I think one of the things that may make things curious by including short-sales is the nature of the option.

One important reason that short-sales are important is that they do indeed remove the lower bound for any given stock’s price. While it’s not totally relevant to this particular subject, it might be enlightening to read (or re-read) the section of Godel, Escher, Bach (by Douglas Hofstadter) where he discusses proofs and Bloop, Floop & Gloop. There, having both lengthening and shortening rules mean that there’s no way to predict if a proof can ever be found since you can’t create a deterministic rule for searching for possible solutions.

Here the problem is (I think) that you can’t determine your investment allocations beforehand. Without short-selling, you might just set up a rule for when to sell a stock based on the price and let it go at that. But if you may have to invest more just to hold on to what you have then it kinda bifurcates the value of the underlying stock and the value of it to you in terms of your investing goals. That is if, as I assume is the point, you both buy a stock and sell it short to protect your investment, you gain the stock’s value if the price goes up, but you also have to make a decision as to whether to give up the short position or not.

BTW, I’m not a stock expert, so I hope the above isn’t laughably naive.

]]>Following the analogy to VS and his tame networks, there really is only one independent dimension there, so the result should be fairly tame. In the real word case there is greater independence between the samples, and that the PCA resolves into eigenvectors. Due to noise these can come out in different orders, so there is lack of robustness introduced by taking a small finite number. The real world series are probably sampled from and infinite dimension population with cross correlation and autocorrealtion, a complexity that is very hard to replicate.

]]>There’s one best optimum, but lots of others that are nearly as good.

True, in most real world examples. But in theory, there is no reason not to have multiple optima – like multiple minima on y= (x^2 – 1)^2.

]]>Still don’t think much of Steve’s point about covariance and correlation getting lost when you look at the larger concept. I think this drives too much from an advocacy and a he-said she-said view of the discussion as just about trashing Mann or Steve. I have no idea if correlation of covariance makes more sense in the given example of MBH. But I do know that we should not tar the sin of off-centering with some of the result that comes from standard deviation dividing. That’s just clear thinking and disaggregation of issues.

]]>Local optima would be mathematical curiousities.

Um, no. This is very common in multivariate non-linear systems. There’s one best optimum, but lots of others that are nearly as good. The most famous example is the traveling salesman problem. What’s the shortest route between N different towns? It turns out to be impossible to solve exactly without simply walking through all possible routes when N is large. But you can get good approximations that are close to the best.

]]>I think one of the things that may make things curious by including short-sales is the nature of the option. In a sense a short sale has unlimited downside. Is the model including this aspect or just the margin at risk? If you consider that they may take your house away from you, then you really have more money at play then just the margin.

]]>We raised the data selection issue with NAS and they dodged it.

]]>In your post, I don’t quite understand the comment about local optimums. From a finance perspective, what matters is the actual optimum (portfolio risk reduction). Local optima would be mathematical curiousities.

Yes, clearly Mann has taken an approach that is very prone to mining and overfiotting and the Bloomfield (name?) comment in the NAS questioning that you can qualify which flavor of BC to use by recent performance fits right in there. The economics article on sinning in the basement seems relevant here as well (as data mining is a sin that is cautioned against, but some argument for a bit of it now and then is made). I think fishing for relationships is interesting. But only if you follow it up with some qualification of what you’ve found. Not just a math mess.

In addition to the mining of the Mann hopper, the whole thing seems rather strange. How did he come up with the overall methdo that he uses for the recon. The varuious steps and combinations. Why are some proxies more equal then others? How does he justify his particular geo-weighting. The whole thing seems like a kludge.

I guess I need to re-read MBH98, but one thing that I’ve always wondered, always bothered me. Does he give a rationale for what series are included, what not? I think this is a standard thing in social science meta-analysis. You describe what the criteria are and then say that you did a lit search and this was what came back.

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