I think one challenge a lot of folks have is calculating cash returns. The problem stems from the intra-day flows that typically occur, from trades, contributions, withdrawals, income, FX transactions, etc.

We recently had a conversation with a software vendor who is trying to get their contributions to work out; that is, that the sum of the contribution effects equals the overall account return. When this doesn’t happen, it’s often because they haven’t captured the transactions, thus the weights and returns of the securities and/or sectors haven’t been properly adjusted. This means they’re using a “holdings-based” rather than a “transaction-based” approach. Residuals are a natural part of holdings-based approaches.

This vendor assured me that they have properly accounted for the security activities, but still don’t always tie out. It appears that the culprit is cash: that is, their cash returns. And so, I think I have a simple solution, but let’s’ start with the “hard way” approach. By the way, they’re doing this on a daily basis.

**The “hard way” approach to cash returns**

If you want to calculate the return on cash, you’ll need to capture your starting value, plus all of your cash flows, as well as your ending value.

It also helps to understand what the provider of the return (often the custodian) is doing; that is, do they provide the income daily or monthly? If, for example, the income is applied irregularly throughout the month, then what you get on a given day isn’t actually from perhaps several days that occurred before that day, meaning you’ll never be able to figure out the return (okay, “never” is a long time, and surely you can, but I think it’ll take some work).

To me, this is fairly complex, thus my preference for the “easy way.”

**The “easy way” approach to cash returns**

There is a fundamental mathematical law that you’re probably familiar with:

- If A + B = C, then
- B = C – A.

It’s basic algebra, right?

Okay, and so, if we let

- A = contribution from everything other than cash
- B = contribution from cash
- C = account return

then *this I know to be true*:

- If the account return equals the contributions from everything other than cash, plus the contribution from cash
- Then, the contribution from cash equals the account return minus the contribution from everything other than cash.

Right? And if we want the return on cash, we can arrive at that by adjusting for the starting weight for cash, plus the weighted flows.

**Contribution analysis steps**

When trying to make sure your math works, I’d start with a period where there are no flows, whatsoever, and see if the sum of the contributions tie out. If they do, then you move to the next step; if they don’t, then something is amiss.

I believe that this is where this vendor spotted issues: that is, they didn’t tie out. And so, if they could confirm that everything but cash worked (that is, if they calculate the return for the account without cash, and were able to tie out the contributions of the non-cash holdings), then that pretty much says that the problem is the cash return.

When you have a global portfolio, with a variety of FX transactions occurring, which only adds more complexity to the mix, why make life harder than it needs to be? Even with non-global, why make it challenging when there’s a simple solution?

To me, simple mathematical truths can be handy tools. Again, why complicate life, when there are easier solutions.

If,

- the sum of the non-cash security contributions equals the return of the account without cash, and
- if the sum of all contributions fails to equal the account’s return
- it would make sense that the problem is the cash return, and so
- if you take the account return minus the sum of the non-cash security contributions,
- you’ll have the contribution from cash.
- And, you can then
*back into*the cash return.

Make sense? I’d love to hear from folks who are dealing with this, and perhaps have different points of view (or, folks that agree!). Please chime in.

Funny: even Sponge Bob Square Pants discusses this topic, well, sort of this topic: https://www.facebook.com/spongebob/posts/257257904364111