Investment advice from the world’s most successful stock picker

Warren Buffett, the Chairman of Berkshire Hathaway since 1970, sometimes called the “oracle of Omaha,” is arguably the world’s most successful stock-picking investor. Under his leadership Berkshire Hathaway has grown to a financial powerhouse, with total market capitalization of approximately USD$420 billion. Buffett has certainly shared in this success — as of this writing (27 February 2017), Buffett’s net worth was USD$76.5 billion, making him the second wealthiest person in the world.

So what advice does Buffett have for the rest of us mere mortals, individual investors as well as institutional investors?

His answer is quite arresting: Invest mainly in

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Backtest overfitting in smart beta investments


In the past few years “smart beta” (also known as “alternative beta” or “strategic beta”) investments have grown rapidly in popularity. As of the current date (January 2017), assets in these investment categories have grown to over USD$500 billion, and are expected to reach USD$1 trillion by 2020. More than 844 exchange-traded funds employing a smart beta strategy are now in operation.

The basic idea behind smart beta is to observe that traditional capitalization-weighted investments (such as S&P 500 index funds) tend to be heavily weighted in favor of securities from large, stable firms. Thus the smart beta community

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How much of hedge fund profits are taken by management?

“Miserable, miserable”

The past few years have been rough on hedge funds. Some have done very well, such as the Medallion Fund, a highly mathematical quant fund operated by Renaissance Technologies. It has produced returns averaging over 30% since its founding in 1988, totaling approximately $55 billion in profits, making multimillionaires of many of its very fortunate investors, who for the most part are professional mathematicians and others employed by Renaissance.

For most other hedge funds, it has been a different story, namely year after year of subpar performance. For example, the HFRI Equity Hedge (Total) Index of U.S. equity

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Erdős Numbers: A True “Prince and the Pauper” story

I still say to myself when I am depressed and find myself forced to listen to pompous and tiresome people: “Well, I have done one thing you could never have done, and that is to have collaborated with Littlewood and Ramanujan on something like equal terms.”

A Mathematician’s Apology (1941). G.H. Hardy (1877-1947)

Mathematics as the great equalizer

What do many of the most successful (and richest) hedge fund managers have in common with a life-long homeless person? That they have worked together, on equal terms, in solving some of the hardest mathematical questions.

Yes, in a stratified world

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Mathematics and economics: A reality check

One of us (Marcos Lopez de Prado) has published the article Mathematics and economics: A reality check in the Journal of Portfolio Management. The article is open-access — there is no fee for viewing or downloading.

Lopez de Prado argues that while economics is arguably one the most mathematical of the social sciences, the mathematical methods of economists may not be up to the task of modeling the complexity of the social institutions and the business/finance world. Outdated and inappropriate statistical methods are of particular concern, with economists and econometricians often drawing very dubious conclusions from the available data.


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The mathematics behind blockchain


In a previous Math Investor blog, we described the emerging world of blockchain, emphasizing how it might impact the financial services and investment world. Already numerous firms, including several startup organizations, are pursuing blockchain to facilitate and streamline many types of financial transactions.

It is worth taking a brief look at the mathematics behind blockchain. The following is based in part on an article by Eric Rykwalder, one of the founders of, a startup blockchain software firm in San Francisco.

The elliptic curve digital signature algorithm

Blockchain is basically a publicly available ledger where participants enter data and

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Is blockchain technology about to upend the financial world?


Many people have heard of Bitcoin, a shadowy form of currency that operates outside normal banking channels. It was introduced in October 2008 by a computer scientist under the alias Satoshi Nakamoto, and later released in the form of open-source software in 2009. Over 100,000 merchants now accept Bitcoin for products and services; the total value of circulating Bitcoins is currently about 10 billion U.S. dollars. In May 2016, Craig Steven Wright, an Australian computer scientist, publicly confessed to being Satoshi Nakamoto, although some skeptics still dispute his claim.

Blockchain: the technology behind Bitcoin

A even more interesting development

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How difficult is it to design a stock fund based on backtests?


Over USD$2 trillion is held in exchange-traded equity funds, just in the U.S., with hundreds of new funds added each year. Strategies vary from simple index-tracking funds to funds that follow sophisticated strategies (e.g., “smart beta”) designed to yield impressive results, based on backtests. According to a Vanguard report, there is concern that many of these funds are not really independent of the indexes they follow, and in any event are not that different from the broad market.

So how hard is it to design a stock fund that will achieve a given performance profile? The present bloggers

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The Mathematical Investor named one of Top 100 Math Blogs

The Mathematical Investor was recently named one of the Top 100 Math Blogs for students and teachers of mathematics, by Feedspot. The full list of the top 100 math blogs can be found HERE. We were awarded this “badge”:

The folly of panic selling

Mark Hulbert has compiled an interesting list of recent market panics:

August 2015: Concerns about the Chinese economy and stock market led to panic selling, with the Shanghai index plunging 8.5% in one day. Soon after in the U.S., on August 24, 2015, the DJIA plunged over 1,000 points in just a few minutes, its most precipitous drop ever, ending the day down 588 points, its worst one-day loss in five years. January 2016: Concerns about the direction of the U.S. economy, and fears that the U.S. stock market was overheated led to a 5.5% drop during January, with the

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