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Author: NoFate One star, 50 posts Old School Fool Global Fool Motley Fool One Everlasting Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 151  
Subject: Re: Basket cases? Date: 5/11/2011 5:10 AM
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Hiya

"One reason why I think there's still opportunity in this sector for "choosy" investors like us is because the sector is all being treated the same. "

I absolutely agree with that - but I think your argument from the start of your message is getting a bit side-tracked with respect to the assessment of probabilities. What my statement referred to was the assessment of probabilities of the return scenarios for the basket chinese small cap stocks, these have already been positively-selected by the team against the rest of the 'potential fraud cases' (or less harshly, the remaining chinese small caps that offer a less favourable risk/return potential according to your research, familiarity, etc.). It is therefore neither academic, nor is it not real-world -- nor does it imply an equal weight for all chinese small caps when one agrees that as a class (now not just the basket ones) they are high risk. Maybe I wasn't very clear on this in my first message.

To make this practical - let's skip to the end of your message. If you assume that you do have selective ability (though not perfect) [which I do otherwise I wouldn't be a paying subscriber] and so you are choosing stocks that you believe offer better than average (=equal weighting) returns and you further weight them according how comfortable you feel (risk/return, handle on management, etc.) then you are still making at least an implicit assessment of the probability attached to each return scenario. You've given various figures in your messages and spoke about expecting one complete fraud, what I was trying to say in my previous message is that from all I can reconstruct out of this
(a) it is simply the case that the assessment of likelihood of returns (to date) was overly optimistic
(b) it appears to me that you assigned an insufficient weight to catastrophic scenarios for otherwise you would've constructed the basket different.

I am not trying to 'finger' you for being wrong - merely trying to point out what the choice made imply (which in itself is not 'fair' in the sense that we're comparing an ex-ante assessment that could've played out as an infinite set of scenarios against the one and only one that materialised.) ... and trying to maybe give you some thoughts around probabilities (it's a topic most humans are dreadful at).

So, let me put it differently:
(a) Yes I do believe that the team has a much better than average chance at avoiding a RINO, CCME, etc.
(b) Because the class of stocks you draw from is treated all the same by the market you will be able to generate excess returns, given (a)
Important part:
(c) However, given the fact that the baseline probability of fraud/catastrophic loss for the class of entities you select from is much higher than normal you also need to adjust your posterior assessment of that risk after you've done your analysis to a level that is higher than, say, if you had started with US stocks (if you want consistent probability assessments, which everyone *should* want)
(d) You can express this assessment in many forms, for the present argument I think it is most conducive to look at it as a fat tail to the -100% return.
(e) Given (c, d) you now try to construct a basked to take away some of that risk - this whole depends on your assessment of the probabilities for each scenario. For the sake of simplicity, let's assume it's only chinese vs. US stocks and the US stocks don't move much and give somewhere between 5 - 10%, the Chinese give -100% to +25%
- Your portfolio construction with a high weight to the latter class implies that you did not believe that anything <0% was very likely, otherwise, why assign so much weight? At 0% you end up with a very low portfolio return and this is fairly stable because the return spread on the US stocks is fairly small, so most of the 'probability' mass in the distributions of outcomes you assume has to sit above the zero line for you to end up with something that's desirable. The downside to your choice is that if you strike out on the wrong stock, you've sustained a 40% loss (as per your portfolio), maybe more, maybe less depending on what the other chinese stocks return (again, the US stocks don't swing this much given their weight). So again, for your expectation to work out to something reasonable, you had to assign a lot of mass to the distribution above 0, with a big chunk sitting right up towards the positive side of your return expectation. That, however, is not consistent with (c). There is no precise formula here and it cannot be optimised generically but only for each individual's combination of assessed probabilities, loss aversion, etc. I do think, however (and you've admitted as much in your email) that this didn't go the way you expected but I would posit that this is not just because the market chose to go this way, but also due to the way the portfolio is constructed.

- The second point I'm making in these messages is that not only do the assessed probabilities appear inconsistent with (c) above but also that the construction may be inefficient. Put another way, precisely because you're faced with such different animals, will you not be able to find a combination that gives you both diversification of risk and returns that are worthwhile in combination that you could not get with a simpler construction (less transaction costs, research time, etc.) In the above example, the US stocks provide 'ballast' but in the scenarios you really care about they don't play that much of a role, so you may as well skip them. In my original understanding of the basket (higher weight to US stocks) [and yes, I know, KO's revenue are increasingly EM .. using this as shorthand only], you end up with a similar problem in that in one of the scenario you really care about (really good) you are not generating enough of an outperformance, being weighted down.

This is a very long winded explanation for the simple fact that I believe the numbers you have provided indicate that the probabilities assigned to very bad outcomes are too low and that baskets don't really work if you're putting things together that have very different return profiles (unless you correct for it by adjusting your probability assessment to give only a narrow range of outcomes that's likely). From a stats perspective, you combine two variables one with a small variance, one with a large one and you end up with a point estimate and still pretty big variance. You've gotten around this by simply reducing the variance of one of your inputs, but that is imprudent. (Note that this doesn't imply some sort of equal weighting, which we dealt with above ... it is just the case that given your research you felt comfortable and narrowed the range of likely outcomes away from -100% more significantly then looks to be justified given the baseline levels of probabilities of all things you started with).

I hope this is understandable ... maybe for those who find it hard to follow draw yourself some distributions or put some numbers on a spreadsheet but be sure to create enough scenarios across the range of all outcomes - then you'll see what I mean.

Cheers - C.
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