A case for a mixed cash flow treatment policy

Most of those who calculate rates of return have settled on either the end-of-day or start-of-day treatment for cash flows. Some time ago I arrived at the belief that a mixed treatment is better:

• Inflows: start-of-day
• Outflows: end-of-day.

While in bed one night, it hit me why this made perfect sense. Thinking I'd recall in the morning what I discovered that night, I didn't bother to write it down. Sadly, I didn't, and haven't been able to recall since.

But the other night, a set of examples came to mind, which seemed, though perhaps not as elegantly, to do a reasonable job justifying this belief. This time I rose from my bed and wrote them down! (The saying pale ink is better than the most retentive memory rules!).

By way of three examples I hope to justify this method, which I'll simply (for the first time) refer to as the "mixed cash flow treatment" approach. We'll use Modified Dietz as our daily return method, where our "weight" is zero, for end-of-day and one for start-of-day.

Gains (or losses) realized on investments made but not recognized until the end of the day.

We host a membership group called the Performance Measurement Forum, which meets twice a year in the States and twice a year in Europe. The subject of cash flow policy has come up a few times, and this example is one that we've discussed at some length.

Let's say your policy is to treat flows as "end-of-day" events; not uncommon. And let's make the example really simple: 

• A portfolio starts the day holding 100 shares invested in a company valued at $10 per share, for a total of $1,000 starting value (there is nothing else in the account). 
• A cash flow of $1,000 occurs and the manager invests it at the same $10 per share price (for simplicity, we'll ignore transaction costs). 
• At the end of the day the stock has risen to $11 per share.

What's your gain?

Seriously, does this make sense? I think you'll agree that it does not. The portfolio is benefiting from the gain of a purchase it hasn't yet recognized. As you can imagine, the same problem can occur if a loss occurred. It's because of examples like this that I came to realize that inflows are start-of-day events. As you can see

it yields the correct result.

When a new account is opened.

A new account gets established with an inflow (e.g., money wired in); there is no starting value without a transaction to create it. 

For our example, let's say that $10,000 comes in to open a new account and that no trading is done, so it ends with the $10,000 it began with. What's the math?

As you'll recall, we cannot divide by zero, and 0/0 has been declared undefined / indeterminate by mathematicians. If you use the end-of-day (EOD) treatment for your inflows, this will occur. And even if the asset had grown during the day, the denominator would remain zero, which is a problem if we use the end-of-day approach. The start-of-day (SOD) method yields the correct result:  0.0 percent.

When an account is terminated.

Okay, perhaps we're not so concerned with getting the returns correct for someone who's leaving, but we at least need to understand the math. Let's assume here that you've adopted the "start-of-day" approach for all flows.

The portfolio begins the day with securities valued at $100,000. We sell them for $101,000 and immediately create a withdrawal in the account (we ignore the issue with settlement, since we're using trade date accounting). 

Clearly the start-of-day treatment fails miserably here, does it not? The end-of-day approach provides the correct return for the last day that we manage money for this client. 

It's my belief that if you use only start- or end-of-day treatment for your flows, your returns are often incorrect; perhaps by just a tad, but wrong, nevertheless. But, if you use the mixed approach as your default, you'll be right much more often. Are there times when this approach is incorrect? Yes, I believe there probably are, but far less than when it's correct. 

I'm happy to report that an increasing number of firms have adopted this approach!

Your thoughts, insights, objections?