The Finance Book Club

TimeTells,
I have added it to the new book list, but I'm anxious to complete all the books that are already on that list. I'm a completionist that way. Time Compression can be the first book after that.

Review
How do I feel about this?

There’s no doubt that Jones is highly clever and his twist on FF MM has been picked up by dozens of trading book authors if not actual traders. I can’t find any fault with his FR method.

However much of the book just seems like good general advice that’s a little too easy. It reminds me of Wyckoff, who can’t be caught in any obvious lie, but to attempt to trade based on his breezy recommendations would likely end in disaster. Especially since he doesn’t even believe in a ‘risk of ruin’ concept.

I think it can’t be so simple as to trade his ‘simple logical system’ from Chapter 13 while applying Fixed Ratio MM and ‘decreasing risk’ during drawdowns. Though I aim to test it. I've begun to test it. Report forthcoming.

The fact that he doesn’t provide more than some tables in a book as proof of the results and that he is OK with using ‘hypothetical’ trades to prove other concepts are both big turnoffs for me.

If it was that simple, why didn’t Jones go on to manage money (instead of selling courses)? Maybe he’s like Marty Schwartz and he just doesn’t want to deal with other people. I can certainly understand that.

If you do a Google search for Ryan Jones you find that he doesn’t maintain a positive reputation among some traders, and this actually puts him higher in my esteem (Clemmo’s Conjecture). At the same time there are some red flags.

You’ll see most of the criticism comes from his sales of an options trading program, not his MM theories. I also have to cite my theorem about book authors who write more than a couple of books. Once you’ve said all there is to say about trading and your method, adding on more methods and more systems, and selling courses on the side, is simply a way to sell more methods and more systems. In this case it appears Jones didn’t write many other books, if any. So that’s a checkmark.

But he did go on to sell courses, a lot of them, for over 15 years, and that’s a big ? except maybe there’s more money to be made selling courses than in trading options or he just can’t resist showing off. It also appears his newfangled ideas don’t work or stopped working quickly. That might not be entirely his fault. The marketplace does that and does it faster than ever before. Lastly, he did have Larry Williams’ confidence, though Williams didn’t use FR to set his trading records. He invented his own MM system.

That right there might be the best lesson of all.

In the end, I guess whether this material has any value depends on how it’s applied, and how faithfully, as well as in how much the markets have changed to adapt to its popularity.

I’m sure you’re all quite sick of the Money Management Topic, but there’s another MM book in my list and I want to get it all out of the way now, so, like it or not, we move straight on to another book about MM. Fortunately (?), as you’ll see it’s more of a refresher than a survey of new topics.

Here's a result from one round of testing the Jonestown EA on AUDUSD

In-sample, 2022 looks too good to be true, as you'd expect.

Out of sample, 2021 just survives, which is better than the alternative. Clearly a couple of years of data is not enough to do a proper backtest.

These use the D1 timeframe. Settings attached. What I'm curious to know is if we can cut down the trading horizon?

The Successful Trader’s Guide to MM by Andreas Unger

What do you do if you don’t make enough profits from trading?
You write books and sell them!
What do you do if you don’t feel like doing all the work to write your own book?
You copy an existing, slightly outdated book, or several in this case!

That’s right, this book is, at least structurally, a retelling of classic works by Ryan Jones, Van Tharp, and Ralph Vince. Right down to the chapter listings, the coin-flipping examples, etc.

At least we know Andreas Unger has the audacity to be a trader…and a plagiarist!

Well, there does seem to be some material that we haven’t covered before so let’s at least look at that.

Note: Unger uses Euros throughout this book and I simply do a straight-up conversion to $ or use the $ interchangeably with the Euro symbol as I don’t want to be bothered trying to produce it using my North American keyboard. I don’t think it matters, but it might.

Foreword
Online trading expanded in Europe in the 1990s.
There aren’t many books about MM at least in Europe, says Unger.
Unger refers to himself in the third person, as ‘the author’. Maybe it’s less incriminating than saying ‘me’ or ‘I’?

Unger repeats Jone’s wisdom that MM is not the same as using stop-losses.

Without MM, TA, systems, and methods are useless.

Unger has a vast trading book collection, he says. Big enough to crib from.

Most traders start as scalpers but then look for something less frantic, Unger claims.

Unger trades almost exclusively with automatic systems, because it’s best suited to planning. Same.

