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Risk of Ruin


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Risk of Ruin

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  #101 (permalink)
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leinster View Post
So does anyone actually use kelly ?

I'd like to also make sure you've seen the webinar:
Webinar: Ernest Chan - Capital Allocation and Risk Management

And the thread:


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  #102 (permalink)
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Hi Mike,

Yes i have seen the webinar and it really peaked my interest in this whole concept.

Hence the reason i ask if anyone is using either optimal f / kelly ?

I am tempted to look at optimal f / kelly on an options spread strategy (where i can exactly limit risk).

I see the researcher in the ppt link i sent on claimed the illustrious Mr Buffett was using fully kelly and Soros .8 if thats true then it certainly is interesting!

Also this betting / money management strategy certainly explains a lot of the ways people get to 1000% in these trading competitions etc.

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  #103 (permalink)
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Fat Tails View Post
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.




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.




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.




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.

is this excell available?
thanks
alejo

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  #104 (permalink)
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alejo View Post
is this excell available?
thanks
alejo

Posted in the thread. Use the attachments link on top right of thread to find it if you don't want to read the posts.

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  #105 (permalink)
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alejo View Post
is this excell available?
thanks
alejo


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Fat Tails View Post

fat tails
i try to use your excell to calculate the max lots with risk of ruin

i have a couple of questions:

i try to compare 2 strategies:
3lots strategy
i practicing this in tradestation
entry 3 lots target 1 2lots at +1 target 21 lot +2
this is the performance report for tradestation
Tradestation considerers 1 trade per exit leg , 2 trades per 1 3lot entry trade


then i have 4 lot strategy, (it is the same than 3lots plus 1 lot more with target +3tick)
i am practicing in S5 and i get this report




here the excell considerers 1 trade per entry=1tradewith 4lots

then i was wondering what i need to entry in your excell to get an useful result to compare both strategy

thank you very much

alejo

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  #107 (permalink)
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alejo View Post
fat tails
i try to use your excell to calculate the max lots with risk of ruin

i have a couple of questions:

i try to compare 2 strategies:
3lots strategy
i practicing this in tradestation
entry 3 lots target 1 2lots at +1 target 21 lot +2
this is the performance report for tradestation
Tradestation considerers 1 trade per exit leg , 2 trades per 1 3lot entry trade


then i have 4 lot strategy, (it is the same than 3lots plus 1 lot more with target +3tick)
i am practicing in S5 and i get this report




here the excell considerers 1 trade per entry=1tradewith 4lots

then i was wondering what i need to entry in your excell to get an useful result to compare both strategy

thank you very much

alejo


The Excel table is a simple tool, which was not meant to be applied to complex trading strategies.

In your case a Monte Carlo simulation can be used for determining the risk levels.

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  #108 (permalink)
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Interesting, however if and when I'm winning not something I look at. I try to keep % of winning trades above 90-95%, and limiting risk exposure strictly upfront try to never get to a point where I'm eroding capital.

I guess my response to the thread would be to not look for a mathematical discussion with myself, but a more psychological one around my own risk aversion levels. But as we are in this thread looking to modelling it a risk aversion factor would need to be a key component. As I guess would be a level of daily VaR level - I guess reflecting the level of drawdown I'd be happy to take, and that a function of the account size.

interesting topic..

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Quoting 
I try to keep % of winning trades above 90-95%

So low?
Below 99.99% I don't trade. Lol

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baruchs View Post
So low?
Below 99.99% I don't trade. Lol

Lol.. 99.999% ideally ;-) sure I get it, nothing is certain very true.

My point coming across badly perhaps.. what I'm trying to get across is that I am willing to accept slightly larger draw-downs if I'm confident in my view of the market but limit my risk exposure to a very small portion of my account. So effectively I can win a lot of my trades whilst I'm progressing my learning curve.

Most people trade more than they should risk wise in terms of proportion of their account and have way too tight stops (in my opinion). they don't give the position space to breathe. As I've seen it - how many times have we all seen a position move against us, close it, and then see it push back.

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  #111 (permalink)
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Hi (and especially @Fat Tails ),

First, thanks a lot for this very interesting thread.

