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Big Ideas

These blog entries offer some big ideas of lasting value relevant for investing and trading.

Perfect Factor Model of U.S. Stock Returns?

How many factors are optimal for modeling future returns of individual stocks? How do these factors relate to conventionally used factors (market, size, value, momentum, investment, profitability…)? In the June 2016 version of their paper entitled “Multifactor Models and the APT: Evidence from a Broad Cross-Section of Stock Returns”, Ilan Cooper, Paulo Maio and Dennis Philip derive mathematically an optimal set of factors for predicting returns of 278 stock portfolios created by sorting U.S. stocks into tenths (deciles) according to 28 market anomalies encompassing aspects of value, momentum, investment, profitability and intangibles. They apply asymptotic principal components analysis to these portfolios to identify the factors. They quantify the premium of each of these factors as the average return spread between extreme deciles of monthly sorts of the 278 source portfolios on the factor. They then examine interactions between this mathematical factor set and several widely used empirical multi-factor models: the Fama-French 3-factor model (market, size, book-to-market); a 4-factor model (adding momentum to the 3-factor model); a second 4-factor model (adding liquidity to the 3-factor-model); a third 4-factor model (market, size, investment, profitability); and, a 5-factor model (adding investment and profitability to the 3-factor model). Using monthly returns for the 278 source stock portfolios during January 1972 through December 2013, they find that: Keep Reading

How Much to Risk?

How should investors balance expected return and expected risk in allocating between risky and risk-free assets? In their short December 2016 paper entitled “Optimal Trade Sizing in a Game with Favourable Odds: The Stock Market”, Victor Haghani and Andrew Morton apply a simple rule of thumb related to mean-variance optimization to estimate the optimal allocation to risky assets. They also note several implications of this rule. Based on assumptions about investor motivation and straightforward mathematics, they conclude that: Keep Reading

Manage Risk by Challenging Assumptions

How can investors, large or small, overcome what appear to be obvious shortcomings in risk management, as occasionally indicated by portfolio crashes? In his November 2016 paper entitled “Managing Risks in Institutional Portfolios”, Andrea Malagoli critiques conventional investment portfolio risk management methodologies and offers precepts for robust risk management. He relies on a few empirical observations rather than abstract theoretical principles. Based on these observations, he concludes that: Keep Reading

Real-world Passive vs. Active

Is a passive investor one who holds all securities in their respective market capitalization weights, or one who never trades? In his October 2016 paper entitled “Sharpening the Arithmetic of Active Management”, Lasse Pedersen challenges the proposition that active trading is a zero sum game that produces an average gross return equal to that realized by passive investors. He argues that holding the market capitalization-weighted portfolio over the long term requires trading as securities enter and exit the market, new shares are issued, old shares are repurchased and authorities reconstitute market indexes. In other words, the market portfolio changes over time such that even passive investors must trade, and they may trade unfavorably with active managers. Also, real passive investors trade for non-investment reasons, again perhaps unfavorably with active managers. Based on the arithmetic of realistic portfolio maintenance, he concludes that: Keep Reading

Effects of In-sample Bias and Market Adaptation on Stock Anomalies

Do stock return anomalies weaken after discovery? If so, why? In the February 2016 update of their paper entitled “Does Academic Research Destroy Stock Return Predictability?”, David McLean and Jeffrey Pontiff examine out-of-sample and post-publication performance of 97 predictors of the cross section of stock returns published in peer-reviewed finance, accounting and economics journals. For each predictor, published confidence in predictive power is at least 95%, and replication is feasible with publicly available data. The publication date is year and month on the cover of the journal. Their goal is to determine the degrees to which any future degradation in predictive power derives from: (1) statistical biases (exposed out-of-sample but pre-publication); and, (2) market adaptation to strategies used by investors to exploit anomalies (exposed post-publication). For each predictor and interval, they employ a consistent test methodology based on average monthly return for a hedge portfolio that is long (short) the fifth of stocks with the highest (lowest) expected returns based on the original study. Portfolios are equally weighted unless the original study uses value weighting. Using extensions to 2013 of the exact or best available approximations of original data for the 97 predictive variables with samples starting as early as 1926 and ending as late as 2011, they find that: Keep Reading

Sharpe Ratio, Alpha or Geometric Mean?

