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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Where are the billionaire financial academics?

Would you believe someone who claims knowledge of how to transform lead into gold, and yet he is not rich? Enter the perplexing world of financial academia, the modern-day “alchemists”

According to the just-published 2016 Rich List of the World’s Top-Earning Hedge Fund Managers by Institutional Investor’s Alpha magazine, eight of the top ten earners fall into the “quant” category, and half of the 25 richest of the year are quants. The firms listed include the likes of Renaissance Technologies, D.E. Shaw, Two Sigma, Millennium, Citadel and Schonfeld, none of which engage in “smart beta” or factor-based investments.

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Tough times for hedge funds

The past few years have not been kind to hedge funds, namely those specialized funds, usually marketed to large institutions and wealthy individuals, which combine a somewhat more risky overall strategy managed by highly professional traders, with a relatively safer “hedge” to limit volatility. (Our comments here refer specifically to investment hedge funds, as opposed to, for example, an airline hedging future fuel prices or an international corporation hedging future currency rates.) Worldwide, hedge funds currently manage USD$2.86 trillion in assets, down from USD$3.2 trillion in September 2015.

Hedge funds typically charge a management fee of 2 percent plus a

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How well does a “robot AI” predict the Japanese stock market?

A recent Bloomberg article reported on the work of Junsuke Senoguchi, who has developed a “robot” artificial intelligence-powered computer program that forecasts the Japanese stock market, in particular the Nikkei-225 index.

Senoguchi, who currently works for Mitsubishi UFJ Morgan Stanley Securities in Tokyo and who has previously worked for Lehman Brothers and also the Bank of Japan, has a Ph.D. in artificial intelligence (AI), and his new investment program employs AI techniques. Senoguchi is delighted when it is working well, “because I feel I can predict the future“.

While we certainly wish Mr. Senoguchi well in his efforts, we need

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How well does the “January barometer” work?

The January barometer

The January barometer is the claim, often mentioned in financial circles, that the performance of the stock market in January is a reliable portend of its performance for the full year — as January goes, so goes the year. The term was first coined by Yale Hirsch in 1972.

Many market analysts take it quite seriously. For example, a BofA-Merrill Lynch Global Research Report asserts “Based on S&P 500 data going back to 1928, January is a good predictor of the year.”

As another example, CNBC reports

The January barometer has been right in 62 of

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High noon for 2015 market prophets

When a prophet speaketh, … if the thing follow not, nor come to pass, … the prophet hath spoken it presumptuously: thou shalt not be afraid of him.” [Deuteronomy 18:22].

In a December 2014 Math Investor blog, we assessed how 2014 market prophets had fared (answer: not very well). Thus with the holiday season once again upon us, it is time to check scores. So how have 2015 prophets performed? Can prophets make profits?

Stock pickers lose

2015 was not a good year for stock pickers. According to Thomson Reuters and FacSet, the ten U.S. stocks that leading Wall Street

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