Is Daily Performance Really More Accurate?

By Travis Morgan, CFA, CIPM

Daily performance has long been considered the most accurate method for calculating investment performance. Its acceptance was primarily based on the assumption that it addressed the issues caused by external cash flows monthly performance methodologies could not solve. In reality, a monthly performance methodology can sometimes produce more accurate results than daily performance, and this is particularly true if the monthly methodology weights cash flows on the day they occur, such as with Modified Dietz. Furthermore, as we’ll see in the hypothetical example below, the time of day assumption used by the daily methodology can be key to its accuracy, or lack thereof.

Let’s take a portfolio with the following factors:

  • December 31st value: $1,000,000
  • January 4th value: $1,010,000
  • January 5th contribution: $500,000
  • January 5th value: $1,590,000
  • January 31st value: $1,600,000

Let’s start by using an end of day timing assumption. This means that all external cash flows are “assumed” to occur at end of day, whether the cash flows did in fact occur at end of day or not. Most portfolio accounting systems will either default to end of day, beginning of day, or a combination of both, depending on the nature of the flow (contribution vs. withdrawal, cash vs. securities, etc.).

First let’s calculate the performance using a daily performance methodology, but because in our example the only flow that occurred was on the 5th we can avoid capturing performance for remaining days.

Step 1: calculate the performance from the 31st through the 4th

$1,010,000 ÷ 1,000,000 – 1 = 1.00%

Step 2: calculate the performance from the 4th through the 5th

(1,590,000 – 500,000) ÷ 1,010,000 = 7.92%

Step 3: calculate the performance from the 5th through the end of the month

1,600,000 ÷ 1,590,000 – 1 = 0.63%

Step 4: geometrically link these returns

(1 + .01) x (1 + 0.0792) x (1 + 0.0063) – 1 = 9.69%

Second, let’s calculate the performance using a Modified Dietz monthly methodology, which weights the flows on the day that they occur and does not consider time of day. Modified Dietz has commonly been used as a way to calculate monthly performance without the need for a sub-period market value.

(1,600,000 – 500,000 – 1,000,000) ÷ (1,000,000 + (500,000 × ((31-5) ÷ 31))) = 7.05%

You’ll notice that these two methodologies produce significantly different results. Common sentiment may lead us to believe that the daily performance result of 9.69% is the more accurate one.

As you’ll recall, we are using an end of day assumption, but what if I knew in this case the flow actually occurred at the beginning of the day? In dissecting  the return for the day of the cash flow you will notice that because the flow actually happened at the beginning of the day that the portfolio made $60,000 with an asset base of 1,510,000. Using our previous end of day assumption instead, the portfolio generated $60,000 with an asset base of 1,010,000. The end of day assumption makes that day’s performance look a lot larger then it really was.

To demonstrate this, let’s calculate the daily performance using a beginning of day assumption.

Step 1: calculate the performance from the 31st to the 4th

$1,010,000 ÷ 1,000,000 – 1 = 1.00%

Step 2: calculate the performance from the 4th through the 5th

(1,590,000 – 500,000 – 1,010,000) ÷ (1,010,000 + 500,000) = 5.30%

Step 3: calculate the performance from the 5th through the end of the month

1,600,000 ÷ 1,590,000 – 1 = 0.63%

Step 4: geometrically link these returns

(1 + 0.01) x (1 + 0.053) x (1 + 0.0063) – 1 = 7.02%

You will notice that the return for the period with the cash flow (January 5th) dropped from 7.92% to 5.30% using a methodology that is more in line with what actually occurred.

We’ve demonstrated that our monthly methodology can be more accurate than the daily methodology, depending on the time of day assumption used by the daily methodology. However, if the daily methodology uses the “correct” time of day assumption, it should be more accurate. Yet as previously mentioned, systems are currently not designed to consider what time of day cash flows actually occur. Therefore, daily performance results can potentially be less accurate than the Modified Dietz methodology’s results. Note that the Modified Dietz calculated a return of 7.05%, which is only 3 basis points away from the accurate return of 7.02% we produced using daily performance and the more appropriate time of day assumption.

Of course specific results will depend on market volatility, cash flow timing, and market movement scale during the day; but isn’t daily performance supposed to solve issues like this? Unfortunately, daily performance is not perfect. Until systems are sophisticated enough to identify the cash flow time of day, performance figures should be considered good estimates at best and likely not quite the true return.

 

2 thoughts on “Is Daily Performance Really More Accurate?”

  1. Ah, beginning, middle, end-of-day . . . the bane of performance professionals.

    The blogpost is correct, although the example is contrived by having the flow occur coincidentally on such an unusual day.

    Internal flows, which occur between segments of the account are important when calculating performance for sectors within the account. Such flows are more frequent than external flows and often represent a larger percentage of the sector of interest than external flows represent for the account.

    The volatility of the sectors being greater than the volatility of the account, daily performance calculations are more accurate than Modified Dietz and thus more important to capturing what actually occurred at the sector level than is the case for the entire account.

    If account-level performance is all that’s of interest, Modified Dietz may be fine. However, if sector-level performance is being calculated, daily is the better method.

    1. Thank you Russ. You do raise good points. However, my example may be more common than you may think. We see this a lot when firms are shadowing a pooled fund within their system. As you would imagine, external flows are pretty common for these types of vehicles and questions start getting asked when performance at month end isn’t in line with their administrator’s return. More often than not, it’s a timing issue where the administrator correctly assumes the flow occurred at end of day and the firm’s system is using a beginning of day assumption.

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