Volatility Trading, + Website, Wiley Trading 2nd edition, Euan Sinclair

Volatility Trading is a practical guide to options trading that is both informative to newcomers to the asset class as well as a valuable reference to the experienced options trader. The mathematics are laid out so that they can be easily followed. The text is readable, clear and offers real world insights into its application and related pitfalls to be mindful of. I highly recommend it to all traders.

Chapter 10 is a standout to me which is expanded from the first edition. It is about trading psychology and this chapter alone is worth the price of the book. Sinclair acknowledges his lack of academic credentials in the field but his experience allows him to present insights that are far more useful than what can be drawn from academic studies. I have read a number of books on the topic and frankly wasted a lot of time in doing so. This is the most practical and concise piece that I have come across on the topic. His plainly stated assertion that confidence comes from competence and competence comes from knowing exactly what your edge is and most everything else is misguided is as accurate as anything I have seen on the topic. Even for the more experienced traders the section on self-attribution bias is a helpful reminder that you are not as good as your results in busy, volatile market and usually not as bad as your results in slow, tight markets, is a helpful reminder when trying to assess your own performance on any time scale. There is a good summary of much of the literature on the most common mistakes made in the evaluation process as well. The points he makes about the importance of finding a partner and what to look for should be strongly considered by every new trader. These relationships have a greater impact on careers than is commonly acknowledged.

This book is worth the time to go through and a valuable guide to have on your bookshelf.

Textbooks on Volatility and the Greeks are often technically correct, but the distance from the flesh, blood, screens, and money of real markets make their arm's length detachment suspect and unpersuasive. They help you understand, but never answer the question: "okay, how do I *do*?"

Mathematical treatments are often more technically rigorous, but take their approach from the demand of proofs common for peer-reviewed perfection. They are, after all, math books.

And then there are Euan Sinclair's books, of which this welcome second edition of Volatility Trading with companion support website speaks of its utility and modernity just in the title alone. Sinclair provides knowledge and tools to create a framework for success: "here is what you need, here is how to do." Euan's prose is accessible, readable, understandable, and lean, but with an expectation that you have the appropriate math background to understand and use what he is explaining. He doesn't use math to obfuscate and show off how smart he is, he uses it as a tool, but it is a tool you need too, and he uses just enough.

As in the previous edition, Sinclair's Volatility Trading Second Edition with Website covers the basics of option pricing, volatility measurement, hedging, money management, and performance evaluation. He demonstrates a robust Black-Scholes-Merton-based quantitative model for measuring volatility that can easily be widely adapted to trading vol for lots of underlyings (not just stocks). These are the same strengths of the first edition, but now includes (in the entirely new Chapter 12) coverage and points to other opportunities in VIX futures, ETNs, and leveraged ETFs. Of course you could have adapted his methods and framework from the first edition of Volatility Trading to these instruments, but their trading volume growth has prompted Sinclair to make the connection more explicit.

Sinclair then continues and expands on the key essential theme of his previous edition: measure volatility for an edge. What differentiates this treatment from a textbook that may cover (poorly) the same areas is Sinclair never loses sight of the fact that 1) this is work, and 2) this is a business. His chapter and continuing reference to the *m*o*n*e*y* * m*a*n*a*g*e*m*e*n*t* of an options book is unique, refreshing, and crucial for success. This is not a textbook waving its hands over these issues with correct formulas and a few exercises: this is a practitioner directly and poignantly telling you that without proper technical money management no edge in the world can overcome your sloppy cash drawer.

Other strengths are that Euan efficiently analyzes the strengths and weaknesses of historical volatility measurements, gives solid methods for forecasting volatility over trade lifecycle, gives solid (money management!) techniques for deducing when to hedge and by how much, shows clever ways to aggregate positions across vol and other Greeks so that you don't have to hedge as much or have an internal natural hedge (this is actually the market-maker's whole game, isn't it?), and then shares some tales from the trader's trench on how to increase profits by trade sizing--techniques borrowed from futures trading, professional gambling and modified workable Kelly criterion, etc.

New or beefier chapters are offered on the dynamics of realized (what actual vol pattern happened versus what was priced at differing points) and implied volatilities, trading variance premiums and using options to trade special situations on equity market when you have a view.

