The Handbook of Portfolio Mathematics: Formulas for Optimal Allocation & Leverage (Wiley Trading)

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The Handbook of Portfolio Mathematics

"For the serious investor, trader, or money manager, this book takes a rewarding look into modern portfolio theory. Vince introduces a leverage-space portfolio model, tweaks it for the drawdown probability, and delivers a superior model. He even provides equations to maximize returns for a chosen level of risk. So if you're serious about making money in today's markets, buy this book. Read it. Profit from it."
� �Thomas N. Bulkowski, author, Encyclopedia of Chart Patterns

"This is an important book. Though traders routinely speak of their 'edge' in the marketplace and ways of handling 'risk,' few can define and measure these accurately. In this book, Ralph Vince takes readers step by step through an understanding of the mathematical foundations of trading, significantly extending his earlier work and breaking important new ground. His lucid writing style and liberal use of practical examples make this book must reading."
� �Brett N. Steenbarger, PhD, author, The Psychology of Trading and Enhancing Trader Performance

"Ralph Vince is one of the world's foremost authorities on quantitative portfolio analysis. In this masterly contribution, Ralph builds on his early pioneering findings to address the real-world concerns of money managers in the trenches-how to systematically maximize gains in relation to risk."
—Nelson Freeburg, Editor, Formula Research

"Gambling and investing may make strange bedfellows in the eyes of many, but not Ralph Vince, who once again demonstrates that an open mind is the investor's most valuable asset. What does bet sizing have to do with investing? The answer to that question and many more lie inside this iconoclastic work. Want to make the most of your investing skills Open this book."
� �John Bollinger, CFA, CMT, www.BollingerBands.com

The Handbook of Portfolio Mathematics: Formulas for Optimal Allocation & Leverage (Wiley Trading) Review

My short advice is if you have any interest in this stuff, read this book, but be very careful what you take away from it. Some of the other reviews worry me with the extravagant unalloyed praise. This is a great book in many respects, but it is an uncommonly dangerous one to absorb uncritically.

The author begins by begging the reader, "[T]o look at everything in this text--as merely my articulation of something, and not an autocratic dictation. Not only am I not infallible, but also my real aim here is to engage you. . ." Taken in that spirit, this is a five-star book, filled with useful advice for any risk-taker, not just financial traders, that will sweep away a lot of dangerous nonsense you may have acquired in other places.

On the other hand, taken as a handbook of portfolio mathematics, it's unrateable. It falls in between what are traditionally called portfolio management and risk management. Portfolio management tries to select positions to build the best (in some sense) probability distribution of return over a fixed horizon. Risk management tries to help the portfolio manager survive long enough to realize her probability distribution; and her other goals as well. These are normally considered orthogonal problems. The portfolio manager needs to know a time horizon, but not the bet size. The risk manager doesn't care about time horizon, only bet size. A simplified toy solution for portfolio managers is maximizing Sharpe ratio, expected return over standard deviation (which is invariant over bet size, but changes over time horizon). A simplified toy solution for risk managers is the Kelly criterion, expected return over variance (which is invariant over time horizon, but changes with bet size).

What this book does is derive a simultaneous solution of both problems, "optimal f." It's a tour de force that will teach you a lot about both portfolio management and risk management, and stimulate a lot of other useful thoughts. But it can't compete with more sophisticated solutions that split the problem up.

While the author correctly throws out covariance-based management, the "scenarios" he uses instead are too crude for most trading strategies. They can work for the trend-following CTAs he discusses, but not for strategies that depend essentially on high-dimensional optimization. This is the bread-and-butter of traditional portfolio management and there are good ways to do it. The author describes only some bad ways.

On the risk management side, the book considers only drawdown in detail, with some vague language about other preferences. But a key early discovery of risk management is that limiting drawdown and other bad events is the smaller part of the problem. It's more important to increase risk enough in good times to generate a cushion to survive the bad. A hedge fund that delivers three years of good Sharpe ratios might survive a 24% drawdown, while another fund with weaker good time performance might be knocked off with a 6% drawdown. Moreover there are many ways for a trader or fund to fail other than to have a big drawdown.

Optimal f might make risk-management sense for a single trader, trading his own money with no interest in raising capital, who is irrevocably committed to staying in the game until it pays off, who would only give up if he ran out of money. But most people have other options, and will benefit greatly from failing fast if they have to fail. A serious risk management analysis, taking into account individual business and life goals, might counsel different bet sizes than optimal f. And some systematic metrics for evaluating portfolios are very useful, if only as a sanity check on subjective scenario results. And finally, rigorous backtesting and performance attribution are essential to efficient portfolio and risk management.

In the end, this comes down to the author's assumption that wealth is both the objective and the constraint. In fact, it is neither one and, more important, the objective and the constraint are different things that have to be managed separately. You can mash them together by asserting everyone has "log utility," but that's neither correct about individual preferences nor a good way to think about managing a business. Another problem is the solution depends on there being a consistent probability distribution not only over all positions, but also over all possible future opportunities. The simplicity of scenarios disguises this requirement. Personally, I don't believe in consistent probability distributions over either one and, if I'm wrong about that, I'm quite confident the two are inconsistent.

This book will make you smarter if you read it critically, there's a lot of great stuff in here. But if you treat it as revealed truth, you could be in big trouble.

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