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The Mathematical Investor: A personal perspective by JMB

[Editorial note: During the next few weeks, each of the editors of the Mathematical Investor will provide, in an essay format, some personal background explaining the origins of their interest and work in this area. This is a perspective essay by Jonathan M Borwein.]

Early interest in economics and finance

I went to Oxford in 1971 to study functional analysis and number theory but ended up (very quickly) working in Optimization theory with Michael Dempster, who even then was running models of the full non-defence US budget. My early history is described in a chapter of a forthcoming book.

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Testing early warning indicators

According to a recently-published article on “early warning indicators,” the gain or loss of the S&P500 index (a widely cited metric of the U.S. stock market) during the seven trading days around the new year (the last five days before and the first two days after the new year) predicts the performance of the index for the entire coming year with 85% accuracy. An accuracy level at 85% is very high by any standard. Nevertheless, scientifically literate investors will find this claim unsatisfactory.

First of all, the period over which this indicator is tested is not specified. More importantly,

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Disclaimer and copyright

Before reading or using material on this site (where, in the following, “material on this site” includes text, papers, blog and software), please note the following important information:

The material on this site is provided for research and informational purposes only, and does NOT necessarily represent the views or policies of the respective institutions or funding agencies of the site editors and authors. The site editors are NOT licensed, professional financial advisors to public clients, although they may provide financial advice to private clients and/or organizations in the course of their professional work. The site editors and other authors of

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Are individual investors equipped to make basic financial decisions?

In discussions of finance and investment, it is routine to see disclaimers such as “may lose value,” and “past performance is no indication of future results.”

However, as we have pointed out in our paper Financial charlatanism: The effects of backtest overfitting on out-of-sample performance, even this may be a bit optimistic, as certain investment strategies, marketed to the public as money-winning, actually might be pretty much guaranteed to be money-losing, particularly when fees and other expenses are considered.

These considerations raise the question: Are individual investors equipped to make the sorts of financial decisions that increasingly are required of

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What Wittgenstein can teach all of us about investing

It is not often that one hears the name of Ludwig Wittgenstein (1889-1951) mentioned in an investment forum. Perhaps it is because the great Anglo-Austrian positivist philosopher gave away his entire inheritance at the age of 30. Quite a brave thing to do, having been born into one of Europe’s wealthiest families, with a fortune comparable to that of the Rothschilds.

You see, Ludwig wanted a do-it-yourself life, he wanted to achieve something based on his own merit. Three of his brothers committed suicide, and poverty probably saved his life and mind (“Tell them I’ve had a wonderful life”).

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Do large cap stocks boost portfolio performance at year’s end?

With the approach of the holiday season, holiday-related investment advice has become increasingly fashionable. Here is the latest: a claim of a ‘less well-known fact’ that large-cap stocks outperform small-cap stocks in December versus the ‘well-known fact’ that the reverse is true in January. The article then suggested a simple strategy to boost one’s portfolio: overweight large-cap stocks in December, then switch to small-cap stocks in January.

How much advantage can one obtain using this strategy? We decided to test it.

We used the SP600 Barra Value and SP600 Barra Growth indices as proxies for small-cap stocks (historical data is

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The Mathematical Investor: A personal perspective by DHB

[Editorial note: During the next few weeks, each of the editors of the Mathematical Investor will provide, in an essay format, some personal background explaining the origins of their interest and work in this area. This is a perspective essay by David H. Bailey.]

Early interest in economics and finance

Although I only recently began to delve into the world of financial mathematics in any technical depth, I have been interested in (indeed, fascinated by) the world of economics and finance for many years. During my senior year at Brigham Young University, I very much enjoyed a course in economics

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The Myth of the Halloween Indicator

Holiday season is coming and so is holiday related investment advice. Right before Halloween (31 Oct 2013), the Halloween Indicator emerged in the Wall Street Journal online site suggesting that during the six months from Halloween (October 31) to May Day (May 1), the market has a higher return compared to the other six months.

Eager to find out how much edge this indicator will provide, we compared a buy-and-hold-the-DJIA strategy from 1915 to 2012 versus taking a position only during the six-month period from October 31 to May 1. The equity curve for these two strategies both starting

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The Art of Investing

Bravery or recklessness?

Investing is often referred to as an Art: The Art of Investing. True artists may object to this analogy, but, in any event, the key implication is that quantitative methods have a very limited applicability to investment problems, and mathematical (i.e., formally rigorous and logical) arguments are essentially misguided. Proponents of this philosophy often assert that investing is just too complex, with too many free variables, for mathematical methods to be of much use. But aren’t biological, chemical or nuclear systems also complex, and yet Mathematics has become the indispensable tool to understand them?

Every human

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Two tales of the Kelly formula

Kelly’s formula is a theoretical benchmark for deciding the appropriate position size when gambling. A divergence in attitude towards this theory illustrates the disconnect between academicians and practitioners, and the necessity of closer collaboration between the two circles, a point we argued in The Two Towers of Finance.

To understand the essence of Kelly’s formula, let us consider the question: Can one lose money in a game in which one has a favorable probability of winning? The answer is, absolutely yes. To see why, think of the simple game of tossing a biased coin: heads means that the player

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