Big Ideas

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Book Preview – Chapter 2

Here is this Friday’s installment of Avoiding Investment Strategy Flame-outs, a short book we are previewing for subscribers. Chapter previews will continue for the next seven Fridays.

Chapter 2: “Making the Strategy Logical”

“Making an investment/trading strategy logical essentially means making it testable and implementable, with inputs, outputs and rules clearly defined, properly sequenced and inclusive of all material factors. Clearly defined inputs, outputs and rules enable verification and extension. Definitions that require subjective interpretation are not clear. Properly sequenced inputs, outputs and rules fit the real world, representing an analysis and implementation scenario available to an investor in real time. Some strategies are more forgiving of tight sequencing than others. Including all material factors means accounting for all significant contributions to (capital gains, dividends, interest) and debits from (costs of data, trading frictions, cost of shorting, cost of leverage) investment outcome. The materiality of factors varies with strategy specifics.

“How can investors make sure their strategies are logical?”

Book Preview – Introduction and Chapter 1

Starting today and continuing for the next eight Fridays, we are previewing for subscribers a short book entitled Avoiding Investment Strategy Flame-outs.

The initial installments are:

“Introduction”

“Why do investment/trading strategies that test well on historical data flame out when put to actual use? Are there steps investors can take to improve the odds that strategies they develop will perform as tested? This book draws upon reviews of hundreds of academic and practitioner studies that seek to predict asset prices and exploit the predictions. It focuses on widespread weaknesses and limitations in these studies to help investors: (1) avoid or mitigate the weaknesses in developing their own strategies; and, (2) perform due diligence on strategies offered by others.”

Chapter 1: “Some Statistical Practices that Make Sense”

“Financial systems, such as stock markets, involve a large number of interacting decisions based on many different time-varying levels of knowledge, processing capabilities, motivations and financial resources. Due to this complexity, theories of financial system behavior cannot determine future prices and returns. Said differently, the models termed “financial theories” are actually just working hypotheses generally formed retrospectively (empirically) to fit the past.

“Lack of solid theories leaves researchers to explore a jungle of empirical data via statistical inference, constructing samples and looking for past conditions (indicators) that relate strongly to future outcomes (returns) within those samples. Investors then make the leap (despite limitations in empirical research and changes in the market conditions) that future data is enough like past data to apply findings from such inferences to investment decisions.

“How should investors generate and interpret research findings in such an environment?”

To make room for Avoiding Investment Strategy Flame-outs on the CXOAdvisory.com main menu, we are retiring our “Investment Demons” (largely subsumed by the book). The demons will, however, remain available here.

Navigating the Data Snooping Icebergs

Iterative testing of strategies on a set of data introduces snooping bias, such that a winning (losing) strategy is to some degree lucky (unlucky). Sharing of strategies across a community of researchers carries the luck forward, with accretion of additional bias from testing by subsequent researchers. Is there a rigorous way to account for this accumulation of snooping bias? In the October 2013 version of their paper entitled “Backtesting”, Campbell Harvey and Yan Liu describe three types of adjustment for snooping bias and apply them to quantify the snooping bias “haircut” appropriate for any reported Sharpe ratio (in lieu of a 50% rule-of-thumb discount). Using mathematical derivations and examples, they conclude that: Keep Reading

Measuring Investment Strategy Snooping Bias

Investors typically employ backtests to estimate future performance of investment strategies. Two approaches to assess in-sample optimization bias in such backtests are:

  1. Reserve (hold out) some of the historical data for out-of-sample testing. However, surreptitious direct use or indirect use (as in strategy construction based on the work of others) of hold-out data may contaminate its independence. Moreover, small samples result in even smaller in-sample and hold-out subsamples.
  2. Randomize the data for Monte Carlo testing, but randomization assumptions may distort the data and destroy real patterns in them. And, the process is time-consuming.

Is there a better way to assess data snooping bias? In their September 2013 paper entitled “The Probability of Backtest Overfitting”, David Bailey, Jonathan Borwein, Marcos Lopez de Prado and Qiji Zhu derive an approach for assessing the probability of backtest overfitting that depends on the number of trials (strategy alternatives) employed to select it. They use Sharpe ratio to measure strategy attractiveness. They define an optimized strategy as overfitted if its out-of-sample Sharpe ratio is less than the median out-of-sample Sharpe ratio of all strategy alternatives considered. By this definition, overfitted backtests are harmful. Their process is very general, specifying multiple (in-sample) training and (out-of-sample) testing subsamples of equal size and reusing all training sets as testing sets and vice versa. Based on interpretation of mathematical derivations, they conclude that: Keep Reading

Insidiousness of Overfitting Investment Strategies via Iterative Backtests

Should investors worry that investment strategies available in the marketplace may derive from optimization via intensive backtesting? In the September 2013 update of their paper entitled “Backtest Overfitting and Out-of-Sample Performance”, David Bailey, Jonathan Borwein, Marcos Lopez de Prado and Qiji Zhu examine the implications of overfitting investment strategies via multiple backtest trials. Using Sharpe ratio as the measure of strategy attractiveness, they compute the minimum backtest sample length an investor should require based on the number of strategy configurations tried. They also investigate situations for which more backtesting may produce worse out-of-sample performance. Based on interpretations of mathematical derivations, they conclude that: Keep Reading

Long-term Investors: Focus on Terminal Wealth?

