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### FIxed fraction sizing conflicts with % risk sizing?

Posted: **Wed Dec 01, 2004 12:13 am**

by **C3PO**

Hello,

I apologize if this is a beginner question, but I seem to be confused about how fixed fraction position sizing (e.g., Kelly ratio) is supposed to work with % risk position sizing. I have spent some time searching the forums but did not find an answer.

It seems to me that the two conflict with one another. Are they completely separate methodologies and are not meant to work with one another?

For example, suppose I have $1,000,000 starting equity. I have determined that my optimal fixed fraction is 0.10. My next trade is a $50 stock with a stop loss at $45.

Using fixed fraction betting, my position size should be $100,000 [$1 million *0.10].

However, suppose I want to limit the % risk per trade to 2% of equity. This means the position size should be 4,000 shares [$20,000/$5] or a position size of $200,000 [4,000 * $50].

So using fixed fraction gives me a $100,000 position size, but using % risk gives me a $200,000 position size. What does one do in this case?

I was under the impression that these two methodologies complement each other, but maybe I am wrong. I would very much appreciate it if someone please clarify this for me? Thanks.

### Re: FIxed fraction sizing conflicts with % risk sizing?

Posted: **Wed Dec 01, 2004 2:13 am**

by **ksberg**

C3PO wrote:Hello,

I apologize if this is a beginner question, but I seem to be confused about how fixed fraction position sizing (e.g., Kelly ratio) is supposed to work with % risk position sizing. I have spent some time searching the forums but did not find an answer.

It seems to me that the two conflict with one another. Are they completely separate methodologies and are not meant to work with one another?

For example, suppose I have $1,000,000 starting equity. I have determined that my optimal fixed fraction is 0.10. My next trade is a $50 stock with a stop loss at $45.

Using fixed fraction betting, my position size should be $100,000 [$1 million *0.10].

However, suppose I want to limit the % risk per trade to 2% of equity. This means the position size should be 4,000 shares [$20,000/$5] or a position size of $200,000 [4,000 * $50].

So using fixed fraction gives me a $100,000 position size, but using % risk gives me a $200,000 position size. What does one do in this case?

I was under the impression that these two methodologies complement each other, but maybe I am wrong. I would very much appreciate it if someone please clarify this for me? Thanks.

Fixed fraction usually refers to the amount risked against the trading equity. So, unless your plan includes losing 10% on a single trade, the first example is incorrect. The fixed fraction approach is sometimes explained in the context of betting (literally), where you actually do stand to lose everything you bet, so it works out to be a straight percentage of equity.

Code: Select all

```
Fixed Fraction
Shares or Contracts = (Account $ Risk) / (Position $ Risk)
Account $ Risk = Equity * (Account % Risk)
Position $ Risk = Stop distance from Entry
```

Fixed fraction is

**not** the same thing as Kelly. As you can see from the formula, there are numerous ways to set account percentage risk. Kelly is one method for assigning a fixed fraction value to the formula; it is not the formula itself (there is a separate formula to determine Kelly Ratio).

Hope that helps,

Kevin

Posted: **Wed Dec 01, 2004 2:28 am**

by **C3PO**

Thanks for the reply. I think I have used incorrect terminology to describe my question so let me clarify.

Please just assume that when I say "fixed fractional", I mean the Kelly ratio.

As I understand the use of the Kelly ratio, you would bet 0.10 of your equity with each trade in the example I provided. This means betting $100,000. However, if I use the formula you've given (which is the same as the % risk method I've described), I would need to bet $200,000.

What should one do in this case? Is the Kelly ratio of position sizing supposed to work with the %risk method? Thanks.

Posted: **Wed Dec 01, 2004 4:31 am**

by **C3PO**

After reading your reply over a few times and other reading, I think I understand now. If I am not mistaken, you are saying that the Kelly ratio is one way of determining the "Account % Risk" in the formula you've given.

So using the numbers from my example, the position size would be

= ($1,000,000 * 0.10) / ($50-$45)

= 20,000 shares

I would very much appreciate it if you can confirm that this is correct. Thanks.

Posted: **Wed Dec 01, 2004 11:34 am**

by **ksberg**

C3PO wrote:After reading your reply over a few times and other reading, I think I understand now. If I am not mistaken, you are saying that the Kelly ratio is one way of determining the "Account % Risk" in the formula you've given.

So using the numbers from my example, the position size would be

= ($1,000,000 * 0.10) / ($50-$45)

= 20,000 shares

I would very much appreciate it if you can confirm that this is correct. Thanks.

If Kelly was 10%, your example would be correct. Typically I find Kelly much higher than 10%.

Code: Select all

```
Kelly Formula:
F = ((R+1)*P â€“ 1)/R
F is fraction of Equity to Risk
R is Win/Loss ratio
P is percent win of trading system
```

Of course, Kelly was not intended to be applied to trading systems (original paper was on signal processing). The probability application is most suitable to bet size for gaming, not trading. In many betting games, the loss and payout is fixed in advance, which is very different from trading.

Cheers,

Kevin