tag:blogger.com,1999:blog-3847775060570505785.post8785998851763815759..comments2024-01-09T01:47:48.175-05:00Comments on Finance Guy: What's wrong with Paul Krugman's arithmetic?Finance Guyhttp://www.blogger.com/profile/00610439870760091838noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-3847775060570505785.post-36653493624141056472009-09-10T17:51:05.010-04:002009-09-10T17:51:05.010-04:00I never saw these comments originally so I'm r...I never saw these comments originally so I'm responding VERY late, but I encourage anonymous April 2 and anonymous April 4 to also see my post here, which is a bit more detailed, if you haven't already: http://homeofthefinanceguy.blogspot.com/2009/03/bad-arithmetic-proliferates.html<br /><br />Justin, I mostly agree with you -- the variance matters tremendously (and you give a good example except I think the investor loses all 19.5 if profits and losses are shared equally yes? Bid is 130, variance is 0, investor automatically takes straight losses down to recourse loan that starts at 110.5 yes?). However, you say that you didn't take Krugman literally that there would be an overpayment of 30%; it was just a "toy example." Krugman's own defense is similar to this, in that he says academic economists use simplified models all the time.<br /><br />I would say "fine," except for two things: 1. the very premise of his model is wrong to begin with, and however simple the model is, that premise must be correct. 2. his "toy example" gives a significantly large overpayment -- 30% -- that is considerably off, I think. I don't think the overpayment would be anywhere near that much.<br /><br />Why that matters (before I return to point #1): if the public thinks there's a huge overpayment (as opposed to perhaps a modest or small overpayment), they will be hostile to this plan, the banks will probably resist as well if for no other reason than because the public will vilify them for getting perceived big overpayments when they know they really aren't (see my nearby entry about 5 reasons the big banks are terrified of Geithner's plan -- which, incidentally, in line with my predictions, has sort of quietly faded out of sight, you may have noticed, as we move into the fall of 2009).<br /><br />Now, point #1: the premise of the model is all wrong. Remember, this is a model of overpayment. All that matters in a model of overpayment is what THE BIDDER THINKS (he's the one overpaying right?). The bidder expects the value to be $100, Krugman says. Okay. Now what will the bidder's thought process be? Something like this: "Hmm, it could be worth $100, but then again, it could be a little more or a little less, and there's a small chance it could be worth a lot more, or a lot less, and there's an even smaller chance the eventual value could lie at one of two extremes, $150 or $50." How many bidders do you think say to themselves, "I'm going to assume its final value will be either $50 or $150"? (And by the way: it doesn't even matter if you posit that the final value IS $150 or $50, and the seller, with a Godlike omniscience, somehow knows this. It doesn't matter because the bidder DOESN'T KNOW THIS and will bid simply based on an expectation that if its expected value is $100, chances are good its final value will come in close to that figure, but could be off some, and could even be way off -- say even $50 high or low). Joe Bidder will probably construct a model of the possible outcomes for the final value, and will get some kind of bell shape-y distribution of points. <br /><br />For more on this, see my blog entry I linked above. In short, I just think Paul (and I love his blog, so no venom here) made a bad assumption: that when you have an asset of uncertain value, a bidder will assume its eventual value will lie at one of two extremes and not anywhere in the middle and make his bid accordingly. And this doesn't really make sense, even at its simple heart.Finance Guyhttps://www.blogger.com/profile/00610439870760091838noreply@blogger.comtag:blogger.com,1999:blog-3847775060570505785.post-32073322885090985902009-04-05T02:16:00.000-04:002009-04-05T02:16:00.000-04:00I tend to agree with a lot of what Krugman writes,...I tend to agree with a lot of what Krugman writes, but it seems this person has a point, and I don't follow the argument in the April 4th post.<BR/><BR/>As a hypothetical example, let's say the variance around the expected value was 0. Then the asset would have 100% chance of paying out $100, meaning I'd always get back $15. But I put up $19.50, so I always lose $4.50. <BR/><BR/>Maybe there's some property of bell curves Krugman is relying on to reach his conclusion, but to me, it seems the variance around the expected value should make a difference. <BR/><BR/>At any rate, when I read Krugman's argument, I didn't take it to mean the Geithner plan actually resulted in the 30% subsidy, and more I take my brother literally when he says he will 'kill me in tennis'. It was just a toy example to illustrate the overpayment would take place, right?justin sarmanoreply@blogger.comtag:blogger.com,1999:blog-3847775060570505785.post-32918639405002987982009-04-04T18:36:00.000-04:002009-04-04T18:36:00.000-04:00Maybe you should do the arithmitic fully out? Beca...Maybe you should do the arithmitic fully out? Because of the binary structure of the payout to the investor, one only has to consider two payout points, that of loss an profits. How the payouts are distributed besides this is irrelevant, since one can substitute it with an expected value and a probability of win/loss, exactly as Krugman has. If you care to elaborate on the different probability structure that you propose, you will see that it comes up with exatcly the same result as KrugmanAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3847775060570505785.post-62308682291091066482009-04-02T20:30:00.000-04:002009-04-02T20:30:00.000-04:00Krugman was only employing a classic binomial mode...Krugman was only employing a classic binomial model used to value options. Actually the numbers were given only to illustrate his case, i.e. to show laymen how the systwm works outAnonymousnoreply@blogger.com