Position management is risk management, not Money Management.

“Personally, I interpret money management only in terms of the science that tells me ‘how much’ to use and not how to do so. Some prefer to call this simply ‘position sizing’ and include risk management also as part of money management, but in my opinion this is a somewhat strained interpretation that does no damage, apart from causing a few misunderstandings.”

I already posted this as a reply to a comment in another thread but where's pure mathematics textbooks here? You cannot talk numbers without knowing what numbers actually are.

I'm curious to know more. Are there any books that deal with the topic you're thinking about? Is it number theory? Are there any books that address the math and the trading together? That would be very interesting.

I am talking about having some grasp on mathematics. From the basics to the advanced topics. And this suggestion came out of your suggestion, correct me if I am wrong, to be able to have some formal way to describe what you are seeing so it can be precise and describable in ways of algorithms.

I recall saying that of the various disciplines that traders should study, statistics is one of the more useful ones. I also think there could be some value in data analysis. I recently finished the Google Data Analysis certificate, in an effort to keep up with what's going on in the field. I'm not sure it was enough.

Quantitative trading is a whole field on its own and I'd be happy to move towards it. One book that's on my personal shelf is Johann Christian Lotter's 'Black Book of Financial Hacking : Passive Income with Algorithmic Trading Strategies. I'd love to go through it, but it would be demanding.

Chapter 1: Martingale and Anti-Martingale
See Jones’ book.

Chapter 2: The Kelly Formula
See my notes on Emerenko, or the review of ‘Fortune’s Formula’.

This is how Unger describes the formula, where R = ratio of wins to losses. W = probability of winning.
He explains everything with coin-flipping and adds the usual warning that theoretical results won’t match expectations especially in trading.

Chapter 3: A Banal Trading System
A moving average crossover system with a fast/slow EMA. on M15, with $20 USD commission and slippage built in to each trade.


The system trades only from midnight to noon, in order to emphasize that a gap loss (from the next day's opening) can be worse than the maximum planned loss.

“In order to further limit the number of system entry points, another filter was used that only allows a long entry if the day’s high hasn’t exceeded the previous day’s high (of course, the high recorded from midnight to midday, as we don’t know the prices outside this range). Vice versa, a short entry is only allowed when the day’s low is still higher than the previous day’s low.”

Recognize this? It’s Jone’s daily high/low break strategy. Actually it’s subtly different as the rule doesn’t enforce a break and then a retrace, it simply requires that the entry not happen above or below the daily break. I’m quite curious to know which one is better or if there is any difference at all. Probably there’s little difference.

Unger tests from 200-2005.

Now we get an interesting attempt to apply the Kelly formula to this system.



Unger gets the inputs from his trading report.



When trading equities it’s not hard to figure this out. However derivatives depend on the leverage being used.

“We calculate the amount of our available capital to invest by applying the percentage obtained using the Kelly formula, and then divide this by the margin, to find out how many contracts we can use.”

Suppose:

1. $100k account
2. K% = 25%

So invest $25k .

Suppose margin is $2500 per contract.

1. 25000/2500 = 10 contracts can be traded.

Suppose K% = 20
Then invest $20k.

With $2500 margin, 20,000/2500 = 8 contracts can be traded.
Round down to limit risk.

The formula to calculate the number of contracts is:
Contracts = ENT(capital ∗ Kelly ∕ margin)

Where ENT = ‘entire part of’ (the whole account)

Suppose we have a $50,000 account.
Contracts = ENT(50k * 0.106265 / 2500) = ENT(2.1253) or 2 rounded down

Recalculate on every trade.

As you can see performance was inferior to not using MM for many trades and then it takes off.

Unger then spends a lot of time examining whether to round up or down or to the nearest fraction (which you can’t do in practical trading anyway. It’s funny what detail-oriented people can get stuck on.)

“You can never put blind faith in a maximum theoretical loss. Even leaving aside the possibility of opening with a gap, and using just intraday techniques, there’s always the risk of losing more than you planned as the technology used to send the orders to the market can cause delays or even be unexpectedly blocked.” Can confirm.

Chapter 4 - MM Models
Fixed Fractional Method
See Jones’ book

Optimal f
See Jones’ book

(although he has a more complex formula for calculating optimal f - possibly straight out of Vince’s book?)

Where

As Unger admits, this is confusing, so it’s better to understand it using concrete examples.

