# Value Premium

Is there a reliable benefit from conventional value investing (based on the book-to-market value ratio)? these blog entries relate to the value premium.

**July 26, 2017** - Fundamental Valuation, Value Premium

Do investors fixate on price-to-earnings ratio (P/E) and thereby create trading opportunities as P/Es change? In his June 2017 paper entitled “P/E Ratios and Value Investor Attention”, Jordan Moore examines market responses to U.S. common stocks sorted by earnings yield (inverse of P/E). He defines P/E as the ratio of stock price to the sum of the last available four quarters of net earnings excluding extraordinary items divided by current shares outstanding. For monthly tests, he assumes that earnings become available at the close of the last trading day of the reporting month. For daily and weekly tests, he assumes that earnings become available at the close of the first trading after earnings release date. He separately analyzes stocks with (published) positive and (generally unpublished) negative earnings yields. For comparison, he similarly calculates current monthly book-to-market ratios and sorts stocks by that alternative valuation metric. Using the specified accounting and price data for a broad sample of U.S. common stocks during 1973 through 2015, *he finds that:* Keep Reading

**June 5, 2017** - Commodity Futures, Currency Trading, Strategic Allocation, Value Premium

Does a carry trade derived from roll yields of futures/forward contracts work within asset classes (undiversified) and across asset classes (iversified)? In his May 2017 paper entitled “Optimising Cross-Asset Carry”, Nick Baltas explores the profitability of cross-sectional (relative) and time-series (absolute) carry strategies within and across futures/forward markets for currencies, stock indexes, commodities and government bonds. He posits that contracts in backwardation (contango) present a positive (negative) roll yield and should generally be overweighted (underweighted) in a carry portfolio. He considers three types of carry portfolios, each reformed monthly:

- Cross-sectional (XS) or Relative – Rank all assets within a class by strength of carry, demean the rankings such that half are positive and half are negative and then assign weights proportional to demeaned ranks to create a balanced long-short portfolio. Combine asset classes by applying inverse volatility weights (based on 100-day rolling windows of returns) to each class portfolio.
- Times-series (TS) or Absolute – Go long (short) each asset within a class that is in backwardation (contango), such that the class may be net long or short. Combine asset classes in the same way as XS.
- Optimized (OPT) – Apply both relative strength and sign of carry to determine gross magnitude and direction (long or short) of positions for all assets, and further apply asset volatilities and correlations (based on 100-day rolling windows of returns) to optimize return/risk allocations.

Using daily data for 52 futures series (20 commodities, eight 10-year government bonds, nine currency exchange rates versus the U.S. dollar and 15 country stock indexes) during January 1990 through January 2016, *he finds that:* Keep Reading

**May 11, 2017** - Value Premium

What’s the best way to combine profitability and value in screening stocks? In their April 2017 paper entitled “The Magic Formula: Value, Profitability, and the Cross Section of Global Stock Returns”, Douglas Blackburn and Nusret Cakici compare performances of a portfolio based on the Magic Formula (MF) and a portfolio based on an Improved Magic Formula (IMF). Both portfolios are long profitable value (PV) stocks and short unprofitable growth (UG) stocks. For MF, profitability is return-on-capital, defined as earnings before interest and taxes (EBIT) divided by tangible capital. For IMF, profitability is gross profitability, gross profit divided by assets. For both, value is an earnings yield, defined as EBIT divided by enterprise value. Specifically, they each month reform a PV-UG portfolio by:

- Ranking stocks by the profitability metric seven months ago (ensuring availability of all inputs).
- Ranking stocks by earnings yield seven months ago.
- Adding the two rankings and sorting stocks into fifths (quintiles) by combined rank.
- Buy the top quintile, sell the bottom quintile (PV-UG) and hold for one month, employing either equal weighting or value weighting.

They test PV-UG portfolios separately in developed equity markets grouped into North America, Europe, Japan and Asia regions. Using the specified firm data and associated monthly stock excess returns (relative to the 1-month U.S. Treasury bill yield as the risk-free rate) in U.S. dollars for 23 developed stock markets during January 1991 through December 2016, *they find that:* Keep Reading

