Category Archives: $$$ Mgmt & Position Sizing
On the subscriber site, there is a fair amount of discussion about stops and position-sizing. The two issues actually go hand-in-hand. I want to address this relationship between stops and position-sizing.
This assumes that a trader uses percent-risk position-sizing. Percent-risk position-sizing means that one risks X% of his account on each trade. In order to manage the amount of money risked, we must know when a trade will be exited so that the account loses the specified amount. A stop-loss is the typical exit method used to ensure that trade risks only X% of the account.
Let’s look at an example.
- $10,000 account, and the trader wants to risk 1% of the account on each trade ($100.00 risked per trade).
- XYZ stock trades for $10.00/share.
- The trader could use a stop 10% beneath his entry: $10.00*.10=$100.00
- In the example above, he would have purchased 100 shares. 100 shares @ $10.00/share = $1000.00 position.
- When this $1000.00 position stops out at 10% loss, he loses his risk of $100.00
However, what if the trader wants to use a stop of 5%? Then his position would be twice as large as using a 10% stop.
- He would have purchased 200 shares. 200 shares @ $10.00/share = $2000.00 position.
- When this $2000.00 position stops out at 5% loss, he loses his risk of $100.00 ($2000.00*.05=$100.00)
So there is a direct connection between the stop-loss level and the size of the position.
With a winning setup and exit strategy, percent-risk position-sizing has multiple, extremely important implications. Hopefully some of these implications will become apparent. If not, I’ll have to do a better job later fleshing it all out.
Let’s look at a real life example.
We’ll use the Power Dip, which uses entry and exit strategies that generate a positive expectancy. This first test used a 5% stop. The tests that will follow will use larger stops. In the end, we’ll draw some conclusions about the effect the stop (and by default, the size of the position) had on system performance
Here are the stats of the backtest:
The most important stats in terms of this discussion are as follows:
- Avg. Profit/Loss %
- Avg. Profit %
- Avg. Loss %
- Risk-Reward Ratio
- Number of Trades
As the stop-loss percentage gets smaller, we’ll see a decrease in the Avg. Loss % and an increase in the Risk-Reward Ratio. We will also see a decreased Avg. Profit/Loss % and a decreased Winners %. So with a decrease in the Avg. Profit/Loss % and decreased Winners %, how does the system make money? Good question…Since the stop is tight at 5%, we have fewer winning trades (59.22% in this example), but the losing trades lose smaller amounts (-4.82%). Despite the fact that the Avg. Profit % (4.84%) and Avg. Loss % are almost equal, the system profits because it has more winning trades than losing trades. The 5% stop keeps the average % losses about the same size as the average % gains.
Profit Distribution of Trades:
In the above graph, the large red spike shows that approximately 923 trades stopped-out. Since there were 2857 trades, this means that approximately 32% of trades stopped-out.
As we increase our stop-loss percentage, we can expect the Winner % to increase and the Avg. Loss % to increase. We will also expect the number of trades to grow. Thus, even though the system will lose more per trade on average, there will be an increased number of trades that win, AND, there will be increased opportunity to trade (remember, as our stop loss widens, our position-size will decrease, meaning we will have more cash available in the portfolio for more positions). Increased opportunity means more chance for profits.
Now, the Obligatory Equity Curve:
Notice that a 5% stop works well when volatility is low (duh?).
Over the next couple of days, I’ll adjust the stop level upwards, and run the same test. By comparing the metrics, we’ll begin to get a sense of the effect of stop-loss and position-sizing on a positive expectancy system.
Your comments are welcome.
Link to Part 1.
Part 1 established the following:
- A stock’s movement is its volatility.
- Average True Range (ATR) is a measure of volatility.
- ATR can be used to position-size to account for volatility.
And we examined the chart below and performed some calculations…
Using the ATR(10) indicator in the bottom pane of the chart, we divided the ATR(10) by the close and multiplied that result by 100 to get a percentage.
