Over the past two decades, I’ve worked on numerous projects in the field of investment performance measurement. These have ranged from customizing existing systems to designing solutions from scratch – covering performance measurement itself as well as the more advanced calculations on – top, such as contribution, attribution and risk metrics.
Along the way, I’ve had to dive deep into the literature. The picture shows an excerpt of the books I’ve collected – and, of course, studied – while working on investment performance measurement.
What astonished me was that across all these books, the performance of a single investment position – or of any aggregated level (e.g. US equities) – is treated as a given, without ever explaining how it is actually calculated.
Most of the literature I found is full of highly sophisticated methods for attribution or risk measurement, yet it rarely explains the very basics of performance measurement. Since I had to implement these basics several times before I could get to the sophisticated numbers, my only sources were colleagues and practitioners who had already done it.
That’s why 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 a simple example: purchasing a share.
On the left-hand side of the image above, you can see the information that is sent to the customer after the share purchase. To determine the resulting cash flows, it’s easiest to start with the cash account position.
The first cash flow is always the amount debited from or credited to the account (green). Since a stock buy transaction is purely internal at portfolio level (i.e. there is nothing performance-neutral at portfolio level), the cash flow on the account must be offset by one or more opposing cash flows so that the sum at portfolio level is zero (red).
In this example, there are three opposing cash flows on the security position (purple): the purchase itself, plus the two transaction-cost components – the stamp duty and the bank’s trading fee.
If these resulting cash flows are classified (orange), the performance calculation can provide additional breakdowns such as costs and taxes, reclaimable taxes, fees, dividends, and interest received, and so on.
It also enables the calculation of gross performance figures, such as:
- 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 purchase occurs (assuming the portfolio consists only of these two positions). The "Sum Cash Flows Net" is taken directly 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 applied using a start-of-day timing, as I find that more intuitive.
As we’re only calculating a single day, the MWR (Modified Dietz) result would be the same.
Since the stock was bought at a lower price (including taxes and fees) than the end-of-day price/value, the performance is positive for the security position and zero for the cash account – as 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 offset. At first glance, it may seem counterintuitive that the dividend is an outflow on the security position. The withholding tax, on the other hand, is an inflow – which reduces the performance of the stock position in a net calculation.
If a gross performance (e.g. before reclaimable taxes) is needed, the cash flows classified as "Tax Reclaimable" (pink) should be excluded from the calculation of the "Sum Cash Flows" => see second example below.
This results in a performance-neutral outflow at portfolio level equal to the withholding tax payment.
The same method applies to interest payments. For transactions involving security deliveries – such as a split – the cash flows on the security positions need to be valued using current market prices.
3.) Payment
For a simple payment, please note that if a fee is involved, then for an accurate net calculation only the payment amount itself should be treated as a performance-neutral flow. The fee should therefore have a negative impact on the performance of the cash account – and on the portfolio overall.
In 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, once you calculate performance at the position level, it becomes straightforward to derive performance for any sub-portfolio aggregation – such as sectors, duration bands, asset classes, etc. – as well as multi-portfolio performance. It also becomes easy to measure, for example, the combined equity portion across several mixed portfolios.
To do so, the positions’ market values and cash flows need to be summed at the desired level, and the performance formulas applied “horizontally” at that aggregation level.
If you find this article of interest, please let me know and I will write a second part covering more complex examples – such as corporate actions, the handling of derivatives, a performance cash-flow classification scheme, cash-flow timing aspects (start of day, end of day, intraday, or mixed), and a few important exceptions to be aware of.
The second article of this series covers the performance cash flow timing.
If you would like to receive the examples as an Excel file, please send me an email.