The basic idea of capitalism is that if individuals make decisions in their own best interest, the total value of the system is maximized. That does not hold true when you have a government structure which allows individuals to take the profit and pass on the risk (such as all the mortgage brokers who got commisions on loans but passed on the actual loan risk to others ; if they actually had to offer the loan capital themselves they would have been more careful and this never would have happened).

I've been thinking about this a while, and something that occurs to me is that there's really no need for the whole idea of a "corporation", nor is a there a need for "stock". The corporation is an artificial construct which acts like an individual but actually has many more rights than an individual.

Who needs corporations? Instead the companies should just be owned by individuals. In the end, that individual owner is fully responsible for the actions of the company. The company can be sold to another, but the legal liability for actions during that time sticks with the single owner. Corporations can no longer do things like pay out dividends when they have massive debt. Sure, they can still pay their owner, but there is no "corporate veil" - the owner is liable for all the corporation's debts, so the money is not being hidden away in a place it can't be retreived.

Who need stocks? Stockholders (and brokers) don't have the ability to really analyze companies and pick stocks well, they're just gambling. What do companies need stocks for? To raise cash for expansion. Well they can do that just by issuing bonds. Individuals can buy the bonds if they have faith in the company. The company gets cash, and the individuals get a return on their investment and capital flows to where it's needed just fine with no need for stock. The good thing about this is the company has a straightforward debt to the bondholders, and the bondholders are offered a clear risk vs return in buying the bond.

Furthermore, bond issues should go through a rating company, and that rating company should be required to insure those bonds! We got rid of stocks so there's no longer a problem of all the bogus stock hawkers, but you still might have a problem of bogus risk ratings on bonds. That's easy to fix - make the bond rater take the penalty for mis-rating the bonds. Boom rating qualities will be far more accurate and more conservative. The insurance goes like this : when you buy a bond you can choose to just buy it normally without insurance, but if you choose, the bond rater is required to give you insurance at a fixed fee based on the rating that they gave, eg. AAA= 1% fee, Baa = 3% fee or whatever; the point is that by assigning a rating they are basically picking how much vig they would need to profitably insure that bond.

You can still have things like "hedge funds" - the hedge fund manger just personally owns the funds, various people give him big loans, he runs the money and pays back the profit.

Now I'd also like to get rid of the Fed entirely and get rid of the FDIC but there may be more complaints about that. Getting rid of the FDIC is relatively easy, you just require banks to purchase insurance at market rate from various insurers instead of giving it away for basically free. Also getting rid of corporations means the owners are personally responsible for debts if the bank defaults so they would be less likely to default.

ADDENDUM : yes I know this is not practical or realistic, but I do think it's interesting as a thought experiment. I believe most of the reasons that people cite for why "we need stocks" are bogus.

1. "We need stocks to create enough aggregate wealth to fund big projects" ; not true, in fact even today those kinds of big capital-intensive projects don't raise money through stocks, they raise money from hedge funds and other large private investors; it's always been that way.

2. "We need stocks to reward entrepreneurs and early employees" ; if you mean that you need stocks to randomly massive over-reward some people and not others, then perhaps, but really this is just a big randomizer. Without stocks entrepreneurs can still get a huge payday by selling their company, or if it's actually a profitable company, they can just keep ownership of it and make a profit with it! NO WAI. In fact, the real benefit of stocks here is for people who create bogus non-profitable companies and somehow manage to convince others that it has good prospects and the stock should be worth more than it is. Early employees could easily be given profit-sharing agreements or conditional bonds which would reward them handsomely. In fact, making all these rewards more accurately tied to the real value of the company would improve the efficiency of capital markets.

3. "Stocks provide a way for the average individual to invest and grow their wealth" ; Individual selective stock ownership has been pretty widely shown to be a bad thing. People don't have the time or skill to invest wisely, and so are best off just investing in large funds. You could just as easily invest in large funds without stock ownership.

In fact, so far as I can tell, the biggest benefit of stocks and public corporations is in fact the exact thing I'm trying to eliminate - that is, responsibility for actions. If the individual running the company really had to take responsibility, they would be far less willing to take risks. Lots of exciting companies might never have happened because they were too risky. The ability to create a diffuse corporate veil is in fact very beneficial in some ways, because some amount of illogical risk is actually good for the economy. (it's an old saying that if people really understood how hard and risky it was to start a company, nobody would ever do it).

Let me illustrate foolish financial risk taking through an analogy to gambling. (Gambling with an edge is just "investing").

Consider a simple thought experiment. You are given the opportunity to bet on a coin flip where you an edge (in this example you win 53% of the time). You start with 1.0 monies. You get to bet a fixed fraction of your bankroll on each flip. eg. you could bet 1/4 of your bankroll on every flip, or 1/5 on each flip, but you aren't allowed to change the fraction. Note that as long as you pick a fraction < 100% you can never go broke. You must always bet all 100 flips.

What is the best fraction to bet ? Well, if you only care about the *average* return, the best fraction is 100%. That should be obvious if you think about it a second. Every extra dollar that you can put in this bet means more profit on average, so you should put as much as possible. But at the same time, if you bet 100% you almost always go broke. In fact only once in 2^100 do you make any profit at all.

