I'd better find that out by myself one day. I'm afraid the opposite of this part would be Also true and valid (mainly due to the other part mentioned above), most of the times. PS: Otherwise, you're contradicting to your own comments made about so called drag (actually I don't really understand what exactly it all means).
I said there is no drag, so I'm not sure which comments you are referring to. Could you indicate which of my points you think are in contradiction? To quickly explain so-called "drag". If I bet 1% on a coin flip, then if you look at alternating results only (i.e. head then tail, tail then head), it looks like you lose money overall on a zero expectation system. For example I start with 100 units of capital, and wager 1% on each trade. I get heads (win) and turn 100 units into 101 units. I then bet another 1% and get tails (lose) - I now have 99.99 units, not 100. Despite making one win and one loss on a breakeven expectation trade, and betting the same in % terms, I am now down. Another example - if I bet 20% on a trade and lose, I now need to make 25% to get back to breakeven...if I bet just 20% then I will only get back to 96% of my original capital if I win. So, some people have mistakenly concluded that betting fixed percentage amounts carries a "drag" in terms of inherent losses on breakeven systems. This is simply the result of errors in arithmetic. I showed a basic example disproving this fallacy a few posts ago. But no need to take my word for it - you can run Monte Carlo simulations and you will get the same result, or you can just build a large probability density function, or simply ask any competent maths professor. Regarding the irrationality of varying bet size despite identical conditions, I'll try to clarify my point clear using a simple example. Take coin-flipper A and coin-flipper B. A starts with $200 and B starts with $50. They have been flipping coins for the last hour. Thanks to a generous benefactor, the payout is 1.1:1, the win rate is 50%. The question is, how much should A and B wager on their next coin-flip? My contention is that, if A and B are identical in all current respects (risk preference, trade odds, win rate, desire for money, size of capital etc) then they will, in *all cases*, bet identical amounts. Their past wins and losses, their past equity curve, is utterly irrelevant to the correct amount to bet in the here and now. A starts with 4 times B's capital, they are identical in all other respects. Logically then, A should wager 4 times what B does. (Actually, because of the shape of typical utility curves for wealth/money, A would wager a bit less than 4 times B's wager, but for the sakes of simplicity we can ignore this factor - it's not relevant to my key point below). Now imagine B had a lucky streak and turned his first $50 into $100. A had a bad streak and his $200 has become $100. They now have identical amounts of money. They are identical in all current respects, the only difference is that A lost 50% to reach $100, whereas B made 100% to reach $100. Given that the odds on the coin are identical, their capital is identical, their risk preference is identical, how much should they wager? Obviously, they should wager an identical amount. Therefore, it is proven that the amount you won or lost in the past has, per se, no bearing whatsoever on how much you should wager now. Acrary's "system" of fixed nominal bets, rather than fixed percentage bets, would have A and B wagering different amounts, based not on the current characteristics of them and the trade facing them, but on their past characteristics - which we have just proven is an illogical approach. Thus Acrary's system has been proven wrong - it is irrational in the end state for A and B to wager different amounts. In other words, even without the maths, we can use a reductio ad absurdum to disprove Acrary's contention that betting fixed % of capital is inferior. In this particular case, Acrary's arithmetic is wrong, and thus his recommend course of action is wrong too. But we can also prove him wrong just by using indisputable axioms and basic logic, without even needing to resort to any arithmetic. Mr Subliminal had pointed out 4 years ago this clear inconsistency and the errors in acrary's thinking, but I see that acrary is still trying to defend his position. Now that he has no mathematical or logical argument to support his contentions, he is resorting to debating tricks and politician's weasel words e.g. my boss won't like it, you're trading like an engineer if you think this way, you have to treat winning streaks like a "bonus" etc. None of these are valid logical arguments, they are just BS and a poor attempt to wiggle out of having to admit he was totally wrong.
