Optimal f
>Controlling risk is the absolute number one priority, not optimization. Although >important, optimization is only secondary in importance.
1. Any problem of risk management/control can be reformulated as some optimization problem.
2. The same risk control procedure that is applied to Kellyâ€™s value or optimal f may be applied to other optimal solutions.
3. Could you please describe the risk control procedure in more detail? I have some doubts that exists a correct procedure, which uses something close to â€œgarbageâ€
1. Any problem of risk management/control can be reformulated as some optimization problem.
2. The same risk control procedure that is applied to Kellyâ€™s value or optimal f may be applied to other optimal solutions.
3. Could you please describe the risk control procedure in more detail? I have some doubts that exists a correct procedure, which uses something close to â€œgarbageâ€
Optimizing Product
PS. Michael Bryant wrote an article some time back for Stocks and Commodities Magazine which described his use of sizing optimization. Here is a link to a page that gives some background and leads to a product that lets you experiment with optimal sizing with limits like you mention. I don't have any ties to the product, but do have experience coding and testing many sizing strategies for custom software similar to this. My recommendation would be to set up something like this and find out what it means for yourself.
Cheers,
Kevin
Cheers,
Kevin
MCT wrote:
What is optimal is not some exact magic number, itâ€™s simply a none stationary line in the sand that separates optimal and none optimal regions; if time wasnâ€™t an issue, we all would have been able to pin down what's optimal. MJ described it best as the cliffofdeath, and it all depends how close youâ€™d like to get.
Assumptions regarding the nature of time are always embedded in any hypothesis, including the one you propose. Iâ€™ll try to take a simple a stab at it.
You might define risk as a worst case loss scenario. It could be based on a run of losses with a less than a one percent probability of occurring, calculated by your expected win/loss ratio. If your luck is running at .40, you have approximately a less than 1% chance you will see ten losses in a row. You could decide the worst drawdown you can stomach and divide that by ten which will give you your allowable risk per trade. Nothing fancy, just straight forward simple math. As you said, just about any fixedfraction betting strategy would satisfy this criterion.
The second criterion is not so simple. 1) You are largely dealing with uncertainty or the unknown. 2) It cannot be defined clearly enough to quantify. 3) Since, whatâ€™s optimal changes with a series of trades, timing of trades becomes an essential element of your strategy. 4) Any statistical study of criterion #2 deals with a form of distribution that has time in it â€“ also known as process. We know very little about such distributions at this stage of our evolution. 5) Stationarity is a much more serious issue, with #2 than #1, with deadly consequences. 6) Last but not least an optimal strategy that takes into account both criterions is a more dangerous route since it could drastically raise the threshold of ones risk of ruin. Unlike risk, reward does not necessarily increase with time, and this distinction is crucial. For example, a position held for a long period of time may simply lose more money, and may never realize any type of reward, but risk will always be present.
In general, the issue you present is EXTREMELY important. Many years ago I concluded Iâ€™d become a hybrid trader. I utilize a more flexible rule based discretion for entries, exits, and market selection. Iâ€™m either aggressive or defensive depending on general market conditions. I find this has maximized the expectancy of my system. I believe, reward is a function of timing of entry and exit rather than simply the length of time a position is held. A well timed trade that runs for a long period of time is nirvana. I guess we all have to find our niche.
PS Wrote:And time, my friend, makes it difficult to determine whatâ€™s really optimal. You can't determine what your profit will be, but you can determine what your loss will be.
Itâ€™s my opinion itâ€™s not a person dependent issue, this is a universal issue. I donâ€™t know anyone who can determine what their profit will be, tomorrow, next month, next year, or any future time. Losing or quantifying something you already possess is much simpler than generating future profits.This is a person dependent issue.
Anyone who know what he want can establish goals and can design strategies which maximize the chances to reach these goals.