What is the single best performance metric an investor can use to rank performances of competing portfolios (such as mutual funds)? In his September 2016 paper entitled “Measuring Portfolio Performance: Sharpe, Alpha, or the Geometric Mean?”, Moshe Levy compares Sharpe ratio, 5-factor (market, size, book-to-market, profitability, investment) alpha and geometric mean return as portfolio performance metric. The widely used Sharpe ratio is optimal when return distributions are normal and the investor can borrow at the lending (risk-free) rate without limit for leverage. However, asset return distributions may not be normal, investors generally borrow at an interest rate above the risk-free rate and Federal Reserve Regulation T restricts borrowing to 100% of an investor’s initial capital. Moreover, investors typically restrict themselves to much lower borrowing levels. His methodology is to compare the ranking of a set of actual equity mutual funds under realistic assumptions based on each of the three metrics with the ranking produced by utility maximizing allocations for each fund paired with the risk-free asset. The better the ranking produced by the metric aligns with the utility maximization ranking, the better the metric. His baseline assumption is that actual annual borrowing rate is 3.5% above the lending rate. For robustness, he considers several levels of investor risk aversion in determining utility maximization and other gaps between borrowing and lending rates. Using theory, monthly returns for 10,145 U.S. domestic equity mutual funds, the risk-free (lending) rate and returns for the five Fama-French factors during July 2005 through June 2015, he finds that: Keep Reading

The Right Math for Analysis of Financial Markets?

Where should investors look for methodological edges in 21st century financial markets? In his brief August 2016 paper entitled “Mathematics and Economics: A Reality Check”, Marcos Lopez de Prado advises finance students (and practitioners) what mathematical/analytical expertise to acquire for successful 21st century investing and trading. Based on his experience with what kinds of analysts and mathematics are most successful in financial markets, he concludes that: Keep Reading

Best Way to Guard Against Investment Strategy Flame-outs?

Can investors avoid strategy flame-outs associated with overly enthusiastic backtesting (overfitting)? In his July 2016 paper entitled “Limitations of Quantitative Claims About Trading Strategy Evaluation”, Michael Harris presents two examples that demonstrate a key limitation of trading strategy backtesting:

  1. U.S. stock market trend following.
  2. U.S. stock market mean reversion.

Specifically, he compares performances of such strategies before and after 1997 to illustrate the interaction of backtesting and change in market conditions. Using daily S&P 500 Index returns (excluding dividends) during January 1950 through December 2015, he finds that: Keep Reading

A Few Notes on Odds On: The Making of an Evidence-based Investor

Matt Hall, cofounder and president of Hill Investment Group, introduces his 2016 book, Odds On: The Making of an Evidence-Based Investor, by stating that: “…the evidence-based movement has been studying market data and academic research to identify the groups of stocks and other investments that provide better odds of long-term success. …I’m inviting you to learn how evidence-based investing could change your life…” Based on his experience, he concludes that: Keep Reading

In-sample vs. Out-of-sample Performance of 888 Trading Strategies

Are any trading strategy backtest performance statistics predictive of out-of-sample results? In their March 2016 paper entitled “All that Glitters Is Not Gold: Comparing Backtest and Out-of-Sample Performance on a Large Cohort of Trading Algorithms”, Thomas Wiecki, Andrew Campbell, Justin Lent and Jessica Stauth compare backtest and out-of-sample performance statistics for 888 algorithmic trading strategies. They first screen a larger set of strategies to remove duplicates, outliers and algorithms unlikely to represent real strategies. They next test the selected strategies in-sample (IS) with data that was available to the developers (from 2010 through deployment dates between January and June in 2015). They then test the strategies out-of-sample (OOS) during June 2015 through February 2016. All tests employ minute-by-minute prices for trade entry/exit and include robustly estimated trading frictions. Performance metrics derive from end-of-day positions/prices. Most tests are linear regressions relating individual IS-OOS performance metrics (such as Sharpe ratio). They also examine abilities of several multivariate machine learning techniques to predict performance, ultimately via an an equal-weighted portfolio of the 10 strategies predicted to have the highest OOS Sharpe ratios. Using position and price data for the 888 strategies during the specified IS and OOS periods, plus the total number of backtest days actually employed by each strategy developer, they find that: Keep Reading

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