Equity Premium

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

Do any equity asset allocation strategies convincingly outperform equal weighting (1/N) after accounting for data snooping bias and portfolio maintenance frictions? In their December 2016 paper entitled “Asset Allocation Strategies, the 1/N Rule, and Data Snooping”, Po-Hsuan Hsu, Qiheng Han, Wensheng Wu and Zhiguang Cao apply tests based on White’s Reality Check to compare out-of-sample performances of 23 basic allocation strategies and 5,490 combinations of these strategies to that of equal weighting (1/N) after accounting for snooping bias and portfolio frictions. The 23 basic strategies encompass: conventional mean-variance optimization; mean-optimization with parameter shrinkage (to avoid extreme allocations); the capital asset pricing (1-factor) model (CAPM); the Fama-french 3-factor model (market, size, book-to-market); the related 4-factor model (adding momentum); CAPM augmented with a cross-sectional volatility factor; a missing factor extension of CAPM; minimum variance; maximum diversification; equal risk contribution; volatility timing; and, reward-to-risk timing. Strategy combinations use two or three of the basic strategies with weights varied in increments of 10%. They apply these strategies to each of seven sets of equity assets: (1) 25 size and book-to-market sorted U.S. stock portfolios; (2) 49 industry U.S. stock portfolios; (3) the stocks in the Dow Jones Industrial Average; (4) 22 developed country stock indexes; (5) the combination of (1) and (2); (6) 93 long-lived stocks from the S&P 500 Index; and, (7) 100 size and book-to-market sorted U.S. stock portfolios. Specifically, they each month estimate model parameters and asset weights in each dataset based on the most recent 60 months, and then calculate respective strategy performances the next month. They set one-way trading frictions for all assets at either 0.05% or 0.50% to estimate net returns. They focus on associated Sharpe ratios and certainty equivalent returns (CEQ) as strategy performance metrics. Using the specified monthly data mostly since July 1969 (but since July 1990 for developed country markets and since July 1996 for S&P 500 Index stocks) through December 2014, they find that: Keep Reading

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

Does trading in exchange-traded funds (ETF) by authorized participants (who may create and redeem ETF shares by exchanging underlying assets) predict associated ETF returns? In their November 2016 draft paper entitled “ETF Arbitrage and Return Predictability”, David Brown, Shaun Davies and Matthew Ringgenberg examine the relationship between ETF share creation/redemption and ETF returns. For their principal analysis, they each week or each month rank ETFs into fifths (quintiles) based on change in shares outstanding and then calculate future returns by value-weighted or equal-weighted quintile. Using daily prices, share creation/redemption data, net asset values, volumes, bid-ask spreads, underlying asset characteristics and fund characteristics for approximately 1,200 ETFs, along with contemporaneous equity factor model returns, during January 2007 through December 2015, they find that: Keep Reading

Is there a unique stock risk factor associated with expectations of a bear market? In the November 2016 version of their paper entitled “Bear Beta”, Zhongjin Lu and Scott Murray relate a put option-based indicator of the risk that the U.S. equity market will enter a bear state to individual stock returns. This indicator is based on two near-term out-of-the-money S&P 500 Index put options: a short position in a put option with strike price 1.5 standard deviations (based on S&P 500 implied volatility, VIX) below a zero excess (relative to the risk-free rate) index return; and, a long position in a put option 1.0 standard deviation below a zero excess index return. Using S&P 500 Index option prices, S&P 500 Index levels, VIX levels, risk-free rates, returns for a broad sample of U.S. stocks and various factor returns during January 1996 through August 2015, they find that: Keep Reading

Is the recent Fama-French augmentation of their classic three-factor (market, size, book-to-market) model of stock returns with profitability and investment factors a major advance? In their November 2016 paper entitled “Five Concerns with the Five-Factor Model”, David Blitz,  Matthias Hanauer, Milan Vidojevic and Pim van Vliet identify five concerns regarding the five-factor model. Based on empirical and theoretical (rationale) grounds, they note that: Keep Reading

Does the term structure of crude oil futures predict stock market returns? In their October 2016 paper entitled “Do Oil Futures Prices Predict Stock Returns?”, I-Hsuan Chiang and Keener Hughen examine the ability of crude oil futures prices to predict U.S. stock market returns. They identify the first three principal components of the nearest six oil futures prices. After finding that one of these components (related to the term structure) predicts stock market returns, they define a simple oil futures term structure curvature factor as:

• Short-term slope (natural logarithm of the second nearest price minus natural logarithm of the nearest price), minus
• Long-term slope (natural logarithm of the sixth nearest price minus natural logarithm of the third nearest price).