What is optimal is not some exact magic number, itâ€™s simply a none stationary line in the sand that separates optimal and none optimal regions; if time wasnâ€™t an issue, we all would have been able to pin down what's optimal. MJ described it best as the cliffofdeath, and it all depends how close youâ€™d like to get.
Assumptions regarding the nature of time are always embedded in any hypothesis, including the one you propose. Iâ€™ll try to take a simple a stab at it.
Your first criterion can be approximated using standard statistics.The first criterion is to minimize the probability to lose the initial capital (bankroll).
The second criterion is to maximize the probability to reach the target profit or sum.
You might define risk as a worst case loss scenario. It could be based on a run of losses with a less than a one percent probability of occurring, calculated by your expected win/loss ratio. If your luck is running at .40, you have approximately a less than 1% chance you will see ten losses in a row. You could decide the worst drawdown you can stomach and divide that by ten which will give you your allowable risk per trade. Nothing fancy, just straight forward simple math. As you said, just about any fixedfraction betting strategy would satisfy this criterion.
The second criterion is not so simple. 1) You are largely dealing with uncertainty or the unknown. 2) It cannot be defined clearly enough to quantify. 3) Since, whatâ€™s optimal changes with a series of trades, timing of trades becomes an essential element of your strategy. 4) Any statistical study of criterion #2 deals with a form of distribution that has time in it â€“ also known as process. We know very little about such distributions at this stage of our evolution. 5) Stationarity is a much more serious issue, with #2 than #1, with deadly consequences. 6) Last but not least an optimal strategy that takes into account both criterions is a more dangerous route since it could drastically raise the threshold of ones risk of ruin. Unlike risk, reward does not necessarily increase with time, and this distinction is crucial. For example, a position held for a long period of time may simply lose more money, and may never realize any type of reward, but risk will always be present.
Iâ€™m of the opinion, subjectivity and assumptions are the very heart of trading, no matter your approach to the markets.On this stage we have multicriteria optimization problem. The solution of this problem is a set of fixedfraction betting strategies. On this set it is possible to consider the next optimization problem: maximize expected value of the total sum (bankroll+profit/loss). This solution is free from artificial assuptions about the criteria.
In general, the issue you present is EXTREMELY important. Many years ago I concluded Iâ€™d become a hybrid trader. I utilize a more flexible rule based discretion for entries, exits, and market selection. Iâ€™m either aggressive or defensive depending on general market conditions. I find this has maximized the expectancy of my system. I believe, reward is a function of timing of entry and exit rather than simply the length of time a position is held. A well timed trade that runs for a long period of time is nirvana. I guess we all have to find our niche.
>What is optimal is not some exact magic number, itâ€™s simply a none >stationary line in the sand that separates optimal and none optimal >regions;
It seems we are talking about different stages in modeling process. There are three stages. On the first stage the assuptions are made about time unit, time interval, probabilities, etc. This is very delicate stage on which we introduce subjectivity and which depend on talents of modellers. Once we do that, we have some mathematical problem. The solution of this problem (for example, optimal solution of an optimization problem) is a concrete solution free from any subjectivity and magic.
The second stage consist in finding the solution, and the third stage consist in interpreting this abstract solution back to real problem and taking actions.
My mentions of optimal solutions were refered to the second stage.
It seems we are talking about different stages in modeling process. There are three stages. On the first stage the assuptions are made about time unit, time interval, probabilities, etc. This is very delicate stage on which we introduce subjectivity and which depend on talents of modellers. Once we do that, we have some mathematical problem. The solution of this problem (for example, optimal solution of an optimization problem) is a concrete solution free from any subjectivity and magic.
The second stage consist in finding the solution, and the third stage consist in interpreting this abstract solution back to real problem and taking actions.
My mentions of optimal solutions were refered to the second stage.
You are correct, in that my focus was on stage 1 as you define it. I think the basics are supremely important. If one impregnates a model with certain assumptions that have nothing to do with reality, the real world results would not be very pleasant. If a doctor did the equivalent he could end up killing his patients. Unlike simulated laboratory experiments, a controlled clinical study of stage one is a more truth revealing approach than blind number crunching.