Secure f
See Jones’ book

Fixed Ratio
Here Unger cites Jones’ book. The cheek!

He also cites a more complex formula for finding the number of contracts using fixed ratio, which is one I’ve seen elsewhere but for obvious reasons prefer not to use.


INT = ENT (entire part of)
Ci = starting capital
Jones plugs in starting capital of $50k with a delta of $2500


While Jones’ formula may have been less mathy, it was far easier to calculate.

Unger mentions that FF is less suited for smaller accounts.

He also models some interesting comparisons of results using different delta fractions.



Percent Volatility Model
Now this is new, and it comes from Van K. Tharp.

The whole theory is based on the maximum size of the fluctuations of the instrument you’re trading.

Measure the daily range, from max. To min. And calculate the average over a number of days. Use more days for longer trading horizons.

4-5 days average is acceptable for short-term trading (open positions from 2 days - 1 week).

20 days average for open positions from 10d - 1 month.

Unger says it’s actually more convenient to use the ATR (it is).

Suppose we have $100k.
We want a maximum fluctuation of 2%.

The allowed fluctuation is $2000.

We measure the ATR over 5 days or so and get an average value of 300 points or $1500.


That’s allowed fluctuation / average ATR. But there’s a more sophisticated formula…



…whose exact meaning is not clear to me. Unger says Vp is the ‘value of the single instrument point’? And in our example it is = 5. So is it the five day period of the ATR? No, surely that’s ATR(period). What other 5 unit value is there? If we interpret this as

Contracts = ENT (0.02 * 50k)/5*5 = 40 contracts

This is way too high. Unger doesn’t add any additional clarification which is annoying as hell. I guess it’s in Tharp’s book and I could go look it up later.

Update: No Unger is on glue and Vp must be the ATR value that we saw earlier around 300.
0.02*50k / 5*300 = ⅔ of a contract if that was even possible. I dunno. Weird.

If he had just stuck with his initial $100k example then it would work out to 1.3 or 1 contract, same as the first example. Ok, I’m moving on.

“This method can be put on standby for periods of time and then start following the signals again in the right volatility conditions.”

Unger spends several pages and dozens of diagrams to reach the conclusion that there is a certain percent of risk beyond which the account will always bankrupt itself. Thanks for that.

Chapter 5 - Refining the Techniques
Unger argues the choice of MM method is largely one that we should tailor to our trading personalities.

However there are other ways to tailor methods to our temperaments.

Reduced f
Just start with %f of 10% until our capital doubles, then reduce to 7.5%, then reduce to 5%, then reduce to 2.5% then 1.25%. A method favoured by con artists who are trading hundreds of accounts with a random system. The few that survive can still appear ‘active’ by drastically reducing their risk and keeping a good looking equity curve for marketing purposes.

The final results actually end up being the same, says Unger.


The bold line is reduced f and the skinnier line is FR with a delta of 6k.It actually looks way better. Maybe there’s something to this. I guess the caveat is getting an account to 300 trades using 10% risk is going to be tricky to say the least.

Timid Bold Equity
Unger shows several other methods that don’t really do much of anything different, but then he shows something by Van Tharp called ‘Timid Bold Equity’.

The idea is to split the equity into two parts. The first is traded at low risk. The second at high risk.
You use FF for both parts, but use a lower percentage with the ‘timid’ portion. You use optimal f for the bold portion.

The initial capital in the account is 100% low risk and then as profits are made in the account they are transferred to the ‘high risk’ portion. Then when your capital has doubled, start again from scratch, withholding double the initial capital for the ‘timid’ portion.

Example
$50k starting balance
Use 5% which is $2000. The optimal f for this system was 23%

Once you get to a profit of $60k you’d calculate as follows:
Contracts = ENT [(50k * 0.05) + (60k - 50k) * 0.23] / 1,250
= ENT(3.872) and round down to 3 contracts.
You see that’s using 5% for the first 50k and then 23% on the 10k in profits you’ve made since you started. 1250 is the max loss I believe?
The original optimal f formula would have had you trading only 2 contracts.

When you get to $100k, apply 5% to that amount and apply 23% to anything you make over that.

Unger compares this method to FF using 5%.

And notes that it doubles the FF method's profits but the DDs are more terrifying. “This is an example of how a more aggressive strategy can produce both damage and benefits.”