Even if I agree that Monte Carlo is a better approach, I wanted to play with the first formula:

where:
a is the level of ruin compared to the initial capital (for instance: a = 0.25)
b is the target compared to the initial capital (for instance: b = 4.0)
k is the fraction of Kelly which is implemented (between 0 and 1)
P(a, b, k) is the probability that target be reached before ruin

I have fixed a = 0.25.
Let’s suppose that we want P >= 0.99.
The above equation gives a relation between b and k.
I wanted to visualize this relations in order to see if we could maximize b (for a given a and P), and see what would be the corresponding value of k.

I have obtained the following chart (with R):


My understanding is the following:
If we choose the Kelly fraction below a certain level, there is at least 99% chance to obtain any target before being ruined.
If I have made no mistake in the calculation, this level for Kelly fraction is:


What puzzles me is this “any target”. Once more, if we use a Kelly fraction below this level, whatever the target we give ourselves, we are guaranteed at 99% to obtain it before being ruined.

This seems confirmed by the Excel sheet (in the last version as modified by Fat Tails).

I guess that the differences lie in the time before reaching the said targets.

In the context of the above model (which is only a model), does it make sense to choose k(max) as an "optimal" Kelly fraction?

Nicolas

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  #112 (permalink)
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Nicolas11 View Post
My understanding is the following:
If we choose the Kelly fraction below a certain level, there is at least 99% chance to obtain any target before being ruined.
If I have made no mistake in the calculation, this level for Kelly fraction is:

What puzzles me is this “any target”. Once more, if we use a Kelly fraction below this level, whatever the target we give ourselves, we are guaranteed at 99% to obtain it before being ruined.

The risk of ruin is not independent from the target chosen. If your starting balance is $ 100.000, if you consider that you are ruined if less than 25% of your initial capital is left (at that stage you abandon the game) and if your target capital is $ 200.000 then

Risk of ruin = the probability that your equity drops below $ 25.000 before you achieve your target of $ 200.000

Now, if you double your target equity to $ 400.000, it is obvious that this increases your risk of ruin. Just consider a tree of all possible outcomes of subsequent trades. All paths that have hit the $ 200.000 equity line and then drop back to an equity below $ 25.000 increase the risk of ruin. You can add their cumulated probability and it to your risk.

Therefore the 99% level you talk about always depends on a target equity. The risk of ruin is a function of 4 input parameters: ruin defined as a percentage of intial equity, target equity defined as a percentage of initial equity, win rate and win-to-loss ratio. The acceptable risk of ruin can be used to determine the Kelly factor, that is the multiplier (< 1) applied to optimal F. The adjustment to the risk of ruin reduces the expected outcome of the series of bets.

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  #113 (permalink)
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I missed this thread for so long. Very interesting information shared and talked about here. I'm wondering how many participants actually trade in a way that lends itself to these various risk models. I had worked with a brilliant programmer from Sweden and he was so adamant about his risk models and the various analysis being discussed here. He would rebel when I told him that is not how it works.

Someone taught me that a target limits your winners and a stop loss guarantees your losers. He asked if I liked the idea of limited wins and guaranteed losers. The process of being "taught" took a long time and was painful at times. Granted equity options are not limited to directional speculation so part of or "risk" was off set by numerous crafty hedges that could be put on and off to change any element of our exposure.

So when I described this to a ES guy years later he taught me how to press my winners. So when most guys are at a target level taking profit some guys are adding aggressively to press the winner and scale out with huge, and I mean huge, gains...the vast majority of which occur after the position has a big lead. I think the only way to test that or do analysis of the outcome is to look at the account statement.

So sometimes in 6E I cut a loser at just 3 or 4 ticks. That depends largely on what has changed since I put the position on...usually killing one that small happens after time has passed and the expected move did not occur. Total discretion. Other times I'll take a position home twenty or thirty ticks against me...only to be "stopped" when I win or by a margin call or visit from risk. That has happened only a few times in 15 years....the margin call or risk mgr call/visit...and always well past 80-100 ticks. Most of the time you can scale that in by trading in and out realizing loss but you still have position enough when it does go the other way. That is NOT advised, and maybe not a "good" practice.

