How is "money management" for traders different from large fund management firms?

Discussion in 'Risk Management' started by ezbentley, May 16, 2009.

  1. rvince99

    rvince99

    Correlation is a good metric for measuring, say, how well two data sets track, and their respective lead/lag, or for autocorrelation of an individual data stream.

    It's a fatal mistake, however -- and I mean FATAL (I say this from firsthand experience on numerous occassions) to use correlation as a metric in allocation.
     
    #31     May 18, 2009
  2. sjfan

    sjfan

    Why in the world would you use correlation for asset allocation? or do you mean it in the sense of using mean-variance type of optimization?

     
    #32     May 18, 2009
  3. I think correlation is used in classical mean-variance allocation optimization.

    If you don't use correlation in asset allocation, I am curious as to what method/framework you use to achieve effective diversification.
     
    #33     May 18, 2009
  4. Maybe you are correct because correlation measures depend on sample size and are subject to time selection bias.

    I think Taleb is saying the same thing from a different angle (or the same).

    But then allocation is impossible.
     
    #34     May 19, 2009
  5. Do you "think" or do you know? Huge difference if we are going to listen to you.

    Your question is a good one though.
     
    #35     May 19, 2009
  6. I have read about mean-variance optimization that involves correlation, but I am not an expert. So I am here mainly to learn from other experts.
     
    #36     May 19, 2009
  7. sjfan

    sjfan

    Well, yes - mean-variance (and its derivatives, like Black-Litterman) uses correlation in the sense that it uses covariance, which is just correlation multiplied by the standard deviation of the two components.

    And to another poster, even if we go Taleb's extreme, we can still do asset allocation. It just gets a little odd and no longer involves the covariance/correlation matrix

     
    #37     May 19, 2009
  8. rvince99

    rvince99

    I KNOW that a matrix of probabilties of cross scenarios has less information loss than the simple, single metric of correlation -- particularly in the tails. I have written about this at length, performed ample studies on it, and have experienced the benefits and consequences of both, firsthand.

    Suppose I have 2 components I am looking to allocate among. Say, 98 periods one component loses 1 unit, the other, gains 2 units (the subsequent period, the reverse occurs, the former now gains 2 units, the latter loses 1 unit. They keep flipping like this, with a net gain of 1 unit, for 98 perdiods. If this were the only data, our correlation coefficient would be -1.0). Then there is the one period where they both lose 10, simultaneously, and the 100th period where they both gain 10. My correlation coefficient in this case, over the 100 periods, is -.04753. That single parameter would be used to describe the relationship of these two streams -- yet, there is a lot of information going on in there -- some really BAD stuff two on that solitary period of -10,-10.

    Contrast using this single metric with the notion of using a matrix of joint probabilities:
    p A B
    .01 -10 -10
    0 -10 -1
    0 -10 2
    0 -10 10
    0 -1 -10
    0 -1 -1
    .48 -1 2
    0 -1 10
    0 2 -10
    .48 2 -1
    0 2 2
    0 2 10
    0 10 -10
    0 10 -1
    0 10 2
    .01 10 10

    Which has more information? Which is more valuable on the disaster days?
    This is only 100 days. The outliers in real life tend to occur far less than .01,
    so your correlation coefficent, r, would typically be far more negative than shown here. (Incidentally, this matrix is the only thing one needs to gather to employ a leverage-space type model)
     
    #38     May 19, 2009
  9. sjfan

    sjfan

    Eh. there are several problems. for one, an explicit table of joint probabilities does not generalize well. You don't know the joint probabilities of anything that hasn't been observed yet. If you want something more generlized, you'll need to make distributional assumptions - by which point, correlation is just a special case.



     
    #39     May 19, 2009
  10. rvince99

    rvince99

    Indeedy -- the past is never the entire sample space, and I am not claiming that it is. However, my point that the joint probability matrix suffers less information loss than a simple, single parameter isn;t nullified by this. The single parameter does NOT prepare me for that -10,-10 period. (And in any attempt to use the past as proxy for the future, we encounter this problem; the only accurate remedy to know the future and amend the inputs accordingly. A less reliable one, to make certain assumptions)

    The matrix forces me to be heads up, budget and prepare for the .01 probability of the -10, -10 joint scenario. The simple parameter of -.04xx does not. Using a model that takes the parameter, r, of .04xx and inputs for both data streams of mean=.49 and variance=4.252424 does not provide enough information for me to budget for and prepare for the -10,-10 scenario.

    However, and MOST IMPORTANTLY, are the criterion employed. Mean Variance -- models that invoke the correlation coefficient, are generally models that seek to maximize expected returns with respect to variance (or semi-variance, or other variance-based risk metric). Using the joint probabilities table, as input to an LSP-style model, allows me not only to attempt to find that allocation set that is growth optimal (or growth optimal with respect to drawdown or risk of ruin, or other risk metric), BUT, allows me to discern functions that permit me to pursue other criteria - criteria that satisfies other investor/trader desires than merely maximizing geometric growth. I cannot do that with models that simply use the correlation coefficient because I am either A. Not smart enough or B. There is not enough information incorporated into such singular measures.
     
    #40     May 19, 2009