I have been dreading writing about this topic. But I noticed there is very little written about optimal f. I think its mainly because the subject is complicated and is deemed impractical anyways by many.

I’m not going to tell you how to calculate your optimal f in the first post. Instead, I will tell you what is the optimal f. Additionally, I will show you what impact it can have on your trading. After that I will examine the benefits and drawbacks of the money management system. I will also provide criticism to the solutions. Finally, I will offer my practical solution that I argue maintains the advantages of optimal f and limits it drawbacks.

[B]What is Optimal f[/B]

Well, it is THE mathematically correct fraction of your balance that you should bet on your trade to get the highest reward. Betting more than that fraction or less than it well yield worse rewards on the same set of trades. So let’s say I have a set of 10 trades, applying the position-sizing of optimal f to those trades will yield the highest result compared to any other way of position-sizing.

I’m not writing this to prove that, it has already been proven by Ralph Vince. So those who want to challenge that notion I would advise them to read Vince’s books. He proves it mathematically anyways, so it is not a matter of point of views. It is a matter of psychology.

[B]Applying Optimal f to your trading[/B]

I did an experiment; I took the first 24 trades I made in 2015 (so the results of those trades were random.) My system’s winning is more than 70% but with the order of those trades the winning % was 66.6%.

The results of the trades were as follows:

1)+37 pips. 2) +133.5 3) 378.6 4) -46.2 5) -103.4 6)-374.3 7) +1053.1 8) -99.6 9) +122 10) +168.7 11) +617.6 12) -113.3 13) +119.6 14) +29.4 15) +135.5 16) -58.1 17) +0.3 18) +26.5 19) +29.4 20) +78.32 21) -5.25 22) -123 23) +128 24) +2

I took those 24 trades and applied two money management systems on it. The first is Larry Williams’ system where the contracts are the relationship between the risk per trade and my biggest loss (again I’m not here to give out formulas. I first want you guys to know what you are in for then give out the formulas for those who are up for it.)

I set a starting account balance of $10,000 and risked a massive 10% per trade (very risky, right?). applying that method yielded me $16629.36. That is a return of 66% which is very good. It is also worth noting that the account never fell below the $10,000 starting balance. So even though the risk was big, the trades played out fine. Risking 4% would have yielded $12,000. With Larry Williams system you can risk more than 1-2% because the system accounts for the biggest loss you have ever encountered.

Next, I applied the same trades to the optimal f position-sizing formula. At the end of the 24 trades I had $58,118.01! Incredible! So why isn’t anyone using that method?

[B]Problems with Optimal f[/B]

Well there are tons of problems with the method. [B]Firstly[/B], even though I had $58,118 in the end, my account had only $6384.5 at one point. The equity swings in optimal f are wild: I literally went from $10,000 to $20,000 in three trades. Then in the next three trades I took it from $20,000 to $6,000.

Optimal f argues that even though we can account for the biggest loss in a system (I have lost 1000 pips before so that would be my worst case scenario for the future), we can never account for the worst case scenario for drawdown or consecutive losses because the answer is losing all (or 99.9%) of our money no matter what.

Optimal f argues that even with using Larry Williams’ method and risking 1%, losing the next 100 trades would almost blow up our account anyway. So since we cannot control the outcome of future trades, we might as well look to get the most gains out of them.

[B]Secondly[/B] The system does not account for spreads, swaps and margin. At one point I was trading 9 standard lots for one trade. Surely holding that trade overnight (or several nights) would have a significant impact on my balance. That is without mentioning the magnifying of spreads as well.

[B]Criticism of Solutions[/B]

There were three main solutions offered to that problem: the first was abandoning optimal f and reverting to the risk% per trade. The second was Larry Williams, a formula that is a mix of the risk% per trade and optimal f. Then there is Ralph Vince’s solution: he presented a formula that finds optimal f within a given drawdown range. Simply put the formula meant if I had a $10,000 account and would only accept a loss of $6,000, based on my previous performances what is my optimal f?

All these solutions are ok, but they do not solve the problem. The real problem is “how do I keep optimal f while limiting its wild swings?” All the three solutions mentioned above limited the drawdown in optimal f, but they also significantly decreased the profits. We want to keep the profits as they are and decrease the losses.

[B]A (Potential) Solution[/B]

The only way around that solution in my opinion, is to use a fraction of your original investment. So in the above example we started with $10,000. Using a fraction of the $10,000 keeps the optimal f as it is while: 1) limiting your losses in dollars. 2) giving you more chances to “wipe out” the account while still having the investment to try again.

Now I tested that idea: with the same 24 trades, I used optimal f position sizing but only depositing $1,000 in the broker and keeping the remaining $9,000 in the bank. Now every time I get a margin call or wipe out the account. I deposit another $1,000. So I’m using optimal f but I get 10 chances before I wipe out the account completely, compared to the 1 chance I had before.

So now applying that method the result was I made $5,811.8. Now unlike the earlier optimal f example this amount is real. The swaps and spreads are that of mini lots so my $10,000 could handle them at any time. The worst drawdown had me at $638.4, so that’s $400 compared to the previous $4000

Comparing this method to using all the $10,000 on a risk% per trade. Only risking 10% or more would have have yielded more profit. More by $81 to be exact.

So you have to risk 10% per trade on regular money management techniques we know to get more or less the same money using the money management method I’m suggesting.

Now once your account gets to $10,000 (remember you get 10 tries at this so it is achievable). It will be up to you whether you want to reinvest your entire or some of the profits to compound your profits further. Or you can take out the $9,000 of profit and start all over again. This topic of deciding when and how much to reinvest deserves another thread on its own.

I hope this provides food for thought for a topic that should be discussed much more by serious traders.