Performance measurement methodology

The total performance of the Government Petroleum Fund is measured with a high degree of precision. An important precondition for this is that the quality-checked market value of the Fund is always calculated when new capital is added. There may, however, be cash flows between the sub-portfolios at other points in time, without the quality-checked market values being calculated at the same time. The measured return on the sub-portfolios will then depend on the method chosen for measuring performance, because adjustments must be made to correct for these cash flows.

What is performance?

The market value of the Government Petroleum Fund consists of the market value of the equity and fixed-income instruments in which the Fund is invested at the time of measurement. The return is calculated as changes in the Fund’s market value from a given date to another, corrected for inflows to the Fund. Any transfers to the Fund are normally made at the end of every quarter, and for that reason are easily identified and excluded from the calculation of the return. On the sub-portfolio level, for example between the equity and fixed-income portfolios, there may be cash flows in the course of the measurement period (ie in the course of the months), and these must be taken into account when calculating the return. The method used will have a sizeable impact on the results (see section 4 below on choice of calculation method).

The market value calculated for the Government Petroleum Fund is based on the trade date, ie the transactions have an effect on the composition of the Fund on the day they are agreed, despite the fact that it takes a few days before settlement of the transactions is completed (the value date). Norges Bank’s accounts also employ a concept of return, but one in which the market value is based on the value date. Up to end-1998, moreover, the securities in the accounts were valued at the lower of market value or average purchase price. There may thus be differences between the book return and the return stated in the reports on investment management.

In addition to the absolute performance of the Government Petroleum Fund, the relative performance is also measured. This is the difference between the performance of the Fund portfolio and the performance of the Fund’s benchmark portfolio(1).

Why do we measure performance?

The performance of the Government Petroleum Fund indicates the contribution of Fund management to the increase in value in a given period. This type of information is of interest to the owners (the Norwegian people), the delegating authority (the Ministry of Finance) and to Norges Bank as manager. In the marketplace, fund managers will use information on investment performance to attract prospective customers. Even though a high historic return does not necessarily imply that the manager will achieve a high return in the future, investors will as a rule attach considerable importance to the historical performance record when choosing managers.

The absolute return on the actual portfolio may be regarded as the sum of the return on the benchmark portfolio, and the difference between the actual return and the return on the benchmark portfolio. It is normally the principal who chooses the composition of the benchmark portfolio, and to a large extent the absolute return reflects this choice. It is not until the relative performance is measured that the skill of the manager can be evaluated. We look at the performance achieved by the manager in relation to the benchmark portfolio that applies to the regions and countries in which the manager is investing, and how much the manager contributes to the total difference in performance. However, in order to determine whether the manager has performed well or just been lucky, a fairly long track record is required.

Normally, a higher expected return can only be achieved by taking higher risk. The performance should therefore be compared with the market risk taken, so that the return per risk unit can be evaluated. For the Government Petroleum Fund, limits have been set for the maximum deviation of the Fund’s investments from the benchmark portfolio, in that a limit for tracking error has been established(2). The limit on tracking error will to a large extent determine the range within which the relative return will vary, including the maximum relative return. Risk correction for return figures is, however, another and complex subject, and will not be further discussed in this article.

Fundamental requirements

The fundamental requirements for reliable performance measurement are that the holdings data employed are correct, that the value assigned to the instruments reflects market value, and that the method used is compatible with the type of management performed. We will revert to the last point in section 4 below.

The market value assessment is based on the size of holdings, market price of instruments, and exchange rates for conversion to a common currency.

Holdings

The Government Petroleum Fund is invested in more than 2,500 different securities. The Fund is managed directly by Norges Bank Investment Management and by external managers. This makes it a considerable challenge to keep track of the holdings. The external managers report all trades continuously to Chase Manhattan Bank, which is the Fund’s custodian institution(3) for externally managed portfolios. Every day Norges Bank Investment Management receives a complete listing of all holdings from the custodian. To provide a complete picture of the Fund’s holdings, information on the capital managed by external managers must be added to similar information on the capital managed by Norges Bank. Information on the internal portfolios is extracted from the internal trading and settlement system and transferred to an internal database, where the information about the externally managed portfolios is also registered. This database therefore contains holdings figures and market values on a daily basis. The quality of the complicated network of information flows and reporting is crucial to the quality of the performance figures(4).

Price sources

Most of the Fund’s equity and fixed-income instruments are liquid securities for which many market-makers quote prices. The derivatives contracts used are liquid standard contracts that are traded on organised exchanges. Because market prices are available, the instruments currently used in the management of the Government Petroleum Fund are generally easy to value. The prices used are closing prices, ie prices quoted by the chosen price source at the end of the day in the local markets. A choice of price source must nonetheless be made. The price source may be a major investment bank or firm, a large brokerage house or an information centre such as Bloomberg. The quality of the various price sources must be evaluated over time, and prices from the various sources must be compared.