What Iâ€™m actually saying is the apparent distributions we observe in process modeling do not have stable properties over time. This is not a problem about fat tails; Iâ€™m actually saying the shape of the curve actually changes. If you move onto stage two without addressing this conundrum, you might not kill a patient but you might end up loosing money . Reality always has a funny way of revealing the truth.It seems we are talking about different stages in modeling process.
One One of the things I find valuable about the Turtle Roundtable is a pragmatic focus. Sometimes members are known to prompt "what do your results say", which is a way to encourage people to share based on actual findings and experiences. So, my question is this: How can we ground the current discussion and move the ball forward in a way that is something beyond opinion and philosophy; in a way that can be implemented, verified, and applied?
Since we're talking about models, what is the mathematics, algorithm, or strategy behind what might be an appropriate model? If you have a model in mind, what information does it reveal?
Cheers,
Kevin
Since we're talking about models, what is the mathematics, algorithm, or strategy behind what might be an appropriate model? If you have a model in mind, what information does it reveal?
Cheers,
Kevin
hi Kevin
I realize, very well, the favorite question on this forum is "what do your results say?" I come from a different and close to datamining free approach grounded in real time historical trading results. I, instead, tend to ask â€œwhat do the results mean?â€
Hi KevinOne One of the things I find valuable about the Turtle Roundtable is a pragmatic focus. Sometimes members are known to prompt "what do your results say", which is a way to encourage people to share based on actual findings and experiences.
I realize, very well, the favorite question on this forum is "what do your results say?" I come from a different and close to datamining free approach grounded in real time historical trading results. I, instead, tend to ask â€œwhat do the results mean?â€
>I think the basics are supremely important.
>If one impregnates a model with certain assumptions that have nothing >to do with >reality, the real world results would not be very pleasant.
I agree with you on 200%. The purpose of my post was to figure out which optimal fixed fraction betting strategy model relies on the most solid and realistic assumptions.
>What Iâ€™m actually saying is the apparent distributions we observe in >process modeling do >not have stable properties over time.
This depends on the type of the market you are trying to model. If you mean stock markets then I agree with you because the nature of stock markets is not statistical it is â€œcooperative (or manipulative) gameâ€
>If one impregnates a model with certain assumptions that have nothing >to do with >reality, the real world results would not be very pleasant.
I agree with you on 200%. The purpose of my post was to figure out which optimal fixed fraction betting strategy model relies on the most solid and realistic assumptions.
>What Iâ€™m actually saying is the apparent distributions we observe in >process modeling do >not have stable properties over time.
This depends on the type of the market you are trying to model. If you mean stock markets then I agree with you because the nature of stock markets is not statistical it is â€œcooperative (or manipulative) gameâ€
Kevin & MCT
Agree with you both, since I was both wondering what the practical benefits were of this somewhat arcane discourse whilst at the same time chiding myself for not revisiting Optimal f with a more open mind.
I am evereager to translate ideas, concepts, theories et al into tangible, realworld practices but am struggling to see any benefit in Optimal f. As a theoretical construct it may have some merit but does anyone really trade it ??
Optimal f seems to offer the optimal route to either googols of dollars or financial oblivion, and not much in between.
Tom
Agree with you both, since I was both wondering what the practical benefits were of this somewhat arcane discourse whilst at the same time chiding myself for not revisiting Optimal f with a more open mind.
I am evereager to translate ideas, concepts, theories et al into tangible, realworld practices but am struggling to see any benefit in Optimal f. As a theoretical construct it may have some merit but does anyone really trade it ??
Optimal f seems to offer the optimal route to either googols of dollars or financial oblivion, and not much in between.
