Big Ideas

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: More…

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: More…

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:

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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: More…

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: More…

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: More…

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: More…

James Weatherall, physicist, mathematician and philosopher, introduces his 2012 book, The Physics of Wall Street: A Brief History of Predicting the Unpredictable, by stating: “This book tells the story of physicists in finance. …It is about how the quants came to be, and about how to understand the ‘complex mathematical models’ that have become central to modern finance.” Tracing the historical stream of key contributions by physicists and mathematicians to finance, he concludes that: More…

Can investors systematically earn a premium by holding relatively illiquid assets? In their December 2012 paper entitled “The Illiquidity Premium: International Evidence”, Yakov Amihud, Allaudeen Hameed, Wenjin Kang and Huiping Zhang examine the illiquidity premium in 26 developed and 19 emerging equity markets. They measure illiquidity as the average ratio of absolute daily stock return to trading volume (price impact per monetary volume traded). They define the illiquidity premium as the average gross return in excess of the risk-free rate for volatility-controlled portfolios that are long (short) high-illiquidity (low-illiquidity) stocks. Specifically, every three months, they: (1) sort stocks into three equal groups (terciles) based on return volatility (standard deviation of daily returns) over a lagged, rolling three-month window; (2) within each volatility tercile, sort stocks into fifths (quintiles) based on illiquidity over the same window; (3) skip one month to avoid any short-term reversal; and, (4) calculate the illiquidity premium as the average of returns of three portfolios that are long (short) the high-illiquidity (low-illiquidity) quintile within each volatility tercile. They groom the sample by excluding stocks that trade infrequently or exhibit extreme movements. They consider equal, value and monetary volume weightings for portfolios. Using daily price, trading volume and shares outstanding data for common stocks in 45 countries, along with estimates of market, size and book-to-market risk factors, during 1990 through 2011 (22 years), they find that: More…

When should an investor favor picking individual stocks over holding a stock index fund? In their November 2012 paper entitled “On Diversification”, Ben Jacobsen and Frans de Roon derive from Modern Portfolio Theory simple rules to compare concentrated investment in a portfolio of one or a few stocks to a broad, diversified (value-weighted) benchmark portfolio. The essential rule is that a concentrated portfolio is preferable to the benchmark portfolio if the product of its expected Sharpe ratio and the expected correlation of its returns with the benchmark’s returns exceeds the expected Sharpe ratio of the benchmark. They apply derivative thumb rules to real stocks to determine conditions under which stock picking is preferable to buying and holding a diversified benchmark portfolio. Using theoretical derivations and monthly returns and fundamentals for the 500 largest non-financial companies as of the end of the sample period with a history of at least five years during 1926 through 2011, they find that: More…