Equity Curve Trading
See Jones’ book and why he dismisses this as not MM, but system optimization. Unger claims this is worth considering because in his tests, not trading during a drawdown produces better results, especially for strategies that use more aggressive values and have ‘marked’ DD periods.

What he doesn’t tell us is what threshold to use to consider equity in a ‘downturn’ and what threshold to use to resume trading in an equity ‘upturn’. He says he is using the MA of 1 contract over a 30 day average, but where is that line?


If you can answer this question you have solved the riddle of trading in general and you wouldn’t need MM at all, just trade nearly all-in all the time. I suspect the only reason that Unger can do it here is because of ‘future leakage’ where he makes use of the pre-existing knowledge of the equity curve. How would you track this if you weren’t trading? Trade a demo system parallel to this one? I know that is something that’s been recommended in the ‘Traders Unplugged’ podcast so maybe.

“Remember, we’re working with a banal moving average crossover system, and it’s well known that these systems work well in trend periods, while suffering heavy drawdowns when the market becomes congested. It’s also well understood that the market alternates trend periods with congested periods, and by ceasing trading below the equity’s moving average we can often stay away from long periods of congestion.” This does make some sense. And what if you, instead of ceasing to trade, switched systems to one that is meant to trade ranges? The problem is when do you know when a range is about to breakout? A filter will cut into your trend profits.

“That’s not all. This type of stop also protects you from the risk of finding yourself with a system that, for whatever reason, no longer works.” Because Big Bro Algo is on to you is why.

Z-Score
I truly believe Unger is out of his depth here, trying to determine what the Hurst coefficient can do more readily, using a technique that was designed for normal distributions, with which market data is definitely not comparable. Still, if you are curious, you should check the book out.

Chapter 6 - Monte Carlo Simulation
Even with a good system, and capable money management, trading too aggressively for your account size can result in ruin.

Being under-capitalized means you are trading with a very aggressive risk profile by default.

Rather than increase risk it’s better to stop using a system that has put you in a condition from which you can’t continue.

Apparently insignificant details like the order in which trades are experienced, or a single percentage point of risk greater or smaller, can have an outsized effect on the future as predicted by chaos theory.

Because the market can change radically there is no definitive way to eliminate all risk.

“The Monte Carlo simulation lets you create a certain number of scenarios, based on the original, simply by mixing up the order in which events happened; so the same might be repeated or some events might not occur at all.”

About the Monte Carlo Simulation, Unger says “this is certainly a very sophisticated method, but in my opinion it goes beyond the spirit of a simulation and almost leaves the world of trading behind to become an exercise in statistics.”

Despite this, he proceeds to examine a bunch of specific cases using a system he hasn’t described - I think it’s the ‘banal’ simple moving average crossover of chapter 3?

First is FF with 5% risk and max loss equal to a SL of $1250. Initial capital of $50,000. He doesn’t say but I assume these figures are retained for all the following examples.


Here’s what Unger (or his original source) takes away from this.

 

1. Outcomes are hard to predict
2. 50% of cases will result in returns over 1000%
3. The other half of the histogram creates a wide range of possibilities, so you can’t confidently aim for 400% for example
4. 3.6% of all cases lose money after six years

The MC simulation also lets us compare the chances of getting a max percent drawdown.

1. This distribution seems much more regular (bell-shaped) than the returns percentage.
2. The most results are in the 34-70 percent DD range.

Now you have to decide if you can live with these probabilities. Nearly 4% chance of ending up behind after six years. DD of 50% or more is likely.

Also keep in mind that this is the result of 1,000 simulations. We can get higher resolution figures by using 5,000 simulations. However the results are largely the same.

Unger looks at a lot of cases where the risk percent is lower than what is needed for the system to continue functioning, but why, I’m not sure. Clearly no one is going to do that. He also looks at cases where the system gets ‘blocked’ due to insufficient capital after the first loss, but again, that’s not going to bear any fruit.

Now Unger looks at Fixed ratio with a delta of 5,000.

1. Returns seem better with fewer loss cases and higher returns in the win cases

Unger also ran a 1,000 simulation test of the DD, but I’m skipping ahead to the 5,000 test, assuming it’s the same deal but more reliable.

1. Results are similar to FF but the curve is wider
2. Average seems to be around 50% DD
3. Some 20% cases are seen that weren’t seen with FF

Unger imagines we are a very prudent (conservative) trader and these high DDs make us nervous (as they should). So we know we can reduce risk by increasing delta.

