Arithmetic vs Geometric Mean: Which to use in Performance Appraisal

Most performance appraisal measures utilize a mean return in its calculation. This can be in the form a geometric mean or a simple arithmetic average. Because both types of means can be used, it raises the question: Which measure should be applied?

When calculating performance, we are accustomed to calculating returns geometrically (i.e., including compounding). Because of this, many investment managers use the geometric mean in appraisal calculations as it is easy to use the reported time-weighted return, rather than separately determining the arithmetic mean. But using geometric mean is not the most appropriate choice when evaluating risk-adjusted appraisal measures.

When calculating performance appraisal measures that compare return to risk, such as Sharpe ratio, the return used in the numerator of the ratio should be the arithmetic mean of the return stream, not the geometric mean. In many cases, the difference between using the arithmetic mean versus geometric mean will be immaterial; however, the greater the volatility in the return stream, the more material the difference will be. Let’s look at a simple example that demonstrates this effect:

Strategies with significant volatility have lower geometric means than arithmetic means (7.5% vs. 8.4% for Portfolio 2 above). This is because the geometric mean penalizes the return stream for risk-taking. In the case of the Sharpe Ratio, the standard deviation (which also accounts for risk-taking) in the denominator will be higher as a result of this higher volatility (1.5% for Portfolio 1 vs. 14.2% for Portfolio 2). In this case, using the geometric mean therefore results in a penalty for risk in both the numerator and denominator of the ratio.

Because risk is already being accounted for in the denominator, there is no need to include it in the numerator; in fact, including it would be double-counting the risk taken. As a result, for measures like Sharpe Ratio, it is more appropriate to use the arithmetic mean than geometric mean.

Although, in many cases, using the geometric return will not have a material effect on the outcome when comparing risk-scaled performance measures, it is technically more accurate to use the arithmetic mean. Its implications are more relevant when evaluating strategies with higher volatility. 

How to Become GIPS Compliant

Many firms are interested in becoming GIPS compliant, but are intimidated by the initial process of bringing their firm into compliance. As long as you know the steps to become GIPS compliant and understand the options you have to complete each step, this process is very manageable. The information provided here is intended to provide you with a high-level overview of the steps you must complete to become GIPS compliant.

holding your firm out to the public as a GIPS compliant firm, there are
three main steps that must first be completed. Firms must:

  1. Document GIPS policies and procedures
  2. Construct composites that consistently follow these policies and procedures
  3. Create compliant presentations to show the results of each composite

Document GIPS Policies and Procedures

are required to document how they comply with the GIPS requirements as
well as any recommendations that the firm chooses to follow in a
document known as the firm’s GIPS Policies and Procedures (“GIPS
P&P”). This document acts as the firm’s internal representation of
their GIPS compliance, and is intended to state the firm’s GIPS policies
as well as describe the procedures the firm follows to maintain their
compliance. Examples of items typically found in this document include:

  • Firm Definition – GIPS is applied to your firm as a whole,
    not to a single product or strategy you manage. How your firm is defined
    for GIPS purposes is primarily based on how the firm is held out to the
    public, which may differ from the legal structure of your firm.
  • Definition of Discretion –Discretion is defined differently
    for GIPS than it typically is for legal or regulatory purposes. You may
    have a discretionary contract for an account that you deem to be
    non-discretionary for GIPS purposes because of restrictions the client
    places on the implementation of the strategy. The “Definition of
    Discretion” section of your firm’s GIPS P&P should outline objective
    criteria for determining the discretionary status of accounts.
  • Policies Regarding Books and Records – Firms must be able to
    support all information included in compliant presentations as well as
    support that their client assets are real. This section of your P&P
    can outline the types of records that are maintained and in what
    format/location they are stored.
  • Calculation Methodology – While GIPS provides a framework for
    how to calculate performance, firms may have different methods for
    handling external cash flows, asset-weighting accounts, calculating
    dispersion, etc. The specifics of the methods used must be documented in
    the firm’s GIPS P&P.
  • Composite Definitions and Rules – Firms must create policies
    to ensure that accounts are placed in the appropriate composite for the
    correct time period. The timing of the movement of accounts in or out of
    composites must be based on objective criteria that is outlined in this
    section of the firm’s GIPS P&P. Other optional rules, such as
    minimum account sizes and significant cash flow thresholds can also be
    documented here to keep accounts out of composites during periods where
    the intended strategy cannot be fully implemented.
  • Error Correction Policies – Firms must create materiality
    thresholds that pre-determine the action required if errors occur in a
    compliant presentation. This section should include thresholds for all
    statistics as well as criteria for determining when errors in
    disclosures are material.

