- Joined
- 22 August 2008
- Posts
- 914
- Reactions
- 20
Yay! I didn't lose the post!.
Ok so lets work through the formula for fixed fractional.
N = f * Equity/| Trade Risk |
So N is what we are looking for. If we use the 2% rule this then becomes our fixed fraction. Equity from our original premise is $100,000, and trade risk is the size of the stop. I usually use a 5% stop loss, but in my example above I gave 10% so lets use that.
N = 2% * $100,000/ 0.925 (10% of $9.25 in the above example)
N = $2,000/0.925
N = 2,162 shares (a trade value of ~ $20K)
Obviously as the position size is five times smaller than our original example, the potential loss is also five times smaller, $2,000 rather than $10,000. We've also limited our potential upside (we only purchased $20,000 worth instead of $100,000), but this is a function of any kind of risk management. We limited the potential gain to increase the certainty involved with the investing activity. That last bit is so important that I bolded it. We have increased the probability of success by managing the risk involved. Cannot be stressed enough how important this is. In my experience investing of any kind, be it trading or investing, is all about managing the risk involved and achieving consistency. Consistency and compounding result in exponential returns over time.
Ok so that is the basic principle behind fixed fractional. If you want more information or greater depth go read Ralph Vince's work I mentioned in the previous post.
Percent volatility position sizing
Percent volatility position sizing came from Van K. Tharp's book "Trade your way to financial freedom" - for the full monty on the subject go get the book, this will be a flyover. The theory is that the percent volatility position sizing method adjusts the risk according to the stock's volatility. Here's the formula.
PositionSize = (CE * %PE) / SV
Where CE is the current account equity (size of portfolio)
%PE is the percentage of portfolio equity to risk per trade.
SV is the stock's volatility (10-day EMA of the true range).
Lets do another example.
(CE) is $100,000,
the percent of portfolio equity we want to risk (%PE) is 2%,
BHP's true range volatility on our original date is....$0.57, then the result is:
($100,000 * 2%) / $0.57 = 3508 shares (a position size of $32,449)
The trap of both of the methods described is that if your portfolio is $100,000 and you are not using any form of leverage, then the number of trades you can have open at any one time is severely reduced. Three stocks with the percent volatility and five with the fixed fractional. In this circumstance the use of a leveraged instrument such as a CFD enables a more efficient use of the position sizing methods, because the calculation is based on your equity, not the size of the portfolio with margin included.
If you hate the concept of leverage then you can avoid the concentrated portfolio problem by dividing the $100,000 of your own equity into allotments. You would use the same formula to determine the position size. Using the percent volatility example and a $10,000 allotment: ($10,000 x 2%) / 0.57 = 350 BHP Shares.
Optimal F position sizing
Optimal F is a step beyond fixed fractional. It uses a classic formula called Kelly's formula, which provides the fixed fraction that maximizes the geometric growth rate for a series of trades where all the losses are one size and all the wins are another size. How often do you think that this occurs when dealing with the market? Here's Kelly's formula:
f = ((B + 1) * P - 1)/B
where B is the win/loss ratio, and P is the percentage of winning trades.
Optimal f position sizing simply extends the Kelly formula so that the wins and losses can be different sizes. Optimal f calculates the fixed fraction that maximizes the rate of return for a given series of trades. It's important to actually have a system that has a positive win/loss ratio before using an Optimal F or Kelly position sizing method.
The trap for Kelly's formula and Optimal f is that no two trade series are the same (where the risk/reward profile remains constant). This can result in a significant drawdown on the account size when a series of losses occurs. The formula is based on win or lose and no intermediate or Gaussian outcome. Don't get me wrong, Kelly and Optimal F have their place in a well designed system, it's just that fat tail events and market corrections tend to kick sand in their faces (as most chaotic events will do).
Sir O's fully sick position sizing method
Ok this is something I do, this will not be for everyone, nor will it work with everything and in all markets. Like Optimal f or Kelly this position sizing will bitch slap you in times of chaos. It's a sort of a combined approach that formed after reading a whole bunch of what others do. It applies to a specific kind of equity investment and works best in the mid tier space. I also use this in a leveraged environment where I don't have to be concerned about portfolio concentration.
Step 1
I use a Fixed Fractional to determine the base number of shares. In the BHP example above that would be 2162 shares.
Step 2
The fixed fractional calculation gives me a trade risk value. I then seek to adjust the number of shares in the position taking into account the variance of the stock to the market. IE. Share price volatility compared to market volatility. Share Price volatility is the daily change of the stock over the last 24 periods which is exponentially averaged. Market volatility is the daily change of the XAO over the last 24 periods exponentially averaged. Essentially what I'm doing is replicating a beta coefficient comparison over a short-term time frame with the nearer term data set given preference.
Step 3
Where the Beta is positive and the position is long, the above beta comparison expressed as a percentage will be applied to the position as an addition. IE Share has a positive beta to market of +0.124 BHP position would then be... (2162 shares * 12.4%) = 2430 shares. (position size increased from $19,998.50 to $22,477.5)
Where the Beta is positive and the position is short, the beta will be applied as a subtraction. IE 2162 - 268 = 1894 share (position size now 17519.50)
Where the Beta is negative and the position is short, once again the beta is an addition.
Where the beta is positive and the position is short, once again the beta is a subtraction.
The reason I do this is so that when I'm trading in a strongly positive or negative position I'm aligned to the overall market's direction. The model is just pants trying to trade neutral trends.
