How can I be your father when I'm only a year older silly? No I don't agree with that...I was agreeing with Alpha's implied suggestion...you are right, it would have been dumb of me to bother saying something patently obvious...which is why I didn't, LOL The strange brew reward to risk profiles you mutter over are real. Contrary to appearances, more risk does not always equate to more reward, neither in trading strategies nor in life strategies. As happens so frequently in all disciplines, initial appearances are not what they seem. Or rather, how it looks first glance ain't always how it is.
That is why I said "up to a point"; a point where it doesn't make sense to take on more risk. Some risk surely needs to be taken if some reward is desired - that is even true of the act of sitting still and doing nothing. There are obviously no hard and fast rules about where the point where adding more risk does not make sense actually lies. In traden4alpha's example, the strategy that risked 1.25% returned more over 2 trades than the strategy that risked 5%. Surely you don't consider risking 5% on a trade to universally (across all trading systems) be beyond the point where adding more risk doesn't make sense. Therefore I was interested to see whether he'd found some strategies that have higher potential returns with very, very low levels of risk than with reasonably high (but not insanely, optimal effly high) risk levels. On reflection, I guess I didn't explain this clearly enough.
This could be one of those times where one guy is talking about the forest and the other is talking about the trees. Before I start going off on wacky tangents like Maxwell's demon, domino chains and profit leverage, let me save myself some typing by just saying 'my bad' and bowing out of this thread....
You said what I was unable to articulate. What Daniel and Darkhorse pointed out was what I was thinking when I suggested the logic was a bit ambiguous on Trade4Alpha's original post. Since everyone seems to agree that margin can be very bad if you aren't careful - I'll toss out a realization that came with having read this thread. Since the beginning of August I've been in a drawdown. The first thing I did to protect myself was chop my size in half. Next, I went on vacation. I'm back now and things are going better. What this thread made me realize was that by chopping size, I wasn't necessarily reducing my overall portfolio exposure to the market. I was still risking 1% of my portfolio per trade. All I accomplished by chopping size was to give my stops more breathing room. If I really want to give myself some protection from the market I should reduce my (controlled risk) exposure to 1/2%. In the future I think we should have far more discussions of this nature (money management).
You are totally right, the examples are totally contrived to illustrate a point. That point is that if you use margin, the losses create a deeper hole to climb out of than if you do not use margin. In that one example a loss of 1.25/sh (on a $100/share stock) has an asymmetric impact on margin vs. non-margin traders. Whereas the non-margin trader needs a follow-on win of 1.31/sh to regain losses after a 1.25/sh loss, the 4:1 margin trader needs a 1.36/sh win to get back to break-even (including commissions, but excluding margin-interest). That said, trading systems with a sufficiently high expectation for profit will do better with margin than without. Using the example of the trade with a 1.25/sh loss, and a second trade with a win, the non-margin trader does better that the margin trader if the second trade has a gain of less than 1.38/share. But, if the second trade exceeds 1.38/sh gain (still on a $100/share stock), then the margin trader will come out further ahead of the margin trader. The issue is that some trading strategies will generate decreasing returns (and at increasing levels of risk) if you use increasing amounts of margin borrowing. (And as with so many aspects of trading, the truth is even stranger than first appears) <b>Returns vs. Margin</b> Yesterday, when daniel_m and darkhorse discussed this, I started to reply but decided to spend some more time analyzing what was happening. The first analysis was a Monte Carlo simulation of 250 trades in which each step had trading returns that where IID normally distributed with some positive mean and standard deviation. The two more analyses used a Pascal's-triangle simulation that computes the distribution of outcomes given a trading system with simple win-loss properties (trade system performance is defined by percent change in share price for win & lose, percent probability of win & lose). One Pascal's triangle sim looked at outcomes after 250 trades, the other was a detailed sim of the evolving pattern of outcomes over 10 trades. These are all SIMPLE simulations (assuming that money management and trade performance do not change as a function of the recent loss-history or account levels). Anyhoo, the results for both sims are: 1) If the expected return is positive, using margin ALWAYS increases long-term expected return