It is important to for anyone wanting to explore ATR position-sizing to know how to figure out what 1ATR equals in percentage terms. If 1ATR=2.3%, then 3ATR=6.9%. I’ll jump a couple of steps ahead and say that if a 3ATR stop is applied to MHP, it will be -6.9% beneath its close of $33.91
We now have most of the information we need to position-size and set a stop using ATR.
Here are the 4 necessary pieces of information to position-size using ATR:
- ATR(10) calculation, readily available at Stockcharts. (I prefer a 10 period setting but the default setting is 14).
- The ATR multiple, or what number you will use to multiply by the ATR (typically between 1.5 to 5).
- The most recent closing price.
- How much $$$ to be risked. (We will use 1% of equity as our amount to be risked).
Here is the ATR Position-Size Calculation:
Where R=risked amount.
ATR = Average True Range with a period setting.
M= Multiple applied to ATR.
C= Most recent closing price.
Assuming account equity of 100K and 1% risk, our 3ATR position-size calculation for The McGraw-Hill Companies, Inc. [[MHP]] would look like this:
($1,000/(.803*3)) =415 shares
415*$33.91 = $14072.65 position-size
The easy part is that the stop is already calculated- it is simply the ATR multiplied by the multiple (we used 3). So the stop is .803*3 = $2.409
Lets look at another example:
Above is [[TPI]] , which was the PDS pick on Wednesday evening. Yes, it is another gorgeous pullback, the kind that the PDS finds daily.
Let’s run through the calculations, using the same parameters, with a 3 multiple for the ATR.
$1000/(.322*3)=1035 shares (We would complete this calculation the night before, and put in the order for that number of shares. Remember that $1,000 is 1% of our equity and the amount we are risking.)
1035*$4.27 = $4419.45 position-size (On Thursday morning, TPI opened at $4.27).
Stop = .966 beneath the entry of $4.27
Let’s Make Sense of It All
Carefully note the following:
Both MHP and TPI used an ATR multiple of 3 to position-size, yet this yielded two completely different sized positions.
For example, the MHP position is over 3x larger than the TPI position, yet the TPI stop is 3x wider than the MHP stop.
MHP position = $14,072 with a -6.9% stop.
TPI position = 4419.45 with a -22.6% stop.
What does it all mean?
The simplest way to understand it is that TPI is more volatile than MHP. Thus, we take a smaller position in TPI and use a wider stop.
Since MHP is less volatile, we might expect it to move 2% in our favor, while we might look for the more volatile TPI to move 6%. (In fact, MHP was closed on 12/24 for a 1.45% gain.)
MHP = 14,072*2% = $281.44 profit.
TPI = 4419.45*6% = $265.17 profit.
Even though the TPI position is smaller, we know that it can earn similar profits to the larger-sized position in MHP.
It is always fun to think about profits, but it is equally important to consider losses. If we took an equal-sized position in TPI as we did in MHP, how would it feel to have TPI move 7-14% against us? It would hurt, yet we should expect that TPI could move that quickly as its average daily range has been over 7%.
Theoretically, building positions that account for volatility help ensure that each position will add the same amount of “heat” to the portfolio. In other words, if you have loaded up with 5 volatile penny stocks, volatility position-sizing will have you buying 5 small positions, leaving a significant amount of cash. Conversely, if you want to fill your portfolio with blue chip stocks (which are typically not relatively volatile), then volatility position-sizing will have you buying a few large positions, and will probably use most of your cash. To see this balance in action, you could buy 7 positions in stocks similar to MHP, using all of your 100K. If you bought 7 positions in stocks similar to TPI, you would have used only 30% of your cash.
Finally, the ATR multiple, be it 1.5, 3, or 5, determines how aggressive your allocations are. A lower ATR multiple will result in larger positions with smaller stops.
Questions and Comments?
If you have any questions or anything I have presented is unclear, please speak up in the comments section.
The PDS site includes a 2% risk, 3ATR model that earned 64.64% annualized, with an average trade profit of 1.65%.