Tom

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 Location: Duluth, MN
Yes, there are those who definitely trade using Optimal f. Option guys like me and offfloor traders who use option constructs to absolutely limit their risk. (Thinkguys like Nassim Taleb)TC wrote: I am evereager to translate ideas, concepts, theories et al into tangible, realworld practices but am struggling to see any benefit in Optimal f. As a theoretical construct it may have some merit but does anyone really trade it ??
If you can be certain that your risk in your optimal f'd trading scenario is limited because of options purchased, the formula works perfectly. What hurts the Optimal f concept is that systemkiller (and systemtraderkiller) losses tend to get bigger as the time factor increases.
You want to become an option trader?
GammaTrader
Hi Gamma
Aint smart enough for that, it's all Greek to me !!
Did briefly consider options on futures to hedge my long exposure on equities but didn't pursue it.
Any good (that means simple) books laying out the basics that you'd recommend ?
Looks to be expensive to trade and seems like the smart money writes rather than trades.
How easy is it (relative to stocks & futures) to find an edge, and what's yours ?
Regards
Tom
GammaTrader wrote:
You want to become an option trader?
GammaTrader
Aint smart enough for that, it's all Greek to me !!
Did briefly consider options on futures to hedge my long exposure on equities but didn't pursue it.
Any good (that means simple) books laying out the basics that you'd recommend ?
Looks to be expensive to trade and seems like the smart money writes rather than trades.
How easy is it (relative to stocks & futures) to find an edge, and what's yours ?
Regards
Tom

 Contributing Member
 Posts: 5
 Joined: Thu Aug 19, 2004 4:13 pm
 Location: Duluth, MN
Being an options trader is a separate world from positional futures trading, but there are important similarities. They are both systems of risk management.TC wrote:Hi Gamma...,
Any good (that means simple) books laying out the basics that you'd recommend ?
Looks to be expensive to trade and seems like the smart money writes rather than trades.
How easy is it (relative to stocks & futures) to find an edge, and what's yours ?
Regards
Tom
Although straight futures traders don't realize it, most professional option traders are very long term traders. Probably longer term than most traders on this forum. When someone buys a USZ5 116 call, the seller is holding the other end for a long time. This is a major component of the option trader edge. Time value of money.
When options are sold (written), they usually stay on the option trader's statements until they expire. This means that the trader has to manage a burgeoning position entering futures and buying offsetting options to balance the greeks to keep potential risks in line.
Then, when another risk selected trade comes along, the process expands. Usually option expiration is a happy time, so most of the sold puts and calls expire and I can take a vacation for a few days.
My edge is the difference between what I receive for the options I sell and what it costs to manage the risk until their expirations. The best management technique is using options to hedge off the options I've sold. It's more dynamic, with a greater likelihood of doing the job with less followup adjustments being needed.
My edge is buying and selling premium with a directional and time bias. I purchase calls/puts in the direction of the working trend and sell others in time periods or price areas less likely to be threatened by future action. Although my "system" is about 8090% mechanical, you do need a fair understanding of what structures are possible in the option world to keep the risk controlled.
I am certain that eventually all competitive long term traders will trade this way. The benefit is you don't get whipsawed as much and you should be able to catch all major trends with less risk and greater size for the same account size that would be trading futures only. The negative is you have to learn more, or have someone on staff to do the derivative work. But for the bigger potential, maybe it is worth it.
There is the additional informational edge which you reap from trading options which mitigates potential drawdowns. You get this because option trading is something very few long term traders are willing to tackle. They figure that it's enough to tinker with money management and diversify amongst many markets instead of branching out in a complicated field.
Here are a couple of decent books which are "simple" but have unique points of view about obtaining and harvesting consistent edges.
The Options Workbook: Fundamental Spread Concept Strategies for Investors and Traders, by Market Wizards's Tony Saliba  He comfortably explains under what circumstances the option markets are exploitable. Great background book.