What happens most of the time is I take an initial profit then I press by adding to the position trying to keep my cost basis on the profitable side of the inside market. Sometimes you get a relatively big position and only get 4-5 ticks net, but other times when the move extends you have as a 10 or 12 lot with bags of ticks hanging off of it. It is okay to set a modest profit lock stop and bring that girl home to mom.

I wonder how that jibes with the regular crew way brighter than I?

So my personal problem now is that I am taking money from the trading account to make up for lost income from another business. Doing that really messes up my psychology and turns me into quite a risk wussy because the 8-10 I'm taking out feels like losing because I am viewing the draw as an expense. Wldman out of balance.

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  #114 (permalink)
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Hi @Fat Tails ,

I obviously agree that, for a given ruin level (a) and a given Kelly factor (k < 1), the probability (p) to reach the target (b) before being ruined decreases when the target (b) increases.

This is visualized by the negative slope on the below 3D surface, when we go from the right (low b) to the left (high b).


However, I have noticed that, for "low" levels of the Kelly factor, this probability does not decrease significantly when the target increases. This is the yellow strip on the chart.

Let's illustrate it with the Excel sheet that you have reviewed. We choose a = 0.25. Let's suppose that we aim at a risk of ruin <= 1%.

With a "high" Kelly factor as 0.6:
- for a target b = 2.0, the risk of ruin is 3.18%
- for a target b = 4.0, the risk of ruin is 3.79 %
The risk of ruin increases with the target. Fine. However, we are above our desired level of risk of ruin (1%).

Now, let's take a "low" Kelly factor as 0.45:
- for a target b = 2.0, the risk of ruin is 0.77%
- for a target b = 4.0, the risk of ruin is 0.84%
The risk of ruin increases with the target. Fine. And we are below our desired level of risk of ruin (1%). Fine again.

And, for this "low" Kelly factor of 0.45, you can input any value you want in the target cell, the risk of ruin will always be less than 1%.

My claim is: for a given ruin level (a), if you choose a Kelly factor k <= kmax (well chosen), then your probability of ruin will always be less than a given threshold, whatever your target.

The reason is that, even if, for given “a” and “k”, the probability (p) to reach the target (b) before being ruined decreases when b increases, it does not decrease to whatever level but tends towards a limit.


It can be calculated that:

(correction thanks to Fat Tails)

So, if you choose

you are guaranteed, in the above model, that the probability of success is above p*.

For a = 0.25 and a desired level of p* = 99% chances of reaching the target before being ruined, if you choose a Kelly factor less than kmax = 0.463, you are guaranteed that your risk of ruin is below 1% whatever your target.

If you are not convinced, you can play with the Excel sheet, and, if I have made no mistake, observe the same phenomenon.



Nicolas

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  #115 (permalink)
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Nicolas11 View Post
It can be calculated that:


So, if you choose

you are guaranteed, in the above model, that the probability of success is above p*.

For a = 0.25 and a desired level of p* = 99% chances of reaching the target before being ruined, if you choose a Kelly factor less than kmax = 0.463, you are guaranteed that your risk of ruin is below 1% whatever your target.

If you are not convinced, you can play with the Excel sheet, and, if I have made no mistake, observe the same phenomenon.



Nicolas

@Nicolas11: You are right, I did not follow you in depth. I have checked your calculations and came to a slightly different conclusion. The main challenge was not to do perform the calculations but to write that stuff with my old version of MS Word. Here is my reasoning:




In the end I find convergence for a Kelly factor < 2 with a slightly different value for the limes. If there is a mistake in my calculations, please let me know.

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  #116 (permalink)
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@Fat Tails ,

I agree with your calculation, and have modified my above message:


I think that it was a kind of transcription error in my message, since my initial formula with kmax is consistent with your correction, which shows that I have found the right expression at a moment, then wrote something else.

Just a note. Since you keep "a" when q --> +oo, it means that you consider that a is constant when the limit is calculated. So your q --> +oo is actually equivalent to my b --> +oo.

Thanks for having noticed the message in my message!

