Some don't agree with the opinion that typing the letters "y o u r e w r o n g d u d e" automatically guarantees correctness. Anybody can type them and attach them to any other remarks whatsoever. They in themselves are not convincing, they confer no special authority. Especially when they are attached to such faulty reasoning as equating "blowing out the first day" to having a position which is 100% long (or 100% short). Many accounts were 100% long yesterday and yet they didn't "blow out". Many accounts were 100% short yesterday (example: the Rydex Ursa mutual fund account) and yet they didn't "blow out". You're wrong dude, period.
This is pretty funny. That statement wasn't his argument, that was his closer because you're being a bit thick. Pretty sure he meant for you to look at his math... and in which case he is correct. There shouldn't be an argument here. Yolanda's chance of a blowout is bigger. Regardless if the odds are small, her risk profile is greater. Consider this. With your logic, a third trader could be introduced who trades 10x less frequently then Yolanda and bets 10x bigger. This would be a 100% bet. Do you still consider their risks equal, or will you add another qualifier saying that betting above a certain percentage is inherently riskier? If you do though, you'll have agreed with onelot that risk is dependent on betsize... which it is, there should be no argument. In fact, I have no idea why you're arguing here. I agree with man as well, the futility of using two non-edge systems as an argument against combining positive edged systems is just dumb. It shows nothing. The only thing it is good for is an exercise in probability theory. So, I have to agree with onelot: you are wrong dude, period.
Some don't agree with the opinion that typing the letters "y o u r e w r o n g d u d e" automatically guarantees correctness. Totally agree. Backed up with sound math and theory though, they're kind of hard to argue with. Maybe if you focus on the math, instead of the ego hit, you might learn something new. Especially when they are attached to such faulty reasoning as equating "blowing out the first day" to having a position which is 100% long (or 100% short). This reasoning was never stated nor implied. The little ^ symbols you see there are called powers. What I wrote was called an expression. Its a short hand way of writing the actual numerical value of getting x trades wrong in a row for 50/50 odds without having to write the really big numbers out. Sorry for not spelling it out. I thought you might have been familiar with the notation. If you're going to come back with another rebuttal, do so directed at the math. That way, other people reading might get something out of it.
I agree, the only thing it is good for is an exercise in probability theory ... an exercise which demonstrates that it is possible to create scenarios where adding more uncorrelated strategies isn't beneficial. More is not always better. I am also glad that you noticed the possibility of imagining a third trader who trades a different number of strategies than either 100 or 5000. I recommend that you imagine this third trader (call him Adam?) trades even more strategies. I recommend you imagine a trader Adam who trades 5001 strategies -- one more than Zack. Does Adam have a superior risk/reward characteristic to Zack? (No.) Is more always better? (No.) I am additionally glad that "man" didn't reflexively add a qualifier that each of the uncorrelated strategies should be profitable by itself, standalone. Because this is untrue; it's well demonstrated that there exist pairs of strategies (A, B) where A is profitable, B is unprofitable and yet the combination of A and B traded simultaneously, has superior risk/reward to either A or B alone. Certainly there are cases where it's beneficial to add losing uncorrelated strategies into the mix. But not always, not in every possible case.
Aren't the equations you stated the probability of flipping 100 or 5000 coins obtaining all heads or tails? Can you explain how that relates to calculating the risk of ruin for the portfolio strategy detailed in this thread? For the portfolio made up of 100 strategies wouldn't you need to calculate the probability the average return of the shorts is +1% and the average return of the longs is -1%? Seems it should be a much higher value than the one you wrote.
i agree in theory. but in practise i do not do it. each strategy must have positive expectation, otherwise i just do not feel good about adding it. i am basically more interested in mid frequency trading. i doubt that there are strategies which trade several times a week, have negative expectation and increase overall return/risk figures. theoretically there might be. practially i do not think so. i experienced that several times in trading related stuff. some things sound compelling in theory yet rarely have practical impact. (which does not mean the theory is "wrong").
why so theoretical? take two systems, add them by taking the average of each days change in capital of the the two. then calc the average 100day VaR for each single and for the composite. if the composite VaR is smaller you reduced your risk. the advantage of doing so is that you using "real" correlation between the two, not an abstract ex post figure.
Well that's a bit of a misunderstanding right there. On the first day, Yolanda's assistants flip 100 coins and Yolanda goes long 1% of her account for each coin that's a Heads, short 1% of her account for each coin that's a Tails. If all coins fall Heads, she's long 100% of her account: she enters into 100 simultaneous Long trades, each trade risking 1% of her account. If all coins fall Tails, she's short 100% of her account: she enters into 100 simultaneous Short trades, each trade risking 100% of her account. The coins are a mechanism for determining Yolanda's net exposure, which is readjusted each Monday. Her exposure can vary from 100% long (all Heads), to 0% long (50 Heads, 50 Tails), to 100% short (all Tails). The calculation (.5)^100 tells the probability that every one of the 100 coins will fall Heads, which is the probability that Yolanda's net exposure is 100% long. But on the first day, there aren't 100 trades "in a row" (red text above). There are 100 parallel trades, each one risking 1% of the account, which sum together to give Yolanda's net exposure. Temporarily let's pretend Yolanda trades SPY, the S&P Total Return tracking stock. In order for Yolanda to "blow out" on the first day, she would need to be 100% long (probability = 0.5^100) and the price of SPY would also have to fall to zero on that day (probability incalculable).
I wasn't referring to the argument in this thread about which portfolio had a lower risk/reward. I just don't understand the connection between onelot's equations and the portfolios risk of ruin. Can you explain it?
not sure i get it either ... you have a hundred coins, at head you win the coin at the other side you lose it, ok? 50% chance you lose the first one, or 0.5. after that you toss the next. 50% or 0.5 you lose this one as well. this adds up to 0.5 x 0.5 = 0.25 or 25%. for two coins your risk to lose both is 25%. it is easy to understand it when you think about all possible outcomes. first one loss, second win. first loss, second loss. first one win, second win. first one win, second loss. four outcomes, one makes you broke, thus risk of ruin is one divided by all cases, which is four, equals 0.25 or 25%. how is it for three coins? 0.5 x 0.5 x 0.5 = 0.125 easier to describe this by 0.5 ^ 3. for one hundred it is accordingly 0.5 ^100 to be broke immediately. now, all these assumes that the coins are completely independent from each other. or, thinking in trading terms, there is no correlation at all between them. and here is my point, why it is very theoretical: trading systems correlate. having ten systems which no corr whatsoever is impossible IMHO. so the coin tossing is nice but not more than illustrative for the statement: diversification pays off.