Euan is also very good at pointing out --particularly in the case of realized volatilities over implied or straight vanilla-Black-Scholes-Merton vol-- that you are still trading against markets that are aggregations of people that have emotional, psychological, and heuristic biases in their behavior. This isn't a full-blown treatment of Behavioral Finance in Options Markets, but Sinclair offers up solid summaries and applications of these biases that the empirics and markets repeatedly say: we skew off log-normal into crazy clown time, and no explanations can capture that. So Euan points to how you spot these and construct an edge.

But Sinclair also correctly emphasizes the wisdom of the long-term robustness of the well established tools and models we do have (expect log-normal), and then demonstrates that trading is about having a more probable success by having a coherent trading philosophy, developing a rigorous system, and being methodical about finding and exploiting (often fleeting) edges.

In that approach alone this treatment beats any textbook or mathematical explication. Volatility Trading second edition couples the formulas and measurement and techniques with an admonition and clarity on management: set a goal and find trades with a clear statistical edge. Then he emphasizes the work: you have to capturing that edge and size each trade (money management!!!) correctly in a way that is consistent with your goal. This is the success framework of trading Volatility (or really, any of the Greeks).

The companion website is a boon: you'll have access to the great premiums already loaded that Sinclair will refresh from time to time as conditions and insights change. It includes valuable well-formatted and de-bugged spreadsheets, models for calculating volatility cones for different time periods, and neat little simulation engines that save you a lot of time from coding it up yourself in Mathematica or Matlab.

Full disclosure: Euan Sinclair is a valued friend who has generously offered his genius and insights both technical and practical to me gratis for decades. Euan is a mensch. If you suspect this review because of that friendship, then sadly that will be your loss: this is an excellent, valuable book that is worth multiples of the cover price. I purchased the book and did not receive a desk copy from the publisher.

Anyone who trades options should own both of Euan Sinclair's books, and Baird. You are welcome to add others to your bookshelf after these (well, never Natenberg), but these are essential for anyone who is serious. The single best investment in increasing your probability for success in option trading is Euan Sinclair's Volatility Trading, + Website. Get it today.

Most finance books are either full of measure theory or the author avoids any mathematics at all.
This book belongs to the rare species which follows - in my view - a reasonable middle ground.
The author filters from the finance-paper glut the practical relevant topics and presents them in a comprehensible way. E.g. there are hundreds of papers about measuring volatility with high-frequency data. The mathematical properties of these methods are very nice. I have played around with these methods. The practical benefit was humble. In real life there exists microstructure, overnight jumps and a strong seasonal daily pattern. The author states about these models: "So as a long-term forecasting tool, using high-frequency data is possibly the wrong approach". This is in line with my own experience.
The author clearly states: There is no silver bullet. All methods and models have pros and cons. He lists explicitely the good and bad points of each major method.
Options (and OTC variance swaps) are the traditional way to trade volatility. With the introduction of VIX-Futures and VIX-based ETNs a new and very interesting volatility playing ground has been created. The 12th chapter deals with VIX-Trading. I liked especially the subchapter about VIX based ETNs. The author covers a very interesting model of Ch. Donninger :-) Generally this part of the book can be expanded in future editions.

The book can not be recommended for absolute beginners and mathematics-grumps. But it is by far the best book I know off for experienced traders and quants. It has a clear leitmotif and is well written.

A good companion to chapter 12 is probably my own homepage godotfinance.com.

Product Details :
Hardcover: 320 pages
Publisher: Wiley; 2 edition (April 1, 2013)
Language: English
ISBN-10: 1118347137
ISBN-13: 978-1118347133
Product Dimensions: 5.9 x 1 x 9.8 inches

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Stochastic Calculus for Finance II: Continuous-Time Models, Springer Finance 1st edition, Steven Shreve