 

1. ‘Respectable’ return %
2. Only 69 cases return better than 1000% (interesting)
3. 295 cases between 500-1000%
4. Most results are 200% or or more
5. 8/1000 negative results, which is very good

The histogram skews towards safety which is encouraging.

Now that Unger has seen a safe (and probably best-case) scenario he wants to see what happens if we get dangerous.




Fixed Fractional with 10% risk.

 

1. Good news - 70% of returns are above 1000%
2. Bad news - 87 cases wiped out more than ½ the starting capital.
3. Over 10% of cases lose money.
4. Few cases are between 0 and 500%
5. Good news is the chance of making a healthy profit is 7x greater than losing

Naturally this good news needs to be balanced out by looking at the DD distribution.

Skews to the risky with a majority of DDs over 80%. This is basically insane. Unger reminds us that this is only looking at daily prices so a mid-day fluctuation could make this even worse.

Now Unger looks to reduce risk with FR, using a delta of 2500 over 1k simulations.

 

1. Potential profits are more limited, with 60% of cases over 1000%
2. Not much noticeable difference between these results and delta of 5,000
3. DD distribution between 48-60%; better than FF but worse than our previous FR test, so Unger keeps hunting

“The Monte Carlo simulation can also make you take quite drastic decisions you might not have taken, based on data from the principal trading system alone. It’s very important to try and take a step back to analyse the results of the simulation objectively, to try and consider the possible scenarios in terms of what your feelings might be at the time. It’s no use kidding ourselves and ‘ignoring’ a 10% possibility that a certain negative event might occur. 10% isn’t exactly a remote chance.”
Maximum Loss
“In our example, we’re using a stop-loss of –€1,250; but, if we take a look at the system performance report (Figure 3.2), you’ll see that the actual maximum loss in the 6 years in question was €2,757.5, more than double that!”

Unger says this shows our percentages are too aggressive.

“From a certain point of view, using the maximum loss instead of the
stop-loss is the same as halving the risk percentage.”

Now Unger will examine Monte Carlo simulations using Max Loss instead of the stop-loss.

The first attempt produces no data, because 5% of $50k is $2500 which is less than the max loss of $2575.50

So he increases to 10%.

1. Very few results under zero
2. Only 40% of cases above 1000% return compared to 70% in Fig. 6.13

This is an improvement over 6.14, with drawdowns skewing to the lower side.

Unger finds this effect even more pronounced when he increases risk to 15%. He says this risk % makes more sense if we’re halving the risk by using max loss instead of stop loss.

“Being able to simulate cases that might occur, but aren’t included in the historical data, lets you analyze more cases you might find yourself in on the basis of your money management decisions.”

Chapter 7 - The Work Plan

1. A strategy is no good without a plan because when under pressure (Mike Tyson’s punch to the mouth) you’ll worry and not know what to do
   
   Attached Image (click to enlarge)

   
   
2. If you know the rules of your strategy (for example because you created it yourself)
   1. You can try to change it during unfavourable periods
   2. A good trader knows how to react during losses

3. If you planned goals but also for hazards, you can remain calm, knowing if this is business as usual or something is wrong
4. People just want to get started so planning is rarely given much thought
5. Unger argues we can create a roadmap by checking in periodically with our six year planned equity curve.
6. However he uses Monte Carlo simulation once again and that’s a bridge too far.
   1. If we simulate the worst loss after a year, and it’s already close to the worst trade loss expected after six years that tells us something is wrong (wrong - the worst loss could happen anywhere, and just because it’s statistically more likely to happen in the greater part of the trading history doesn’t mean you can know anything about the future based on where the max loss happens - this is a convoluted form of gambler’s fallacy)

7. Unger suggests simulating the profits year by year
8. Have parameters to halt trading before it’s too late
9. “For lovers of statistics let’s say the distribution of the natural logarithm of the percentage drawdowns is normal, so the percentage drawdowns are distributed log-normally.” This is a terrible assumption. The only thing it could tell you is if your system is better or worse than a natural (coin-flipping) system.
10. Unger goes on to explain e, and normal distributions, standard deviations.
11. He somehow arrives at a risk level of 4%
12. He somehow arrives at exact drawdowns to expect per year, 46.1% in the second year.
13. He continues to fantasize in this way arriving at made-up values for his entire history.