Customary position-sizing has the trader buy X number of shares and set a stop to so that he does not lose more than X dollars. One drawback of this method is that it does not account for the volatility of the security being traded. Volatility is a measurement of change in price over a given period. It is usually expressed as a percentage and computed as the annualized standard deviation of the percentage change in daily price. The more volatile a stock or market, the more money an investor can gain (or lose!) in a short time.
Consider then that our positions can be built to account for the volatility of each security we are trading. For example, if we have two stocks, both priced at $25, and ABC moves on average 1% per day and XYZ moves 3% per day, do we want to take equally sized positions in both stocks? Do we want to use the same stop level for both stocks? If the answer is not immediately clear, think about this: If we use a 1$ stop loss for both stocks, XYZ stock is much more likely to hit the stop, yet this movement may be entirely within a normal range (remember, it moves an average of 3% a day).
We can account for this volatility and position-size accordingly.
The easiest way to do this is to use the Average True Range. ATR is popular as it is readily available in most free charting programs, such as Stockcharts. “The Average True Range (ATR) indicator measures a security’s volatility. As such, the indicator does not provide an indication of price direction or duration, simply the degree of price movement or volatility.”
There is no absolute need to understand exactly how the ATR indicator makes its calculation, as long as there is a basic understanding of what it is calculating. In simplified terms, it is calculating the average daily movement of a security. This is just what we need to position-size for volatility.
Lets take a look at a chart with a plot of ATR(10), where 10 is a user-definable setting. 14 is standard, but I prefer 10.
Above we have a chart of The McGraw-Hill Companies, Inc. [[MHP]] , which just happened to be one of today’s PDS picks. (Yes, it is a sweet pullback setup. The PDS will find these daily.) In the bottom of the chart, ATR(10) is plotted. We can see that ATR has been steadily decreasing since September. Remember that this means that volatility, or how much the stock moves on average, has been decreasing.
We can complete a quick calculation and get an idea, in percentage terms, of the average daily movement of [[MHP]]. All we need to do is divide ATR(10) by the price.
On average over the last 10 periods, MHP has traded in a daily range of 2.3%. Obviously, using a 2% stop would be foolhardy with this stock.
I’ll quit here to allow digestion of the principles of building positions around volatility using the ATR indicator.
The next post will detail exactly how to use ATR to calculate your stops and build positions that are sized according to the volatility of the stock.
Access to ATR position-sizing and stop models are included in both the trial and full PDS memberships.
Parts One and Two established the framework and system to use for the study. Now it is time to get to the meat of the study: How can we combine elements of trend-trading to a system that often trades counter-trend?
First, what measure constitutes the trend? Deciding the best measure for the trend can be somewhat subjective; since many, many traders use the 50 day simple moving average, that is what will be used in this study.
With the 50 day average as our trend indicator, the close must be monitored. If the close is above the 50 day average, we have a long bias. If the close is below the 50 day average, we have a short bias.
The final question then is how to capture the bias? While there are likely many ways, what will be proposed here is a combination of leverage and position-sizing. Thus, if the trade is with the trend (above the 50 day and going long, or below the 50 day and going short), as much as 2x leverage will be used. If the trade is against the trend (long and below the 50 day moving average or short and above the 50 day moving average), the position size will be decreased.
Finally, how will performance be measured to determine if the there are any improvements to the system?
Performance will be measured by 4 criteria: Net Profit, Largest Intraday Drawdown, Largest Trade Drawdown, and Average Drawdown. For each of these calculations, the drawdown figure will be divided into Net Profit to create a ratio.
For example: Net Profit = $10,000 and Largest Intraday Drawdown = $2,000. $10,000 / $2,000 = 5.0
As the ratio increases, the Net Profit is rising and the drawdowns are decreasing. Thus, the higher the ratio the better.
Using the system described in Part Two as the baseline, varying combinations of position-sizing and leverage will be used to trade with the trend while trading against it.