**March 24, 2017** - Momentum Investing, Value Premium, Volatility Effects

Are widely used stock factor premiums amenable to timing based on the ratio of aggregate valuation of stocks in the long side to aggregate valuation of stocks in the short side of the factor portfolio (the value spread)? In their March 2017 paper entitled “Contrarian Factor Timing is Deceptively Difficult”, Clifford Asness, Swati Chandra, Antti Ilmanen and Ronen Israel test a strategy that times factor portfolios based on the value spread, in single-factor or multi-factor portfolios. They consider three annually rebalanced factor hedge portfolios: (1) value (High Minus Low book-to-market ratio, or HML); (2) momentum (Up Minus Down, or UMD); and, (3) low beta (Betting Against Beta, or BAB). Their main measure for calculating the value spread is book-to-market ratio, so that a high (low) value spread implies a cheap (expensive) factor. To standardize the value spread, they use z-scores (number of standard deviations above or below the historical average, with positive values indicating undervalued). They use the first 120 months of data to calculate the first z-score. They compare performances of factor portfolios without timing to performances of the same portfolios with a timing overlay that varies capital weights for a factor between 50% and 150% of its passive weight according to the factor’s value spread (scaled to total portfolio weight 100%). They consider variants that are and are not industry neutral. Using factor and return data for large-capitalization U.S. stocks during 1968 through 2016, *they find that:* Keep Reading

**March 22, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

How diversifying are different equity factors within and across country stock markets? In his January 2016 paper entitled “The Power of Equity Factor Diversification”, Ulrich Carl analyzes diversification properties of six equity factors (market excess return, size, value, momentum, low-beta and quality) across 20 developed stock markets. He defines each factor conventionally as returns to a portfolio that is each month long (short) stocks with the highest (lowest) expected returns based on that factor. He considers: (1) cross-country correlations for each factor; (2) cross-factor correlations for each country; (3) cross-country, cross-factor correlations; (4) dynamics of cross-country correlations for each factor based on rolling 36-month windows of returns; and, (5) cross-country correlations for each factor for the 30% lowest and 30% highest market excess returns (tail events). He also applies principal component analysis as another way to evaluate how diverse the 120 country-factor return streams are. Finally, he constructs cross-factor and cross-country portfolios to assess economic value of diversification properties. Using monthly returns in U.S. dollars for the six factors in each of the 20 countries during January 1991 through April 2015, *he finds that:* Keep Reading

**March 15, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Are the returns of factors widely used to predict the cross-section of stock returns themselves predictable? In the January 2016 draft of his paper entitled “Equity Factor Predictability”, Ulrich Carl analyzes predictability of market, size (market capitalization), value (book-to-market ratio), momentum (returns from 12 months ago to one month ago), low beta (betting against beta) and quality factor returns. All factor returns derive from hedge portfolios that are long (short) stocks with high (low) expected returns based on their factor values. He employs a broad range of economic and financial variables in four sets and multiple ways of testing predictability to ensure robustness of findings and limit model/data snooping bias. Predictability tests he applies include: combinations of simple forecasts (mean or median of single-variable regression forecasts); principal component analysis to distill forecasting variables into a few independent predictive factors; and, methods that adjust variable emphasis according to their respective past performances. He considers several predictability evaluation metrics, including: mean squared error compared to that of the historical average return; utility gain of timing based on predictability; and, information ratio (difference in return divided by difference in risk) relative to the historical average return. He mostly examines next-month forecasts with a one-month gap between predictive variable measurement and forecasted return over two test periods: 1975-2013 and 1950-2013. Using monthly returns for the six factors (start dates ranging from 1928 to 1958), a large set of financial variables since 1928 and a large set of economic variables since 1962, all through November 2013, *he finds that:* Keep Reading

**March 10, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

How attractive are purified factor portfolios, constructed to focus on one factor by avoiding exposures to other factors? In their January 2017 paper entitled “Pure Factor Portfolios and Multivariate Regression Analysis”, Roger Clarke, Harindra de Silva and Steven Thorley explore a multivariate regression approach to generating pure factor portfolios. They consider five widely studied factors: value (earnings yield); momentum (cumulative return from 12 months ago to one month ago); size (market capitalization); equity market beta; and, profitability (gross profit margin). They also consider bond beta (regression of stock returns on 10-year U.S. Treasury note returns) to examine interest rate risk. They each month reform two types of factor portfolios:

- Primary – a factor portfolio with weights that deviate simply from market weights based on analysis of just one factor, with differences from market portfolio weights scaled by market capitalization.
- Pure – a factor portfolio derived from a multiple regression that isolates each factor, ensuring that it has zero exposures to all other factors.