It's a little unclear exactly what metric to use to decide which strategy is best, so lets go ahead and look some numbers :

winPercent : 53% , num bets = 100, num trials = 262144

fraction | average | sdev | profit% | median |

1/ 2 | 19.22 | 1051.56 | 1.69% | 0.00 |

1/ 3 | 7.24 | 422.89 | 13.48% | 0.02 |

1/ 4 | 4.43 | 58.10 | 24.17% | 0.18 |

1/ 5 | 3.30 | 20.66 | 30.92% | 0.44 |

1/ 6 | 2.70 | 10.43 | 38.30% | 0.67 |

1/ 7 | 2.35 | 5.79 | 46.10% | 0.85 |

1/ 8 | 2.11 | 3.94 | 46.03% | 0.97 |

1/10 | 1.82 | 2.30 | 54.18% | 1.10 |

1/12 | 1.64 | 1.61 | 53.96% | 1.17 |

1/14 | 1.53 | 1.24 | 61.69% | 1.19 |

1/16 | 1.45 | 0.99 | 61.75% | 1.20 |

1/19 | 1.37 | 0.77 | 61.94% | 1.19 |

1/22 | 1.31 | 0.62 | 61.76% | 1.18 |

1/25 | 1.27 | 0.53 | 62.10% | 1.17 |

1/29 | 1.23 | 0.43 | 69.36% | 1.16 |

1/33 | 1.20 | 0.37 | 69.22% | 1.15 |

1/38 | 1.17 | 0.31 | 69.21% | 1.13 |

1/43 | 1.15 | 0.27 | 69.40% | 1.12 |

1/49 | 1.13 | 0.23 | 69.25% | 1.11 |

fraction = fraction of bankroll placed on each bet average = average final bankroll sdev = standard deviation profit = %% of people in the trial who had any profit at all median = median average bankroll (note the sdev for the 1/2 and 1/3 bet cases is very inaccurate ; I foolishly did a monte carlo simulation rather than just directly counting it which actually is easy to do with the binomial theorem; the average return is exact)

It's easy to see in the table that the average profit is maximize for very large (risky) bets. But if you look at the profit% to see what portion of the population is benefiting, you see that in the risky bet cases only a tiny part of the population is benefiting and the high average is just because a very few people got very lucky.

It seems to me just intuitively that maximizing the median seems to produce a pretty solid strategy. For a win percent of 53% that corresponds to a bet fraction of 1/16. Another sort of reasonable approach might be to choose the point where > 50% of the population shows a profit, which would be at 1/10. (these both also occur right around the area where the sdev becomes smaller than the mean, which might be another good heuristic for picking a strategy). Using much smaller fractions doesn't really increase the profit% very much, while using larger fractions very rapidly increases the variance and descreases the profit%.

In any case I believe the analogy to finance is amusing. In a simple experiment like this it's trivial to see that when everyone is taking too much risk, it might be very good for the *whole*, but it's bad for almost every individual. It can be very profitable for a tiny portion of the population. It's also trivial to see here that any measure of the sum of the population (such as the GDP) is pretty useless when really measuring how well your strategy for the economy is working.

ASIDE: I used the fast median code from here . There are basically two sane fast ways to find a median. In most cases the fastest is the histogram method, which is basically just a radix sort, assuming you have 32 bit values or something reasonable like that. Basically you do a radix sort, but rather than read the values back out to a sorted array, you just step through the histogram until you've seen half the values and that's your median. If you can't do a radix for some reason, the other sane way is basically like quicksort. You pick a pivot and shuffle values, and then rather than descending to both sides you only need to descend to one side. This is actually still O(N) , it's not N log N, because N + N/2 + N/4 ... = 2*N which is of course O(N). Both of these methods can find the Kth largest element, the median is just a special case.

## 5 comments:

http://en.wikipedia.org/wiki/Kelly_criterion

And also, your quicksort-style median-select explanation is a bit hand wavey, since there is nothing to prevent bad partitions.

http://www.ics.uci.edu/~eppstein/161/960130.html

That Kelly thing is sort of interesting, but the article has a lot of mistakes. These statements :

"so in the long run, final wealth is maximized by setting Δ to zero, which means following Kelly strategy."

are just wrong/misleading. As is this :

"The "long run" part of Kelly is necessary because you don't know K in advance, just that as N gets large, K will approach pN. Someone who bets more than Kelly can do better if K > pN for a stretch, someone who bets less than Kelly can do better if K < pN for a stretch, but in the long run, Kelly always wins"

In fact, *mean* return is maximized by always betting 100%.

The Kelley bet maximizes the mean of the logarithm of the return, or if you prefer, it maximizes the geometric mean.

This is interesting because the geometric mean is much closer to the median than the arithmetic mean.

log-utility is also intuitive and makes good sense and has lots of writing to back it up.

The reason the "Proof" section is misleading is that he's talking about only the case where K = pN exactly, while even for large N you need to be adding in all the terms. The Kelley bet only maximizes the return for the exact case of K = pN.

Anyhoo, the interesting thing to me is just to look at the curve of how mean, median, and profit% change as you bet different amounts.

It intrigues me that geometric mean (aka antilog of the mean of the logs) is almost identical to median in this case.

Apparently that's well known, and is a standard part of the black art of people who do statistics :

http://www.childrensmercy.org/stats/model/log.asp

http://www.cyto.purdue.edu/hmarchiv/1998/0824.htm

Hmm.. Kelly's original paper (link on Wikipedia) is really good. There's a lot of stuff on this that I don't understand.

http://www.stanford.edu/~cover/portfolio-theory.html

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