“A well-constructed work plan helped bring our work to a successful conclusion and, above all, get through a very ugly period without getting into a panic (there were of course a few frayed nerves, but having a plan helped in the decision-making process).” Oh bravo! You got through your imaginary sequence.

Chapter 8 - Combining Forces

1. Use a combination of systems
2. Unger introduces a new system - the Donchian Channel breakout
3. It “is based on hourly bars, and simply buys on the breakout of the 50-bar high and sells on the breakout of the low in the same period.” A classic trend-follower.
4. The idea is if a market is strong enough to break the highest highs or lowest lows it is likely to continue (momentum)
5. Crude Oil, Gold, and Soybeans
6. 1500 USD stop loss per contract

Unger then shows us pages and pages of charts like this:

And this:

For each market.

“Now, to evaluate the effect of both the application of position sizing on the systems, and whether a portfolio approach is effective or not, first we’ll consider the individual systems applying different money management algorithms, starting with the Crude Oil system and evaluating the performance with a percent f of 2% calibrated to the stop-loss, a fixed ratio with a delta of 10,000 USD and a percent volatility of 2%”.

He checks each market, and then checks the results with varying risk levels and varying MM methods.

I don’t think there is any value to any of this as we don’t know all the ins and outs of his system, the details of the Donchian channels (does he use them) and other devilish details. As he noted before, small differences can have an outsized impact on overall long-term performance. I suspect this is merely book padding. Lots and lots of charts quickly fill up the pages.

“In money management, you don’t think in terms of single systems. Always remember that the number of contracts depends on the available capital.” I think this means that more successful systems should fund less successful ones, and the reason you keep them around is because in different regimes they will pay off?

Unger describes a few more Van Tharp inventions. However, he does so very quickly. I’m sure it would be better to get this info directly from Tharp.

The Core Equity Model
The available capital is the capital remaining after deducting the potential losses allowed by the MM strategy.
Suppose the account is $500k.
Using 2% risk
Enter with six contracts:
Capital risked = 500k * 2/100 = 10k
Contracts = ENT(10k/1500) =6 (1500 is the largest loss?)
“This means you’d be willing to withstand a loss of 9,000 USD.” (because 1500 * 6 = 9000 ? This is not explained in sufficient detail!)

Now suppose you want to enter a crude oil trade.
Initial capital is still 500k but deduct 9k risked and use 491k to figure the oil contracts.

Total Equity Model
“In this case, the capital of reference is the total available liquid capital added to the current value of the portfolio.”
Use the values from the previous example.
Suppose you have a gain of 2k for each gold contract when you decide to enter the crude oil position.

500k + (6 * 2000) = 512,000
The situation is different when we look at things this way, and different situations require different choices which could result in different outcomes. Well duh.

Reduced Core Equity Model / Reduced Total Equity
Based on the core equity model reasoning.
Subtracts the risk values from initial capital.

Again, use the previous case.
“If, for example, in the above case you reached a point in which the Gold contract provided for a move to a closer exit level (this isn’t provided for by the system we’re taking as an example but is often used in many other systems), and instead of a loss of 1,500 USD now provided for a loss of 500 USD, the 1,000 USD ‘gained’ from the dynamics of the trade for each contract would be added to the value of the capital to be considered.”

Prior case:
500,000 − 6 ∗ 1,500 = 491,000.

New Case
491,000 + 6 ∗ 1,000 = 497,000.
OR
500,000 − 6 ∗ 500 = 497,000. Is the other way to look at it.

So we’re basically borrowing from the total allowable loss by exiting from a position earlier than we originally planned? That seems nuts.

Now imagine that the gold contracts increase in profits. We gain $500 from each contract.

Change risk by another $1000 per contract (from $500 loss to $500 profit).
497,000 + 6 ∗ 1,000 = 503,000
OR
500,000 + 6 ∗ 500 = 503,000.

The Nameless Method
A name I've given it, because Unger doesn’t have a name for it.

“for every trade, [...] consider the equity when the last trade closed. In practice the evolution of the open trades and their potential repercussions on the capital, aren’t considered. As far as I know, this method doesn’t have a name, and I do sometimes use it as the calculations are intrinsically very simple.” And that’s all the explanation given! I’m not going to try and guess what he means. I should have skipped this last one.