Option SecretsNever Before Seen Techiques, by David Rivera  This is a book with option software included, with effective structures for trading futures and stock trends with low risk. Rivera explains how relative beginners can get an edge identical to that of pros.
There are much more complex books available, but if you can't understand them very well, it is hard to get the information they contain. Like everything, there is a learning curve to trading options profitably.
For every $1000 of option premium I sell, I buy $666 of options to hedge it. This enables me to let wasting time value work for me, while having the potential of making money if an extreme move takes place in any direction because of the deltas I buy to hedge myself.
But, as in everything in trading, there are tradeoffs. Complexity has costs too. We all have to make our own choices.
GammaTrader
Gamma
Thanks for the informative post, you have piqued my interest sufficiently that I'm going to get Saliba's book, I've always wanted to learn a new language !!
How many markets do you have to trade to diversify your risk and what strategies would you recommend to neophyte options traders ?
Also, if I may indulge with a followup, assuming that the oftquoted statistic that 90% of options expire worthless is broadly correct, wouldn't writing options offer a more appealing risk:reward profile than buying them ?
Thanks
Tom
Thanks for the informative post, you have piqued my interest sufficiently that I'm going to get Saliba's book, I've always wanted to learn a new language !!
How many markets do you have to trade to diversify your risk and what strategies would you recommend to neophyte options traders ?
Also, if I may indulge with a followup, assuming that the oftquoted statistic that 90% of options expire worthless is broadly correct, wouldn't writing options offer a more appealing risk:reward profile than buying them ?
Thanks
Tom

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This 90% number strikes me as entirely meaningless unless we know the net value of those that expire worthless vs those that are in the money.TC wrote: Also, if I may indulge with a followup, assuming that the oftquoted statistic that 90% of options expire worthless is broadly correct,
Imagine an option seller sells 10 options at an average price of $1. If 9 expire worthless, while the last one is in the money for $11 at expiration, your option seller is a net loser even though 90% of his options expired worthless.
bbc
Read the prior posts and you'll see that I am not an advocate of trading straightup Optimalf. I also mention some alternative practical applications, such as system metrics. For instance, given two systems with roughly equivalent MAR ratio, I will always choose the system that yeilds the highest Optimalf ratio.TC wrote:I am evereager to translate ideas, concepts, theories et al into tangible, realworld practices but am struggling to see any benefit in Optimal f. As a theoretical construct it may have some merit but does anyone really trade it ??
Getting back to practical optimization, I think the framework and mechanics for Optimalf offers a great starting point. The core problem with straight Optimalf is not the mechanics, but how it defines "what is optimal". It optimizes net return at all costs (Terminal Wealth Relative, or TWR in Optimalf lingo). I think the first example to rewiring Optimalf is discarding all values that result in drawdown greater than X%.
Take a look at the code for Optimalf, and modify this section ...
Code: Select all
double X = 0.50;
for(i=0;i<len;i++) {
hpr = 1 + (f * (trxns[i]/_absLargestLoss));
twr = twr*hpr;
if (twr < X) { // <== NEW CODE BLOCK
twr = 0.0;
break;
}
}
Not so abstract, and not all that hard.
Cheers,
Kevin
One more thing ...
Ok, I'll add one more twist ... Turn the above constrained optimal fraction into a simple Monte Carlo run by selecting permutations of the transactions input array, building a distribution of constrained optimal result values, then picking the distribution median. These techniques should go a long way toward finding a stable optimal bet size.
Cheers,
Kevin
[edit: Rather than picking the median, it's probably more useful to pick a value based on confidence interval. For example, pick the optimal fixed fraction value with a 95% chance of not seeing a 50% drawdown].
Cheers,
Kevin
[edit: Rather than picking the median, it's probably more useful to pick a value based on confidence interval. For example, pick the optimal fixed fraction value with a 95% chance of not seeing a 50% drawdown].
Last edited by ksberg on Wed Sep 22, 2004 12:37 pm, edited 1 time in total.
