Sharpe ratio and Skew

Discussion in 'Strategy Development' started by minmike, Feb 16, 2007.

  1. minmike


    I have been working on system that has a pretty good Sharpe ratio. ~.5 The backtest results also have a skew of .2.

    I'm not sure how to think about this. I think the skew means that a greater than averge portion of the volatility is to the positive side. I know that volatility will lower the sharpe ratio, but I am happy to get extra profit. Any idea on how to think about this? Does it mean that the system is better than the sharpe says?

    I ran a Sortino, it was higher than the Sharpe.

    I'm having a hard time understanding the Sortino ratio. It only has negative volatility. That would appear to me not to take into acount the size of the lose. I.E. if Ilost the same amount everytime, the ratio would go to infinity.

    Any Idea how to think about all of these together?

  2. First of all, 0.5 is not a good Sharpe Ratio. Think about the definition of SR...return per unit of risk. So, your SR means that as you increase your risk, your returns only increase 1/2 as much. What you want is a SR>1.0, and ideally >2.0. You want your returns to increase more than the risk you use to achieve those returns. Anyone can crank up the volatility (through leverage) of a system to get some marginal additional return.

    As far as the Sortino, that is just a measure of return against downside volatility. In other words, you only care about the portion of your return profile that is "bad" (as you choose to define that level). This is for the guy that thinks, "I don't care about how I make money, but I'll definitely lose sleep over how my losses occur." Sortinos>3.0 are generally considered acceptable.

    One last point. These ratios mean comparatively little other than as a way to "remove" the effects of leverage from your returns so that funds' performance can be better compared. Don't get stuck on them...they are only one set of metrics.
  3. man


    out of 100 random systems, 3 will have a modified sharpe above
    1.0, just to put your result in proper perspective.
  4. man


    what do you use in addition, if i may ask?
  5. minmike


    Thanks for the advice guys. I appreciate it. When people do a Sharpe ratio, what time period is normal?

    I don't have many parameters in the system, so I don't really worry about over fitting the data. I also just did an out sample test which had a slightly better sharpe than the original. I have actually been running the Sharpe on the daily values. I don't have enough months to make any observations on that time peroid valid.

    I'm waiting another couple of weeks so that I have a month worth of forward data to test on.

    Man, I was curious how you how you came to the conclusion that 3 out of a 100 randomly will have a sharpe over 1. How many trades would that be taking, etc.

    I'm still a little new to all of these statistical methods so all the help/opinions is greatly appreciated.

  6. If all your returns are identical and negative, both the Sharpe and Sortino ratio will go to <b>negative</b> infinity (because the mean return, the numerator, is negative).

    Timeframes for Sharpe ratios can sometimes be confusing. E.g. most Sharpe ratios are reported on an annual basis, but usually you can get more precise estimates when using daily returns to calculate it. You have to multiply the daily Sharpe ratio by sqrt(250) to get the annual equivalent.

    It's also helpful to calculate a confidence interval (or standard errors), to give you a sense how stable your outcome is (or whether it's statistically different from zero). You have to use a numerical method (monte carlo) to get a confidence interval for the Sortino ratio as no closed form solution exists afaik.
  7. minmike


    Thanks for the insights Noworries. So If I understand correctly you mulitple the daliy by the square root of the amount of days a period would have. So if you were looking for monthly, it would be daily time the square root of 20?

    That helps a lot. Do you worry about skew at all? How does that affect your calculations, or do you just disregard it.?
  8. Exactly, however multiplying by sqrt(n) assumes you're not compounding.

    Wrt higher moments, I think people are more worried about kurtosis. The higher this is, the more likely your variance (and thus Sharpe) is due to some extreme outliers. Usually people don't like this. Thus if you have 2 trading systems with similar Sharpe but with different kurtosis, you'd prefer the one with the lower kurtosis.

    Using options, or dynamic replications, you can mold the distribution of your returns *in theory* in many different shapes, i.e. you can improve a Sharpe ratio by selling options, at the cost of an increase in kurtosis (which many people won't notice until a rare spike happens in the market) . In practice it's often not feasible for retail traders due to transaction cost and spreads.

    There's also this new "Omega" measure that quantifies return/risk by the entire distribution, rather than some of its moments. See for example:
  9. virgin



    What do you use yourself for quantifying reward/risk ?
  10. I use the Sharpe ratio and calculate a 95% confidence interval around it (using the bootstrap method). I closely watch the lower bound of this interval (I never trade a system if the lower 95% bound is less than zero). Sometimes I calculate a rolling Sharpe ratio, i.e. if I have 250 returns, I take r1-r50, calculate Sharpe, then take r2-r51, calculate Sharpe and plot the results in a graph, together with the confidence intervals. If the graph looks stable then I'm quite satisfied.

    I might try that Omega measure in the future.
    #10     Feb 20, 2007