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Equity Premium

Governments are largely insulated from market forces. Companies are not. Investments in stocks therefore carry substantial risk in comparison with holdings of government bonds, notes or bills. The marketplace presumably rewards risk with extra return. How much of a return premium should investors in equities expect? These blog entries examine the equity risk premium as a return benchmark for equity investors.

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Equity Risk Premium and Investment Horizon

How should an investor’s view of the equity risk premium vary with investment horizon? In the December 2017 update of their paper entitled “Volatility Lessons”, Eugene Fama and Kenneth French examine how the U.S. equity risk premium (difference in returns between the expected equity market return over some horizon and return on U.S. Treasury instrument of matched duration) varies across investment horizons ranging from one month to 30 years. To generate distributions of equity risk premiums for horizons longer than one month, they employ bootstrap simulations. Specifically, for each matched horizon/duration, they randomly draw 100,000 pairs of stock market and U.S. Treasury instrument returns with replacement from a base sample of monthly data, without or with an adjustment for uncertainty in associated equity premiums. They repeat analyses on three value portfolios (Market Value, Big Value and Small Value) and on a Small stock portfolio with no value tilt, defining size and value as follows: (1) big (small) stocks are U.S. listed stocks with market capitalizations above (below) the NYSE median; and, (2) value stocks are U.S. listed stocks with book-to-market ratios above the 70th percentile of those for NYSE stocks. All style portfolios are capitalization-weighted and rebalanced annually at the end of June. Using monthly U.S. stock returns and and U.S. Treasury instrument yields across durations during July 1963 through December 2016 (642 months), they find that: Keep Reading

P/E10 for Country Stock Market Timing?

“Usefulness of P/E10 as Stock Market Return Predictor” investigates whether P/E10 (or Cyclically Adjusted Price-Earnings ratio, CAPE) usefully predicts U.S. stock market returns over the long run. That analysis employs Robert Shiller’s data set, which defines P/E10 as inflation-adjusted S&P Composite Index level divided by average monthly inflation-adjusted 12-month trailing earnings of index companies over the last ten years. Do more timely country P/E10 series work for timing country stock markets and trading pairs of country stock markets? Within each country market, higher (lower) P/E10 suggests overvaluation (undervaluation). Across countries, variation in P/E10 gaps arguably indicates which country markets are relatively overvalued and undervalued. To investigate, we consider:

  • P/E10 time series for Germany, Japan and the U.S. evaluated separately over available sample periods using DAX, Nikkei 225 and S&P 500 indexes, respectively. We also look at separately timing SPDR S&P 500 (SPY) and iShares MSCI Japan (EWJ).
  • Japan P/E10 versus U.S. P/E10 for pair trading of SPY versus EWJ over the available sample period.

Using monthly data for the three P/E10s, the three associated stock market indexes, SPY, EWJ and 3-month U.S. Treasury bill (T-bill) yield as available during December 1981 through December 2017, we find that: Keep Reading

Simple Sector ETF Momentum Strategy Update/Extension

“Simple Sector ETF Momentum Strategy” investigates performances of simple momentum trading strategies for the following nine sector exchange-traded funds (ETF) executed with Standard & Poor’s Depository Receipts (SPDR):

Materials Select Sector SPDR (XLB)
Energy Select Sector SPDR (XLE)
Financial Select Sector SPDR (XLF)
Industrial Select Sector SPDR (XLI)
Technology Select Sector SPDR (XLK)
Consumer Staples Select Sector SPDR (XLP)
Utilities Select Sector SPDR (XLU)
Health Care Select Sector SPDR (XLV)
Consumer Discretionary Select SPDR (XLY)

Here, we update the principal strategy and extend it by adding equally weighted combinations of the top two and top three sector ETFs, along with corresponding robustness tests. We present findings in formats similar to those used for the Simple Asset Class ETF Momentum Strategy and the Simple Asset Class ETF Value Strategy. Using monthly dividend-adjusted closing prices for the sector ETFs and SPDR S&P 500 (SPY) and 3-month U.S. Treasury bill (T-bill) yields since December 1998, and S&P 500 Index levels since September 1998, all through December 2017, we find that: Keep Reading

Stock Anomaly Short Side Costs Manageable?