Kevin
You have adroitly, and with some ingenuity, proved the point I was trying to make !!
Optimal F itself needs some "optimising" before it becomes a useful tool for the average trader
You have demonstrated in the above posts and elsewhere that your analytical skills far exceed my own and I would be very interested in a simple (remember, I'm a simple guy) exposition of your portfolio optimisation process, within the limits of what you consider proprietary of course.
Using TradeStation I run singlestrategy/single market optimisations (max. 8,000 parameter value permutations) and then export to Excel for further analysis.
The optimisation & analysis of systems and markets at the portfolio level and data import capability are the prime reasons I will likely buy VT 2.0.
Thanks
Tom
You have adroitly, and with some ingenuity, proved the point I was trying to make !!
Optimal F itself needs some "optimising" before it becomes a useful tool for the average trader
You have demonstrated in the above posts and elsewhere that your analytical skills far exceed my own and I would be very interested in a simple (remember, I'm a simple guy) exposition of your portfolio optimisation process, within the limits of what you consider proprietary of course.
Using TradeStation I run singlestrategy/single market optimisations (max. 8,000 parameter value permutations) and then export to Excel for further analysis.
The optimisation & analysis of systems and markets at the portfolio level and data import capability are the prime reasons I will likely buy VT 2.0.
Thanks
Tom
The meaning of all this ...
Tom,
I'm unsure whether you were looking for an explanation of the modified Optimalf algorithm (I'll call this ConstrainedF), how ConstrainedF gets used in Monte Carlo, or the whole ball of wax.
In a prior post, Ted uploaded a nice graph that compares the bet size fraction to equity growth (his 1st graph). The LHS label reads "Equity Growth", but we would get the same curve using CAGR, $ return, or even TWR. What OptimalF is doing is walking that curve, testing each fixed fraction point, and finding the point at the top. What the ConstrainedF example is doing is also walking the same curve left to right, but it stops somewhere left of the point on top. It stops precisely where we see initial capital decrease by more than 50%. That gives us a more conservative bet size.
Life is good, and we go about trading. Say we repeat the optimization 10 trades later: we would find that our optimal value moved because of the new trade data. Another few trades and it moves again, and so on, and so on. After a while we would question if we should be using an optimal value that keeps moving, because we'd always be trading on past information. Enter Monte Carlo.
Monte Carlo is a technique to randomize probable outcomes based on the future behaving somewhat like the past. At the core, MC asks "What if our trades had occured in a different order?". We could repeat the optimization process on the randomized data, and get a probable optimal value. Record this value. Randomize again, optimize and record. Keep repeating this process hundreds or more times. Graph the recorded values and you will get a statistical distribution, like a bell curve, that represents what we believe to be all probable optimal ConstrainedF values.
Finally we use statistics to help pick a point on that curve, which will be our final ConstrainedF fixed fraction. Remember that our constraint or "cut off" condition was anything beyond 50% drawdown of initial capital? That implies all optimal values beyond ConstrainedF resulted in 50% drawdown or more, so our belllike curve also closely represents the occurances of seeing 50% drawdown. To cut exposure to 5% chance of seeing that happen, choose a point on the lefthand tail of the distribution which represents 5% or less of all occurances. We now have an optimal value that gives a 95% confidence of keeping initial capital drawdown to less than 50% (according to MC).
My "one more twist" comments add some effort to ConstrainedF algorithm, but not as much as you might think: The ConstrainedF algorithm needs to be put in a loop. The input values need to be permuted (shuffled). The outputs need to be collected in an array. After the loop, the collection needs to be sorted lowtohigh. Calculate 5% as an index into the sorted array. Voila! The value at the index is the answer (at least for this example).
Excel VBA is sufficient for the task. I think the hardest part is a producing a decent shuffle. Mr. Google always has an answer.
Hope that helps,
Kevin
BTW: OptimalF TWR = Final Stake / Initial Stake ... it's a gain ratio for the portfolio.