As new instruments are adopted, such as derivatives contracts that are not traded on organised exchanges and bonds issued by private companies, it may become increasingly difficult to find reliable prices in the market, and it may then be necessary to use theoretical pricing models instead of market prices. Such models will provide prices that are theoretically consistent with the market prices of other instruments, but which do not necessarily reflect the actual market price of these derivatives contracts or private bonds, because the models can never provide a correct picture of all relevant factors.

Whether market prices or a model are used, a crucial criterion for obtaining comparable performance results is that the same price source is used over time, and is not changed to obtain the most favourable price. On the other hand, if the price source used fails to capture actual market conditions, a change should naturally be considered. A change in price source is indicated if, for example, there is consistent overpricing or underpricing by comparison with other price sources in the market and no daily price quotations for certain instruments. Responsibility for the valuation of the portfolios should be kept separate from responsibility for management.

As mentioned, the Government Petroleum Fund is managed by many external managers in addition to Norges Bank. This means that several managers frequently have the same instruments in their portfolios. Chase Manhattan Bank currently prices and measures the performance of all equity portfolios, thereby ensuring that the same price is used. Moreover, the entire fixed-income portfolio is managed by Norges Bank. As a result, a situation cannot arise whereby Chase and Norges Bank use different prices for the same instruments. In the first half of 2000, external portfolios will again include fixed-income instruments, for which Chase will perform pricing and performance measurement. It should then be ensured that the same price sources are used by Chase and Norges Bank.

The same price sources used for the benchmark portfolio are used in the pricing of the Fund’s holdings to the extent deemed appropriate. This means that any errors in the price sources for the instruments included in both the Fund and the benchmark portfolio have no effect on the relative return.

Exchange rates

The return on the Petroleum Fund is calculated in Norwegian and foreign currency. The return measured in NOK does not provide an adequate picture of changes in the Petroleum Fund’s international purchasing power. Fluctuations in the Norwegian krone affect the return measured in NOK, but are of no significance for international purchasing power. Norges Bank therefore primarily emphasises return figures in a foreign currency basket. The return in local currency is weighted together with the individual countries’ weightings in the benchmark portfolio, distributed on equities and fixed-income instruments.

It is also important that the same source is used over time for exchange rates. For the Petroleum Fund, the same source is used for exchange rates in the performance measurements of both Chase and Norges Bank.

Global Investment Performance Standards (GIPS)

An international standard has been developed to ensure greater confidence that the investment performance information presented is complete and correct, and to facilitate the comparison of figures from different institutions, using the same methods and principles. This is of benefit to owners, managers and to prospective investors who are choosing managers.

GIPS are a set of standards for companies managing assets on behalf of a third party. GIPS have been drawn up by the Association for Investment Management and Research (AIMR) and the Global Investment Performance Standards Committee. The Norwegian Financial Analysts Association has decided to replace the Norwegian standard with GIPS from January 2000. However, at the beginning of 2000 no Norwegian managers were GIPS-certified.

The objectives of GIPS are:

• to ensure that the figures are presented in a comparable format, that they are correct and that they provide full disclosure
• to ensure accurate and consistent investment performance data is reported and presented
• to promote fair competition among investment firms in all markets
• to foster the notion of industry self-regulation on a global basis.

GIPS have several key characteristics:

The input data shall be consistent, both across portfolios and over time. This is essential if the investment performance data are to be complete and provide a fair representation. Valuations must be based on market values, and the standard will require trade-date accounting at a later stage. Portfolios must be valued at least quarterly. For periods beginning 1 January 2001, portfolios must be valued at least monthly and from 2010 firms will be required to value portfolios on the date of any external cash flow.

Total return, including realised and unrealised gains plus income, must be used. Time-weighted rates of return must be adjusted for cash flows, see further discussion of time-weighted return in section 4 below. Periodic returns must be geometrically linked, ie, the returns in each period must be chain-linked in order to find the performance for the entire period.

In addition to information on the performance, information must be provided on market value. An overview and description of portfolio groups(5) must be provided. It must also be specified whether the market values are based on value or trade dates, the currency in which the return is calculated and whether the return is calculated before or after the deduction of management fees or other charges.

A firm is required to present, at a minimum, five years of annual investment performance that is compliant with GIPS. If the manager has been in existence less than five years, firms must present performance since the inception of management activity. After presenting five years of compliant history, an additional year of performance must be added each year so that after five years of claiming compliance, the firm presents a ten-year performance record. The total return on the benchmark portfolio must be stated for the same period as the return on the actual portfolio. In addition, the cumulative return on both the actual and the benchmark portfolio must be reported.

