
When numbers of any sort are presented, whether in mathematics, science, business, government or finance, the default assumption is that the data presented are reasonably reliable to the last digit presented. Thus, if a light bulb is listed as using 3.14 watts, then its actual usage is presumably between 3.13 and 3.15 watts, and certainly not 2.8 or 4.2 watts. Or if the average interest rate paid on a set of securities is listed as 2.718 percent, then a reasonable reader presumes that the actual figure is between 2.717 and 2.719 percent.
The total number of significant digits can vary
Continue reading Dubious digits: Is this data really that accurate?
One central difficulty of investing, both in the U.S. and internationally, is that most individual investors are not sufficiently wellinformed on financial matters (or else are not sufficiently disciplined in their approach), and thus often make lessthanoptimal choices in managing their longterm savings. The 2014 DALBAR report, for instance, concluded that over the past 20 years, individual U.S. stock fund investors achieved only a 5.02% average annual return, which is considerably less than the 9.22% they could have achieved simply by investing in a S&P500 index fund. Results for other asset classes are similar.
In fact, analyst Richard Bernstein has
Continue reading Index investing: “Confidence in the mathematics”
Challenging times for hedge funds
Recently attention has been drawn to the fact that the advantage enjoyed by hedge funds over more conventional investment vehicles has been eroding. For example, the annualized “excess return” of the HFRI equity hedge fund index (adjusted for certain factors, 60 month rolling average) has declined from approximately 15% in 2000 to less than 2% in 2010, and actually has been negative over the past two years. In particular, the average yeartodate hedge fund return (as of September 2014) is only 2%, compared to the 7.27% rise in the S&P500 index. Similarly, only 23% of
Continue reading Is “cherry picking” a factor in hedge fund performance?
Introduction
We are pleased to announce the availability of a new online tool to demonstrate and analyze the phenomenon of backtest overfitting. It is available HERE. It was developed by researchers at the Scientific Data Management Group at Lawrence Berkeley National Laboratory, with contributions and suggestions from several other persons. A complete list of contributors is given below.
In finance, “backtest overfitting” means using historical market data (i.e., a “backtest”) to develop an investment strategy, where too many variations of the strategy are tried, relative to the amount of data available. Overfit strategies typically work well when tested against
Continue reading New online tool to demonstrate backtest overfitting
Introduction
A June 2014 study released by the Employee Benefit Research Institute concluded that many U.S. Baby Boomer and Gen Xer households are expected to run short of money in retirement (assuming 35 years in retirement): 83% of those in the lowest income quartile, 47% in the second quartile, 28% in the third, and 13% even in the highest income quartile. Another study concluded that more than half of future U.S. retirees will rely on Social Security for at least 50% of their income.
Part of the difficulty stems from the fact that many workers, both in the U.S. and
Continue reading How financially literate are individual investors?
On 12 July 2014, David H. Bailey and Jonathan M. Borwein (two of the bloggers on this site) presented the talk Scientific Integrity in Mathematical Finance at the Workshop on Optimization, Nonlinear Analysis, Randomness and Risk, held at the Centre for ComputerAssisted Research Mathematics and its Applications (CARMA), University of Newcastle, Australia. The viewgraphs for the talk are available here.
In this talk, Bailey and Borwein summarize research outlined in their paper (coauthored with Marcos Lopez de Prado and Qiji Jim Zhu), Pseudomathematics and financial charlatanism: The effects of backtest overfitting on outofsample performance. The talk also includes a series
Continue reading Bailey and Borwein give talks on integrity and reproducibility in mathematical finance
On 7 July 2014, the New York Times ran a feature story on James H. Simons, the wellknown geometer, hedge fund founder, billionaire and philanthropist. Here are some of the fascinating facts uncovered in the Times story and elsewhere:
Simons was born in 1938 in Newton, Massachusetts, the son of a shoe factory owner. Simons graduated from the Massachusetts Institute of Technology in three years, then received his Ph.D. in mathematics from U.C. Berkeley in three more years, finishing at the age of 23. Simons worked on cryptographic mathematics at the Institute for Defense Analyses in Princeton, New Jersey, but
Continue reading New York Times features story on James Simons
On June 5, Mary Jo White, Chair of the U.S. Securities and Exchange Commission, sketched some proposed changes to regulate highfrequency trading (HFT). Her full speech is available from the SEC website. Some analysis can be read in the New York Times and Bloomberg News.
Synopsis of White’s comments
White surprised many observers by stating that investors are doing better in the algorithmic trading regime today than they did in the “old manual markets.” She noted that for institutional investors, the cost of executing a large order is roughly 10% lower than in 2006, and the spreads between bid and
Continue reading SEC to propose new rules for highfrequency trading
As we emphasized in a December 2013 Mathematical Investor blog, individual investors are not very well equipped, and certainly not very effective, in managing their own investment portfolios.
This is unfortunate, because fewer workers than in the past, particularly in the U.S., are covered by a “definedbenefit” retirement system, namely a pension that guarantees a certain proportion of one’s income at retirement, based on the number of years in service, in perpetuity until one’s death. Instead, the majority of the growing army of American baby boomers (according to the Population Reference Bureau, 76.4 million Americans were born in the period
Continue reading Latest DALBAR report underscores poor longterm performance of individual investors
Many investors, individual and institutional, have come to the conclusion that indexlinked investments are a rational and, in the long term, profitable investment strategy.
It is certainly true that many individual investors could do far worse that merely investing, say, in a S&P500 index fund or exchangetraded fund (ETF). As we described in a previous Mathematical Investor blog, the typical U.S. equity investor has significantly underperformed the S&P500, with similarly dismal results in other asset categories. In particular, the average equity investor has a 20year return of 4.25% per annum, compared with a 8.21% average return of the S&P500, for
Continue reading Do new backtested index ETFs outperform the market?

