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The Breakout Bulletin


The following article was originally published in July 2003 issue of The Breakout Bulletin.

Fixed Ratio Position Sizing


    In my previous discussions of position sizing, I’ve always assumed that the number of contracts was determined based on the risk of the trade.

    For example, you might decide to risk 3% of your trading equity on the next trade.
    If the trade has a potential loss of $500 per contract, and your account equity is $50,000, you would take 3% of your equity (0.03 * $50,000 = $1,500) and divide the result by the trade risk of $500.

    The result is $1,500/$500 = 3 contracts.
    This is known as fixed fractional position sizing and is widely used in futures trading.



3%(0.03 * 50000 = 1500ドル)

すると1500 / 500 = 3枚となる。

    Basing position sizing on risk makes intuitive sense in that we know the greater the risk, the greater the reward. We expect that if we risk more of our equity on each trade, we will earn a higher return.

    This is the case with fixed fractional trading, provided we don’t risk more than the so-called “optimal f” (see reference 1) and presuming our trading method is inherently profitable.

    Fixed fractional trading also helps us relate the risk of individual trades to the drawdown risk.

    By drawdown risk, I mean the largest percentage decline in equity from the most recent equity peak.

    Most traders have a limit to how much drawdown they can tolerate; e.g., 30%.
    By using a method like Monte Carlo simulation, which I discussed last month, it’s possible to relate the trade risk, as represented by the fixed fraction, to the drawdown risk.



これは固定分割トレーディングでのケースであり、我々がいわゆる【optimal f】(参考1を参照)以上のリスクをとらないということであり、そして我々のトレーディング方法が潜在的に収益性をもつということを前提としている。





    However, fixed fractional position sizing is not the only method of position sizing available.

    I often get questions about fixed ratio position sizing, so this month, I’ll discuss the concept of fixed ratio position sizing and compare it to the fixed fractional method. 

    In his book “The Trading Game” (reference 2), Ryan Jones introduced the fixed ratio method, which he developed to address some of the limitations he felt existed in fixed fractional position sizing.




Ryan Jones氏が書いた“トレーディングゲーム”(参考2)の中で、固定比率法について書いてあり、これは固定分割ポジションサイジングに存在すると彼が思ったいくつかの限界に取り組むために開発したものである。

    The key concept of the fixed ratio method is the delta.
    The delta is the profit per contract needed to increase the number of contracts by one.

    For example, starting with one contract and with a delta of $5,000, you need a profit of $5,000 to increase the number of contracts to two.
    With two contracts, you need a profit per contract of $5,000 or $10,000 total from the two contracts to increase the number of contracts to three.

    With three contracts, you need a profit of $15,000 to increase the number of contracts to four.

    With four contracts, you need to profit of $20,000 to increase the number of contracts to five, and so on.





    Based on the relationships presented by Jones, it’s possible to derive the following equation for the number of contracts in fixed ratio position sizing:


N = 0.5  * [1 + (1 + 8 * Profit/delta)^0.5]

    where Profit  = total closed trade profit in dollars, delta = profit/contract to increase by one contract, and “^0.5″ means that the expression in parentheses is raised to the power of 0.5.

    It’s interesting to compare this equation to the corresponding equation for fixed fractional trading:

ここでProfitは最終合計トレード利益(ドル)であり、デルタ=利益÷枚数 これは枚数を1枚ごと増やすためのもので、”^0.5″は括弧[ ]の中のものを0.5乗したものである。

N = ff * Equity/| trade risk |

    where “trade risk” is the possible loss in dollars for the trade, and the vertical bars (|) represent absolute value.

    Notice that the relationship between the number of contracts and the profit is linear with fixed fractional trading. As the profits accrue, the number of contracts increases linearly.

    The rate of change of N with respect to account equity is constant with the fixed fractional method; e.g., a $10,000 increase in profits results in the same increase in the number of contracts regardless of whether that profit occurred with a $15,000 account or a $150,000 account.

ここで“trade risk”はトレードで損失となる可能性のある金額(ドル)で、垂直線(|)は絶対値を表している。


    With fixed ratio trading, on the other hand, as you accrue more profits, the number of contracts increases more slowly.
    A $10,000 profit with a $20,000 account will increase the number of contracts more than if a $10,000 profit is made on a $200,000 account. 

    For small account sizes, you’ll increase the number of contracts more quickly with fixed ratio position sizing.

    However, when the account equity becomes larger, the number of contracts will increase more slowly than with fixed fractional position sizing.

    This is why fixed ratio position sizing is sometimes preferred for small accounts.




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