GIPS require that a manager fulfil all GIPS requirements to claim compliance with GIPS. Norges Bank Investment Management does not meet all the requirements today, but is seeking to satisfy the key requirements.

Calculation methods

There are different methods used to calculate portfolio performance for a given period. The various methods will yield the same results when returns are calculated for a period in which there have been no external cash flows. The periodic return will then be the difference between end-of- period and beginning market value divided by beginning market value.

In periods with cash flows, however, the various methods will yield divergent results. We present two methods below that are often used to calculate performance in periods with cash flows:

• Time-weighted method (ideal method)
• Money-weighted method (an approximation of the time-weighted method)

To illustrate the differences in the results obtained by these methods, we will give two examples. Both examples have the same return in the periods before and after a cash flow has been added to the portfolio. The difference between the two examples is that the second example includes a much larger cash flow.

Example 1 (Government Petroleum Fund in millions of NOK):   Initial value 1/1-99: 171 832 Value 30/6-99: 174 726 (before cash flow) Final value 30/9-99: 186 016 Cash flow 30/6: 8 000 Return 1/1-30/6: 1.6842 % Return 30/6-30/9: 1.8005 % Example 2 (constructed):   Initial value 1/1-99: 171 832 Value 30/6-99: 174 726 (before cash flow) Final value 30/9-99: 585 074 Cash flow 30/6: 400 000 Return 1/1-30/6: 1.6842 % Return 30/6-30/9: 1.8005 % Table 1: Results from different calculation methods  Method    Example 1  Example2 Time-weighted RT = 3.51% RT = 3.51% Money-weighted Modified Dietz RM = 3.54% RM = 4.32% Money-weighted Internal rate of return method RM = 3.57% RM = 4.37%

Time-weighted method

The ideal method for calculating performance is the time-weighted method. This calculation method is used to eliminate the effect of the portfolio’s external cash flows. The method makes it possible to compare performance data between portfolios, portfolio managers and/or benchmark indices.

Chart: Time-weighted method for calculating performance

The time-weighted return is calculated by dividing the calculation period into sub-periods, so that each sub-period equals the interval between two cash flows. The return in each sub-period is found by dividing the portfolio’s final value by the initial value in the sub-period. The return in the entire reporting period is found by chain-linking the rate of return in the different sub-periods, as shown in the box below:

The advantage of the time-weighted return method is, as shown in Table 1, that the method yields identical results even if cash flows vary widely. The disadvantage is that the method may demand extremely frequent - even daily - valuations, and it can often be costly to develop systems that can provide data of sufficient quality for this kind of valuation.

Money-weighted method

The money-weighted method is often used to calculate the return in sub-periods. To find the performance for a longer period, the return figures for the various sub-periods are chain-linked in the same way as under the time-weighted method.

There are several methods for calculating the money-weighted return. The two commonest are the modified Dietz method and the internal rate of return method:

Chart: Money-weighted method for performance calculations (modified Dietz)

In the modified Dietz method the individual cash flows in the course of the period are weighted on the basis of the date they entered the portfolio. Cash flow is divided between the beginning and end-of-period value, weighted by the number of days the cash flow has been in the portfolio in relation to the total number of days in the measurement period.

The internal rate of return is the interest rate that makes the present value of all cash flows in the period plus the value of the portfolio at the end of the period equal to the portfolio’s initial value.

The modified Dietz method is an approximation of the internal rate of return method and the two methods thus yield more or less the same results for the two examples (see Table 1). Calculating the internal rate of return is somewhat more complicated and it is more common to use the modified Dietz.

The accuracy of the internal rate of return and modified Dietz methods depends on the size of the cash flows in relation to the portfolio value and the length of the measurement period. If the cash flows are larger than 10 per cent of the portfolio value, or if the measurement period exceeds one month, then the use of these methods is not recommended(6). In our second example, the methods are not recommended.

Table 1 shows the results of the two examples using the different methods. The second example has a very large cash flow in relation to the value of the portfolio, and a smaller cash flow would have yielded far smaller differences in the results derived from the time-weighted and money-weighted methods.

In both examples, the periodic returns 1/1-30/6 and 30/6-30/9 are identical. However, the second example shows a higher return than the first. This is due to the different sizes of the cash flows. A manager does not normally have any influence on the timing of portfolio cash flows, but under the money-weighted method the manager is “rewarded or punished” depending on the timing and size of the cash flow. In the example above, the return in the period 1/1-30/6 is lower than that in the period 30/6-30/9. The money-weighted method thereby gives the highest return for the portfolio that has the relatively highest inflow of capital. The opposite would have been the case if the period 1/1-30/6 had had a higher return than the following period.

