Hey Best Friend,
I can see where your discomfort with the weighted average equations lies. "Statistics" is about predicting outcomes. The "100% of 3% vs. 3% of 100%" model, is simply predicting outcomes, with no underlying capital at risk. So, with no risk to capital, 100% of 3% yields 3%, and 3% of 100% yields 3%, with the caveat that the statistical sample is properly sized. Having said that, in the real world, our capital is typically at risk. If we were to apply the "all or nothing" approach, meaning a straight 3% v. losing 9700% and winning 300%, you were spot on. Your comment about not knowing the outcome of the other 97% (potentially negative) would be relevant if we were discussing dynamic variables, but that is outside of the purview of this "simple" weighted average discussion. BTW, despite the fact that I understand weighted averages, I would take the 3% every time. Thanks for helping me to "refine" my earlier post.
P.S. Feel free to feed the "Goat"
http://www.google.com/images?client=safari&rls=en&q=p icture+of+old+pontiac+GTO&oe=UTF-8&um=1&ie=UTF-8&source =univ&sa=X&ei=uyiVTYv8HZOztwf2_siNDA&ved=0CCAQsAQ&biw=1 219&bih=686
Don't forget counterfractional regret (the haunting sense of what could have been). This might bias an investor's rational decision making ability on subsequent, similar transactions, e.g., "I'm not going to miss it this time".
there's a concept in law:
>In contract law, a mistake is an erroneous belief, at contracting, that certain facts are true. It can be argued as a defence, and if raised successfully can lead to the agreement in question being found void ab initio or voidable, or alternatively an equitable remedy may be provided by the courts. Common law has identified three different types of mistake in contract: the 'unilateral mistake', the 'mutual mistake' and the 'common mistake'. It is important to note the distinction between the 'common mistake' and the 'mutual mistake'.<
We have indeed been talking about different things. I believe you are correct in your argument and I plead guilty to reading over your point. What I meant originally, and what Tversky discussed, was the mathematical equivalence of a 100% chance of making $.03, and 3% chance of making $1.00. Thus the relevance of my comments about a tangential colloquy.
While the example is renovated the original point about cognitive bias obscuring rational assessments of quantitative differentials and equivalents, and their potential role in investment theses, remains.
>The facts are friendly regarding the "100% chance of 3% return v. the 3% chance of 100% return". You are correct that from a purely statistical perspective, the "weighted" return is the same.
No. You can't say that. You don't know what the other 97% of the chance is. If it's less than 0% return, the expected value is not 3%.
Example, assuming no compounding and unlimited availability of credit:
100 trials of 100% chance of 3% = 100*3% = 300%, and you still have your principal.
100 trials of 3% chance of 100% return but 97% chance of -100% return (i.e., losing your principal) = 3*100% + 97*(-100%) = -9400%, i.e. you're in hock for 93 times your original principal.
This is an extreme example, but it's enough to disprove the tautology "p(3%)=1 <==> p(100%)=.03".
Anyone not recognizing the difference between 100% chance of 3% gain and 3% chance of 100% gain is not dealing in cognitive bias so much as feeding their cash to a goat.
I agree - and thanks for your equable reply. I have no problems with DD's observations except insofar as they were offered to refute a theoretical observation.
Probabilities of outcomes go to the application - only math is needed for valuation of specified outcomes.
Basically cognitive bias explains many theories of market behavior - fear/greed, efficient market, lemmings, etc. My investing experience has been that often fear of loss, and sometimes fear based on aversion to specific threats, leads to greater valuation discounts than can be rationally or quantitatively assessed. Sometimes that leads to an investable thesis and sometimes it doesn't.
I completely agree on the bias theory of board discussions.
I try to find situations where undue aversion to certain types of risks occludes rational analysis and sets up favorable reward risk profiles, whether from perceived company specific problems or exogenous factors (e.g. fear of rising interest rates).
That's the essence of psychoarbitrage.
I make lots of decisions - many wrong - some right - but enjoy the challenge of cutting through the fluff, which works every now and then.
Smart money would say that is WAY too much invested in one stock, but then again, the fewer stocks (and moves) you make, the less your fees, so another argument would be in your favor. No one knows absolutely the "right" answer or we would all have the same opinion.
Thanks for sharing the salient parts of Tversky; cognitive bias plays a critical role in every decision we make. I've read some of those studies, and it is fascinating how counter-intuitive some of the behavior is. The key is to learn to exploit the cognitive bias, cognitive dissonance, etc. vis a vis investor behavior, looking for the arbitrage opportunities. The facts are friendly regarding the "100% chance of 3% return v. the 3% chance of 100% return". You are correct that from a purely statistical perspective, the "weighted" return is the same. Having said that, DDerinnger3 is also correct. The key to achieving the weighted return is a sufficient statistical sample. It's as simple as that. Pretty much an irrefutable fact in statistics (as long as we have eliminated dynamic variables-see retired Statistics Prof. "Jack" on the LINE board). Ironically, much of the discussion around this statistical "equation" is self proving in that it demonstrates cognitive bias on the part of the respondents.
Your original question received some excellent information, but you need to glean the good info from the overall replies. Do you manage your own portfolio and do your own taxes? If so, remember the extra paperwork involved with MLPs and REITs can be less than enjoyable. Diversify, but in moderation. I have near-retirement friends who are so over-diversified that they can't even beat the S&P. 20% in AGNC (or any other stock) is just fine if you stay tuned and understand the need for stop-loss orders. But AGNC combined with NLY and a very few MLPs can bring a great return. Combined with vigilence and stop-loss orders (that are mathematically calculated to your loss % calculation), a 10 stock portfolio is not unreasonable. If you can only check your portfolio once a week, don't like tax documents, and occasionally forget to enter the stop-loss; find some nice intermediate term tax exempt funds and open up a cold beverage.
I give up.
"Any extrapolation to compare the two situations on a mathematical basis is completely unfounded."
The two values are equal. Yes, there are other outcomes than these two - but these are the two I chose to compare.
I was speaking theoretically, you are in an applied mode.
The fact that the mathematical values are equal does not mean the application values are equal. My point had nothing to do with the "real-world investment climate", which is another discussion, a few steps away from the theoretical insight.
In any event we've beaten this to death with our tangential colloquy.
No. In the risk-seeking/aversion study, which is merely summarized in that article, the rules are clear and simple. In my example the rules are not clear and therefore nothing is simple. I gave you no reason to believe that your only choices were 0 or 3%, or 0 or 100%. I only told you what your chances at 3% or 100% were. Any extrapolation to compare the two situations on a mathematical basis is completely unfounded.
But my example is much more like the real-world investment climate. Dozens of different choices, few understood properly by anyone but the people selling them. If you are risk-averse, and you understand the risk of dealing in ambiguous investments, you'll stay away from anything more complicated than a savings account (which, truth be told, ain't that simple, and kind of locks you into very low returns, but that's better than simply being swindled).