ROE

jptardif2jptardif2
in MSA.Ratios

Hi Graham,

Back in college when I learned about return metrics such as ROE, we divided the net income earned during year t by the equity we had at the beginning of the year. That tells us how much income we were able to generate with a certain amount of equity to start with. In these problems we are dividing by the equity we have at the end of the year. Thoughts?

Regards,

Comments

  • grahamgraham

    Hey @jptardif2,

    That's an interesting question. I poked around on the internet for information about the measurement of equity in the ROE formula but couldn't find anything satisfactory. One article seemed to say you should take the average of the beginning and ending equity for the period. Anyway, here are a few of my own thoughts:

    1. All of these financial ratios: MSA, MCT, BCAR, and whatever others there might be, are all very imperfect ways to measure the financial health of a company. It's like trying to understand a painting but being only allowed to look at 1 tiny area at a time. Maybe 1 part of the painting is a sunny sky and you think it's a painting of something nice. But maybe another part of the painting that you can't see shows storm clouds approaching. You have to start with the assumption that any 1 numeric measure of a company's health is by itself not going to tell you very much.
    2. But getting back to your point, I see the logic in what you're saying. You have a certain equity at the beginning of the year and you make business plans based on that amount. Then at the end of the year, you tally your income and see how it compares to the equity you started with. On the surface, that seems sensible, but the time period of 1 year is completely arbitrary...
    3. ...the equity doesn't stay the same over the course of the year. If in January you generate a certain amount of income, it would be nice to measure the ROE as of the end of January just to see if the company is on the right track. You might then invest this new equity to generate more income in February. Then at the end of February, you could calculate ROE using February's income divided by the equity at the start of February. In general, you can calculate ROE for any time period you want. So rather than trying to figure out whether the annual ROE should use the beginning or ending equity (or an average of the two) you could get a much more accurate answer by doing the ROE calculation monthly and then summing the 12 monthly values.
    4. This reminds me of the definition of the derivative in calculus. You start by calculating the slope of the secant line over the interval "delta x", but this is just an approximation to the slope of the tangent. If you then take the limit as "delta x" approaches 0, you get the exact value of the slope of the tangent. Here, calculating ROE over finite intervals like a year or a month is like calculating the slope of the secant, but what you really want is the slope of the tangent. If you calculate ROE over smaller and smaller intervals (weeks, days, hours, minutes!!) then you will get a better and better picture of how the company is doing at any particular instant in time (versus approximating with an average over a longer period.) Of course, it doesn't make sense to calculate ROE on a small interval like 1 minute...
    5. ...the best you could probably do is quarterly because abbreviated financial statements are done at the end of each quarter, but even that is probably too short a time frame. It takes a certain amount of time for a business plan to play out and it could be that nothing much happens in 3 months, especially in insurance where claims might have a long tail.

    My final thought on this is that the MSA definition of ROE (using ending equity) is simply for convenience. There probably isn't a justifiable reason for saying the beginning or ending or average is better. For certain scenarios, using the beginning value might give you a more accurate picture of the company but for other scenarios the ending value might be better. You don't know in advance, so you need to take any calculation with a grain of salt and not rely too much on any single number.

  • jptardif2jptardif2

    I agree 100% with what you said. I'll take these metrics with a grain of salt. If it were up to me though, I'd use the beginning equity, just because I can translate into simple words that it means (You have a certain equity at the beginning of the year and you make business plans based on that amount...). But since I'm just trying to get the FCAS title, I will bow before the MSA and do as they say.

    Thanks so much again!

  • grahamgraham

    Yes, the CAS requires bending the knee. :-)

Sign In or Register to comment.