Construct Composites

the GIPS P&P is created, firms can use these policies to construct
the composites defined in the policy document. To do this, firms must:

  1. Identify all of the accounts that meet the definition of a
    composite. In other words, group all accounts by strategy, but then
    remove accounts that do not meet the firm’s definition of discretion or
    that do not meet a composite-specific rule, such as a minimum account
  2. Determine the correct time to include each account as well as remove
    any account that closed, changed strategies, or otherwise caused you to
    lose discretion. Portfolios must only be included in composites for
    periods in which they were considered discretionary for GIPS purposes.
    This helps ensure that the composite results accurately represent the
    firm’s management of the composite’s strategy and does not include
    outside noise created from client-requested restrictions.
  3. Asset-weight the monthly account-level results for each account
    included in the composite to calculate the composite-level performance
  4. Calculate all required composite-level statistics (see the list
    below) that must be included in the composite’s compliant presentation.

Create Compliant Presentations

presentations act as the firm’s external representation of their GIPS
compliance and must be provided to all prospective clients. Each
composite has a separate presentation that includes all of the required
statistics as well as the required disclosures. Statistics included in
compliant presentations include:

  • Annual composite performance (gross and/or net)
  • Annual benchmark performance
  • Number of accounts in the composite as of each year-end
  • Total assets in the composite as of each year-end
  • Total assets of the GIPS firm as of each year-end
  • A measure of internal dispersion for each annual period
  • Three year annualized ex-post standard deviation of both the composite and the benchmark based on monthly returns

Other statistics may also be required such as the percentage of
non-fee paying accounts or the percentage of bundled fee paying accounts
as of each year-end, where applicable.

Want to Learn More?

If you have any questions about how to become GIPS Compliant, we would love to help.  Longs Peak’s professionals have extensive experience helping firms become GIPS compliant as well as helping them maintain compliance with the GIPS Standards on an ongoing basis. 

Are fee-related admin issues causing errors in your investment performance?

Calculating gross and net investment performance should be simple, right? Yes, however, firms often face fee-related portfolio accounting or administrative issues that cause complications, resulting in inaccurate performance. It is essential that all types of fees are accounted for correctly to ensure reported performance can be relied upon and properly evaluated by clients and prospective investors.

Which Fees and Expenses Reduce Investment Performance?

Gross-of-fee performance represents a portfolio’s return net of transaction costs only. Net-of-fee performance is net of transaction costs and investment management fees, so the only difference between gross and net performance is the investment management fee. According to the Global Investment Performance Standards (GIPS®), investment management fees are defined to include both asset-based and performance-based fees that are earned for managing a portfolio.

If your firm is GIPS compliant, it is important to reduce performance by both types of fees when calculating net-of-fee performance. For non-GIPS compliant firms, this is still considered a best practice; however, it is common for firms with both types of fees to report performance reduced only by the asset-based fee as “Net” and performance reduced by both the asset-based fee and performance-based fee as “Net Net.”

Administrative fees, such as custody fees, do not reduce performance. This is the typical practice because clients have some control over selecting a custodian and, therefore, the administrative fees charged to their portfolio. For this reason, administrative fees are excluded from performance calculations and instead are treated like external cash flows that do not reduce their return.

The most common exception to this is net performance reported for mutual funds, which is typically calculated based on the change in the fund’s net asset value (NAV), resulting in performance that is net of all fees and expenses. Mutual fund investors do not have control over the custodian used or administrative fees charged (i.e., the manager selects the custodian), so these fees do reduce performance when calculating net returns for mutual funds.

What Are the Most Common Fee-Related Administrative Issues and How Can They Be Addressed?

The most common administrative issues that affect performance results usually are derived from:

  1. Clients paying their management fee by check or from another outside source
  2. Accounts with bundled fee structures (e.g., wrap accounts)
  3. Accounts paying asset-based fees for transactions in lieu of per-trade commissions

We will examine each of these issues below.

1.  Clients Paying Their Management Fee by Check or from Another Outside Source

In an ideal world all clients would have their management fees directly debited from the account that earned the fee; however, this is not always the case. Some clients prefer to pay their management fees by check or out of one of their multiple accounts managed by your firm. Since many firms record their accounts receivable in an accounting system separate from their portfolio accounting system (which calculates performance), a matching entry must be added to the portfolio accounting system when fees are paid. If this fee is not recorded in the portfolio accounting system, the client’s gross and net returns will be equal (neither being reduced by the management fee), which is inaccurate.

How to Add Adjusting Accounting Entries to Ensure Net-of-Fee Performance Is Accurate

When a client pays their fee by check, to correctly record this, two entries are needed in the portfolio accounting system:

  1. An external cash inflow matching the management fees paid by check.
  2. A management fee expense for the same amount.

After these two transactions are made, the portfolio’s market value will be the same as it was before entering these transactions since the two transactions offset each other. While these entries do not change the value of the portfolio, an expense is recorded that will allow the system to report the correct net-of-fee performance for the period.

Similarly, when the management fee is directly debited from another account, adjustments need to be made to both the account that paid the fee and the account that earned the fee. The account that paid the management fee will need two accounting entries:

  1. A negative management fee expense for fees paid on behalf of a different account.
  2. An external cash outflow for the same amount.

The account that earned the management fee will also need two accounting entries (note that these are the same as the entries when paid by check):

  1. An external cash inflow matching the fees paid by the other account.
  2. A management fee expense for the same amount.