From the reviews of the first edition: "Steven Shreve’s comprehensive two-volume Stochastic Calculus for Finance may well be the last word, at least for a while, in the flood of Master’s level books.... a detailed and authoritative reference for "quants” (formerly known as "rocket scientists”). The books are derived from lecture notes that have been available on the Web for years and that have developed a huge cult following among students, instructors, and practitioners. The key ideas presented in these works involve the mathematical theory of securities pricing based upon the ideas of classical finance. ...the beauty of mathematics is partly in the fact that it is self-contained and allows us to explore the logical implications of our hypotheses. The material of this volume of Shreve’s text is a wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach. It is accessible to a broad audience and has been developed after years of teaching the subject. It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." (SIAM, 2005) "The contents of the book have been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise Statements of results, plausibility arguments, and even some proofs. But more importantly, intuitive explanations, developed and refine through classroom experience with this material are provided throughout the book." (Finanz Betrieb, 7:5, 2005) "The origin of this two volume textbook are the well-known lecture notes on Stochastic Calculus … . The first volume contains the binomial asset pricing model. … The second volume covers continuous-time models … . This book continues the series of publications by Steven Shreve of highest quality on the one hand and accessibility on the other end. It is a must for anybody who wants to get into mathematical finance and a pleasure for experts … ." (www.mathfinance.de, 2004) "This is the latter of the two-volume series evolving from the author’s mathematics courses in M.Sc. Computational Finance program at Carnegie Mellon University (USA). The content of this book is organized such as to give the reader precise statements of results, plausibility arguments, mathematical proofs and, more importantly, the intuitive explanations of the financial and economic phenomena. Each chapter concludes with summary of the discussed matter, bibliographic notes, and a set of really useful exercises." (Neculai Curteanu, Zentralblatt MATH, Vol. 1068, 2005)

Think of this as a thank-you letter to Shreve for helping to teach me applied quantitative finance. This is a truly wonderful book and a great place to start learning the subject, regardless of your previous exposure to the subject or mathematical maturity, and has plentiful opportunities in the exercises to practice important results.

The first three and part of the fourth chapter serve as the mathematical preparation for the book. Shreve reviews basic concepts from probability, introducing just enough measure-theoretic concepts to understand the motivation behind the concepts of a filtration and its relation to conditional expectation, martingales, and later in a brief chapter on American options, stopping times. Since the book's main emphasis is on the application of the Ito-Doeblin calculus in solving SDE generated by Brownian motion, Chapter 2 covers the necessary elements of conditional expectation for risk-neutral pricing. Chapter 3 covers Brownian motion, although not rigorously - he gives just enough properties of the canonical continuous stochastic process to know how to identify it and to understand its crucial properties. This chapter is important for the first part of Chapter 4, which uses the properties of Brownian motion to develop the notion of quadratic variation and its role in the calculation of the Ito Integral. After developing the Ito integral and demonstrating its key properties, such as the martingale property and the Ito isometry, Shreve has enough math to start developing the Black-Scholes-Merton framework for actual finance.

Chapters 5 covers risk-neutral pricing as a more general case of the BSM model, and in addition to demonstrating important results to finance such as Girsanov's theorem and its role in the Martingale Representation Theorem, Shreve also covers extensions such as the relationship between Forwards and Futures prices. In addition, he extends the classical BSM formula to include dividends, a generalization which plays a key role in the pricing of currency options in the Garman-Kohlhagen model.

Chapter 6 shows how, through the application of the Feynman-Kac formula to Markov processes, the probabilistic (here, the martingale) approach can be connected to the PDE approach whenever a problem is (or can be made) Markov. At the end of this chapter and in the next chapter on Exotic Options, Shreve shows how adding additional states can reduce the pricing problem of a path-dependent option, such as an Asian option, to the Markov case. The presentation is particularly nice and through playing with some of the exercises, the reader can build the ability to reduce a seemingly complicated payoff to a simpler case and see how it's just another case of the same general theme.

Chapters 7 and 8 cover Exotic and American options, respectively, although each are meant only as introductions. One can see through the pricing of various exotic options that the difficulty lies more in algebra and basic calculus than in actual abstraction; the idea emphasized here is that setting up the problem correctly is the hard (although certainly less tedious) part of the problem. Chapter 8 only touches on the important concepts of American options, namely that to price them one must know how to identify a stopping time, understand what it means in non-mathematical terms, and understand its application to pricing.

Chapter 9, a generalization to the chapter on Risk-Neutral pricing, covers change of measures. While this isn't terribly difficult to grasp, it is important not just for currency pricing problems but also for more advanced Market Models through the use of forward measures.

