We teach how to annualize rates of return in our Fundamentals of Performance Measurement course. Invariably, someone will ask whether using trade days might be better than calendar days. I normally give a brief explanation as to why it wouldn’t, and then move on.
But a funny thing happened recently:
While conducting a “non-GIPS” verification for a client, I discovered someone who uses trade days when annualizing rates of return. I found this quite curious, and so gave this topic more thought than before.
My first question was “why?” Interestingly, no clear or decisive answer could be given; perhaps it just seemed like the right thing to do at the time. Whoever was responsible for making the decision apparently is long gone, and no record of its basis apparently exists.
Let’s consider this topic a bit and see if we can decide whether annualizing rates of return with trading days rather than calendar days would work okay.
Before we proceed, let’s ensure that we understand why this is even a topic
When annualizing periods, especially ones that involve from and to dates that aren’t month-ends, we need to know the number of days for the period [as an aside, some insist on using days even when whole months are involved, since the number of days from one month to another can vary; this is an interesting idea, worthy of further reflection, but not today]. A formula we can use to annualize is:
RCum is the cumulative return for the period. We’re raising it (plus one) to the 365/T power, where “T” is the total number of days in the period. [As a further aside, the use of 365 is a totally different topic, as we might want to adjust it for leap years, something I’ve briefly addressed.]
If you’re using trade days, then instead of 365, you would use the number of trading days in the year: something like 252.
Here are the issues I have raised regarding this idea for annualizing rates of return
There are several:
- Why? I think it’s safe to say that the standard “convention” is to use calendar days. And so, to switch to trading days for annualizing rates of return must be based on some belief that it’s better; what is it? None that I could discover.
- The number of trading days per year changes from year-to-year: How will you handle these switches? What number do you then use in your “power”?
- The number of trading days can vary from region to region, country to country: While we generally agree that there are 365 days in a year, except for leap years when one is added, there is no agreement to the number of trade days across countries. This is partly because we celebrate different holidays. For example, in the USA Martin Luther King’s birthday, as well as Presidents’ Day, are holidays, while in the UK they celebrate Boxing Day. If you have a global portfolio, how will you handle these variations across countries?
- The number of trading days can vary within a country, depending on who’s doing the trading: In the USA, there are times when the banks are closed while the stock exchange remain open (and vice versa); as a result, folks who work for a bank may have fewer or more trading days than those who work for an asset manager; will there be differences within the system to account for this?
- How will you handle half-days? In the USA, there are times when the exchange closes at noon: will this be a half day?
- How do you handle dynamic changes to the number? Following 9/11, the stock exchanges in the States closed for a few days, thus reducing the number of trading days: do we alter the original number? Also, some countries will introduce “banking holidays”: will their introduction result in a change in the original number for the year?
- Income accrues over weekends and holidays; shouldn’t these days be included with the annualization? Even though we may not be trading, income accrues. Why would this be ignored? The return includes these accruals.
- What about inception-to-date – how do you determine the number of days? Imagine if you’re deriving a return for someone whose inception date was, for example, June 8, 1997, and you’re reporting to them through July 15, 2015. How many days are there in the intervening period? The number of calendar days is quite easy to derive: Excel will even do the counting for you. But coming up with the number of trading days? That seems like a lot of work.
- If you thought leap year was bad enough already… There is no standard way to handle leap years. However, whether you’re using 365, 365.25, or 366 as your standard term in your equation, the difference will be slight. As you lower the number, however, the impact will be greater.
- How do you explain differences in results? I’ve done some preliminary testing, and for the most part I get the same answer. I did a test for inception-to-date and had a one basis point difference, which isn’t huge, but it’s still a difference. More testing might reveal greater differences. If a vendor has adopted what we believe is a much more difficult way to do annualization, they have to have a good reason: what is it?
I’m a bit excited to have learned of this, as it gives us a chance to consider the possible merits of using trading days. I’m open to your thoughts. Please chime in! Should we have a RULE that says ALWAYS use calendar days? I suspect, “yes.” Let me know what YOU think!