Again, these transactions will not change the market value of any account as these entries simultaneously adjust cash and management fee expense by the same amount. While this has no effect on the total portfolio’s market value, it will allow net-of fee performance to be accurately reported, regardless of the source or method of the actual payment.

Forgetting to make these adjustments is very common and often leads to erroneously overstating net-of-fee performance for clients paying their fees from an outside source. It will also result in an overstatement of net-of-fee performance for any composite that includes these accounts. To avoid regulatory deficiencies or non-compliance with GIPS requirements, it is best to look into whether your firm has accounts paying management fees from outside sources and ensure proper adjustments are made.

2.  Accounts with Bundled Fee Structures, Such as Wrap Accounts

As previously discussed, gross-of-fee performance is reduced by transaction costs and net-of-fee performance is reduced by transaction costs and management fees. This can become complicated when fees and expenses are bundled together and accounted for as one bundled fee.

What to Do If Fees and Expenses Are Bundled Together and Cannot Be Separated

If fees and expenses cannot be separated, gross-of-fee performance is calculated by reducing performance by transaction costs and any fees or expenses that cannot be separated from those transaction costs. Net-of-fee performance is then calculated by reducing performance by transaction costs and management fees, as well as any fees or expenses that cannot be separated from the transaction costs or management fees. This often results in identical gross-of fee and net-of-fee performance, as both performance measures are reduced by the entire bundled fee.

This most commonly occurs with wrap accounts, where the client pays one bundled fee and the individual fees for transaction costs, management fees, etc. cannot be separately determined. When this occurs, disclosures should be included with the performance to clarify if any fees other than transaction costs and management fees have been used to reduce performance.

Alternative Presentation Options for Gross-of-Fee and Net-of-Fee Performance With Bundled Fees

Instead of presenting gross-of-fee performance that is equal to net-of-fee performance, firms often only include net returns as their official performance, but then also present “pure gross” returns as supplemental information. Pure gross returns are gross of all fees and expenses and must be disclosed as such.

3.  Accounts That Pay Asset-Based Fees for Transactions in Lieu of Per-Trade Commissions

As discussed earlier, gross-of-fee performance is reduced by transaction costs. Typically these transaction costs are the commissions tied to each executed trade; however, there has been a trend towards using asset-based fee structures for transaction costs, instead of per-trade commissions.

If an account is actively managed and trades frequently enough that an asset-based fee structure results in lower expenses than paying commissions on each trade, an asset-based fee structure may be a good option for your client. However, properly accounting for this kind of fee structure in your portfolio accounting system may be challenging, as many portfolio accounting systems have not caught up with this trend, leading to errors in the client’s reported performance.

With a commission-based structure, portfolio accounting systems typically account for each trade net of commissions, which ensures that gross-of-fee performance is net of transaction costs. All other fees and expenses are recorded as separate line items that are coded as either “performance affecting” (e.g., management fees, which reduce performance to arrive at net-of fee-returns), or “non-performance affecting” (e.g., administrative fees, which are treated as external cash flows that do not have an effect on performance).

When asset-based fee structures replace per-trade commissions, the asset-based fee is commonly accounted for as a line item, similar to management fees or other administrative expenses. The problem with this is that neither of the two options available (“performance-affecting” or “non-performance-affecting”) reduce gross-of-fee performance to account for trading costs. Instead, these options were only designed to reduce net-of-fee performance or reduce neither performance measure (i.e., there is often no transaction code that only reduces gross-of-fee performance).

How to Make Adjustments to Properly Account for Asset-Based Transaction Costs

Many systems have not created a solution for asset-based transaction costs, leaving firms to develop their own workarounds to reduce gross-of-fee returns. One example of a workaround that firms use is to record these fees as negative dividends, which results in the desired effect of reducing gross-of-fee performance. While this approach works, it is not ideal since the dividend transaction code is not intended to be used for this purpose, and should only be used as a short-term solution until your portfolio accounting system provider can offer an appropriate transaction code that will properly account for this type of fee.

Firms that have accounts with this type of fee structure for transaction costs should check with their portfolio accounting system provider to confirm if there is a way to ensure these fees are accounted for properly. Ideally, this should be addressed with a system developer or senior representative from your system provider, as this question is likely beyond the knowledge of a typical helpdesk associate, and may not be addressed in the reference materials they have available to them.

While this post is focused on fee-related administrative issues that affect performance, there are many other fee-related issues that firms face in reporting investment performance. We intend to cover additional fee-related topics in future posts, including: determining whether to use cash basis or accrual accounting for management fees, and considerations for determining when it is appropriate to use hypothetical or model management fees instead of actual management fees to calculate net-of-fee performance. If you would like to receive periodic information on these kinds of topics, please subscribe to our blog by submitting your email at the bottom of the webpage or check back frequently for new posts.

For more information on fee-related administrative issues or to discuss other investment performance or GIPS® topics, please contact Sean Gilligan at