Chapter 10, one of the longer ones in the book, covers a full range of term structure models. Shreve covers the older class of models, which require only the use of previously developed SDE, as well as an introduction to the HJM framework and its application to Modern Market Models. This is a subject not just of importance to quants working in the vast universe of fixed income derivative pricing, but also for all students wanting to test the power of risk-neutral pricing in a modern setting. Shreve's presentation seems to be a natural extension of the risk-neutral framework and makes a relatively difficult concept easy to grasp. Despite the emphasis on the HJM framework and the use of forward measures, Shreve doesn't neglect the classical term structure models, covering many of them both in the text and giving their solutions and some of their statistical properties through exercises.

The final chapter comes with a warning: Jump processes aren't easy to understand. Shreve succeeds wildly in teaching a very difficult subject quite well, building up from Poisson processes to compound processes, and then extending the same change-of-measure techniques to show how the risk-neutral approach works in this case too. While the book would have been complete in a pedagogical sense without this chapter, its inclusion reflects the increasing importance of jumps in everything from credit models to the volatility smirk/smile. It's no secret Levy processes and generalized jump models will play an increasingly important role in financial modeling, and Shreve is trying to show how the first 10 chapters of the book in some way provides some of the general ideas useful for these extensions.

The problems in this book are excellent and range in difficulty, length, and purpose, although the harder ones have copious hints; this book is clearly meant to learn how to apply a few basic ideas to models through applications, not to provide deep abstractions on the subject. Nonetheless, they span a range of topics and in some cases fill blanks in areas not covered in the text, ranging from the construction of the volatility surface to the portfolio dynamics of an arbitrage strategy.

Sometimes we like books which are both terse and mathematically elegant. This isn't one of them, nor does it pretend to be either. It's a way for a hard-working student to get up to speed on the basic mathematical tools and concepts used in derivative pricing and in other areas of asset pricing in finance. The emphasis is on learning by doing, many of the problems are extensions of examples in the text, while others are very long problems with plenty of hints, meant to encourage the reader to learn by "filling in the blanks."

Again, Shreve deserves my thanks as well as those of anyone who learned from this great book (or its predecessor, the lecture notes...). For those who want to complement this book with a more rigorous treatment of the SDE given in the book, Oksendal's book is about a half a step higher in mathematical rigor and covers important concepts not covered in Shreve related to PDE and diffusions, as well as applications to optimal control and other subjects important outside (and in!) derivative pricing. If you feel comfortable with PDE and Real Analysis, complement Shreve with this text to get a fairly strong background in stochastic calculus and its applications.

Although I work in a major global bank at a senior level I don't use stochastic calculus in my job. My maths and physics background goes back to the 1970s when stochastic calculus was not part of undergraduate studies. Indeed, one usually did stochastic theory at postgraduate level. I have memories of reading Halmos for measure theory, Feller for probability theory, Wiener and others. None of this was easy.

Suffice it to say that there were a lot of abstract building blocks one had to erect first before one could actually do anything useful.

Stochastic calculus is not easy. It is less intuitive than ordinary calculus. The vast majority of textbooks launch into a wall of definitions that seem divorced from the motivation for them. I am always suspicious of authors who do that. It's fine if you are writing for a very specialised audience but I am with Richard Feynman who reckoned that if you can't provide a simple explanation you don't really understand what is going on. In that context read his PhD thesis - it is most readable and understandable.

What Shreve has done - and this is a significant achievement in my view - is to present something that is rigorous enough (and we all know that in this and other areas of mathematics one can go on and on with minute points of detail all in the name of rigour) yet grounds the concepts in something that is understandable.

The simple pedagogical fact of life with this type of material is that there is a large overhead in getting to a particular point and Shreve had done a very good job in getting readers to a good standard without destroying their will to go on!

When one looks at areas of mathematics with much longer pedigrees - and Fourier Theory is an example - there are some extremely good presentations of the theory at both mathematical and physical levels. Elias Stein, for instance, has done some marvellous work in the area. Stochastic calculus is really very young in terms of mainstream appeal. I can recall actuarial subjects I did in the early 1980s that had no stochastic calculus at all in them. All that has changed and I think Shreve's attempts in this area can be improved upon too but this will only happen over time.

My colleagues in quant like Shreve's books so I guess that says something too.

In the old time, students in Finance or Financial Engineering who want to study SDE has few choices.