Unger points out that the Core Equity Model can be tracked in Excel. The Total Equity model needs to be updated in real-time. Core Equity is more conservative.

Unger goes on to simulate the results of portfolios using Monte Carlo though he is sparing with the details. The most important conclusion he reaches is that where Fixed Ratio wasn’t very impressive when using individual systems it fares far better when combining systems but at the cost of worse drawdowns.




Just imagine pages and pages of charts and tables like these looking at different percentages of fixed fractional, 2% volatility model, and you have the rest of the chapter. Again, this would all vary based on the system used, by so much that to select a method based on his sample model would be…foolish? At best?

Unger does prefer the percent volatility model though as it ends up with a DD < 25%. (in this case).

Chapter 9 - MM Trading Stocks
Futures are not any riskier than Stocks once you know them.

Risking more with stocks paradoxically can improve performance, because unlike with futures, the commission costs don’t necessarily increase with more volume.

Unger provides code for his stock-trading system, which, interestingly, does not use fixed-ratio MM because it’s too complex to calculate with shares.

Chapter 10 - Portfolio Management
I thought this was lifted from Jones’ book but it’s actually about managing money for other people. It reinforces Schwartz’s suggestion that the public cannot tolerate much DD at all. I think if you get to this point you’ll probably want to consult a tome dedicated to this specific subject. Or two.

Chapter 11 - Discretionary Trading
Unger doesn’t want anyone to feel left out so we get this mega-chapter.

After reading the previous chapter, you’ll probably think the money management techniques in it must be combined with a trading system. Certainly, in order to plan things in an effective way, you should simulate the strategy you’re thinking of using to see how it behaves, so it’s always a good idea to draw up a trading system before you start trading on the Market.” In other words, yes you bloody well do need a trading system even if that ‘system’ is just tons of experience.

Unger points out that people usually start by improvising and don’t have a clear idea of what they’re doing. That’s true.

Then he decides he needs to define what he means by discretionary trading. Well, let me do what he takes a page to do. It’s trading without a system. Trading by the seat of your pants. Trading based on how the wind/moods/ascension of Venus moves you. If it sounds like I’m being snarky, maybe, but I know at least a few people are very good at it. I’m not.

Unger doesn’t count scalping as discretionary, but of course it is.

Entries are chosen selectively. Exits are chosen haphazardly, for ‘most’ discretionary traders.

Discretionary training doesn't give you historical data to base decisions. Well, it does. But it’s harder to evaluate because it’s all different. Somewhat random.

Unger dissuades the reader who trades discretionarily (?) from using Fixed Ratio because it’s more complex. He advises using percent vol or fixed fractional.

On using FF:
“When using a very tight stop-loss, the loss will be quite limited and, for the same percentage impact, you can enter the trade with more contracts.” I think this is terrible advice, for reasons I think I’ve mentioned before, because the larger your trade, the more inherent opposition it will receive. Your tight stop loss is like a tissue barrier against a machine that is oiled and ready to consume your money. The larger the trade, the more leeway it needs to be given except in the most liquid (volatile) of situations. At least for those of us stuck on the retail side of things.

On using percent vol:
It “doesn’t consider the potential loss, but measures the movements of the stock and calibrates the entry based on the Average True Range of the last period. If you want to use this method, you will have to have already calculated the average at n days of the true range for the stock.”

Unger describes a sample stock trade using FF.
Fixed Fractional example
He decides to enter at 9.30 and set his stop at 8.75.
Assume account size is $100k.
Risk is 2%.
First evaluate the stop-loss in percentage terms.




Now calculate the amount to risk.


“With these two parameters, we can now calculate the amount to invest in the trade. The capital used for the trade must be equal to an amount 5.91% of which is €2,000 because, if the stop is triggered, losing 5.91%, we don’t want to lose more than €2,000.”



Now Unger uses the word ‘contracts’ but he means ‘shares’, no?

So we enter at 9.30.


If he hits his stop.
Well, that’s 90 cents off, but good enough.

If he hits his target:


Some might say at 1:1 R:R this is not a good trade but that’s a matter of risk management, not money management and beyond the scope of this treatise. Of course it depends on the system/discretion of the trader.

Here’s a formula you can use to directly calculate the number of contracts on the basis of the entry price and stop if used, as well as obviously the risk chosen and available capital:


Now what about
Percent Volatility?

