Hey man, save the cheap attacks on academicians! If it weren't for them, you'd still be looking at the stars to figure out what an option is worth! There have been other options around? Yeah, and I wonder who came up with them first! I bet someone with at least one PhD. Anyone knows that stock returns are not normal - limited liability etc create the skewness. In most decent work by academics (pick up a journal like the Journal of Financial Economics or something of similar rigor) any biases are checked and double checked, whenever a simplifying assumption is made. A battery of nonparametric robustness checks is also carried out. Secondly, if your sample is large enough, things <b>will (and do)</b> become distributed normally - simply by the virtue of the central limit theorem. Most of the research that is done now involve gigantic samples b/c of more data available and greater computing capacity (my Pentium IV machines run for several days sometimes to process the sample), given that number of obs, the assumption of normality is very warranted.
I don't quite understand what you mean when you say that stock are an increasing function of time. Are you using the idea (1.) that since the stock MARKET has an expectation over time to rise, that every individual stock also has that expectation, or (2.) that: (s) = t*x. Where s is the function of a stock, and t is the time value paired with some multiplier that is always positive, in which case I will NEVER short a stock again since I had no idea that every stock always goes up with time. If you are subscribing to the first idea, I agree that the stock MARKET is expected to rise over time because of the success of the American Economy, but even though the market is a representation of individual stock movement, the relationship is NOT reciprocal, meaning that individual stocks are NOT representative of a market, so the same generalization of the time value of the MARKET is not applicable. Chris P.S. As before if you want to talk more about that, PM me so we don't bore everyone else with this point as it is not on the same subject of the thread.
The zero long term expectation only comes true if you bet the same amount every single time and you have a risk:reward of 1:1. Give me 1.5:1 payoff and allow me to vary my bet size and I could make a living betting on coin flips. I would have an edge in expectation even with a perfectly fair coin toss. Do it 1,000 times and I make x amount, do it 2000 times and I would make more. I would only need to manage my bet size so that I wouldn't go broke if say I hit tails 10 times in a row.
Let me get this straight, you want a situation where there's a fair coin toss and if you guessed wrong you lose 100% of you bet, but if you got it right it gets doubled (or whatever asymmetry you might have in mind)? A toddler can understand you can make money in such a situation b/c the expected value of your gain will be 0.5*(-100%)+0.5*(200) = 100%. That's nice to ponder over, just as it is to think of how nice it would be to buy an in the money option for less than the value by which it is in the money. The point is, who's dumb enough to take the other side??? If you have an asymmetric payoff of the kind you want, then the likelihood of getting it right will be driven to the appropriate level where you'll break even at best (in expected value terms.) Unless the counterpart of your transactions hasn't taken math101 and is filthy rich. If so, you have found your money pump and what are you still doing on this bouard? You should be flying to Hawaii in your own jet. The situation I was discribing in previous posts assumed you traded in a <b>realistic</b> mostly rational world. Where you have to keep in mind that many traders are really smart and have abundant resources/tools to know better.
The most interesting concept I've come across is a variation of the martingale system. It is based on the almost certain statistical probabllity that over time, the coin will streak. The idea being that after each win you increase your size, but after a loss you go back to one unit. Thereby taking advantage of the certain streak. Very difficult however to find a game with exactly 50/50 odds.
Speaking of the Martingale system, I played Roulette this weekend on the West Coast and used a modified version of the Martingale system. I don't know if it can be mathematically supported, but playing just Red/Black (47.2% win rate), when I lost a bet, I would double it the next time, and then again. But unlike the Martingale, I held my triple bet steady until I won then went down to double until I won, then back to the original bet. The results were that the inevitable streaks never took me out and I was able to more than double my money in a couple hours. Mathematically I'm sure I just moved the bell curve of destruction out farther and didn't hit the inevitable large trend that would've crushed me, but it was nice to gamble and get paid for it.
The second part is sufficient by itself man, I've been trying to tell you this over and over! If the ratio is one to one (and I don't see why it would not be, unless you trade in derivatives where payoffs are not symmetric), the whole "position sizing" idea is pointless. Read the other post. <b> Give me 1.5:1 payoff and allow me to vary my bet size and I could make a living betting on coin flips. I would have an edge in expectation even with a perfectly fair coin toss. Do it 1,000 times and I make x amount, do it 2000 times and I would make more. I would only need to manage my bet size so that I wouldn't go broke if say I hit tails 10 times in a row. </b> If the probabilities of head/tails are 50-50 and someone is dumb enough to play against you <and> allow you to have a higher gain than loss - then I entirely agree. But, that is only good as a hypothetical example, for obvious reasons. In reality, if the payoff is as asymmetric as you want it, the probability of you being right will be correspondingly lower - a good example is a lottery.
You are getting me deeper into the realm of fundamental analysis than I like to go ... I don't agree with the not reciprocal part. The reason the market is expected to rise is b/c it's components are. And it really has nothing to do with the success of the economy. If the company retains even a portion of cash instead of paying it out as dividends, the price (or mkt cap) will go up b/c of reinvested funds. The market is representative of the <b>average</b> company and <b>vice versa</b> since the former is a liner function of the latter. The only reason someone would buy a risky asset such as a stock is if they expect to earn a commensurate <b>positive</b> return. That works for any time horizon you consider. Let's say it's one day. If you only plan to hold the stock for one day, there are no mkt frictions like transactions costs etc to simplify things - the only reason you would hold it would be if you expected to earn a return commensurate with the level of systematic risk the stock exposes you to. The more time passes, the more you <b>expect</b> to earn. That of course, will not necessarily materialize in any particular case, but the expected return IS positive <b>always</b>. If you expect the return to be negative, why get exposed to any risk???? Noone would hold it in that time period. That's why the observed lower returns on Mondays are an anomaly. Given that more time passes from the close of Friday to the close of Monday, you'd expect the Friday to Monday return to be higher than those of the weekdays....