by an amount more than linear in the amount margin used. 2) Use of margin leads to a skewed heavy-tailed distributions in the long-term -- increasing chance of extreme drawdowns, decreasing chance of modest returns and some chance of increasingly extreme-high returns 3) The probability of ending with less money that one started with goes to 100% with increasing levels of margin and increasing time. So, <b>daniel_m was right,</b> the more you risk (on average), then more you gain (on average). BUT this rule works by converting the trading system to a lottery-type gamble as margin usage increases. With high levels of margin borrowing, one faces an extremely high chance of losing everything that is offset by a low chance of winning a high multiple of the original account size. That the results contradict my examples, show just how dangerous contrived examples can be (or do they show how dangerous simplistic simulations can be!?!?!?!). In doing this analysis I did hit several ugly hard-to-resolve issues that reduce the benefits of margin. <b>Ugly Issue 1: Unfair Comparisons</b> Its very hard to create fair comparisons of margin vs. non-margin trading. If one assumes a trading system (with fixed rules about entry and exit based on dollar values, TA indicators, or % changes in the price of the tradable) then the trader using margin will be risking a much greater fraction of their account on each trade. In the example with trading a $100/sh stock and a 1.25/sh stop, the 4:1 margin trader is risking 5% and the non-margin trader is risking 1.25%. (NOTE: the sims that I described above assumes a trading system with fixed rules that define returns in terms of % change in position value). The alternative is to equalize risk in terms of potential loss of actual capital at risk (as darkhorse puts it). Yet to try to equalize risk to, say 2% for both traders, the 4:1 margin trader uses the 0.50 stop (on a 100/sh stock), but the non-margin trader can use a stop of $2/share (on a $100/sh stock). Under the scenario of equal-risk, the trading results for the two traders will be extremely different because the non-margin trader will not be stopped out as often. (This actually means that margin traders have a higher chance of loss than non-margin traders, which could make the use of margin counterproductive). <b>Ugly Issue 2: Continued Trading After Massive Drawdown</b> These simulations assume that the trader keeps trading even after an arbitrarily large drawdown or long string of losses. It also assumes that they enjoy the same trading returns, regardless of how small the account is drawn-down to. In reality, a massive drawndown is likely to both reduce trading performance (fixed costs like commissions, spreads, data service fees will drag on returns) and increase the chance of the trader dropping out or trading smaller size. Reducing trade size after a drawdown or string of losses puts a downward bias on expected returns because trading trajectories that would have reverted to the higher value after a loss do not revert as far because the trader stops trading or trades smaller positions. (A few preliminary sims confirmed this effect, but still margin did increase average returns) <b>Ugly Issue 3: Continued Performance After Massive Gain</b> The flip side of ugly issue 2 is that the sims assume that trading performance is unchanged as the account grows too. For high levels of margin, the aggregate average level of performance depends on rare winning streaks producing extraordinary levels of return (i.e., the account grows to tens or hundreds of times its original size). Yet other discussions on ET clearly highlight the fallacy of unlimited compounding. Many trading techniques only work (or return consistent profits) when the trader is quickly getting into and out of relatively small positions. If spectacular returns are denied to the high-margin trader, then they can never get the "lottery win" that pays off the large percentage of losing outcomes. Thus, we have another downward bias on the outcomes for aggressive users of margin. (A few preliminary sims confirmed this effect, but still margin did increase average returns) <b>Ugly Issue 4: Trader's Utility Function</b> These numerical simulations use arithmetic averages to compute the expected outcome of trading with margin. A simple arithmetic average assumes that the trader is indifferent to extreme losses or extreme gains (e.g., they are indifferent to a 50:50 bet in which they either lose ALL their trading capital with a 50% chance or double their total trading capital with a 50% chance). That traders might be risk-averse or risk-seeking (or some complex combination that is dependent of streaks of wins or losses) is NOT factored into these results. A risk-averse trader would find the chance of a 95% drawdown over an x-year time-frame abhorrent and negatively weight those losing outcomes more than is suggested by the arithmetic average used by my sims. Prudent traders will find that margin has lower expected utility even if it has higher expected dollar returns. <b>Ugly Issue 5: Freak Losses</b> As darkhorse points out, freak losses hurt the aggressive user of margin more than they do the non-margin trader. All of these sims assume that the trading system obeys a simple statistical law for profit and loss (the Monte Carlo used normally distributed returns, the Pascal triangle sim used binomial returns). Neither sim allowed for freak losses due to price gaps, trading halts, order imbalance, typos on order entry, broker failures, computer failures, etc. Although one could argue (and hope) for freak wins, I suspect most ET traders would agree that freak losses outnumber and outweigh freak wins. Again, this issue is another strike against using margin. <b>Conclusion: Messy Impact of Margin = Test Carefully!