newbie, You're making a good point. Basically, you're just adjusting position size based on volatility. A trader's expected loss can be expressed as the position size times the stop value times the percentage of losers . Example, 100 share position, $1.00 stop, 65% losers system=$65.00 loss expectancy /trade. If the volatility is such that you must increase the stop size, then you have to decrease the position size to keep risk constant. It is a common misconception that one can control risk through stop sizing. It doesn't work, because too small a stop will dramatically increase your loss percentage.
Yup, exactly. That's why I recommend that for various different stop sizes (based on % volatility) you need to run separate simulations to determine what the % loss will be for that specific stop loss amount. The % wins and risk factors on a very wide stop are very different than the % wins and risk factors on a very tight stop. Only with this information, now you can adequately adjust your position sizing because you know the true risks for that specific trade.
Precisely what I was saying in my previous post. How can you reconcile this with the adoption of an optimal f strategy?
Keep in mind that optimal f is an extremely aggressive strategy that is a product more of academia than it is of real-life trading. The drawdowns will either kill you or require margin calls if you are leveraged. Still, there are traders who use (optimal f / X) where X is their comfort level. If your optimal f is 0.4, obviously risking 40% per trade is very risky. Some traders will use X = 10 so if f=0.4 then you actually risk only 4% of your equity on each trade. *** Important Point: Remember that optimal f assumes a <A HREF="http://www.ruf.rice.edu/~lane/hyperstat/A6929.html">normally distributed</A> and <A HREF="http://www.sjsu.edu/faculty/watkins/stable.htm">stable distribution</A> of your trade results. If you were playing computerized blackjack with a true RNG and perfect strategy you could rely on optimal f without hesitation. In systems trading, you never know exactly how well that system will perform in the future, hence the problem with optimal f is that your underlying assumptions are always not correct. How far they deviate from the normal and stable distributions will affect the system's performance using optimal f. Regarding your question about how to apply optimal f to a position sizing strategy. What you have with position sizing is really several separate systems. You group each set of system by a factor of their stoploss, which is your risk per trade. For example, if you use a variable stoploss, use Average True Range (ATR) of past X bars as your volatility measurement, now you can separate your stoploss as a factor of ATR into separate "buckets". Each bucket will have a different win/loss & risk factor. You have to run optimal f for each bucket. When a new trade setup comes up, you determine what your stoploss factor is and use the corresponding optimal f. Let me give you concrete example. Your system says to buy SUNW at 12.5, the ATR(10) is 0.75, your variable stop loss says for this trade it should be placed at 12.0. Hence your "factor" will be 0.50 / 0.75 = 0.67. If you had a 1.50-pt stoploss then your "factor" would have been 2.00. You determine this factor for all of your trades and then group them into corresponding buckets. The more trades you have to produce a statistically significant analysis, the more buckets you can have, but generally speaking you could group them like: factor = 0.00 to 0.20 factor = 0.21 to 0.40 factor = 0.41 to 0.60 etc... The "standard" recommendation is at least 35 trades per bucket to produce statistically signifcantly results. Your mileage may vary here. The more the better. There are methods where you can determine what is the best interval to use to separate your factors into different buckets based on the distribution of stop sizes. The wider your min & max stoploss factor the larger your interval and/or the more buckets you will have to have. This makes sense -- a trade that uses 10x ATR(10) for a stoploss will have much different risk characteristics than a trade with 1x ATR(10) as a stoploss. Some form of volatility (I used ATR) is the common way to measure your factor, but there are other methods too. I hope that makes sense.