The graph above shows the results. The left most column shows the varying combinations of leverage and trend where T = trend and CT = counter-trend. We see on the first row the results of the baseline system where no leverage or position-sizing were used (T = 1.0 and CT = 1.0).
The second row shows leverage with the trend of 1.5x and a decrease in the position size when trading counter-trend of .5x. Assuming 10K per trade for the baseline system, with the trend a position of 15K is taken, while against the trend only 5K is used.
The third row shows 2x leverage with the trend (20K position) and .5x position against the trend (5K). This row shows the best drawdown ratios (in purple) for Largest Trade Drawdown and Average Drawdown. This version will have a position that is 4x larger with the trend than when trading against the trend.
Already it should be evident that Net Profit is increasing, due mainly to the leverage. However, the ratios show that drawdowns are decreasing. The 2nd row shows a ratio of 6.32 (in purple) which is the highest ratio of the study for max intraday drawdown. By simply using 1.5x leverage with the trend and cutting position-size in half against the trend, Net Profit increases while all drawdown measures decrease. In fact, for the 1.5 / 0.5 row, the largest intraday drawdown and max trade drawdown are decreased by roughly 1/3rd.
The row showing 2.0 / 2.0 is the baseline system using 2x leverage on all trades, regardless of the trend.
After the 2.0 / 2.0 row, the leverage and position-sizing are switched so that now the system is using leverage against the trend and decreasing position size with the trend. Note that Net Profit stays very close while the drawdowns increase (causing a decrease in the ratios).
I believe that the last three rows prove that leveraging with the trend makes up for the lost gains from taking smaller position sizes, while smaller position sizes when trading against the trend improves the drawdown characteristics of the system.
Beauty is in the eye of the beholder…I like the 2.0 / 1.0 version as net profit is improved by 33% over the baseline system while the drawdown ratios improve 25%, 22%, and 17% respectively.
If one is satisfied with the baseline system and just wants to improve the drawdown characteristics, then the 1.5 / 0.5 version might be appropriate.
Avenues for future research could include using the distance of the close from the trend to calculate more advanced position-sizing / leveraging algorithms. Perhaps the slope of the trend indicator could also guide position-sizing / leveraging.
In Terms of Real Life…
The baseline system gave a long entry signal for Thursday’s (February 19th) open. Had the 1.5 /0.5 version been used, only a HALF position would have been purchased. Based on the recent market action, I would personally feel better about sitting on a half long position rather than a full long position going into Monday.
Now I will present the system to be used for the study that was described in Part One.
The system uses an entry and exit signal generated from the CCI (Commodity Channel Index) indicator. For more information on the CCI, here is a helpful explanation: Commodity Channel Index.
As systems go, this is not one of my favorites, although it is profitable. I have not spent an inordinate amount of time developing my version of it. As the system makes money from being contrarian, it will work well for this study.
All entry and exit signals are based on the end-of-day CCI(8) reading and will be triggered on the next market open.
A Buy signal is generated when CCI(8) crosses above -150 from below. This means that the system is buying weakness.
A Sell Short signal is generated when CCI(8) crosses below 90 from above. This indicates that the system is shorting on strength.
An exit signal for any long position is generated when CCI(8) is rising and crosses above 40 from below, meaning the system is selling the long position into strength.
A Buy to Cover signal for any short position is generated when CCI(8) falls to below 50, meaning the system is covering into weakness.
System Specifics and Results
Period Tested: 10 years back ending on 12/31/2008 using the SPY.
10,000 per trade with no compounding of gains. Gains are purposely not compounded during back testing. It will be best to cover the rationale for not compounding gains during proof-of-concept testing in a future post.
Commissions of .01/share are included. I have not included any returns generated from the cash available when the system is out of the market (It is only in the market about 50% of the time).
Some Chart Porn
The equity curve is fairly smooth, except for the end of 2008 (This will be improved in Part Three).
The weekly drawdowns are not awful, but will also be improved in Part Three.
