Is volitility linear vs position size

Discussion in 'Risk Management' started by Hooked2000, Aug 9, 2007.

  1. For example if the Vix, Atr or even actual volatility of an instrument doubled, would cutting position size in half keep the net p/l fluctuations the same as before the increased movement?

    This question was brought up at the office today and I didn't have the answer for this. The trader claims even after cutting his size in half in response to a doubling of ATR, his p/l swings are still greater. Is Volatility exponential? Or is there some formula that we could use?

  2. BENG


    Bigger trading range is just a result of volatility, they are not the same thing. Imagine a W shape day is more volatile than a V shape day with the same trading range.

    Your calcuation of ATR could also be too long when compared to the volatility generated by some very recent market sentiment. ATR is lagging behind the volatility movement.
  3. I assume your trading multiple stocks or instruments and its the "portfolio" as a whole that matters.

    It seems intuitive that if you use any leverage at all in the portfolio that an increase in volatility takes on a greater than linear change in your portfolio losses.

    Plus there are hard to show things like marketwide volatility in the positions as a whole, and liquidity may not be so good as your spreads may increase.

  4. Volatility in not exponential, it is a random variable. Some believe daily vola is a gaussian distribution, others don't. The two things to be aware of are 1) high volatilty is usually followed by high vola and the same for low vola following low vola, 2) vola is mean reverting process.

    Anyhow; the type of analysis you are looking for actually requires quite a bit of sophisticated math. You need a vola forecasting method - lookup "GARCH", or, if you want something quick and dirty just use IV from the options. That should provide you a good enough short term forecast. Then backtest that forecast with the instrument you are interested in to find the degree of correlation (some products will have minor cor, some will have high cor).

    As a side note, given the high occurence of outliers in historical/actual volatility, I happen to think that a cauchy distribution might be more appropriate for certain products. If you don't know what a cauchy dist. is I highly recommend you look it up.

    This stuff does require some advanced stats, but, I find it very helpful in assessing future risk.

    Hope that makes sense, feel free to ask any questions.

    Good luck.

  5. Its good he cut his position down relative to volatility.

    I have also been getting wider p/l swings due to more trading signals being generated.