Nicolas

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  #117 (permalink)
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Ernie Chan had a good blog on this recently

Quantitative Trading: Kelly vs. Markowitz Portfolio Optimization

He will be back on futures.io (formerly BMT) for another webinar soon.

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  #118 (permalink)
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sharpe ratio = (MeanAnnualReturn-RiskFreeRate)/StandardDeviationOfReturns

continuous Kelly = (MeanAnnualReturn-RiskFreeRate)/StandardDeviationOfReturns^2

discrete Kelly just gives meaningless numbers for trading systems IMO.

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I believe any moment you enter the market is different. I mean it can favor or unfavor you. Thus it also differ from playing a coin for example, or doing something that is mathematically driven. I saw some raw uneducated guys trading forex, using some simple ploys that don't require any calculations and make decent profit.. consistently.. seeing that I want to throw my math book to the garbage

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Code
# +------------------------------------------------------
# |         Portfolio:  Kelly vs Markowitz 
# |           ( epchan.blogspot.com )
# +------------------------------------------------------

library(quantmod)
library(PerformanceAnalytics)

# Download Monthly Data
syms = c(
  "SPY",     # US SP500
  "TLT",     # US bonds
  "GLD"      # US Gold 
)

Rf <- 0.002  # Risk-free 2.4%  year

getSymbols(syms, from="1970-01-01")
p <- do.call(merge, lapply(syms, function(x) {
               Cl(to.monthly(Ad(get(x)), drop.time = TRUE,
               indexAt='endof'))
               }))
colnames(p) = paste(syms, ".Ad",sep="")
r <- na.omit(ROC(p,type="discrete")) # monthly return

M <- apply(r,2,mean)-Rf # excess return vector
C <- cov(r)             # covariance matrix
KW <- (solve(C)%*%M)/2  # (Half)Kelly-weigths vector
KW                      # H-Kelly Portfolio W's 

MW <- KW/sum(KW)          
MW                      # Markowitz Tangency Portfolio W's

# Results *IN-SAMPLE* :

# Markowitz Portfolio Ret
xx <- t(apply(r,1,function(x) x*MW))
my <- as.xts(apply(xx,1,sum))

# H-Kelly Portfolio Ret
xx <- t(apply(r,1,function(x) x*KW))
ky <- as.xts(apply(xx,1,sum))
z <- merge(my,ky) 
colnames(z) <- c("Markowitz","H-Kelly")

table.AnnualizedReturns(z, Rf=Rf, scale=12)
charts.PerformanceSummary(z,ylog=T,lwd=1,
       main="Markowitz vs H-Kelly")
maxDrawdown(z)
# +---------------------End----------------------------------

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Big Mike View Post

Kaufman gives us the following formula for calculating the risk of ruin:
risk_of_ruin = ((1 - Edge)/(1 + Edge)) ^ Capital_Units
Edge is the probability of a win.

There are a few different formulas floating around, and I've seen some requests to incorporate

I thought I would give a recap of online calculators that are out there since this post, as things have changed:

1) Chris Capre has updated his site to show an interactive calculator instead of just the published tables. The weakness of the calculator as well as the formula it is based on ignores the number of trades placed, and makes no provision for a profit target to be reached before being ruined.

2) The Au.Tra.Sy blog has an interactive calculator based on a monte carlo simulator. It does take inot account the number of trades (periods). It additionally allows you to set a drawdown level instead of ruin. However, it does not allow for a profit target.

3) Forex Scam Alerts has an online risk tool based on monte carlo simulations. It also considers the number of trades, and allows you to set a drawdown level as well. Further, it includes profit targets (retirement), which allows you to see what the probability is of hitting that target before reaching your drawdown limit. The downside of this tool is that it doesn't allow you to set an value you want, but only predetermined values that the tool looks up in a huge database on Monte Carlo simulations.

There are other similar calculators, but they are on blackjack sites, so are not built to be as applicable for traders.

Let me know if I have missed any good ones.

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Dear All,

I just want to say this:

"Risk of ruin has absolutely zero practical application in trading. Running through the calculations to determine the risk of ruin on any particular method is also completely useless."

'The Trading Game' by Ryan Jones.

Don't waste your time fellas.