</b> The cautionary contrived examples, optimistic simplistic simulations, and list of "ugly issues" make my original point. Margin is dangerous and can skew trading system results in unfavorable ways. Yet, daniel_m's point about generally enjoying higher returns for accepting high probability of ruin also seems right. The question is, what are the results of more realistic simulations of margin use (ones with parameters and features to model all 5 ugly issues). I have not done these yet and I wonder if anyone really has? Anyway, sorry this got so long. I hope everyone trades carefully and profitably, -Traden4Alpha P.S. I am intrigued by darkhorse's wacky tangents on Maxwell's demon, domino chains, etc.
I know it seems odd to question the seemingly linear reward to risk relationship...and the tangents I mentioned are directly related to that, though more of the 'consider this' and 'look at that' variety than roads that lead anywhere meaningful. I have a mental image of what I want to convey, but as I try and put it down on paper I realize the words aren't fully there. I don't like to lay out a line of reasoning if it's incomplete and I feel like this theory isn't "done" yet. Still baking in the oven. The best I can suggest at moment is that a large real world trade sample is less like a linear series and more like a population of organisms that respond and react to each other within a controlled environment- like those computer designed amoebas that either thrive or die depending on small tweaks to their rule sets and positioning, that sort of thing. When you add asymmetrical reward to risk ratios and the concept of profit leverage into the picture, I think the net result is potentially just as surprising as the way small changes in those computer amoeba programs can lead to dramatically varied results due to sensitive dependence on initial conditions. And then there is the other real world stuff and psychological stuff on top of that, but again I don't have a concrete sense of it yet, or at least not one firm enough to articulate here. Maybe after I read Wolfram and chew on it some more I'll be able to offer something more tangible. Or maybe not, LOL
Interesting analogy, darkhorse (I like 'consider this' and 'look at that' tangents). It seems, to me, that a trading system is similar to the computer designed amoeba that you mentioned. In both cases a notional set of rules defines the thing's behavior in some environment (either the markets or a simulated petri dish). Under this analogy, leverage does two things. First, leverage accelerates the success or failure of a particular trading system -- good trading systems excel under leverage, bad trading systems blowup all the faster with leverage. Second, leverage increases the system's sensitivity to the vagaries of the environment (= the market). One freak loss or an unlucky string of regular losses can send even a good trading system into a deadly drawdown. And you are totally right, that this only accounts for the objective side of trading. The psychological issues in borrowing a whole wad'o money from a broker can certainly adversely impact trading performance and adverse impacts on trading are the last thing an overleveraged trader needs. Gotta go work on my trading system's fitness function, -Traden4Alpha
Hmm u got me musing again. Now take the above and combine it with the profit leverage concept that allows theoretical room for the opposite- that a freak string of wins from the base could send that trading system into a parabolic UPtrend due to further gains fueling themselves. Add this potential for parabolic reward based on microcurved profit leverage to the high danger downside concept, and is it not possible that you get an optimization shift away from More initial capital risk and towards Less initial capital risk? i.e. does the spiraling/reflexive concept that works in both directions though for different reasons not potentially argue for a system with smaller per trade risk potentially outperforming a system with larger per trade risk over a number of test runs even with the 'risk of ruin' element not a factor? to speak more plainly, what if we focus on using our own money to get a foot in the door and then only use the market's money after that? instead of optimal F we thus have 'ghost F', LOL or maybe i'm just smoking banana peels. fun to think about anyway.