Is optimal stock anomaly exploitation long-only or long-short? If not long-short, does shorting the market rather than individual stocks work as well as shorting individual stocks? In his November 2017 paper entitled “How Do Short Selling Costs and Restrictions Affect the Profitability of Stock Anomalies?”, Filip Bekjarovski explores effects of short selling costs and constraints on the viability of exploiting seven U.S. stock anomalies: size, value, profitability, investment, momentum, accruals and net issuance. He constructs all anomaly portfolios via market capitalization weighting of stocks sorted into tenths (deciles). He measures portfolio alphas relative to the market excess return (1-factor). He considers long-only (long the top decile), conventional long-short (long the top and short the bottom deciles) and hybrid long-short (long the two highest alpha deciles, tilted toward the highest, while short the market). Anomaly portfolio rebalancing is annual for all except momentum (monthly). He analyzes effects of shorting costs based on an April 2017 proprietary snapshot of institutional stock borrowing fees. He specifically estimates a shorting cost threshold above which investors should switch between long-short and hybrid long-short exploitation methods. Using the stock borrowing fee snapshot and data required to construct seven anomalies from a broad sample of U.S. common stocks during July 1963 through December 2016, he finds that: Keep Reading

Smartest Beta?

What is the smartest way (having the lowest prediction errors) to estimate market beta across stocks for the purpose of portfolio construction? In their November 2017 paper entitled “How to Estimate Beta?”, Fabian Hollstein, Marcel Prokopczuk and Chardin Simen test effects of different return sampling frequencies, forecast adjustments and model combinations on market beta prediction accuracy across the universe of U.S. stocks. Their primary goal is to identify optimal choices. They focus on a beta prediction horizon of six months. They consider past beta estimation (lookback) windows of 1, 3, 6, 12, 24, 36 and 60 months for daily data, 12, 36 and 60 months for monthly data and 120 months for quarterly data. They measure beta prediction accuracy based on average root mean squared error (RMSE) across stocks. Using returns for a broad sample of U.S. stocks during January 1963 through December 2015, they find that: Keep Reading

Exploitability of Deep Value across Asset Classes

Is value investing particularly profitable when the price spread between cheap and expensive assets (the value spread) is extremely large (deep value)? In their November 2017 paper entitled “Deep Value”, Clifford Asness, John Liew, Lasse Pedersen and Ashwin Thapar examine how the performance of value investing changes when the value spread is in its largest fifth (quintile). They consider value spreads for seven asset classes: individual stocks within each of four global regions (U.S., UK, continental Europe and Japan); equity index futures globally; currencies globally; and, bond futures globally. Their measures for value are:

  • Individual stocks – book value-to-market capitalization ratio (B/P).
  • Equity index futures – index-level B/P, aggregated using index weights.
  • Currencies – real exchange rate based on purchasing power parity.
  • Bonds – real bond yield (nominal bond yield minus forecasted inflation).

For each of the seven broad asset classes, they each month rank assets by value. They then for each class form a hedge portfolio that is long (short) the third of assets that are cheapest (most expensive). For stocks and equity indexes, they weight portfolio assets by market capitalization. For currencies and bond futures, they weight equally. To create more deep value episodes, they construct 515 sub-classes from the seven broad asset classes. For asset sub-classes, they use hedge portfolios when there are many assets (272 strategies) and pairs trading when there are few (243 strategies). They conduct both in-sample and out-of-sample deep value tests, the latter buying value when the value spread is within its top inception-to-date quintile and selling value when the value spread reverts to its inception-to-date median. Using data as specified and as available (starting as early as January 1926 for U.S. stocks and as late as January 1988 for continental Europe stocks) through September 2015, they find that:

Keep Reading

Underestimating Left-tail Persistence Among Individual Stocks?