Please demonstrate how there is drag. To keep it simple, perhaps you'd want to use my coin flipping example that I posted on this thread. 50% chance of heads or tails, 1:1 payout, 1% of capital risked per coin flip, 2 flips/trades made in total. The possibilities are: H H H T T H T T Add up the results across the whole space and you get an expected end value of 100% of starting capital, not less. Where is the drag? Or we can do it another way. Let's pretend for a moment that there is drag. Since we are looking at a zero-sum game, where is that drag going, who is collecting it? Imagine a market where all the traders in it use fixed % of capital as their bet sizing principle - you are effectively saying that money will leak out of this population of traders, due to drag. Where is the money going, and how is it leaving this closed system? The unavoidable answer is that there is no net drag across the whole population of traders in this example. Since there is "drag" for those who bet 1%, lose, then bet 1% and win, this means there must be the opposite of drag for people not doing that i.e. those who get win 1%, win 1%, and lose 1%, lose 1%. The streaky traders do better than they would if they were using fixed nominal amounts.
Perhaps you base on your own assumptions too much, such as either fixed amount or %. Since one has an upwards equity curve and the other has a downwards equity curve, A and B may have two individual systems that highly possibly have quite different characteristics, in response to their market analyses based on current market consditions including interpretations and projections of latest price movements. Therefore No, they don't have to bet the same size all the times. That depends on your decisions of risk and money management approaches. Just my 2 cents.
Finally, after hundreds of hours of reading, researching and testing I've managed to grasp the idea of strategic trading. It really doesn't look that complicated now. Big thanks to Alan
There is no drag. Expected return does not change after taking into account negative and positive compounding. I'm going to nitpick for a minute here and point out that your example of coin flipping is flawed and more likely just a a poor example. To recap: trader A starts with 200, trader B with 50. Probability of win is the same for each, set at 0.5. Payout is 1.1:1. To answer your question, Kelly criterion is the optimal position sizing method with respect to return (a fraction or percentage of existing capital). See http://www.racing.saratoga.ny.us/kelly.pdf for original manuscript. It is not without its flaws, namely the high risk of ruin. This has led to others adding additional constraints to the initial objective profit maximizing function, namely probability of blowup =< some arbitrary threshold. I will assume unconstrained Kelly to illustrate my point. Given the above, Kelly = .5-.5/1.1 ~= 4.55%. Thus 4.55% of each trader's capital would be the ideal bet size in each round. However, the convergence rates of each of these strategies to 100 is different, for both your suggested method and Kelly criterion. In other words, the length of each of their 'streaks' or respective consecutive wins/losses is different. See attached excel for illustration. In short, trader A converges from 200 to 100 in about 14.9 turns (n=ln(100/200)/ln(1-4.55%)) while trader B converges from 50 to 100 in 15.6 turns (n=ln(100/50)/ln(1+4.55%)). This is assuming both use Kelly. If trader A instead uses 4x trader B's bet, notice that trader B's capital is growing while trader A's is decreasing - convergence occurs after approx. 10 rounds. Furthermore your assumption that each trader is in the same condition is also weak from the very fact that they have different initial starting capital. Each trader faces different risk profiles. As in poker, trader A will have the advantage in that he can bet less in terms of percentage of capital to achieve the same dollar returns as trader B. As a result, trader A will have less volatility. On the flip side, if trader B wanted to match trader A's dollar returns, he would have to lever up and be exposed to increased risk. You are however correct that the ideal position sizing will have to be a function of total capital at each period. I do not recall Acrary ever saying that the ideal position size should be a fixed amount. As a matter of fact I recall one post (http://elitetrader.com/vb/showthread.php?s=&postid=384111&highlight=position+sizing#post384111) in which dynamic position sizing was referenced. This seemed to me to take into account utility as well as capital. Other considerations for sizing a directional position would likely incorporate other factors such as liquidity in the constraints. To bring this thread back on topic I think that Acrary's posts have been very likely the most enlightening on this board, especially for those new to systems development. However if you blindly believe what you read on an internet forum without testing it yourself then any consequences that may arrive from your actions are your own responsibility.