Notice that the chart in figure 11.1 has the ATR listed.
%Vol limits the fluctuations in the total capital. Unger chooses to limit capital flux to 0.5% of total capital.

Check the ATR indicator each morning. On Jan. 4 it was 0.1230

First, calculate the admissible range.



“On the basis of our observation we know that the volatility of 1MS share is €0.1230; so, in order to remain within the limit of a max. range of €500 we could buy:”



Not too different from the FF example.

The general formula is


If Unger hits the target:


“Note that the percent volatility model doesn’t in fact consider the strategic levels of the trade you are going to open. The formula doesn’t consider the entry level (the number of contracts is calculated without even considering the entry price) or where the stop-loss is positioned, and it only considers how much the stock moved in the latest period, so how much it could move while we have a position open.”

And so Unger doesn’t calculate the loss we’d suffer if we used the same stop loss as the FF example but that’s trivial.
(8.75-9.30) * 4065 = -2,235.75, again, fairly similar to a 1:1 RR trade.
The important difference is the stop loss is not part of the %vol formula, where it is integral to FF.

Also, if you keep a position open for a while the volatility might change and need to be recalculated. That might necessitate selling off some part of the position.

Unger goes on to quickly look at a wider stop using FF, for some reason, and then hastily touches on Core Equity, Total Equity examples, but in so little detail that I got nothing from it, and summarizing it would be even worse.

However Unger does consider a FR trade using DAX futures which I will summarize as this could be quite useful.
Fixed Ratio Example

Unger decides to enter here, going with the trend after an indecisive triangle.


The added wrinkle of trailing stops!


Eventually the stop is hit and the trade exits.

Unger tells us this is the gain from the trade.

But what MM was used?

Again, assume $100k account.
The FF method would use the entry at 5249, a stop-loss of 5153 which is 96 DAX points. Each DAX point is = 25 euros.


So every DAX contract is risking $2400.

Suppose we want to risk the usual 2%.



The exclamation points aren’t factorials, they are astonishment as we can’t take this trade at this risk. Actually it’s 0.83 but gets rounded to zero.

“Remember that rejecting a trade for this sort of reason is part of money management and shouldn’t be seen as something stupid.”

You can

1. Ignore the trade (simplest)
2. Increase the risk (imprudent)
3. Move the SL level so you wouldn’t lose more than $2k (needs a level of 5169 which is possible but ‘pushing it’)
4. Wait for a retracement to enter at a level where you wouldn’t lose more than $2k (limit buy at 5233, using SL of 5153) (most advisable)

The result:


Ok, whew, now let’s look at percent volatility for this DAX futures trade.

Percent Vol Example
Unger has already told us that a percentage of 0.5% which was fine for stocks is not suitable for Futures. Let’s see why.

First, consult figure 11.1. The ATR the day before the trade is at 53.6 points.
DAX points are 25 euros.


This gives us the volatility in euros. We didn’t have to do this with stocks because 1 point = $1 in that case.

“Now, if we take this path with the percentage we considered at the time of 0.5% we’d have a maximum limit range of:”


So we are limited to movements of $500 when the instrument itself has an expected average true range of $1340. This is just setting ourselves up for heartbreak (and why the tight SL crowd is usually disappointed).

To trade like this the ATR would have to be under 20. However waiting for volatility to drop is futile. Volatility in DAX is rarely this low.

We either need more capital (you always do) or you need a different percent.
Unger chooses to increase the starting capital to $500k. Lucky guy.



That’s right, you can trade 1 contract with half a million.

Now Unger absolutely twists himself into knots, trying to track volatility over time, and comparing it to FF, but since the FF example only used $100k capital, we need to do another comparison using FF but at $500k. Then he takes that and adjusts it over several days of varying volatility.


It looks like this and I don’t care! This needs to be automated. Ultimately he finds that all this adjustment is pointless as we would make more money using Fixed Fractional. It seems to me that Fixed Fractional isn’t such a bad trading method after all. It is simpler and often comes out on top in cases where you have adequate capitalization, but then, who has that?
“If you use the percent volatility model, while the trade is open you can monitor the level of exposure on the basis of the current volatility and, by using suitable calculations, adjust the number of contracts used. This procedure can involve some difficulties but also be very effective to make the most of market trends.” I would just love to see that thread and its single follower (me) on ForexFactory!