Six Sigma Events

Discussion in 'Trading' started by ASusilovic, Jan 3, 2008.

  1. Six Sigma Events

    The discrepancy between normality and reality !
    Six Sigma Events have nothing to do with the Six Sigma Practice, This concept has been around since the inception of Probabilistic Risk Modeling, much before the name was borrowed to to sell business books!

    A Six Sigma Event was coined from observation of the normal distribution to describe extreme movements in market prices that contradict normal distribution assumptions.

    A six sigma event is characterized by a price drop of six times the volatility (or standard deviations) of the asset , thus the name six-sigma, sigma being the Greek letter representing volatility.


    According to normal distribution assumptions, This type of events should happen EXTREMELY rarely.

    We've actually seen quite a few in the past decade!

    - Crash of '87.
    - .....
    - Mexican Crisis. Tequila Effect.
    - Russian Devaluation .
    - Asian Crisis.
    - Technology bubble....

    The following table draws the probability that an event will occur according to the normal distribution versus the number of standard deviations and Value-at-risk
    No of Standard Deviations Probability of Occurrence Value at Risk
    1 94 600'000
    ... ... ...
    1.65 95 1'000'000
    1.96 97.5 1'200'000
    2.99 99 1'410'000
    6 99.99996 > 3 Mio
    From this, a six sigma event assumes a 99.99996 % probability of occurrence. For a daily horizon this translates into one event happening once every 2'500'000 days. All the recent market slumps i.e. '87 Crash, Mexican Tequila effect, Russian Devaluation, Asian Crisis and Internet speculative bubble, .. have all been six sigma events and they've all happened in the past two decades.

    Financial Instruments carry many risks.... and rewards for those who master them!
  2. These are the same math models that economist are using to tell us that "the us economy can stand $150 oil just fine"??
  3. I always wondered what made these researchers proclaim stock returns are distributed normally just like the heights of random adults or the weights of newborn kittens. Once they throw away the normal distribution assumption in the garbage bin the "6 sigma excuse" for money managers would disappear automatically.

    Dear Renaissance Investor,

    As promised in my July letter, posted today on the RIEF website, I want to share some thoughts on August-to-date performance in order to provide perspective on a most unusual period.

    RIEF results through July 31 were below expectations, but not extraordinarily so. I’ve previously stated that the low volatility Basic System, to which our predictions are added, was not in sync with the market during much of this period. Nonetheless, we remain confident that over time the Basic System will match the return of the S&P and, enhanced by our predictive signals, should exceed it. Since we do not attempt to track this or any other index there will be periods of positive and negative relative returns.

    August (down 8.7% through today) is a different story. The culprit is not the Basic System but our predictive overlay. While we believe we have an excellent set of predictive signals, some of these are undoubtedly shared by a number of long/short hedge funds. For one reason or another many of these funds have not been doing well, and certain factors have caused them to liquidate positions. In addition to poor performance these factors may include losses in credit securities, excessive risk, margin calls and others. All of this may not influence the direction of the overall market, but it may certainly alter the relationships of stocks to each other in a dramatic way. Given the undoubted partial overlap of our portfolios, these liquidations have had a negative impact on RIEF.

    Other examples of such liquidations are the meltdown of risk arbitrage positions in the October 1987 crash, the forced liquidation of junk bonds around 1990 and the collapse of European bonds in 1994. Some of these were in the midst of a bear market, some not.

    Such events tend to occur extremely infrequently. We cannot predict the duration of the current environment, but usually such behavior causes first pain and then opportunity. While we may hedge out some market risk, our basic plan is to stay the course and, as conditions revert to the norm, we anticipate the possibility of an attractive opportunity for RIEF. Our firm remains strong, and although Medallion has experienced some losses in August, it is solidly profitable year-to-date.

    We are confident in our approach, and we urge you to contact our staff should you have any questions.

    Jim Simons

  5. avarus


    Based on the likelihood that 98 percent of the moves will stop at two standard deviations is an easy bet in my book. If it goes beyond that, risk control will take care of the rest. The ones who blow up are those who have no idea what their VARs are at any point in time. If you have your VARs worked out properly, a six sigma event should just be a blip in the equity curve.
  6. Old news