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Yes, this is possible. The formula supposes fixed fractional betting, which typically leads to geometrical growth. What you need to calculate is the account growth g expected from a single bet. If the target account is 400% of the initial balance, the total growth factor would be t = 4. The number of required trades would then be

N = log t / log g

It is probably easier to understand this by following an example, so let us come back to the spreadsheet:

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In the first example there is a win rate of 45% and multiple R of 2, the expected gain per contract traded is therefore

With 20 contracts traded the expected gain would be 20 * $ 8.50 = $ 170 for an initial balance of $ 50,000. The growth factor g is (50,000 + 170) / 50,000 = 1.0034 and the required number of trades would be

N = log 4 / log 1.0034 = 408.4

This is quite a large number of trades that are required. However, the edge (45% win rate with an R-multiple after slippage and commissions of 1.54) is not impressive. The risk adjusted Kelly factor is therefore small and it takes some patience to achieve the target account of 400%.

@TheTrend: If you wish you can include this calculation with your Excel sheet as expected number of trades to reach the target.

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The following user says Thank You to Big Mike for this post:

I hope I'll be trading full time again in a few weeks and will be able to look into this.

By the way, I mainly swing trade stocks for the moment so I've built this spreadsheet mainly for the benefit of the group and to better understand the figures behind the formulas (and I encourage you to build it yourself if you intend to use it).

You can freely update and adapt this spreadsheet to your needs, there's no copyright on it

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As @TheTrend is busy, I have enhanced the spread sheet.

The left part of the spreadsheet is used to adjust Optimal F for the tolerated risk of ruin, when you start off with your trading strategy.

The right part of the spreadsheet allows to calculate the position size. Optimal F assumes that you follow a fixed fractional betting strategy to achieve optimal geometric growth. The number of contracts that should be traded thus depends on the risk parameter (last line of left part of spread sheet) and the current balance of your trading account. The spread sheet now also includes an estimate of the number of traders required until the target account is reached.

All orange fields are entry fields. The Kelly Factor requires manual adjustment, until the calculated risk of ruin matches the tolerated risk of ruin, as entered above.

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The spreadsheet is attached below.

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Harking back a couple of pages, it seems to me we need to define what is meant by risk tolerance in the context of this statement. If I understand correctly, the "risk" here is now something quite specific - it's the chance that your "Edge" assumption is not correct. Otherwise there would be no long-term risk if you size correctly - assuming the short-term performance is not too wild. I guess we now need a measure of strategy volatility

cheers,

BB

The following user says Thank You to BenosBanderos for this post:

@BenosBanderos: Thank you for putting up this question, as it is really the key to the problem.

The risk here is NOT the chance that the edge assumption is not correct.

The risk of ruin as defined per the Kelly criterion is the risk that you will lose money although your assumptions have been correct.

To make that clear: In a card game there is a known probability depending on the number and values of the cards. Even if you have an edge in your card game - such as the Casino has, when distributing Black Jack cards or operating a Roulette table - there is a risk of ruin, which depends on your initial capital and the Kelly factor calculated from your bet size and your edge.

In particular these risks are NOT covered by the above approach:

The risk that you have made a false evaluation of your edge. The risk that markets have changed and your edge is reduced or no longer there. Operational risk (power failure, disrupture of data lines, failure/crash of exchange), which leads to an outcome which cannot not be described within the framework of the Bernoulli distribution.

The Bernoulli distribution, on which the model is based, is derived from two possible outcomes of your trades only. So if you have a bad fill, an overnight gap or anything which is beyond the model, it is not covered.

This means that the real risk is much higher, than the above calculated risk. Therefore a quarter Kelly approach as shown in the Excel table above, is the maximum risk that you may assume in accordance with your risk appetite. In view of the additional risk that is not covered you should further reduce your bet size and exposure below the model values suggested.

The point is that you cannot easily calculate a probability of a power failure, the evaporation of your assumed edge or technical errors committed during a backtest.

The calculation of the risk of ruin is therefore limited to the risks that can be evaluated.

It is a model risk, and its meaning is limited to the features of the model. Ask an economist what that means.

The following 12 users say Thank You to Fat Tails for this post:

I wanted to respond more in depth to this but I confess I need to go back to school and understand Kelly, Opt F from first principals before I can do so. But thanks for clarifying my guesswork there.

I guess as with any model it's important to know it's limitations, how to use it and how to interpret results. So perhaps that is the best question I can ask. How should we use this model/spreadsheet to inform our trading?

One thing that stood out to me by playing with the numbers, is that there seems to be a stronger inverse relationship than I thought between Win Loss ratio and Avg Win vs Avg Loss. For example if you are trading a 1:1 RR you need MUCH better than 60% Win ratio to be profitable - perhaps difficult to achieve. This again emphasised the importance of reducing the number of losing trades and maximising profits on winning ones.

cheers,

BB

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Absolutely. The main limitation of the model in its current shape is

- that it only applies to Bernoulli distributions, that is trade setups where you either win X or you lose Y
- that some of the risks that cannot be quantified (changing markets, false evaluation of edge, operational risk, gaps)

The much better than 60% win ratio is needed to overcome slippage and commissions. The case shown above refers to a win/loss ratio of 2:1. After accounting for slippage and commissions, this win/loss ratio becomes 1.54:1, which is a significant deterioration. This suggests that with a retail account you should go for more than 10 or 20 points. However, most retail traders are undercapitalized and prefer to trade with a narrow stop loss. If you are a scalper, a small edge is easily converted into no edge by slippage and commissions.

Contrary to what most people think, I believe that the win/loss ratio is more important than the R multiple. The key to understanding this is the standard deviation of returns. A low standard deviation of returns reduces the risk of ruin and allows you to increase leverage. Now if you compare

(1) trading a system with a high R multiple, where the average winning bet is much larger than the average losing bet, but a low win/loss ratio with less than 50% of successful trades (just as the example which I had selected above)

(2) trading a system with a low R multiple, that is an average winning bet similar or equal to the average losing bet, but a high win/loss ratio with something like 75% of successful trades

you will probably find that the latter system has a lower standard deviation of returns. This implies that the drawdowns are not as large, which in turn has a favourable impact on the risk of ruin.

In the end you might be able to trade (2) with a higher leverage, if you specify the same risk of ruin. This might lead to the conclusion that systems which generate regular small returns are preferable to systems that generate an occasional home run. I am saying "might", because I have not yet shown it mathematically. Any comments would be appreciated.

Last edited by Fat Tails; April 12th, 2012 at 09:05 AM.

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How Bankers define risk of capital. Funny a Swiss Bank using Swiss Chees Model to explain risk of capital. Some points might be interesting for retail traders and automated systems.

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