Investment Performance Measurement on a Single Position and Aggregations

In the past two decades I have been working on numerous projects in the investment performance measurement field. They included the customizing of systems as well as designing systems from scratch, for performance measurement and all the fancy calculations on top like contribution, attribution, risk figures etc.
Evidently I had to study quite a bit of literature regarding these topics. The picture shows an extract of the books which I gathered, and of course also studied, while working on the topic of investment performance calculation.

What astonished me is that in all these books, the performance of a single investment position or any aggregated level (e.g. equity US) is a given fact, without explaining how it is calculated.

All literature I found is packed with very sophisticated methodologies for attribution or risk measurement, without explaining the very basics of performance measurement. As I had to implement those very basics several times, before doing the fancy stuff, the only source of input were other people who already implemented it. Therefore I decided to write this short introduction to the subject.

Three typical examples

On a portfolio level (which is fully covered in all the books) the key to any performance calculation are the performance cash flows. On a portfolio level these are typically payments or security deliveries which are considered as performance neutral. On a positon level things are a bit trickier, as any transaction has one or more performance cash flows with reference to one or more positions.

1.) Buy Stock

I will start with the easy example of buying a stock.

On the left side of the picture above you see the information which will be sent to the client after buying the stock. To determine the resulting cash flows it is easiest to start on the cash account positon. The first cash flow is always the amount debited or credited to the account (green). As a stock buy transaction is a solely portfolio internal matter (nothing performance neutral on the portfolio level) the cash flow on the account has to be compensated with one or more opposed cash flows, so that the sum on the portfolio level is zero (red). In this example we have three opposed cash flows on the security positon (purple). The first is the buy itself; the two other ones are the stamp duty and the trade fee of the bank.

If those resulting cash flows are classified (orange) the performance calculation will provide additional information like costs & taxes, reclaimable taxes, fees, dividends and interest received etc.
It will also allow you to calculate gross performances like

  • Performance before reclaimable taxes
  • Performance before management fee
  • Performances before management fee and reclaimable taxes
  • etc.
    => See example dividend further down.

The next picture shows the performance calculation for the cash account and the security positon on the day the buy occurs (We assume the portfolio only consist of these two positions). The “Sum Cash Flows Net” is simply taken from the preceding picture.

The “Daily Profit” is:
Value End of Day – Value Start of Day –Cash Flows

The “Daily Net Performance” for a TWR Calculation is calculated as:
Value End of Day / (Value Start of Day + Cash Flows) -1

The Cash flows are taken with a start of day timing as it is more intuitive in my point of view.
As we are calculating only one single day, the MWR (modified Dietz) performance would be the same.

Because the stock was bough cheaper (including tax and fee) as the end of day price, the performance is positive for the security positon, and as presumably expected zero for the cash account. The green figure shows the sum of all cash flows and as long as it is zero, there are no performance neutral cash flows on the portfolio level.

2.) Dividend

The second example shows a dividend payment.

Again the flow on the cash account has to be compensated. On first sight it might seems strange that the dividend is an outflow on the security positon. The withholding tax is on the other hand an inflow which decreases the performance of the stock position in a net calculation.

If a gross performance (e.g. before reclaimable taxes) is needed, the cash flows which are classified as “Tax Reclaimable” (pink) need to be ignored in the calculation of the “Sum Cash Flows” => see second example below. This will result in a performance neutral outflow on the portfolio level which equals the withholding tax payment.

The same method applies to interest payments. If there are transaction with security delivers like e.g. a split, the security postions cash flows need to be evaluated with the current market prices.

3.) Payment

For a straightforward payment I would like you to consider, that if there is a fee involved, for an accurate net calculation only the amount of the payment should be taken into account as a performance neutral flow. Hence the fee will have a negative impact on the performance of the cash account and the portfolio. According to my experience, some standard software packages do not handle that properly.

The amount itself is not mapped to a cash flow, in contrast to the dividend payment discussed above.

Aggregations

If you are calculating the performance on a position level, it is consequently easy to calculate any sub portfolio aggregation like sectors, duration bands, asset classes etc. as well as multi-portfolio performances. It is also easy to measure e.g. only the equity parts of several mixed portfolios together.
The market values and cash flows of the positions need to be summed up on the intended level and the performance formulas have to be applied in a horizontal way.

If this article is of any interest to you please let me know, then I will write a second part covering more complicated corporate action examples, the handling of derivatives, a performance cash flow classification scheme, cash flow timing aspects (morning, evening, mid of day or mixed) and some exceptions which should be considered.

The second article of this series covers the performance cash flow timing.

If you would like to have the examples as an Excel file please send me an email.

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2 Gedanken zu „Investment Performance Measurement on a Single Position and Aggregations“

  1. Volkmar,

    I like your choice of books! I think it is a fair criticism there isn’t a great deal of individual security performance in my books at least – but there are others including the CIPM curriculum that goes into more detail (although more is probably needed). I will ensure there is more content in the 3rd edition – so please provide more material I’m sure it will give me good ideas.

    You have chosen one particular return methodology (in effect assuming cash flows occur at the start of day – not the most common) there are others each with their pros and cons ( in my experience you need a rules based approach that allows for a change of methodology in certain conditions). It is of course essential that you use a consistent methodology throughout to ensure contributions and attributions actual add up.

    Best regards

    Carl

    • Carl,

      I feel flattered that you read and also commented my post, thanks!

      Regarding the cash flow timing:
      – You are right with the fact that start of day is presumably not the most common one
      – As I wrote, I choose it since it is especially for examples the most intuitive one, in my point of view
      – You are also right in regards of the conditions where it should not be used. As announced at the bottom of the article, I intend to write in the second part* about some exceptions. One apparent one I thought of is the day a position is closed, where end of day timing has to be used, since otherwise you will end up with a performance of -100%. With End of day Cash Flows you have obviously also to implement an exception when opening a position (use start of day this time) otherwise you will end up with a division by 0. I am also aware that there are certain transaction types where it can be considered as a fixed rule.

      *I will also write in the second part about
      – Tricky examples like options assignment or closing of FX forwards
      – Considerations about economical exposure valuations for derivatives in performance calculation
      – A scheme for cash flow classification which will satisfy most investment reporting aspects

      Best regards
      Volkmar

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