Investment Performance Measurement on a Single Position and Aggregations

Over the past two decades I have worked on numerous projects in the field of investment performance measurement. They included customizing systems as well as designing systems from scratch, for performance measurement and all the fancy calculations on top like contribution, attribution, risk figures etc.
Obviously I had to study quite a bit of literature on these subjects. The picture shows an excerpt from the books that I collected and of course also studied while dealing with 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 the literature I found is full of very sophisticated methods for attribution or risk measurement without explaining the very basics of performance measurement. Since I had to implement these basics several times before I could get into the sophisticated numbers, the only sources of my input were other people who had already done so. Therefore, I decided to write this brief introduction to the topic.

Three typical examples

At the portfolio level (which is covered in detail in all 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 position 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 simple example of buying a share.

On the left side of the above image you can see the information that will be sent to the customer after the purchase of the share. To determine the resulting cash flows it is easiest to start on the cash account position. 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 position (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 image shows the performance calculation for the cash account and the security position 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 image.

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.

Since the stock was bought cheaper (including taxes and fees) than the end-of-day price, the performance is positive for the security position and zero for the cash account, as presumably expected. The green number shows the sum of all cash flows, and as long as it is zero, there are no performance-neutral cash flows at portfolio level.

2.) Dividend

The second example shows a dividend payment.

Again the flow on the cash account has to be compensated. At first glance, it may seem counterintuitive that the dividend is an outflow on the security position. 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 transactions with security deliveries like e.g. a split, the security positions cash flows need to be evaluated with the current market prices.

3.) Payment

In case of a simple payment I would like you to consider, that if a fee is 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 this properly.


In the payment example, the amount itself is not mapped to a performance cash flow, unlike in the dividend example.

Aggregations

Consequently, when you calculate performance at the position level, it is easy to calculate any sub-portfolio aggregations 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.

DE