Tuesday, July 14, 2009

Arithmetic and Geometric Mean

I completed my undergraduate work at the excellent University of Illinois, where I majored in English (Rhetoric) while secretly in awe of all the engineering students who actually had to, like, study. Starting with first semester, these students had to take a five-day-a-week Calculus class, which seemed to meet only at 8 o'clock . . . in the morning! Obviously, Calculus pops up in an engineer's daily work about as often as half the Series 65/66 material will pop up in yours. Ultimately, they are both weeding-out processes designed to thin the herd of professionals to a workable number. The students who got through Calculus 101 with an A or a B went on to enjoy technical careers, and the ones who didn't apparently now write questions for the Series 65 and 66 exams.
Like the following gem that you might actually see on your test:

If an investment adviser representative needs to calculate a portfolio's expected return, he will be working with which of the following?
A. geometric mean
B. arithmetic mean
C. mean reversion
D. harmonic mean

EXPLANATION: mean reversion can be eliminated. This is what the geniuses at Long Term Capital Management based their trading strategy on, allowing them to lose $500 billion dollars 15 years ago when something happened that their models didn't, like, factor in. I don't know what the "harmonic mean" is, and I'll probably indulge in a rare academic treat of not looking it up. If we calculated an "arithmetic mean," we would be figuring a simple average that would be misleading for investing. For example, if you put $10,000 into your brokerage account and had the following returns, what would your account be worth at the end of the third year?
Year 1: -10%
Year 2: -20%
Year 3: +30%

If we try to take a simple "arithmetic mean" or average of -10, -20, and +30%, it might seem that the account should be back at $10,000. But, in fact, the account would be worth only $9,360. When the value dropped 10%, the account went to $9,000. When it lost 20%, it dropped to $7,200. If that account rises 30%, we're only back to $9,360.
So, in order to avoid this mistake, we would need to find the so-called "geometric mean," rather than the "arithmetic mean." And, if you can choose the right term on this possible test question, you will be that much closer to passing. So, there you have it.


  1. I'm not a Calculus person. I hope I'll be okay in stock/trading/finance field!

    Anyways, I've been curious. I'm in the middle of looking for a new career (kind of). I was wondering if there are any websites that you can suggest. I'm looking for jobs specifically in the finance field that requires a Series 7. I've spend too much time studying for the Series 7. It would be a waste for me not to do anything with it. I've found a site called Broker Hunter. Are there any other sites you can recommend?
    If not, that's fine.
    Thank you, again.

  2. I would try http://www.sevenhelp.com/

    And, you might draft a cover letter to various banks, insurance companies, and full-service financial firms asking their HR department which jobs they have that require or favor a Series 7.

    Did you get your 66, too? That would open up some doors in the financial planning/money management arena.

  3. Great site! I'll look into it in more detail soon.
    My firm doesn't sponsor the Series 66. They only sponsor the 7, 63, and 55. I'm studying for the 55 right now.

    I'm guessing that an additional license(s) would help. But a Series 7 license is still better than no license, don't you think?
    I hope so.

  4. Hi, Daniel

    I don't think I've ever seen anyone devalue a SERIES 7 quite to that degree before ;).
    The SERIES 7 is the grand-daddy of all securities licenses. The 65/66 is also very useful. You can sponsor yourself for the Series 66, unless your firm has an issue with that. You use the U10 as opposed to the U4.