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Usually, when discussing risk of ruin, we talk about (1) and not that much about the other two points. All customer of MF Global know that (3) exists and should not be neglected. Do you know how your funds are protected, if your broker collapses? Have you splitted your funds between several brokers for risk diversification? (2) is more linked to computer failure, disruption of data feeds, bad internet connectivity. For many cases of (2) preparation is possible

- have a second PC
- have a second internet connection (fixed line + mobile)
- have a second broker
- have the phone numbers of the trade desk of your broker(s) ready to close your positions
- be prepared where to enter correlated trades in case that the exchange has an operational problem

But the items referring to (2) and (3) are not easily quantifiable. That means, if we talk about risk of ruin, we focus on market risk, more or less excluding operational and counter party risk. But it is definitely there, although it cannot be calculated from a Kelly formula or the standard deviations of the trades.

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Comparing Different Systems with the Same Expectancy

Now let us play a little with the Excel application and compare three different trading systems that have exactly the same expectancy per trade!

System 1:

- Average Win : 30 points
- Average Loss : 10 points
- Winning Percentage: 40%

Expectancy per contract traded is E = 0.4 * 30 points * $ 5 - 0.6 * 10 points * $ 5 = $ 30

System 2:

- Average Win: 12 points
- Average Loss = 12 points
- Winning Percentage: 75 %

Expectancy per contract traded is E = 0.75 * 12 points * $ 5 - 0.25 * 12 points * $ 5 = $ 30

System 3:

- Average Win: 20 points
- Average Loss = 20 points
- Winning Percentage: 65 %

Expectancy per contract traded is E = 0.65 * 20 points * $ 5 - 0.35 * 20 points * $ 5 = $ 30

All expectancies are before slippage and commission. Slippage and commission is identical for all three systems and would be $ 9 per roundturn based on 1 point slippage and 0.8 points commission. This leads to a net expectancy of $ 21 per trade. The important point here is that the net expectancy for all three systems is the same. System 1 is typical for a breakout system or a trend follower, system 2 is not unusual for a scalping system. System 3 could be a system that uses retracement entries.

All three systems are traded with a Kelly factor of 0.25

This fixes our risk of ruin at 078%. Note that the risk of ruin does not directly depend on the R-Multiple or the win/loss ratio, as the Kellycrieterion already adjusts for it. The three systems now

- have the same expectancy per contract traded
- have the same risk of ruin via the 0.1 Kelly approach

The best system is that one, which allows us to trade size for the same risk appetite. Now we just need to put the figures into that Excel table, and here are the results:

System 1: The optimal position size would be 3.72% of the initial balance, the system would start trading 32 contracts and the target would be reached after 104 trades.

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System 2: The optimal position size would be 10.29% of the initial balance, the system would start trading 75 contracts and the target would be reached after 45 trades.

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System 3: The optimal position size would be 5.77% of the initial balance, the system would start trading 26 contracts and the target would be reached after 128 trades.

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Conclusions

We have compared three different trading systems with the same expectancy per contract traded, that is $ 30 before commission and slippage, and $ 21 after commission and slippage.

We have then adjusted position size to our predefined risk appetite in order to maintain a level of 0.78% for the risk of ruin. The results are interesting.

System 1 allows us to trade 32 contracts, system 2 allows us to trade 75 contracts and system 3 allows us to trade 26 contracts for the same risk. Clearly system 2 is my favourite, as it allows to trade larger position size and I may reach the target account after only 45 trades.

Have written all this to show that my assumption as per last sentence of post #69 was correct, and because @Hotch has encouraged me to do so.

Last edited by Fat Tails; April 13th, 2012 at 06:19 AM.

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@Fat Tails, if you modify the win/loss figures to include commission and slippage, wouldn't it be easier?

Just using net profit or net win/loss vs gross.

Mike

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- System with 2,000 trades, and net expectancy after commission and slippage of $5 per trade.
- System with 200 trades, and net expectancy after commission and slippage of $50 per trade.

I tend to always lean towards the system with the greater number of trades, as I like to imagine such a system is less curve fitted and has provided me more samples.

What are your thoughts? I suppose in terms of risk alone, trading 200 times is less risk than trading 2,000 times.

