Real-World Probability Books: Stock Market and Finance

Malkiel, Burton Gordon. A Random Walk Down Wall Street. Norton, 2003 (original 1975).

Perhaps the only book in existence whose reading may be both intellectually and financially rewarding. Episodic history of markets and their occasional excesses; distinction between technical and fundamental analysis; wonderful discussion of "how good is fundamental analysis" and explanation of what efficient market theory means; description of portfolio theory and capital asset pricing model. Last part gives more concrete advice for the individual investor. Dear Student: read now to get a general overview of markets and their hazards; read again when you have money to invest.

Wilmott, Paul and Orrell, David. The Money Formula: Dodgy Finance, Pseudo Science, and How Mathematicians Took Over the Markets. Wiley, 2017.

See my review.

Brown, Aaron. Red-Blooded Risk: The Secret History of Wall Street. Wiley, 2011.

See my review.

Brown, Aaron. Financial Risk Management for Dummies . For Dummies, 2015.

A little outside the academic theme of my course, but a fascinating guide to the actual job of Financial Risk Management with insightful comments on the mathematics components. See my detailed Wilmott magazine review.

Shiller, Robert J. Irrational Exuberance. Princeton University Press, 2005 (original 2001).

Argues that fluctuations in stock market indexes over (say) 5 year periods are not determined primarily (as standard theory asserts) by changes in consensus rational assessment of future profits etc, but instead are determined by non-rational psychological shifts in investors' perceptions of markets. Argues that current (2005) U.S. house prices reflect speculative bubble analogous to late-90s dotcom stocks, and suggests 12 factors underlying such bubbles (e.g. expansion of media coverage; analyst's optimistic forecasts; expansion of defined contribution pension plans; decline of inflation and effect of money illusion). Well argued and thought-provoking throughout.

Shiller, Robert J. The New Financial Order. Risk in the 21st century. Princeton University Press, 2003.

One of the best books for a big picture of the present and future. Points out that the financial risks facing typical individuals are badly addressed by existing instruments. Has bold suggestions: an index fund of entire world economic value; insuring against your College major subject becoming redundant, insuring against regional house price declines,

Poundstone, William. Fortune's Formula. Hill and Wang, 2005.

"Fortune's formula" is the Kelly criterion. Much of the book is entertaining episodic anecdotal history of characters like Shannon, Kelly, Thorp, Milken, Boesky and Long Term Capital Management. The formula-free discussion of mathematical aspects of the Kelly criterion is rather good. Entertaining account of dispute between the proponents of Kelly (math types) and economists led by Samuelson who viewed it as too risky even in the long run. Memorable slogan: 100% Kelly strategy marks the boundary between aggressive and insane investing.

Zuckerman, Gregory. The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution. Portfolio, 2019.

See my review.

Swensen, David F. Unconventional Success: a fundamental approach to personal investment. Free Press, 2005.

Explains in careful detail why certain assets (U.S. equity, foreign developed equity, emerging market equity, real estate, U.S. treasury bonds, inflation protected bonds) should be considered "core" and others (corporate, municipal or foreign bonds; asset-backed securities; venture capital or hedge funds) should be disregarded by the individual investor. Advocates choosing a percentage allocation amongst core assets and then sticking to it long-term via rebalancing, rather than market timing or ``chasing performance". Despite a flat prose style, this first half constitutes invaluable practical advice for the investor. Though, like a similarly sophisticated book on (say) poker or dating, you will only appreciate it after you have played the game for a while. The second half is a damning critique of the for-profit mutual fund industry and associated institutions (Morningstar ratings, SEC). Both halves contain useful recent historical data, though only passing allusion to math theory.

Bookstaber, Richard. The End of Theory: Financial Crises, the Failure of Economics, and the Sweep of Human Interaction. Princeton University Press, 2017.

Review reformatted on

This is one of many books criticizing textbook Economic theory, engendered by the 2008-9 financial crisis. It's easily readable, mostly reasonable, and informative to someone who has not read similar works. Classical Economic theory is certainly unrealistic in many ways, so it's interesting to see his list (section 2) of four unrealistic ways relevant to financial crises.
Radical uncertainty is certainly a better phrase than Black Swan, though surely unknown unknowns is even better.
Non-ergodicity is better explained as the opposite of "the future will be statistically the same as the past", and it would have been worth emphasizing that all quant finance assumes the latter.
Emergent means "properties of a model not obvious from its definition", used in the context of interacting entities. This is one of those words adopted by 1980s theoretical physicists that are thoroughly annoying to mathematicians like me: everything one studies as research is emergent in that sense ..... we don't waste our time on the obvious stuff!
Computational irreducibility means "you can't hope to figure out how a process will behave except by watching it actually run".

This categorization is fine, though the continuation involves descriptions of Godel incompleteness, Heisenberg uncertainty, Turing, and quotes from some of Borges's literature. Such material is all rather familiar in books like this, and seems to serve only as analogies to knock down some "straw man" of simplistic deterministic economic modeling.

Eventually the book gets to its intended novel and positive point, advocacy of agent-based models. We can all agree these would be great if one could make them work. Their introduction via traffic models is misleading: drivers have few and known actions available and there is a vast amount of traffic data from different times and places available -- surely diametrically opposed to the case of financial crises. It is interesting to see his models of past crises, but as he finally writes I am presenting the concept of agent-based models, and specifically how it relates to crises, as a paradigm rather than an engineering how-to treatise. This allows me to bypass the difficulty aspects of how you estimate the parameters of the model and how you test it empirically. How do you do that if ...... the world you want to model will not look like the past? Indeed. So where's the beef? Only a few final pages give interesting concrete suggestions for deflecting future crises (e.g. have the world's largest asset owners agree in advance to start buying when prices drop 20 or 30 percent).

As with most other such books, it's a critique of Econ 201 by someone who has never volunteered to develop and teach their preferred alternative. Though I do admire the brave choice of title, after Fukuyama's The End of History proving spectacularly wrong.

Brown, Aaron. Financial Risk Management For Dummies. For Dummies, 2015.

This is rather out of the mainstream for these reviews, being aimed at a reader interested in a career in Financial Risk Management, but is also fascinating for a reader curious about what that job entails. Here is my review for the FRM professional journal Wilmott magazine.

Taleb, Nassim Nicholas. Fooled by Randomness: The Hidden Role of Chance in the Markets and in Life . Texere, 2001.

Entertaining read from a cheerful egomaniac Wall Streeter, recounting misadventures of people in the business and combining his real-world experiences with his broad reading of theory and psychology of randomness. Fascinating to see what bits of theory impress him: survivorship bias, data snooping, using Monte Carlo to see alternative futures.

Weatherall, James Owen. The Physics of Wall Street: A Brief History of Predicting the Unpredictable . Houghton Mifflin Harcourt, 2013.

See my review.

Paulos, John Allen. A Mathematician Plays the Stock Market. Basic Books, 2003.

An odd book. Jaunty style, framed by (a) the author's investment experience, contains (b) a variety of math topics related to the stock market, mixed with (c) brief accounts of classic (prisoners dilemma, regression effect) and recently fashionable (power laws, Parrondo's rachet) probability topics. Perhaps a decent read if you haven't read anything else, but this material is covered much better by (a) Taleb, (b) Malkiel and (c) Peterson.

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