Equity curves and the effect of compounding

Discussion in 'Risk Management' started by tireg, Mar 20, 2006.

  1. tireg


    Hmm wasn't sure how to categorize this... but something interesting that we may have all thought about before.

    Why a time-based average (5 year average) might be misleading.. and why smoother equity curves are better for the long run due to compounding.

    Haven't done any sharpe or sortino calculations... just whipped this up in excel.

    Trader A has the smoothest equity curve, with consistent 10% gains year over year.
    Trader B has an almost-smooth curve.. fluctuates from 12% gains to 8% gains yearly.
    Trader C is more volatile, going from -10% drawdown to 30% gain.
    Trader D is the most volatile, experiencing a 20% drawdown and 50% gain.

    All traders' results are displayed on a 5-year chart. Average gain for each trader per year? 10%. Results? Way different.

  2. esuperbo


    I don't believe that 1-3-5 year (or whatever) average returns are based on a simple arithmetic average.

    They are calculated by determining the % change, then adjusting it to be in terms of an annually compounded rate.

    In short, you have a good point, which is exactly why mutual funds/etc do not report average annual gains as such.
  3. You need to look at geometric average, not arithmetic. See attached

    Edit: we both forgot to subtract 1 from the compounded 5 yr returns. So they should be 61.05%, 60.94%, 51.63%, and 43.64% respectively
  4. tireg


    Dynamic, thank you for your insight.

    My original and uninformed line of thinking showed the fallacy of using arithmetic averages to evaluate portfolio performance over multiple timeframes.

    Geometric averages should instead be used because they show annualized measures of the proportional change in equity that actually occured over the time horizon being analyzed, as if the equity grew at a constant rate of return equal to the geometric mean.

    IE for Trader C in the flawed comparison, 151.63 = compounded steady return of 8.68%, or the geometric mean of their performances.. that's why it was lower than the compounded mean of 10%, or 161.05%.

    As such, any scenarios in which geometric mean is the same across different trader comparison results would mean that equity curves would all end up at the same place, and thus have the same compounded yield...

    I've plotted this out on the attached and updated excel file.

    We find that the question now becomes how much drawdown can one tolerate to achieve similar performance using various R/R scales. One can now also use the idea of geometric averages to compare the performance of a portfolio to its equivalent steady-rate-return or 'smooth-equity-curved' portfolio.
  5. tireg


    oops. updated excel file attached, demonstrating what I just said above.

    EDIT: You're right again dynamic.. fixed excel file for compounded returns; forgot to subtract 1.
  6. Suppose YOU are trader C. What steps can you take or changes can you make, that will transform you into trader A with absolutely guaranteed 100% certainty?
  7. tireg


    Find a nice fixed income instrument like... bonds or something that pays 10% compounded.