What does everyone else use?
Cheers
Sir O
Ok so lets work through the formula for fixed fractional.
N = f * Equity/| Trade Risk |
So N is what we are looking for. If we use the 2% rule this then becomes our fixed fraction. Equity from our original premise is $100,000, and trade risk is the size of the stop. I usually use a 5% stop loss, but in my example above I gave 10% so lets use that.
N = 2% * $100,000/ 0.925 (10% of $9.25 in the above example)
N = $2,000/0.925
N = 2,162 shares (a trade value of ~ $20K)
Obviously as the position size is five times smaller than our original example, the potential loss is also five times smaller, $2,000 rather than $10,000. We've also limited our potential upside (we only purchased $20,000 worth instead of $100,000), but this is a function of any kind of risk management. We limited the potential gain to increase the certainty involved with the investing activity. That last bit is so important that I bolded it. We have increased the probability of success by managing the risk involved. Cannot be stressed enough how important this is. In my experience investing of any kind, be it trading or investing, is all about managing the risk involved and achieving consistency. Consistency and compounding result in exponential returns over time.
Ok so that is the basic principle behind fixed fractional. If you want more information or greater depth go read Ralph Vince's work I mentioned in the previous post.
Percent volatility position sizing
Percent volatility position sizing came from Van K. Tharp's book "Trade your way to financial freedom" - for the full monty on the subject go get the book, this will be a flyover. The theory is that the percent volatility position sizing method adjusts the risk according to the stock's volatility. Here's the formula.
PositionSize = (CE * %PE) / SV
Where CE is the current account equity (size of portfolio)
%PE is the percentage of portfolio equity to risk per trade.
SV is the stock's volatility (10-day EMA of the true range).
Lets do another example.
(CE) is $100,000,
the percent of portfolio equity we want to risk (%PE) is 2%,
BHP's true range volatility on our original date is....$0.57, then the result is:
($100,000 * 2%) / $0.57 = 3508 shares (a position size of $32,449)
The trap of both of the methods described is that if your portfolio is $100,000 and you are not using any form of leverage, then the number of trades you can have open at any one time is severely reduced. Three stocks with the percent volatility and five with the fixed fractional. In this circumstance the use of a leveraged instrument such as a CFD enables a more efficient use of the position sizing methods, because the calculation is based on your equity, not the size of the portfolio with margin included.
If you hate the concept of leverage then you can avoid the concentrated portfolio problem by dividing the $100,000 of your own equity into allotments. You would use the same formula to determine the position size. Using the percent volatility example and a $10,000 allotment: ($10,000 x 2%) / 0.57 = 350 BHP Shares.
Optimal F position sizing
Optimal F is a step beyond fixed fractional. It uses a classic formula called Kelly's formula, which provides the fixed fraction that maximizes the geometric growth rate for a series of trades where all the losses are one size and all the wins are another size. How often do you think that this occurs when dealing with the market? Here's Kelly's formula:
f = ((B + 1) * P - 1)/B
where B is the win/loss ratio, and P is the percentage of winning trades.
Optimal f position sizing simply extends the Kelly formula so that the wins and losses can be different sizes. Optimal f calculates the fixed fraction that maximizes the rate of return for a given series of trades. It's important to actually have a system that has a positive win/loss ratio before using an Optimal F or Kelly position sizing method.
The trap for Kelly's formula and Optimal f is that no two trade series are the same (where the risk/reward profile remains constant). This can result in a significant drawdown on the account size when a series of losses occurs. The formula is based on win or lose and no intermediate or Gaussian outcome. Don't get me wrong, Kelly and Optimal F have their place in a well designed system, it's just that fat tail events and market corrections tend to kick sand in their faces (as most chaotic events will do).
Sir O's fully sick position sizing method
Ok this is something I do, this will not be for everyone, nor will it work with everything and in all markets. Like Optimal f or Kelly this position sizing will bitch slap you in times of chaos. It's a sort of a combined approach that formed after reading a whole bunch of what others do. It applies to a specific kind of equity investment and works best in the mid tier space. I also use this in a leveraged environment where I don't have to be concerned about portfolio concentration.
Step 1
I use a Fixed Fractional to determine the base number of shares. In the BHP example above that would be 2162 shares.
Step 2
The fixed fractional calculation gives me a trade risk value. I then seek to adjust the number of shares in the position taking into account the variance of the stock to the market. IE. Share price volatility compared to market volatility. Share Price volatility is the daily change of the stock over the last 24 periods which is exponentially averaged. Market volatility is the daily change of the XAO over the last 24 periods exponentially averaged. Essentially what I'm doing is replicating a beta coefficient comparison over a short-term time frame with the nearer term data set given preference.
Step 3
Where the Beta is positive and the position is long, the above beta comparison expressed as a percentage will be applied to the position as an addition. IE Share has a positive beta to market of +0.124 BHP position would then be... (2162 shares * 12.4%) = 2430 shares. (position size increased from $19,998.50 to $22,477.5)
Where the Beta is positive and the position is short, the beta will be applied as a subtraction. IE 2162 - 268 = 1894 share (position size now 17519.50)
Where the Beta is negative and the position is short, once again the beta is an addition.
Where the beta is positive and the position is short, once again the beta is a subtraction.
The reason I do this is so that when I'm trading in a strongly positive or negative position I'm aligned to the overall market's direction. The model is just pants trying to trade neutral trends.
What does everyone else use?
Cheers
Sir O