darkhorse, <b>Bootstrapping</b> Your bootstrapping concept (using our own money to get a foot in the door and then only use the market's money after that) sounds very intriguing. The tricky key to bootstrapping, though, is to ensure that one's very first trades are winners. A drawdown at the very beginning puts he trader "in the hole" and trading on their own capital until they get back to break-even. Hmmm.. perhaps traders would want to use a split trading strategy -- trade their own money using a conservative, high P(Win) strategy and trade "the market's money" with a high-margin, high expected return strategy. <b>When Margin has Low Utility</b> Me, I'm more partial to thinking in terms of utility functions as a means of thinking about the actual value or danger of accepting risk (although I admit that I cannot quite pin-down my own personal utility function, I do know that I am risk averse). One common risk-averse utility function is U(V) = ln(V), which is the natural log of the dollar value of the account after the trade and U(V) is the utility assigned to that outcome. This utility function displays constant relative risk aversion and would have the trader invest a constant percentage of assets in risky endeavours, regardless of wealth level. Thus U(V) = ln(V) jives with the common trading advice of risking a constant 2% or so on each trade. To give an example, a person with this utility function would accept a 50:50 bet in which they lose 1/2 of their trading capital with a chance of 50% or double their trading capital with a chance of 50%. Note that the dollar expectation on this bet is strongly positive and reflects the risk premium that this risk-averse trader demands. For very small wins and losses, this utility function is nearly linear -- the person would be indifferent to a 50-50 bet with outcomes of 2% loss vs. 2.04082% win. (Of course this utility function also implies that the trader would accept a 50:50 bet that gave either a 95% drawndown(YIKES!) or a 20X increase in the account (WOOHOO!). OK, maybe I'm more risk averse than this "risk averse" utility function implies. ) Anyway, when I rerun the sims using this utility function, the expected utility of trading with margin has very different properties. A person with this type of risk aversion would have some optimal margin level (i.e., excessive margin has negative utility because the high chance of ruin outweighs the the slim chance of lottery-like winnings). With a bit'o analytic work, one can show that a binomially distributed trading system has an optimal margin level of: Optimal Margin = -(Pwin*Dwin + Ploss*Dloss)/(Dwin*Dloss) where: Pwin = the probability of a winning trade Dwin = the positive delta-% for a win Ploss = the probability of a losing trade (Ploss = 1 - Pwin) Dloss = the negative delta-% for a loss (e.g., Dloss = -0.02 if we risk 2% loss) Notice that the numerator is just the expected return for the trading system and that the negative value of Dloss in the denominator corrects the negative sign on the equation to give a positive value of optimal m. Note also, that m can be any positive number for a trading system with positive expected return. If m > 1, then the optimal strategy for a risk averse trader (who obeys the U = ln(V) utility function) is to borrow margin at a rate of m:1. If 0 < m < 1, then the optimal strategy is to only devote only a fraction of trading capital on any one trade. Note also that this formula is restricted to cases where m < -1/Dloss -- i.e. it does NOT apply to extreme combinations of over-leverage and excessive loss that can leave the trader with a negative account value (the U = ln(V) utility function means that the risk averse trader will avoid this case at all costs). <b>BIG DISCLAIMER</b> This "optimal m" still carries with it a distinct possibility of very nasty drawdowns (the utility = ln(V) is not completely risk-avoiding and will accept arbitrarily large drawdowns if the chance of extremely large winnings is large enough). And this optimal m still has ALL of the problems mentioned in the "Ugly Issues" list of my previous posting. Furthermore, this formulation assumes that the trading system obeys the simple statistical model of binomially distributed returns (wins and losses always have exactly the stated returns with exactly the stated probability with no correlation between successive trades). YOUR MILEAGE MAY VARY, but at least this formulation of a risk-averse value for optimal margin under a set of assumptions gives one some idea of how much margin to use. OK, now my head hurts, -Traden4Alpha