The above graph shows the recent trades and the CCI indicator in the lower pane. Also plotted is the 50 day moving average. The 50 day moving average will be the intermediate trend indicator. Note the long entry (LE) that was made on 10/1/08. The CCI system entered long in oversold conditions, and then the market cratered, getting more and more oversold. This particular stretch of market history caused a lot of angst for traders of mean-reversion systems.
Presented above is a mean-reversion (contrarian) system. As such, it seeks to buy when the market is going down and sell when it is going up. Unfortunately, as shown in the October trade, the system will often take a trade against the intermediate trend (as shown by the declining 50 day moving average). Occasionally these trades against the trend will result in large drawdowns.
Now that the system has been presented, Part Three will use the intermediate trend (50 day average) to determine position-sizing and leverage. The final result will be the proof-of-concept of a “best of both worlds” system with decreased drawdowns and increased profits.
Traders who have not added to their arsenal some form of mean-reversion trading methodology really missed a banner year (2008) for that style of trading. Traders considering making the transition from momentum and breakout strategies to mean-reversion methodologies may have a difficult time as the shift requires them to be contrarian. Taking a contrarian approach requires a transition to an alternate mindset as the trader has become psychologically accustomed to trading with the trend.
Even once this shift to contrarian mode is accomplished in the trader’s mind, taking a contrarian approach can still hit his wallet. For example, most mean-reversion approaches would have had the trader positioned long during September 2008, as the world was staring headlong at an economic maelstrom. A contrarian trader would have been positioned for a short term bounce within the context of a longer downtrend.
The best of both worlds then, or trading with the trend while trading against it, would be a system that benefits from the regular short-term swings of a mean-reverting market but is not punished by severe drawdowns when the market does not revert (swing) as quickly or as completely as the trade requires.
In Part 2 I will show a system that is contrarian and trades against the short-term trend. The system will use position-sizing and leverage to accentuate returns when trading with the intermediate trend. Similarly, position-sizing will be used to decrease drawdowns when trading against the intermediate trend. What will then be presented is a system that attempts to capture the best of both worlds: Mean-reverting, yet leveraged with the trend.
When the market is range-bound and whipsawing I find it more productive to read and do research about trading rather than practice trading in a difficult environment. While searching around the web, I recently discovered some research about position-sizing, as well as another blogger’s informative post on the subject.
The following research is a must-read. It measures how position-sizing effects trader performance when trading a system with positive expectancy. In other words, when trading a winning system, bet-size will determine whether one survives, thrives,Â or goes bankrupt.
“One purpose of this study was to find evidence for the importance of position sizing. The results showed that in order to survive trading in a simulated stock market, using a trading system with expected value of < 1.0, one should take positions in sizes of approximately 3.7% – 6.6% as the surviving traders, rather than 22.9% – 23.7% as the bankrupt traders. Further, to be able to increase oneâ€™s account over the long run and actually make money by trading the simulated market, one should not risk much more than 6% as the winning traders did on an average (2000, Ginyard, pg. 20).”
I encourage taking the time to read the research in order to understand the experimental design.
Max takes a positive expectancy system as described by Van Tharp in the November, 2005, Active Trader magazine article Meeting Your Trading Objectives with Position Sizing andÂ models it in Excel. His results may challenge some assumptions about bet size.
Max writes, “Since it’s a Monte Carlo model the results are random, but here’s a typical set of results:”
“The charts on the left model a group that risks 16% of capital on each trade, the middle is 8%, and the right models the results of a group of individuals who risk only 4% per trade. The top row of charts are the ending money of each individual in the group, and the bottom charts are the average capital of all group members after each marble comes up.”
“It is not surprising that the number of people in the red (below the starting money) is the most for the group that risked the most and the least for the most conservative group on the right. What is surprising is that the group of people who risked 8% had among them more big winners (dark green) than the 16% group, which had none (no dark green on the pie chart). So you can actually win more by betting less, and therefore lasting longer.”
Please visit his blog for the rest of the article as well as a link to the excel spreadsheet he created to model the system.