Kazartas & Shreves' classic text book is too rigorous and very demanding, it would give readers solid theoretical background, but I think only few readers can really master in those material.

That's why books like Oksendal's SDE come into the market, they are easier than Kazartas & Shreve but deeper than many undergrad Financial Mathmetics in theory. Oksendal is easy reading and good for self study; however, it's Finance part is relatively weak.

For those Finance or Financial Engineering people, Steele's book fits well, It is right at the level like Oksendal, and root at Finance application. It's story telling style makes it joyful in reading, but bad in reference.

Finally we have Shreve's new book. This book is at the level of demanding as Oksendal and Steele's books. You may still need some grad-level mathematics training to understand the stuff well. But unlike other stochastic calculus books, it is designed for Finance field. Finance guy nomatter practitioners or researchers can soon find help they need in this books. Also it is well-organized and with nice writing style. Although the first couple chapters are a little too condense, I still highly appreciate this book.

Product Details :
Hardcover: 569 pages
Publisher: Springer; 1st edition (June 3, 2004)
Language: English
ISBN-10: 0387401016
ISBN-13: 978-0387401010
Product Dimensions: 6.1 x 1.2 x 9.2 inches

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Technical Analysis of Stock Trends 9th edition, Robert D. Edwards

“With a focus on pragmatic portfolio theory, editor Charles Bassetti significantly contributes t the technical analysis body of knowledge especially related to tactics, and has created a book worth a space on every technican’s bookshelf.”

-Technically Speaking (Market Technicians Association monthly newsletter)

If you ask any stock broker, investment banker, or financial advisor, for resources to learn about trading, its very likely that this renowned book would be on their list. More than six decades and nine editions later, Robert Edwards and John Magee's Technical Analysis of Stock Trends is still considered the gold standard of technical analysis based trading. The current 9th edition has been updated to stay relevant in the current environment.

The editor starts off with an introduction on how he went about adapting this classic. However, it quickly jumps into a lot of theoretical trending information with very detailed coverage of the Dow Theory from the basic theory to specific examples in the past. The authors then discuss various trends including my favorite the Head and Shoulder trend line to help you predict which direction a stock will move based on past data. Several examples (over 200) are introduced to make sure the reader has understood this concept. I really liked that the editor pointed out the uncertainty with following such a trend system but at the same time promoting its benefits. The authors also outline the different strategies (options- either put or call) based on the predicted movement of a particular stock.

The second half of the book is devoted to specific tactics that can be utilized during different market conditions. Essentially, the authors break up the different theories into ways that you can apply them. For example, if you are deciding to invest in an energy sector company during a bear market with a Triangular Trend pointing to an upwards movement in price, you can navigate through to figure out the various metrics you need to chart (P/E ratio, revenue, profits, etc) in order to determine the optimal time to invest and the investment tool (stock versus option). The authors also devote a short time to explaining similar trending patterns and tactics in the commodity market.

Overall, I have mostly positive things to say about this book. However, this book is more useful as sort of an instructional manual when trading stocks. If this is your first time investing I would not recommend reading this book. Instead, get something like Stock Trading for Dummies, so that you can be familiar with all various investment terminology. Then, open an investment simulator account for free using Investopedia or a similar platform and as you start reading this book practice the tactics on your simulated investments. Keep referring to the book as you make decisions about your portfolio. The tactics in the book, although they might seem technical at first, are actually very easy to chart using Google Finance, Morningstar, or similar. So, hold on to this book as a reference so that you can finally start making data driven decisions instead of just trading based on a stock tip from your buddy!

In the age of overdeterming macroeconomic factors, ETFs, high frequency trading, hedge funds, etc., technical analysis is a total waste of time for the average Joe sitting at his workstation trying to day trade. For every chart that shows a meaningful pattern, there are 5 that show no pattern at all. The technician, out of necessity of his methodology, is forced to make meaning of a chart which is likely just a random collection of observations. Just because a price happened to bottom or top twice consecutively at the same point doesn't mean that there's 'support' or 'resistance' at that level. Sometimes there are legitimate support and resistance levels, but more often than not, those are illusory. Support or resistance levels evaporate and reset all the time.

