The Global Investment Performance Standards (GIPS) quite correctly point out that valuing the portfolio and calculating interim returns each time there is an external cash flow is the most accurate method for calculating the time-weighted rate of return. 

However, the standards are silent about the timing assumptions of intra-day cash flows. As a consequence firms can make their own assumptions about the timing of cash flows. An end of day assumption is perhaps the most common but the beginning of day assumption is also frequently used. The spirit of the standards clearly requires a policy to be established, documented and applied consistently.

To my knowledge there are at least six different approaches that portfolio managers might use to determine the time of an intra-day cash flow, which may result in a surprising large variation of return, so care must be taken. The six methods are:

1. End of day
2. Beginning of day
3. Intra-day weighted – normally a half day weighted Simple Dietz method but might also include a modified weighting approach weighting by the hour
4. Differentiated – beginning of the day for a cash inflow and end of day for a cash outflow or the far less common end of day for a cash inflow and beginning of day for a cash outflow
5. Actual – genuinely true time-weighted the portfolio is valued at the actual time of the cash flow – 11:15 for example.
6. Rule based – for example normally end of day but beginning of day if the cash flow is greater than 20% of the beginning value.

These different methods will result in a different denominator in the return calculation and hence the differences will be more pronounced for larger cash flows. The end of day method is perhaps the most common method and for me the most logical, I find it difficult to use any method that makes the assumption that the portfolio manager has received the cash flow before it is actually received. The portfolio manager may not be at his desk at the time of cash flow and will probably not act instantly in any event. In terms of cash outflows the portfolio manager has more influence over the timing therefore an end of day assumption that does not exclude the weight of cash flow that day is probably the most appropriate.

It should be noted that the return methodology used for part of a portfolio (sectors or even individual securities) should be consistent with the methodology used for the entire portfolio thus ensuring the sum of the parts will equal the whole, a requirement for successful attribution analysis.

The beginning of day assumption is favored by some asset managers, not so much because of its economic relevance or even the impact on calculating the return of the total portfolio but more because of the impact of calculating returns for parts of portfolios. The main problem with the end of day assumption is that if there is no money in a sector at the start of the day and there is a cash flow during the day, the denominator will remain zero, which means a return cannot be calculated, yet profits or losses may have be generated. Of course the beginning of day assumption would allow the calculation of a return. The reverse might be true for a cash outflow, if the entire value of the sector is removed there may also be a zero denominator, however this situation is rarer.

Intra-day weighting avoids any problem by ensuring there is a denominator present in the almost all situations. Half weighting the cash flow, equivalent to the simple Dietz method for longer time periods is straight forward. I’ve not seen an intra-day modified Dietz method in use but logically why not weight the average capital available to the portfolio manager by the hour.

Determining the valuation at the actual time of the cash flow and calculating a return prior to the cash flow, after the cash flow and then chain linking is the most accurate, but also the most difficult, it assumes the portfolio manager can value the portfolio accurately minute by minute.

To understand the differences in return that might result, take the following example of a portfolio with a beginning value of $100, a cash inflow of $10 at 11:15am, at which point the portfolio value immediately before the cash flow is $100.5 and a valuation at the end of the day of $110. The returns for the day using each timing assumption are as follows:

There is clearly a big difference in this example because the cash flow of $10 is quite large (but not unrealistic) compared to the start value of $100. The question the asset management firm must answer is which of these methodologies is most realistic economically.

The differentiated approach is often preferred by system designers, the more common version being beginning of day for cash inflows and end of day for cash outflows. This method ensures that the denominator always has a value in order to calculate a return, even for a new sector with zero assets at the beginning of the day. It also ensures a structurally higher capital employed which mildly dilutes returns. In the long term returns are expected to be positive (if not why invest at all), therefore this method should result in structurally slightly lower returns. Assuming beginning of day for cash outflow and end of day for cash inflow ensures a structurally lower capital employed which mildly leverages returns.

To demonstrate this effect I’ve added an extra day to our previous example in which the portfolio suffers a cash outflow at 11:15am of $10 on the second day, the value of the portfolio immediately before the cash flow being $111.5 and at the end of the day $102. The linked two day return for each method is as follows:

In this particular example the actual return is midway between the end of day and beginning of day methodologies and both differentiated methods are significantly different from the actual return. In my opinion the differentiated methods are by far the worst because they introduce a structural bias in the long term.

A further variation on the timing of cash flow, is responding to the notification of cash flow rather than the receipt of cash (or assets). In this instance the portfolio manager can trade in advance of actual receipt of cash trusting that the cash will be received before settlement is required. If trading in advance is allowed, and frequently it is not, the asset manager must make a policy decision to assume the cash flow occurs at the time of notification or receipt. If the policy decision is for the time of receipt it means in effect the portfolio is leveraged by the transactions undertaken at notification but prior to receipt of the cash.

In the absence of clear guidance from GIPS, firms must establish and document their own policy ex-ante, decisions are clearly too easily influenced ex-post. I prefer the end of day assumption for the economic rationale I described earlier, however this can cause minor issues for parts of portfolios so I do allow a rule based change if and only if the denominator would otherwise be zero. This rule allows a beginning of day assumption for that sector only in that instance, assuming there is an equal and opposite effect in the cash sector of the portfolio, thus ensuring the attribution will still add up.

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