I'm unsure whether you were looking for an explanation of the modified Optimalf algorithm (I'll call this ConstrainedF), how ConstrainedF gets used in Monte Carlo, or the whole ball of wax.
In a prior post, Ted uploaded a nice graph that compares the bet size fraction to equity growth (his 1st graph). The LHS label reads "Equity Growth", but we would get the same curve using CAGR, $ return, or even TWR. What OptimalF is doing is walking that curve, testing each fixed fraction point, and finding the point at the top. What the ConstrainedF example is doing is also walking the same curve left to right, but it stops somewhere left of the point on top. It stops precisely where we see initial capital decrease by more than 50%. That gives us a more conservative bet size.
Life is good, and we go about trading. Say we repeat the optimization 10 trades later: we would find that our optimal value moved because of the new trade data. Another few trades and it moves again, and so on, and so on. After a while we would question if we should be using an optimal value that keeps moving, because we'd always be trading on past information. Enter Monte Carlo.
Monte Carlo is a technique to randomize probable outcomes based on the future behaving somewhat like the past. At the core, MC asks "What if our trades had occured in a different order?". We could repeat the optimization process on the randomized data, and get a probable optimal value. Record this value. Randomize again, optimize and record. Keep repeating this process hundreds or more times. Graph the recorded values and you will get a statistical distribution, like a bell curve, that represents what we believe to be all probable optimal ConstrainedF values.
Finally we use statistics to help pick a point on that curve, which will be our final ConstrainedF fixed fraction. Remember that our constraint or "cut off" condition was anything beyond 50% drawdown of initial capital? That implies all optimal values beyond ConstrainedF resulted in 50% drawdown or more, so our belllike curve also closely represents the occurances of seeing 50% drawdown. To cut exposure to 5% chance of seeing that happen, choose a point on the lefthand tail of the distribution which represents 5% or less of all occurances. We now have an optimal value that gives a 95% confidence of keeping initial capital drawdown to less than 50% (according to MC).
My "one more twist" comments add some effort to ConstrainedF algorithm, but not as much as you might think: The ConstrainedF algorithm needs to be put in a loop. The input values need to be permuted (shuffled). The outputs need to be collected in an array. After the loop, the collection needs to be sorted lowtohigh. Calculate 5% as an index into the sorted array. Voila! The value at the index is the answer (at least for this example).
Excel VBA is sufficient for the task. I think the hardest part is a producing a decent shuffle. Mr. Google always has an answer.
Hope that helps,
Kevin
BTW: OptimalF TWR = Final Stake / Initial Stake ... it's a gain ratio for the portfolio.

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Forum Mgmnt wrote: If 3% is considered conservative, it's no wonder most traders lose money.
My guess is that a high % of traders have had experience with equities before venturing into futures in search of higher returns.
For a nonmargin equities account 3% is a reasonably conservative amount to risk as this would imply a porfolio of ca 30 different stocks. Given the high correlation of all stocks there is little value in increasing the number of equities in a portfolio above this number and many would recommend trading fewer stocks at larger size (traditional buy & hold stock investing). Thus, an investor could have an orthodox equity portfolio of 1520 stocks, with 5  7 % of his equity in each stock.
This same individual then starts trading futures, and recognizing the higher risk, decides to halve the amount of equity in each trade. The result is a "conservative" 3% of equity/trade.
As he rakes in the cash on the first few trades he may be tempted to increase his bet size to where it used to be when investing in equities. In his more thoughful moments this trader may ponder why some of the more experienced traders appear willing to forgo the profits he is making by trading a paltry 1% of equity compared with his 3%+
And then Alan "The Real Hurricane" Greenspan begins his testimony on Capitol Hill ..............
Of course before Sir Alan has even finished his prepared statement our traders account has taken such a severe beating he'll likely bail at the height of the turmoil and retreat to the safe world of anythingbutfutures