Big Ideas

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

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

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

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

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

Is downside risk the critical driver of investor asset valuation? In the January 2013 version of their paper entitled “Conditional Risk Premia in Currency Markets and Other Asset Classes”, Martin Lettau, Matteo Maggiori and Michael Weber explore the ability of a simple downside risk capital asset pricing model (DR-CAPM) to explain and predict asset returns. Their approach captures the idea that downside risk aversion makes investors view assets with high beta during bad market conditions as particularly risky. For all asset classes (but focusing on currencies), they define bad market conditions as months when the excess return on the broad value-weighted U.S. stock market is less than 1.0 standard deviation below its sample period average. To test DR-CAPM on currencies, they rank a sample of 53 currencies by interest rates into six portfolios, excluding for some analyses those currencies in highest interest rate portfolio with annual inflation at least 10% higher than contemporaneous U.S. inflation. They calculate the monthly return for each currency as the sum of its excess interest rate relative to the dollar and its change in value relative to the dollar. They then calculate overall and downside betas relative to the U.S. stock market based on the full sample. They extend tests of DR-CAPM to six portfolios of U.S. stocks sorted by size and book-to-market ratio, five portfolios of commodities sorted by futures premium and six portfolios of government bonds sorted by probability of default, and to multi-asset class combinations. They also compare DR-CAPM to optimal models based on principal component analysis within and across asset classes. Using monthly prices and characteristics for currencies and U.S. stocks during January 1974 through March 2010, for commodities during January 1974 through December 2008 and for government bonds during January 1995 through March 2010, they find that: Keep Reading

Does use of alphas from linear factor models to identify anomalies in U.S. stock returns mislead investors? In the February 2013 draft of their paper entitled “Using Maximum Drawdowns to Capture Tail Risk”, Wesley Gray and Jack Vogel investigate maximum drawdown (largest peak-to-trough loss over a time series of compounded returns) as a simple measure of tail risk missed by linear factor models. Specifically, they quantify maximum drawdowns for 11 widely cited U.S. stock return anomalies identified via one-factor (market), three-factor (plus size and book-to-market ratio) and four-factor (plus momentum) linear models. These anomalies are: financial distress; O-score (probability of bankruptcy); net stock issuance; composite stock issuance; total accruals; net operating assets; momentum; gross profitability; asset growth; return on assets; and, investment-to-assets ratio. They calculate alphas for each anomaly by using the specified linear model risk factors to adjust gross monthly returns from a portfolio that is long (short) the value-weighted or equal-weighted tenth of stocks that are “good” (“bad”) according to that anomaly, reforming the portfolio annually or monthly depending on anomaly input frequency. Using monthly returns and firm fundamentals for a broad sample of U.S. stocks, and contemporaneous stock return model factor returns, during July 1963 through December 2012, they find that: Keep Reading

In his 2013 book The Little Book of Market Myths: How to Profit by Avoiding the Investing Mistakes Everyone Else Makes, author Ken Fisher, chairman and CEO of Fisher Investments, “covers some of the most widely believed market and economic myths–ones that routinely cause folks to see the world wrongly, leading to investment errors.” His hope is that “the book helps you improve your investing results by helping you see the world a bit clearer. And I hope the examples included here inspire you to do some sleuthing on your own so that you can uncover still more market mythology.” Some notable points from the book are: Keep Reading

How should investors measure the value of tactical deviations from a strategic asset class allocation? In their December 2012 draft paper entitled “A Framework for Examining Asset Allocation Alpha”, Jason Hsu and Omid Shakernia decompose sources of alpha for a diversified portfolio. Their decomposition assumes prior determination of the strategic asset allocation (policy portfolio), consisting of indexes that proxy for broad asset classes. They define tactical asset allocation (tactical portfolio), also consisting of indexes, as deviation from the strategic allocation. They define manager selection (implemented portfolio) as the set of tradable assets used to implement the tactical allocation. Total alpha is the return of the implemented portfolio in excess of that for the policy portfolio, a combination of excess returns from tactical allocation and manager selection. The excess return of the tactical portfolio over the policy portfolio is the asset allocation alpha, the focus of the paper. Based on prior research, they conclude that: Keep Reading

How special is the Fama-French three-factor model (market, size, book-to-market ratio) compared to other possible three-factor models? In their November 2012 paper entitled “Firm Characteristics and Empirical Factor Models: a Data-Mining Experiment”, Leonid Kogan and Mary Tian systematically compare explanatory breadth for all 351 three-factor and 2,925 four-factor (linear) models for predicting stock returns that can be formed from 27 firm characteristics other than size and book-to-market ratio. They measure explanatory breadth of a model by how well it captures the average future return differences across value-weighted deciles from annual sorts on the characteristics not used in the model. Using monthly returns and annual/quarterly firm characteristics for a broad sample of non-financial U.S. stocks during 1971 through 2011, they find that: Keep Reading