Fundamental analysis puts the investor in a much better position to actually succeed in my opinion. Earnings, price, book value, growth, forward earnings, debt levels, etc. are not subject to any interpretation. They are what they are. It might take any given stock a long time for it to align w/ its fundamental valuation, but the relative predictability that one sees in P/E levels for different types of businesses of varying sizes and growh prospects makes the fundamental school the more rational approach.

Also, anyone who believes that markets are 'efficient' hasn't paid much attention to markets. Lacking a material event (earnings release, management shake-up, etc.) a company's price will largely be pulled around in lock-step w/ the broader market.

These are known as the facts. The subject book is probably ok, but it starts w/ the wrong premise.

I am a former student of Professor Bassetti; I took his FI 498S Building Efficient Trading Systems class this summer at Golden Gate University. During the course, in his widely-read weekly newsletter on edwards-magee.com, Professor Bassetti correctly predicted the August 2011 correction, which was picked up by MarketWatch on July 27th.

Technical Analysis of Stock Trends was a textbook for the FI 498S course, along with his other investment and trading books -- StairStops and Zen Simple. StairStops and Zen Simple are available on Amazon (Kindle versions available), and I found them helpful in clarifying concepts from Technical Analysis of Stock Trends.

This is one of the best books on trading ever written! The book contains two parts. In the first part you learn the theory of technical analysis such as price and volume action. In the second part you do practice. I know a lot of books that give you just fundamentals without saying how to apply those fundamentals in practice. This book is a perfect exception! Authors did a great job! Though a book has been written in 1940s, it still remains in print and contains valuable insights into how market really works. The only chapter that I would exclude from the book is chapter about trading in futures which has been added to this edition of the book. You can tell by reading this chapter that the language is different, more difficult to comprehend and tells a lot of different indicators that you don't even need to know. So, skip that chapter and enjoy the rest of the book!

4 stars for the volume of thoroughly well researched examples and exhaustive coverage of basic patterns.
This book is comprehensive but not complete. There is no information on some modern indicators or, for example, candlesticks or point and figure.
I have the 8th edition.
This book is good to have and I did learn valuable things from it but if you are only going to buy a few books, I would not recommend this as one of them.
On the plus side, there are many many actual stock chart examples. That adds to the length in a good way.
Writing style is very much early 20th century; leisurely rather than short and to the point.
This book is geared toward stocks and commodities but not forex. (although the stock patterns also apply to forex)

I'd recommend this book to anyone wanting an introduction to technical analysis. It is written like a textbook with topics addressed in logical order. This book covers detailed descriptions and analysis of many traditional chart patterns and some attendant trading strategies. Numerous examples are given in annotated charts. Technical terms are defined and explained.

In the ninth edition (©2007), Appendix E contains a Turtle Trading System manual written by Curtis Faith (one of Richard Dennis' original Turtles) - a dated but nevertheless instructional description of a mechanical trading system.

Though this book is a great educational tool, I feel it would be a mistake to take it all literally as a guide to trading. The original author, Magee, last updated the book in 1966. He goes out on a limb regularly in his advice on how certain patterns 'typically' resolve. The probabilities with which his rules apply to today's markets would undoubtedly vary from pre-1966 markets. William J. O'Neil, in his renowned How to Make Money in Stocks (©2009, p.-146), said that many patterns discussed by Edwards & Magee such as triangles, coils and pennants have, in recent times, shown to be "unreliable and risky" patterns "without sufficient time or price correction to become proper bases."

I found the book a frustrating slog to get through because Magee uses a very formal, wordy and repetitive writing style. In the eighth and ninth editions professor Bassetti has added numerous editor's notes and extra chapters to the original, but frequently uses awkward, incomplete sentences to belabor the obvious. More annoying were Bassetti's repeated attempts to be clever, e.g. p.- 415: "The wild frontier of the Internet and of the gunslinger speculators. Amazon bucks on. Give us a slug of rotgut whiskey and get out the ruler", or "one might almost say awesome, if the word were not in such currency on `Saturday Night Live' and the `Comedy Channel'". This sort of running commentary gets tiring after 800 pages.

Product Details :
Hardcover: 840 pages
Publisher: AMACOM; 9th edition (February 26, 2007)
Language: English
ISBN-10: 0814408648
ISBN-13: 978-0814408643
Product Dimensions: 6.5 x 1.8 x 9.6 inches

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