Hi Ray -- The answer to your question is a couple of chapters in my next book, Advanced AmiBroker. While waiting for me to finish (no definite date for release), you might read: 1. any of Ralph Vince's books. All are worth reading. His most recent is "The Leverage Space Trading Model". 2. Van Tharp's "Trade Your Way to Financial Freedom". Get the second edition. In the first edition his explanation of expectancy is wrong. In the second, it is more nearly correct, but still non-standard. If you read his "Definitive Guide to Position Sizing", be aware that all of his examples are artificial and unrealistic. There is a thread on Aussie Stocks Forum discussing that book with many of my comments. 3. Nassim Taleb's "Fooled by Randomness". 4. David Aronson's "Evidence Based Technical Analysis".
Several authors correctly point out the importance of position sizing in the long-term profitability of a trading system. The very important point to keep in mind is that estimates of trading results used to determine the position sizing must come from unbiased out-of-sample data. Using in-sample data will seriously underestimate the risk and lead to significant losses or bankruptcy. There are two components to the risk analysis, and they must be kept in balance. One is the risk a trader is willing to take in his or her account on any single trade. The recommended maximum risk is often in the 1 or 2% range. If a person has a (notional) $100,000 trading account, 1% risk is $1000. This means that the trader should hold the maximum loss of any single trade to $1000. The other is the risk associated with the trading system. Measure the (out-of-sample) mean and standard deviation of trades, or mean and maximum adverse excursion of trades. The standard deviation or MAE is (almost) always significantly greater than the mean. Per trade risk is, or at least can be, determined as some multiple of standard deviation or MAE. If a trading system has an expectancy of 0.5% with a standard deviation of 1.5% (not an untypical ratio), and maximum risk is computed as 2 times standard deviation, the risk associated with this system is 3%. Assume the system gives a signal to buy some issue -- say an ETF that trades at $50.00 per share. The maximum risk is 3% or $1.50 per share. If the entire $100,000 is allocated, 2000 shares could be purchased. If the trade goes bad, $3000 could be lost. Since the $3000 risk associated with the trading system is greater than the $1000 risk associated with the account, the position size is too big. The maximum position size that can be taken is the ratio of the account risk to the trading system risk -- 1:3. To keep the two risk components in balance, the trader can take a position of 1/3 of $100,000, or 666 shares. Even without using leverage or margin, a trader who takes a position with all of the funds in his or her account is seriously at risk. In this example, the trader allocating all the funds is trading at 3 times leverage in a cash, un-leveraged, account All trading systems that have a non-zero probability of unlimited loss on any single trade have a non-zero probability of going bankrupt. The probability of that system going bankrupt increases to certainty as trading continues. Aggressive position sizing is necessary if a trader hopes to accumulate serious wealth. Ralph Vince developed / popularized "optimal f", an algorithm to calculate the fraction of a trading account that should be "bet" on any single trade in order to maximize terminal wealth. Systems that trade at optimal f are expected to have drawdowns in the 80% range on their way to the final wealth. Trading at optimal f, or anywhere near it, will create drawdowns that most traders cannot tolerate. In fact, when applying statistical methods to determine whether a trading system is broken or not, most systems would appear to be broken before they recovered. As Vince points out, trading at a risk level higher than optimal f assures bankruptcy. And, as he points out in "Leverage Space", if a multisystem is being traded (either multiple systems or multiple tradables), if any one of the systems is traded at a level higher than optimal f, the multisystem is assured of bankruptcy. The topic is a little more complex than explained here, but this should be a reasonable start. Thanks for listening, Howard On Tue, Jul 20, 2010 at 1:55 PM, raymondpconnolly < raymondpconno...@gmail.com> wrote: > > > Hi Howard, > > When deciding on position size vs. Max. Sys % Drawdown is it advisable to > use the minimum (minimum negative value) or the mean of Max. Sys % Drawdown? > Does use of the control chart methodology you outline in the ATAA > presentation alleviate the risk of a minimum Max. Sys % Drawdown scenario so > that more aggressive position sizing can be taken based on mean rather than > the minimum of Max. Sys % Drawdown ? > > My system seems be able to recover even when minimum Max. Sys % DD = -33% > which based on OOS results occurs with less than 1% probability but it still > occurs. My average profit drops 75% if I constrain Position Size as % of > equity to 2% in order to achieve minimum Max. Sys % DD = -18% . My objfn is > RAR/MDD, I'm happy with my equity curve and have expectancy > 0 with 99% > confidence but not sure how far I can push the position size. > > Thanks for your thoughts. > > Regards, > Ray > > >