Should long-term investors focus on terminal wealth and ignore interim volatility? In his August 2013 paper entitled “Rethinking Risk”, Javier Estrada compares distributions of terminal wealths for $100 initial investments in stocks or bonds over investment horizons of 10, 20 or 30 years. He utilizes mean, median, tail (extreme 1%, 5% and 10%) and risk-adjusted performance metrics. He employs real returns for 19 country markets adjusted by local inflation and in local currency for individual country markets, and adjusted by U.S. inflation and in dollars for the (capitalization-weighted) World market. Using real annual total returns for indexes of stocks and government bonds in each country during 1900 through 2009 (101, 91, and 81 overlapping intervals of 10, 20, and 30 years), he finds that: Keep Reading

Unified Carry Trade Theory

Does the carry trade concept provide a useful framework for valuation of securities within and across all asset classes? In their July 2013 paper entitled “Carry”, Ralph Koijen, Tobias Moskowitz, Lasse Pedersen and Evert Vrugt investigate expected return across asset classes via decomposition into “carry” (expected return assuming price does not change) and expected price appreciation. They measure carry for: global equities; global 10-year bonds; global bond yield spread (10-year minus 2-year); currencies; commodities; U.S. Treasuries; credit; equity index call options; and equity index put options. Their measurements of carry vary by asset class (based on: futures prices for equity indexes, currencies and commodities, modeled futures prices for global bonds, U.S. Treasuries and credit; and, option prices for options). They further decompose carry returns into passive and dynamic components. The passive component is the return to a hedge (carry trade) portfolio designed to capture differences in average carry returns across securities, and the dynamic component indicates how well carry predicts future price appreciation. Finally, they determine the conditions under which carry strategies perform poorly across all asset classes. Using monthly price/yield data for multiple assets within each class as available during January 1972 through September 2012, they find that: Keep Reading

Capturing Factor Premiums

How can investors capture returns from widely accepted risk factors associated with asset classes and subclasses? In the June 2013 version of his book chapter entitled “Factor Investing”, Andrew Ang provides advice on capturing risk premiums associated with factors such as value, momentum, illiquidity, credit risk and volatility risk. Based on the body of research, he concludes that: Keep Reading

Taming the Factor Zoo?

How should researchers address the issue of aggregate/cumulative data snooping bias, which derives from many researchers exploring approximately the same data over time? In their April 2013 draft paper entitled “. . . and the Cross-Section of Expected Returns”, Campbell Harvey, Yan Liu and Heqing Zhu examine this issue with respect to studies that discover factors explaining differences in future returns among U.S. stocks. They argue that aggregate/cumulative data snooping bias makes conventional statistical significance cutoffs (for example, a t-statistic of at least 2.0) too low. Researchers should view their respective analyses not as independent single tests, but rather as one of many within a multiple hypothesis testing framework. Such a framework raises the bar for significance according to the number of hypotheses tested, and the authors give guidance on how high the bar should be. They acknowledge that they do not (cannot) count past tests of factors falling short of conventional significance levels (and consequently not published). Using the body of published and near-published (working papers) research that discovers new factors explaining the cross-section of future U.S. stock returns from the mid-1960s through 2012, they find that: Keep Reading

Index Investing Makes Stock Picking Harder?

How does growth in equity index investing affect the stock market? In their March 2013 paper entitled “Indexing and Stock Price Efficiency”, Nan Qin and Vijay Singal examine the relationship between equity index investing (driven passively by liquidity trading and index changes, not actively by private information) and stock price efficiency. They estimate equity index investing from holdings of 663 equity index mutual funds, enhanced index mutual funds, exchange-traded funds and closet indexers. They measure each stock’s index ownership as the percentage of shares held by these funds at the end of each quarter, with passive trading volume the absolute quarterly change in holdings of these funds. They measure stock price inefficiency as volatility of the deviation of daily and intraday price from a random walk. For robustness, they also consider autocorrelation of daily stock returns and the weekly-to-daily variance ratio as measures of price inefficiency. Each quarter, they relate price inefficiency to index ownership across stocks. Using intraday and daily returns of S&P 500 Index constituents from the time they enter the index and quarterly fund holdings during 1993 (inception of intraday stock price data) through 2011, they find that: Keep Reading

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