They test the ability of this curvature factor to predict U.S. stock market performance and industry performance in-sample (based on returns) and out-of-sample (based on R-squared explanatory power) at a one-month horizon. They compare its out-of-sample predictive power with those of nine other widely used predictors: dividend-price ratio, dividend yield, earnings-price ratio, book-to-market ratio, long-term U.S. Treasuries yield, long-term U.S. Treasuries return, U.S. Treasuries yield spread, U.S. Treasury bills yield and default yield spread. Using daily prices for the six nearest WTI light crude oil futures contracts and monthly returns for the broad U.S. stock market, 49 value-weighted industries and stocks in four crude oil subsectors during March 1983 through December 2014, they find that: Keep Reading

Do global equity funds generate alpha after accounting for both equity and currency factors? In their October 2016 paper entitled “Global Equity Fund Performance Evaluation with Equity and Currency Style Factors”, David Gallagher, Graham Harman, Camille Schmidt and Geoff Warren measure the performance of global equity funds based on their quarterly holdings after adjusting for market return, six widely used equity factor returns and three widely used currency exchange factor returns. The six equity factors are size (market capitalization), value (average of book-to-market and cash flow-to-price ratios), momentum (return from 12 months ago to one month ago in local currency), investment (quarterly change in total assets), profitability (return-on-equity) and illiquidity (impact of trading). The three currency exchange factors are trend (3-month average exchange rate minus 12-month average exchange rate), carry (reflecting short-term interest rate differences) and value (based on deviation from purchasing power parity). They also test developed and emerging markets holdings of these funds separately. Using quarterly stock holding weights for 90 institutional global equity funds priced in U.S. dollars, and contemporaneous equity and currency exchange factor return data, during 2002 through 2012, they find that: Keep Reading

Do stocks entering (exiting) factor indexes experience a price jump (drop) due to increased (decreased) demand? In their October 2016 paper entitled “Price Response to Factor Index Decompositions”, Joop Huij and Georgi Kyosev examine price impacts for stocks entering and exiting MSCI Minimum Volatility factor indexes covering U.S., European, global and emerging markets. To isolate the factor index effect, they exclude changes affecting both a factor index and its parent broad market index and changes due to corporate actions (such as spin-off or acquisition). They distinguish between the effective day (ED) of a change (first day the change occurs in the index portfolio) and the announcement day (AD) of a change (nine business days before ED). They define daily abnormal return of a stock as return in excess of the return of its factor index. They define daily abnormal trading volume of a stock as the ratio of dollar trading volume of the stock to dollar trading volume of its factor index, multiplied by the ratio of average dollar trading volume of the index to average dollar trading volume of the stock during a 40-day window ending 10 days before AD. Using index changes and daily returns and trading volumes of all stocks in the Minimum Volatility factor indexes and their parent broad market indexes during November 2010 through December 2015 (11 index rebalancings), they find that: Keep Reading

Do the realities of trading (bids and asks, stale prices, large orders, noise traders and technical traders) that may drive asset price away from fundamental value affect some stocks more than others? If so, is the effect exploitable? In their October 2016 draft paper entitled “(Priced) Frictions”, Kewei Hou, Sehoon Kim and Ingrid Werner assess the impact of such microstructure frictions on the cross-section of stock returns. Using a rolling 250-day window, they first estimate a stock’s friction-free average daily return as average two-day return divided by average lagged one-day return. They then compute the stock’s microstructure friction (FRIC) as average daily return minus friction-free average daily return over the same 250-day rolling window. To explore cross-sectional effects, they each month sort stocks into tenths (deciles) based on FRIC and construct a hedge portfolio that is long the high-FRIC decile and short the low-FRIC decile. They also perform double-sorts of FRIC and other stock return factors/predictors into fifths (quintiles) to investigate interactions. Using daily returns and firm data for a broad sample of U.S. stocks, and monthly returns for various stock return factors/predictors, during July 1963 through June 2013, they find that: Keep Reading