Fitness Metric: Sharpe == RAR?

Discussion in 'Strategy Development' started by jazzguysoca, Aug 12, 2010.

  1. Stupid Question:

    Are Sharpe (trade expectation/stddev) and RAR (return/maxDD) pretty much interchangeable as fitness metrics?

    ie: All things being equal does a higher Sharpe always guarantee a higher RAR and/or lower drawdowns?

    I think the answer is "yes", as conceptually at least they seem to be measuring the same kind of thing, except that maxDD is the maximum deviation from the mean, rather than the average deviation.

    Any thoughts?

    (I'm sure acrary knows the answer and has probably already tested it, but I'm not sure if he hangs out here anymore)
     
  2. MGJ

    MGJ

    System simulators usually offer dozens of different measurements and statistics, that give you different ways to analyze the results of a particular backtest run. Here is a perturbation study of a 3-parameter system run on a simulator, for a total of 4200 different parameter settings. The two ratios are plotted against one another in a scatter plot.

    [​IMG]
     
  3. MGJ

    MGJ

    There are a few things to notice about the scatterplot.
    1. The system with the highest (CAGR% / MaxDD%) ratio ("C") does not have the highest Sharpe ratio; that honor goes to system "D". You can maximize Sharpe ratio, or you can maximize (CAGR% / MaxDD%) ratio, but you can't maximize both simultaneously.
    2. When you traverse from system "A" to system "B", Sharpe ratio rises but (CAGR% / MaxDD%) ratio falls. On the other hand,
    3. When you traverse from system "A" to system "C", Sharpe ratio rises and (CAGR% / MaxDD%) ratio also rises.

    [​IMG]
     
  4. But judging by the line of best fit, which is sloping at almost 45 degrees, you can answer that yes the two metrics are highly correlated, a high number in one means a high number in the other.
     
  5. dloyer

    dloyer

    Yes, but they are different and you still need to pick one thing to optimize for. There are a number of other risk adjusted measurments as well, such as UPI. You will get slightly different results depending on the one you pick.

    They all seem to perform slightly better than CAR for predicting out of sample performance.
     
  6. It's your 1st day at work. You hit a red light at some corner.

    Doesn't mean you'll hit it every day.

    ...................


    You hit the bus and some hot chick stands next to you. A week later, she's next to you again.

    Doesn't mean you'll have sex with her the next week.

    .......................


    Pattern and tendency...
     
  7. MGJ, thanks a bunch for posting your results - much appreciated.

    Based on your tests at least, it appears the two metrics are correlated enough to be used interchangeably. And if that's the case, what's more interesting is that it supports the notion that higher trade Sharpe ratios implies equity curves with higher overall RARs.

    Interesting..

    But I guess this shouldn't be too surprising, as its intuitive that systems which generate trades that scatter nearer their expectation will have smoother equity curves than those that are more disbursed.
     
  8. Agreed. But I think I personally lean more toward RAR, as the classic Sharpe assumes that all volatility is bad. Thus for example Sharpe will penalize systems that are more disbursed on the positive side than they are on the negative side, which is counter to what most trader's want (I don't know about you but I don't really care how much volatility there is in my positive trades - I'll take all the positive outliers I can get).

    One could use the Sortino ratio instead of the Sharpe, which I'd bet is also correlated to RAR (probably moreso).

    But for my purposes at least, RAR is more a direct measurement of what concerns me most: a system's maximum drawdown relative to its total return.