They measure factor portfolio performance based on: average difference in monthly returns between each factor portfolio and the market portfolio; annualized standard deviation of the underlying monthly return differences; 1-factor (market) alpha; and, information ratio (alpha divided by incremental risk to the market portfolio). Using return and factor data for the 1,000 largest U.S. stocks during 1967 through 2016, *they find that:* Keep Reading

**February 27, 2017** - Momentum Investing, Size Effect, Value Premium, Volatility Effects

Are there plenty of exchange-traded funds (ETF) offering positive or negative exposures to widely accepted factor premiums? In his February 2017 paper entitled “Are Exchange-Traded Funds Harvesting Factor Premiums?”, David Blitz analyzes the exposures of U.S. equity ETFs to market, size, value, momentum and volatility factors. Specifically, he calculates factor betas (exposures) from a multi-factor regression of monthly excess (relative to the risk-free rate) total returns for each ETF versus market, small-minus-big size (SMB), high-minus-low value (HML), winners-minus-losers momentum (WML) and low-minus-high volatility (LV-HV) factor returns during 2011 through 2015. His overall sample consists of 415 U.S. equity ETFs with least 36 months of return history as of the end of 2015. He also considers subsamples consisting of: (1) 103 smart beta ETFs that explicitly target factor premiums, including fundamentally weighted and high-dividend funds; and, (2) the remaining 312 conventional ETFs, including sector funds and funds with conflicting factor exposures. He includes lists of the 10 ETFs with the most positive and the 10 ETFs with the most negative exposures to each factor from among the 100 largest ETFs. Using monthly Assets under Management (AuM) and total returns for the specified 415 ETFs, along with the monthly risk-free rate and the selected factor premiums during January 2011 through December 2015, *he finds that:* Keep Reading

**February 3, 2017** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Does suppressing unrelated risks from stock factor portfolios improve performance? In their January 2017 paper entitled “Diversify and Purify Factor Premiums in Equity Markets”, Raul Leote de Carvalho, Lu Xiao, François Soupé and Patrick Dugnolle investigate how to improve the capture of four types of stock factor premiums: value (12 measures); quality (16 measures); low-risk (two measures); and, momentum (10 measures). They standardize the different factor measurement scales based on respective medians and standard deviations, and they discard outliers. Their baseline factors portfolios employ constant leverage (CL) by each month taking 100% long (100% short) positions in stocks with factor values associated with the highest (lowest) expected returns. They strip unrelated risks from baseline portfolios by:

- SN – imposing sector neutrality by segregating stocks into 10 sectors before ranking them for assignment to long and short sides of the factor portfolio.
- CV – replacing constant leverage by each month weighting each stock in the portfolio to target a specified volatility based on its actual volatility over the past three years.
- HB – hedging the market beta of the portfolio each month based on market betas of individual stocks calculated over the past three years by taking positions in the capitalization-weighted market portfolio and cash.
- HS – hedging the size beta of the portfolio each month based on size betas of individual stocks calculated over the past three years by taking positions in the equal-weighted market portfolio and the capitalization-weighted market portfolio.

They examine effects of combining measures within factor types, combining types of factors and excluding short sides of factor portfolios. They also look at U.S., Europe and Japan separately. Their portfolio performance metric is the information ratio, annualized average return divided by annualized standard deviation of returns. Using data for stocks in the MSCI World Index since January 1997, in the S&P 500 Index since January 1990, in the STOXX Europe 600 Index since January 1992 and in the Japan Topix 500 Index since August 1993, all through November 2016, *they find that:* Keep Reading

**September 26, 2016** - Size Effect, Value Premium, Volatility Effects

Do investors exploiting common stock return anomalies risk extraordinarily large drawdowns during market crashes? In their May 2016 paper entitled “Can Exposure to Aggregate Tail Risk Explain Size, Book-to-Market, and Idiosyncratic Volatility Anomalies?”, Sofiane Aboura and Eser Arisoy investigate whether portfolios based on the size, book-to-market ratio and idiosyncratic volatility effects bear elevated stock market tail risk. They measure market tail risk as change in VIX Tail Hedge Index (VXTH), which hedges extreme drops in the S&P 500 Index by holding the index and one-month far out-of-the-money (30-delta) call options on the CBOE Volatility Index (VIX). They test sensitivity of size and book-to-market factors to overall risk and tail risk by adding change in VIX (market volatility risk factor) and change in VXTH (market tail risk factor) to the Fama-French three-factor (market, size, book-to-market) model of stock returns. They consider two equal subperiods, one containing the 2008 financial crisis, to check robustness of findings. Using monthly values of VIX and VXTH, factor model returns and U.S. Treasury bill yields during January 2007 through February 2016 (110 months), *they find that:* Keep Reading