Do investors underestimate the adverse import of large left tails for future stock returns? In their November 2017 paper entitled “Left-Tail Momentum: Limited Attention of Individual Investors and Expected Equity Returns”, Yigit Atilgan, Turan Bali, Ozgur Demirtas and Doruk Gunaydin investigate the relationship between left-tail risk and next-month returns for U.S. and international stocks. They measure left-tail risk at the end of each month via either of:

  • Value-at-risk (VaR) – daily return of a stock at the first (VAR1) or fifth (VAR5) percentile of its returns over the past one year (250 trading days).
  • Expected shortfall – average daily return of a stock for the bottom 1% (ES1) or bottom 5% (ES5) of its returns over the past year (250 trading days).

They then sort stocks into tenths (deciles) based on left-tail risk and examine variation in next-month average gross returns across deciles. Using daily prices and monthly firm characteristics and risk factors for U.S. stocks with month-end prices at least $5 during January 1962 through December 2014, they find that: Keep Reading

Emptying the Equity Factor Zoo?

As described in “Quantifying Snooping Bias in Published Anomalies”, anomalies published in leading journals offer substantial opportunities for exploitation on a gross basis. What profits are left after accounting for portfolio maintenance costs? In their November 2017 paper entitled “Accounting for the Anomaly Zoo: A Trading Cost Perspective”, Andrew Chen and Mihail Velikov examine the combined effects of post-publication return deterioration and portfolio reformation frictions on 135 cross-sectional stock return anomalies published in leading journals. Their proxy for trading frictions is modeled stock-level effective bid-ask spread based on daily returns, representing a lower bound on costs for investors using market orders. Their baseline tests employ hedge portfolios that are long (short) the equally weighted fifth, or quintile, of stocks with the highest (lowest) expected returns for each anomaly. They also consider capitalization weighting, sorts into tenths (deciles) rather than quintiles and portfolio constructions that apply cost-suppression techniques. Using data as specified in published articles for replication of 135 anomaly hedge portfolios, they find that:

Keep Reading

Quantifying Snooping Bias in Published Anomalies

Is data snooping bias a material issue for cross-sectional stock return anomalies published in leading journals? In the September 2017 update of their paper entitled “Publication Bias and the Cross-Section of Stock Returns”, Andrew Chen and Tom Zimmermann: (1) develop an estimator for anomaly data snooping bias based on noisiness of associated returns; (2) apply it to replications of 172 anomalies published in 15 highly selective journals; and, (3) compare results to post-publication anomaly returns to distinguish between in-sample bias and out-of-sample market response to publication. If predictability is due to bias, post-publication returns should be (immediately) poor because pre-publication performance is a statistical figment. If predictability is due to true mispricing, post-publication returns should degrade as investors exploit new anomalies. Their baseline tests employ hedge portfolios that are long (short) the equally weighted fifth, or quintile, of stocks with the highest (lowest) expected returns for each anomaly. Results are gross, ignoring the impact of periodic portfolio reformation frictions. Using data as specified in published articles for replication of 172 anomaly hedge portfolios, they find that:

Keep Reading

Financial Distress, Investor Sentiment and Downgrades as Asset Return Anomaly Drivers

What firm/asset/market conditions signal mispricing? In the November 2017 version of their paper entitled “Bonds, Stocks, and Sources of Mispricing”, Doron Avramov, Tarun Chordia, Gergana Jostova and Alexander Philipov investigate drivers of U.S. corporate stock and bond mispricing based on interactions among asset prices, financial distress of associated firms and investor sentiment. They measure financial distress via Standard & Poor’s long term issuer credit rating downgrades. They measure investor sentiment primarily with the multi-input Baker-Wurgler Sentiment Index, but they also consider the University of Michigan Consumer Sentiment index and the Consumer Confidence Index. They each month measure asset mispricing by:

  1. Ranking firms into tenths (deciles) based on each of 12 anomalies: price momentum, earnings momentum, idiosyncratic volatility, analyst forecast dispersion, asset growth, investments, net operating assets, accruals, gross profitability, return on assets and two measures of net share issuance.
  2. Computing for each firm the equally weighted average of its anomaly rankings, such that a high (low) average ranking indicates the firms’s assets are relatively overpriced (underpriced).

Using monthly firm, stock and bond data for a sample of U.S. firms with sufficient data and investor sentiment during January 1986 through December 2016, they find that: Keep Reading

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