Mike

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Lots of good information in this thread and thank you for the spreadsheet as well.

Makes me wish I had a Bernoulli distribution in my trading; could leverage a lot higher. Though it did confirm that the size have been trading is likely a bit low.

For those that don't have a hard profit target and stop loss, I am wondering if there would be a way to consider the standard deviation of wins and losses in order to make the same risk of ruin and size calculations. I could probably come up with something, but it would likely be using bad statistics.

Luger

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The question is not obvious to answer, I need to make a lot of assumptions first.

(1) First of all the model relies on fixed-fractional betting. If you say I have a system doing 2,000 trades with an expectancy of $5, you assume that all those trades are the same size. Otherwise your expectancy would rise with your account size, as you take advantage of trading more contracts. If you don't increase the bet size, you don't need any models.

So the question, correctly put would be that you trade a system with an initial expectancy of $5, which will do 2,000 trades.

(2) The model which is based on the Kelly criterion above was used to find the optimal position size compatible with a predefined risk appetite. It compares risk adjusted returns. Your question fixes the position size before you start trading and you ask about the risk for a given number of trades with identical returns before adjusting position sizing. If you do not adjust position size, when the bet starts, then you forego the opportunity to adjust the position size to risk allowance. Of course you can ask the question backward: If I am trading this, what would have been the Kelly factor that would have produced the same initial position size and what would have been the corresponding risk of ruin.

(3) The expectancy and the number of trades does not tell me anything about the dispersion of those trades around the mean return, the information you have given is therefore not sufficient to evaluate the risk of ruin.
Information is needed on the characteristics of the two systems regarding the R-Multiple and winning percentage.

(4) I also need to assume that the 200 and the 2,000 trades are approximately taken over the same period, so that both systems are in the market for about the same time.

Answer to your question:

Even without calculating, it is obvious that the drawdowns produced by the system with 200 trades are typically larger than the drawdowns produced by the system with 2,000 trades. Statistically this is described by the variance of the logarithmic returns, which is smaller for the 2,000 trade system. The smaller variance allows to increase position size and the system performing 2,000 trades can be leveraged higher for the same risk allowance.

I will now try to reverse-select a Kelly factor to allow to compare the two systems for their risk of ruin. As I said above, the information given is not sufficient, so I will make some additional assumptions before applying the Excel model.

System 1:

average win : 10 points
average loss : 10 points
winning percentage: 65%
slippage and commision : 2 points

Expectancy after slippage and commission: 0.65 * (10-2) * 5 $ - 0.35 (10+2) * 5 $ = 5 $
The Kelly factor is now adjusted in a way that the system produces approximately 2,000 trades.

Result: The system can be traded with a Kelly factor of 0.07, which represents a risk of ruin of 0.000005 %.
It would require 1981 trades to attain the target account of $ 200.000.

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System 2:

average win : 40 points
average loss : 40 points
winning percentage: 65%
slippage and commision : 2 points

Expectancy after slippage and commission: 0.65 * (40-2) * 5 $ - 0.35 (40+2) * 5 $ = 50 $
The Kelly factor is now adjusted in a way that the system produces approximately 200 trades.

Result: The system can be traded with a Kelly factor of 0.11, which represents a risk of ruin of 0.000673 %.
It would require 199 trades to attain the target account of $ 200.000.

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Comparing the results:

Both systems start trading with 7 contracts. However, the 200 trade system represents a risk of ruin which is about 1,350 times higher than the 2,000 trade system. This is essentially due to the larger variance of returns.

The 2,000 trade system uses a Kelly factor of 0.07, the 200 trade system uses a Kelly factor of 0.11.

But now comes what is really important. If you apply the same Kelly factor to the 2,000 trade system, you may increase the number of contracts traded from 7 to 11. By increasing leverage, you will achieve your target after 1,261 trades.

However the 2,000 trade system only comes out winner, if the 2,000 trades are taken over the same period as the 200 trades of the other system. Actually it wins, if the 1,261 trades that result from adjusting the position size for risk appetite are completed prior to the 200 trades of the other system.

Last edited by Fat Tails; April 12th, 2012 at 08:31 PM.

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