The accuracy of the money-weighted method also depends on the degree of fluctuation in the portfolio value. The method presupposes an equal return over the entire period, ie every krone will count the same regardless of how long it has been invested. When values fluctuate widely in the course of a period, with cash flows during the period, the money-weighted method will yield a less accurate result.

The total return in NOK on the Government Petroleum Fund is calculated by means of the time-weighted method. Transfers of capital from the Ministry of Finance are made only on set dates (normally at the end of each quarter) and the market value before and after the transfer is accurately calculated.

The return on the sub-portfolios (per asset class, manager and currency) is calculated by means of the modified Dietz method in sub-periods (months), which are geometrically linked. The reason for the use of the modified Dietz method for sub-portfolios is that cash flows between portfolios occur in the course of the months.

The market value of the Government Petroleum Fund is currently measured on a daily basis, but so far not based on quality-checked data. Our long-term goal is to have quality-checked market values daily, and then the time-weighted method for calculating the return can also be used for sub-portfolios.

Relative performance The actual performance of the total Fund and on all sub-portfolios are compared with the performance of the benchmark portfolio. The relative performance is measured as relative geometrical return, ie the krone value of the relative return is calculated as a percentage of the krone value of the benchmark portfolio at the end of the period. This yields the following equation: Relative return = (1+ RF)/(1+RR)-1 = (RF-RR)/(1+ RR) RF = return on the actual portfolio RR = return on the benchmark portfolio

Decomposition

In many cases it will be of interest to divide a portfolio’s total return or excess return into different components. The aim may be to elucidate to what extent various components of the portfolio have contributed to the total return or the excess return. This will provide valuable information for both the principal and manager. For the principal, such information will make it easier to assess whether investment performance is the result of good management or luck. For the manager, the information will be useful input in the investment process.

The Government Petroleum Fund consists of both equities and fixed-income instruments in 21 countries. The Fund is managed both externally and internally, and the management is subdivided into many separate mandates. There are thus many options with regard to decomposition.

Today, the return is measured on the actual portfolio and on the benchmark portfolio for each asset class. This provides an indication of the absolute and relative return on each asset class. If the composition of assets has been the same for the Petroleum Fund and the total benchmark portfolio, this will show what contribution each asset class has made to the overall performance. If the actual portfolio has been over-weighted or under-weighted in relation to the benchmark portfolio within each asset class, adjustments must be made for this effect.

Decomposition can distribute the actual and relative return between internal and external management. A further decomposition may show the contribution to the relative return from each externally managed mandate. Alternatively, the mandates can be grouped according to type - for example, geographical region or industry sector.

Most of the equity portfolio of the Government Petroleum Fund is managed by external fund managers. Some of these are index portfolios, for which the aim is to have the risk and the performance closely track the benchmark portfolio, and some of them are active portfolios, for which the aim is to take risk in order to achieve a higher return than the benchmark portfolio. Both the index mandates and the active mandates may be restricted to countries or regions or specialised in particular sectors or industries. The same division can be made for the portion managed internally.

At present, the entire fixed-income portfolio is managed internally by Norges Bank and is approximately indexed. As active management increases, it will be natural to decompose on internal and external management in the same way as for equities, and also by management type.

A third type of sub-portfolio is used to take positions by changing the weightings of different markets and asset classes in the Petroleum Fund. This is called tactical asset allocation, and in the course of 2000 the Petroleum Fund will have external portfolios of this kind in addition to the internal allocation portfolio that is already being managed by Norges Bank Investment Management.

Performing this type of decomposition may provide a picture of the contribution made by different types of management to excess return. It is important to assess on a continuous basis the weighting assigned to each type of management style. Decomposition must be undertaken with this objective in mind.

(1) See section 1 in the Annual Report. A more thorough discussion of the Fund’s benchmark portfolio may be found on the Internet website of Norges Bank/Petroleum Fund, in the article The Composition of the Government Petroleum Fund’s Portfolio.

(2) The web site of Norges Bank/Petroleum Fund contains a feature article Tracking Error as a Measure of Market Risk, which discusses this concept.

(3) The most important task of a custodian institution or a custodian is to ensure that the individual client’s securities are correctly registered and “stored” in the securities registers of the various countries in which the paper is issued. A custodian has important functions in the settlement of securities trades and also provides accounting services. Various types of supplementary services, such as monitoring of external managers and lending of securities, may be agreed.

(4) The Internet website of Norges Bank/Petroleum Fund contains an article Management of Risk in the Petroleum Fund, with a more detailed description of the various information flows that are necessary for obtaining a full overview of the composition of the Government Petroleum Fund.

(5) Portfolio groups are constructed in accordance with similar investment objectives and/or investment strategies.

(6) According to GIPS, see above.