dottom, thanks for the detailed and helpful reply. It's funny that you mention blackjack as it was in this context that I first came across the concepts of the Kelly criterion and optimal (f/X). I will take your advice and leave optimal f to the academics at this stage, though I may need this or another sophisticated strategy in a couple of years, by which time my sims show I should have amassed about $2 billion
Orignally Posted by Newbie: The example is to show that if on average if you made 100 trades and only had 35 winners and 65 losers-yet your winners averaged 2 to 1 risk to reward..... you would still be profitable. Hi Newbie, I am glad to see you started this thread because I have been thinking about these concepts a lot lately. Unfortunately you seem to have made a critical mistake in your math that nobody noticed, if I understand your quote above as a correct component of your position sizing. What I am assuming here is that every profit you take is 2X every loss. I would call it a 1:2 Risk/Reward ratio. Every risk you take is worth 1 and every reward you take is worth 2. In the example you gave there were 4 trades and only 1 was a winner. It appears you incorrectly listed your profit on Trade #4 as 4X your risk, not 2X. To list your example using the 1:2 Risk/Reward ratio we get: Trade # 1 (Loss) = -1,000 Trade # 2 (Loss) = -1,000 Trade # 3 (Loss) = -1,000 Trade # 4 (Win) = +2,000 The total is -1,000 In your example your winning Trade # 4 used a .50 stop loss. Your 1:2 Risk/Reward scenario would only show you a dollar profit, but you listed your profit as $2 a share or $4,000. This is 4X your risk of .50 cents. So for your original example to be correct every profit taken would have to be 4X your risk, or a 1:4 Risk/Reward ratio. Your example was not quite appropriate for your concept because it is based on winning 1 out of four trades. A more appropriate example in line with your 35% winning percentage idea would be based on winning 1 out of three trades: Trade #1 (Loss) = -1,000 Trade #2 (Loss) = -1,000 Trade #3 (Win) = +2,000 But...the total is Zero. However, you are correct in saying that only winning 35% of the time would make you a winner using a 1:2 Risk/Reward Ratio: 65 Losers = -65,000 35 Winners = +70,000 The total is +5,000 But as in the zero example above if your winning percentage slipped a mere 1.67 % (You only win 33.33% of the time): 66.66% Losers = -66,660 33.33% Winners =+66,660 The total is Zero. The bottom line is in order to win with your position sizing strategy and 1:2 Risk/Reward ratio you need to win at least 33.34% of the time. Regards, Alex
Hi Dottom, You kind of lost me with the optimal f thing. Could you please post a link that tells what an optimal f is? I am not a math guy, but I have come up with some real-life trading ideas based on the concepts you mentioned in your post, I would be interested in seeing what you and others think about it: I have come up with three rules to help me âposition sizeâ or more accurately manage the actual dollar risk in my account. I use these rules because I need an effective way to manage overnight risk. I designed a spreadsheet based on these rules and I can enter my account balance on a daily basis to determine the actual dollar amounts and share size I can afford/trade for any combination of Share Price and Average True Range of the stock. The rules I have are: 1. The ATR (Average True Range in dollar amount) should not exceed my maximum per trade risk (1.5% of my account). Rationale: If a stock gaps against me overnight ordinarily it would be contained within the ATR, but certainly not always. On an average this helps protect me from gaps resulting in a drawdown of more than 1.5% of my account. 2. The dollar amount of any one trade should not exceed the value of 1/3 of my account. Rationale: If a cataclysmic event were to happen and a stock lost half its value, I would only lose a maximum of 1/6th of the equity of my account. Even if I was long and the stock went to zero, I would only lose 1/3 of my account and would still be able to continue trading. Of course if I was short up to 1/3 of my account and the stock quadrupled in price, I would lose my entire equity. However, since I donât short low priced stocks, this is unlikely to happen. 3. My largest stop should not exceed the value of 1% of my account. Rationale: 1% of my account is the most I am comfortable (on an average) with losing on each trade. Sometimes I will lose more because of overnight gaps. But sometimes stocks gap in your favor so you take the bad with the good. You could adjust all these rules (per trade risk, dollar amount of any one trade, and percentage of account as a stop) to your comfort level. These are simply the numbers I am comfortable with, and I believe they are conservative enough to keep me in the game while allowing for significant profits. I am attaching the spreadsheet. I started with a minimum atr of .5 Here are the instructions: 1. Enter your account balance in cell A3 2. Change the Share amount in the Shares column (Column B) so the 1.5% of the account (Column C) is no more than the value of cell C3. 3. Change the Maximum Price column (Column E) so the Dollar Value (Column D) is no more than the value of cell D3. 4. Adjust the formulas in C3, D3 and E3 to reflect your risk tolerance as necessary. Note: You may need to add addtional rows to the spreadsheet based to add additional ATRs and Share sizes. Let me know if you have questions. Regards, Alex
Your rules look well thought out. The important think as we all know is to have a plan that works for you and stick to it. Optimal F is the quickest way mathematically to increase your account balance by betting an "optimal fixed fraction" of your account equity on each trade. This is an offshoot of the Kelly Criterion. As I mentioned, an optimal f approach is designed for theoretical research into what could happen. The reality is you do not know if your system will continue to perform at the same level with the same distribution and variance in the future as it did in the past (heck, you're lucky just to have a profitable system, let alone ask for a stable distribution!). Also, the better the system, the larger the drawdown because you will be betting a higher optimal fraction, hence more of your account is at risk. Another note, 'optimal f' assumes that your largest lost in backtesting will be your largest loss going forward, which we know is not necessarily the case. Vince says to "pad" your largest loss with some amount so that you can be reasonably certain that your system will not generate a larger loss. For detailed analysis of optimal f, refer to one of Ralph Vince's books. He covers it in all of them. You can get a calculator to help determine optimal f & z-score <A HREF="http://www.futuresmag.com/industry/downloads/downloads.html" target="_blank">here</A>. Remember that optimal f is a theoretical approach, designed for normally distributed and stable systems, of which a trading system is NOT. Those traders who seriously utilize some for of optimal f recalculate their 'f' periodically to make sure the 'f' is within their confidence limits. The 'f' will move slightly with every new trade.
aldrums, your next step should be to modify your rules and spreadsheet to take into account multiple positions.