A random walk on the base4 digits of pi (see http://gigapan.com/gigapans/106803)
A Random Walk Down Wall Street
Fifty years ago, Princeton economics professor Burton Malkiel published A Random Walk Down Wall Street. He boldly asserted that a blindfolded chimpanzee throwing darts could pick a stock portfolio that would do as well as one created by many expert practitioners in the field.
At the time, Malkiel envisioned a strategy of owning a broadbased set of stocks, saying mimicking a major stock index such as the U.S. Standard and Poor’s 500 index (S&P 500). At the time, such investment vehicles
Continue reading Active versus index funds: Latest results
Introduction
Suppose, in a national TV newscast, instead of citing data, analysis and predictions from major government agencies, the weatherperson displayed a chart of recent temperatures, noting “trends,” “waves” and “breakout patterns.” Most of us would not have confidence in such a dubious and unorthodox forecast.
Or suppose, at a medical clinic, that a cardiologist made some hand measurements of events on an electrocardiogram and noted a “triangle pattern” or “Fibonacci ratio” between them. If this were to happen, most of us would start looking for another cardiologist. [Note: The “Fibonacci ratio,” also known as the “golden ratio,” usually
Continue reading Major brokerages and news media feature technical analysis
A new paper, Causal factor investing: Can factor investing become scientific?, has been written by our esteemed colleague Marcos Lopez de Prado of Cornell University, Abu Dhabi Investment Authority and True Positive Technologies.
In his 75page preprint, Lopez de Prado argues that almost all journal articles in the “factor investing” literature make assertions that are merely associational observations from statistical analyses, with no attempt to connect these findings to any coherent underlying theory. In other words, these authors justify their chosen model specification merely in terms of correlations or other statistics, and they do not propose experiments for falsifying causal
Continue reading Can factor investing become scientific?
Labyrinth at Schonbrunn Garden, Vienna; Credit: Andrea Schaufler and Wikimedia Commons
Origin of longshort hedge funds
“Hedge funds” were pioneered some 70 years ago by Australian financier Alfred Winslow Jones. His idea was to combine a “long” position (i.e., one that profits if the securities go up in price), typically a set of growth stocks, with a “short” position (i.e., one that profits if the securities go down in price) on the other part of the portfolio. Jones argued that this “longshort” strategy is more stable that either of the two parts by themselves — if the overall market
Continue reading Are hedge funds losing their hedge?
Credit: Onov3056 and Wikimedia Commons
The mathematics behind cryptocurrency
In a previous Mathematical Investor blog, we presented an overview of the mathematics behind blockchain technology, which is the basis of all cryptocurrency systems. At the present time, most systems are based on the SHA256 algorithm, which is a specific instance of the Elliptic curve digital signature algorithm.
To attempt to break SHA256 by brute force computation, one would need to exhaust over 2256 ≈ 1077 possible private keys, which is comparable to the number of atoms in the visible universe. In other words, while the computations necessary to actually
Continue reading How safe are cryptocurrency investments?
Credit: Mutual Fund Advisors
Introduction
For the vast majority of individuals investors, investing in one or a small number of mutual funds or exchangetraded funds makes more sense than directly owning a set of stocks or bonds. For one thing, investors often sleep better with mutual funds, rather than fretting whenever one of their stock or bond holdings is mentioned in a news report. Also, for many individuals, mutual fund holdings are less likely to run afoul of conflictofinterest difficulties in their professional work.
In a previous Mathematical Investor blog, we presented data on actively managed versus passive fund
Continue reading Active mutual funds underperform passive funds, again
A 13card hand dealt “at random”
Introduction
In several articles on this site (see, for instance, A and B), we have commented on the dangers of backtest overfitting in finance.
By backtest overfitting, we mean the usage of historical market data to develop an investment model, strategy or fund, where many variations are tried on the same fixed dataset. Backtest overfitting, a form of selection bias under multiple testing, has long plagued the field of finance and is now thought to be the leading reason why investments that look great when designed often disappoint when actually fielded to investors.
Continue reading Backtest overfitting and the posthoc probability fallacy
The present author, together with Marcos López de Prado, has just published the article How backtest overfitting in finance leads to false discoveries in Significance, a journal of the British Statistical Society. The published article is now available at the Significance (Wiley) website.
This article is condensed from the following manuscript, which is freely available from SSRN: Finance is Not Excused: Why Finance Should Not Flout Basic Principles of Statistics.
This paper introduces the problem of backtest overfitting in finance to the general reader who may be trained in the basics of statistics but not necessarily familiar with the application
Continue reading How backtest overfitting in finance leads to false discoveries
Block function approximation to normal distribution
Introduction
Today, arguably more than ever before, the world is governed by the science of probability and statistics. “Big data” is now the norm in scientific research, with terabytes of data streaming into research centers from satellites and experimental facilities, analyzed by supercomputers. “Data mining” is now an essential part of mathematical finance and business management. Numerous public opinion polls, expertly analyzed, guide the political arena. Covid19 infection rates, immunization levels and r0 factors are a staple of nightly newscasts.
Yet the public at large remains mostly ignorant of the basic principles
Continue reading The brave new world of probability and statistics
Venice astrological circle; credit Wikimedia
Astrology in finance?
In a previous MathInvestor article, we mentioned how absurd it would be if someone offered predictions of stock or bond prices or cryptocurrency rates based on astrological signs.
Consider for a moment that financial market prices are based on a confluence of many thousands of factors worldwide, including developments in science and technology, changes in consumer sentiment and preferences, changes in prices of production, public health emergencies (e.g., Covid19), political developments, competition with other financial instruments and even changes in weather. These prices are negotiated electronically, on behalf of millions of
Continue reading Can astrology predict financial markets??

