regime. To ensure that the conditional regime is adequately transparent, it is therefore important to formulate the guidelines precisely.

The Ministry of Finance defines the benchmark for the Petroleum Fund. Therefore, under the new regime it is important that the Ministry of Finance precisely and unequivocally stipulates the rules for defining the benchmark. This means, among other things, that the Ministry must prepare detailed rules about the optimal composition of the transfer portfolio and the conditions that must be satisfied to trigger full rebalancing. Norges Bank will provide the Ministry of Finance with further advice about formulating these rules.

Yours sincerely,

Svein Gjedrem

Harald Bøhn

Table 1: Alternative rebalancing regimes for the Petroleum Fund

Quarterly transfers

Quarterly rebalancing

(current regime)

Monthly transfers

Annual rebalancing

Monthly transfers

Conditional rebalancing

Net simple return, annualized (%)

6.50

6.52

 

6.53

Volatility

(%)

8.94

8.99

 

9.01

Sharpe ratio

(return/

volatility

0.710

0.708

 

0.707

Value of rebalancing transactions over 5-year period,

and contribution bonds/equities

(in NOK billions)

572.9

275.4 / 297.5

295.8

138.2 / 157.6

122.8

56.0 / 66.8

Average (over time) value of rebalancing transactions relative to current value of Fund (%)

 

2.2

 

4.2

 

 

9.6

Transaction costs over 5-year period,

(in NOK billions)

 

0.91

 

0.48

 

 

0.20

Probability of one or more rebalancing operations over a 5-year period (%)

 

100

 

100

 

61.5

Expected number of rebalancing operations over 5-year period

20

5

0.83

Average (over time) equity share

(%)

40.1

40.4

40.6

Average (over time) share in Europe/N.Am./Asia (%)

50.0/30.0/20.0

49.8/30.0/20.2

49.7/30.0/20.3

Fund value at horizon, and 95% confidence interval

(in NOK billions)

1704.3

(1226.8 -

2324.5)

1710.6

(1227.5 -

2340.5)

1711.6

(1229.4 -

2349.1)

Probability of negative return over a 5-year period (%)

5.7

5.8

 

5.8

 

Chart 1.

Cumulative transaction costs (in NOK billions) in connection with rebalancing over a five-year period

Chart 2.

Expected transaction value for each rebalancing (in NOK billions) over a five-year period. Dots: current regime (quarterly transfers and rebalancing). Circles: monthly optimal transfers and annual rebalancing. Squares: monthly optimal transfers and conditional rebalancing. Under the conditional rebalancing regime, the time of rebalancing is uncertain, so that every month has an associated expectation value. The fluctuations are due to statistical uncertainty.

 

Chart 3.

Expected equity portion and 95% confidence interval (drawn lines), over a five-year period.
  1. Current regime
  2.  

  3. Monthly optimal transfers and annual rebalancing
  4.  

  5. Monthly optimal transfers and conditional rebalancing


Footnotes:


1 The strategic weightings of these six asset classes are: European bonds (30%), North American bonds (18%), Asian-Oceania bonds (12%), European equities (20%), North American equities (12%) and Asian-Pacific equities (8%).
2 Autocorrelation means that the return over time will tend to follow a certain pattern. A positive autocorrelation usually means that a sizeable return over a period is followed by a large return in the next period as well. A negative autocorrelation usually means the reverse: a large return is often followed by a small return.
3 As a result of the large transfers to the Fund this year, however, transfers have been made several times each quarter since May, and this will continue until the end of the year. Rebalancing is still undertaken quarterly.
4 We find that the differences between the regimes are qualitatively the same if we use the historic return rates in the period 1986-2001 instead of our assumptions about returns on equities and bonds.
5 The transaction costs for bonds are a share-weighted sum of costs for government and non-government-guaranteed bonds. Costs for equities take into account pure commissions and the bid-ask spread.
6 Transaction costs in connection with transfers (purchases) have been set equal to zero for the sake of simplicity. Since transferred capital must be invested regardless of the choice of rebalancing and transfer strategy, the purchase costs will not affect the choice of an optimal rebalancing strategy.
7 We have not taken market impacts into account in the simulations.
8 95 per cent confidence interval (which shows the interval within which the equity share will remain in 19 of 20 periods.
Published 22 August 2001 11:02