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The Mathematics of Money Management: Risk Analysis Techniques for Traders

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Title: The Mathematics of Money Management: Risk Analysis Techniques for Traders
by Ralph Vince
ISBN: 0-471-54738-7
Publisher: Wiley
Pub. Date: 17 April, 1992
Format: Hardcover
Volumes: 1
List Price(USD): $70.00
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Average Customer Rating: 3.25 (8 reviews)

Customer Reviews

Rating: 5
Summary: This Book is Must Read for those Mathematically Inclined
Comment: ... I must have close to a 100 trading books and this one is a gem. As Elder points out in one of his books there are three legs that support successful trading: Trading Strategy, Psychology and Money Management. Optimal F which is well explained in this book is the best measure of your Risk/Reward. Knowing the optimal f of a trade allows you to compare apples and oranges. I can tell if trading a stock option with a potential return of 1000% is better than trading a stock with a potential return of 20%.

Rating: 1
Summary: mathematical myopia
Comment: In my view trading is NOT about fancy mathematics any more than running a business is about knowing tax laws (of course, I am assuming that a basic knowledge of statistics and probability concepts is not considered 'fancy' here). Trading is about trading, you have to have a basic concept of math but you don't have to be a quant, unless you are trying your hand at some high powered form of arbitrage. Ralph Vince's theory is off in its assumptions because it overlooks the fact that controlling risk is the absolute number one priority, NOT optimization. This very topic is discussed and wrapped up nicely in a few paragraphs in Jack Schwager's interview with scientist/money manager William Eckhardt in 'New Market Wizards' (Eckhardt has a few hundred million under management; I don't know how much Vince does, if any).

I am not a math superstar, I was a literature and philosophy major in college. But even a liberal arts joker like me can see that the math element is way overdone here. The idea that money management is a mysterious and complex issue is proliferated by books like this. I can sum up effective money management in two steps: First take your worst case loss scenario, which will be based on a run of lossses with a less than one percent probability of occurring, as calculated by your expected win/loss ratio. For example, if you reasonably expect to win 40% of the time and lose 60% of the time, there is a less than 1% or "worst case" probability, that you will see ten losses in a row at some point in your trading (this may look like hard math but the calculations are actually grade school level). Next, determine your max desired drawdown. What's the biggest hit you could possibly stand? Ten percent down? Twenty five? Fifty? Let's say you are moderately aggressive and able to deal with a twenty percent drawdown without losing your nerve. Divide twenty percent by ten, and you see that your max allowable risk is 2% of your account balance, including calculated slippage and commissions per trade. If you can stomach a 40% drawdown you don't risk more than 4%, and so forth. Simple, straightforward, no hidden gimmicks, gizmos or geekspeak. The only other bogey you have to deal with is the once in a blue moon nasty price shock that blows your stop to kingdom come (a simple and emphatic argument for less risk per trade, not more).

Most CTA's could double their returns very easily, simply by doubling the amount of risk they take. Why don't they do it? Because the reward is not worth the risk. If you get a huge win, it will help your profits but it will not change your world. A string of fat losses or a single huge loss, however, can kill you, take you out for years, maybe for good, leave you wandering the streets muttering 'if only I had taken a smaller risk on that trade with my name on it, I would have survived'.... Not to mention that bigger ups and downs throw your sharpe ratio all out of wack, which few investors like. If you double your money in eleven months and then take a 50% loss in December, where have you gotten? Nowhere. I recall an anecdote a while back about how George Soros' fired one of his currency traders after a huge score because the trader took on way too much risk with the trade. Even though he won, he got canned for being reckless. If I had someone trading for me and he wasn't thinking defense first, I would can him too. So you've had a reliable win/loss ratio in the past, so what. How do you know a string of losses or a price shock isn't going to bite you when you least expect it? You don't know, and no one is completely immune to a streak of misfortune. Optimization is for gamblers, not professionals. The 'F' in Optimal F should stand for a word that rhymes with 'sucked.'

Rating: 2
Summary: Some gems, but very poorly presented
Comment: I just read the "not for the innumerate" review on this book, and I agree. But I would like to clarify why the book disappoints. It's not that there are too many equations, but that there are too few equations and way too much jargon-laden hand waving. The hand waving, unfortunately, does not compensate for the clarity sacrificed by omitting the math. Vince's thesis that optimal f will maximize geometric returns is a valuable one, as is the concept of trading at dynamic fractional f to control risk. Unfortunately, he does not get specific enough to show us how to define and use optimal f in real life stock trading. I have an extensive math background, but I cannot get convincing quantitative results in Excel using his presentation, even after re-deriving for myself all the equations he deigns to show us. Perhaps if I had a futures trading background I would find his prose easier to follow, but I would have been much better off with the equations, in an appendix at least.

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