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virgo739 View Post
Dear All,

I just want to say this:

"Risk of ruin has absolutely zero practical application in trading. Running through the calculations to determine the risk of ruin on any particular method is also completely useless."

'The Trading Game' by Ryan Jones.

Don't waste your time fellas.


Risk of ruin is the key to position sizing. Position sizing is the key to growing a trading account, once you have found an edge and mastered trading psychology.

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virgo739 View Post
Dear All,

I just want to say this:

"Risk of ruin has absolutely zero practical application in trading. Running through the calculations to determine the risk of ruin on any particular method is also completely useless."

'The Trading Game' by Ryan Jones.

Don't waste your time fellas.

I would like you explain in details what you find useless about it. Do you understand what it truly measures for each trader?

Matt Z
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virgo739 View Post
Dear All,

I just want to say this:

"Risk of ruin has absolutely zero practical application in trading. Running through the calculations to determine the risk of ruin on any particular method is also completely useless."

'The Trading Game' by Ryan Jones.

Don't waste your time fellas.

I 100% disagree with that statement. If you don't know your risk of ruin then you can't possibly size your positions.

The probability of ruin matrix is a calculation based on several pieces of data. First, it assumes 100 events; in this case that would be 100 trades. Next, it defines ruin as 50% drawdown from starting equity. Last, it assumes that the methodology used to initiate each event is always the same in every event; in other words each trade done during the 100 trades in the sample set is executed for exactly the same reason.

According to this matrix, if you do 100 trades, and have 42% winners and pull two dollars out for every dollar you give back, your probability of ruin is a little less than 14%. If you calculate the numbers yourself you will find that (42 x 2) - (58 x 1) actually yields a profit of $26, but the ruin matrix is using the full scope of probability theory. That includes the possibility that all the losing trades will come in the first 50% before the sample set of 100 trades is complete.

Notice that a high percentage of winning trades is not an indication that you will make money net in your account. Someone who has 55% winning trades to losing trades has a worse risk of ruin if he wins about the same amount as he loses every time. It actually has a better probability for your account if you have fewer winning trades but hold those winners for a higher profit/loss ratio. Of course, the best of all worlds is to be in the far right side of the matrix. A trader with 60% or more winning trades and only a slightly better profit/loss ratio than 1:1 has no chance of ruin.


--------------------------------------------------------
- Trade what you see. Invest in what you believe -
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Silver Dragon View Post
Found this out of the Internet. Numbers look in line but would like some verfication.


Notes:
  • Cells highlighted in Yellow are what you fill in.
  • All other cells have formulas. Do not change!!
SD

You actually have mistake in your spreadsheet when calculating Z and A.
Pay attention to signs.

It must be like this:

Z = %profitable * avgwin% + %losing * avg loss%,
where avg loss% should be already with minus.

The same logic for A...

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From another post.
SMCJB View Post
Then I built a quick Monte Carlo/Risk of Ruin spreadsheet. The spreadsheet calculates 500 simulations of 100 trades. The two illustrations show the impact of starting account size of a theoretical trading system with an average trade PnL of $500 and Standard Deviation of $1500. Notice how better the starting account size of $10k is than $5k. This is driven by the much lower number of simulations that get 'ruined'.




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A very interesting thread that I'm obviously late to.

Just thought I would share something I read a while back on Johann Lotter's (aka jcl) "Financial Hacker" blog.

He uses a long-run theoretical math approach to argue that however you determine your % risk for each trade, the % should scale sub-linearly with the size of your account. Specifically, he suggests that % risk should scale proportionally to the square root of account size. i.e. if you double your account, the absolute amount risked should increase by (1.41/2) or approx 70.5% instead of 100%.

If you do scale linearly, in the long-run (and he does mean LONG run aka infinitely long), the risk of ruin is 100%. This may be too conservative for practical purposes because as Keynes said we're all dead in the long run... but I think it's still worth keeping in mind if scaling linearly makes you feel uncomfortable.

In addition to authoring this blog, jcl is the author of the "Black Book of Financial Hacking" and one of the lead developers of the zorro backtesting tool.

See section 9 in this blog post: https://financial-hacker.com/build-better-strategies-part-3-the-development-process/

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