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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.

Bear Market Expectation Risk Factor

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

Critiquing the Five-factor Model of Stock Returns

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

Oil Futures Term Structure and Future Stock Market Returns

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

Equity+Currency Factors and Global Equity Fund Performance

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

Returns for Stocks Entering and Leaving Factor Indexes

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

The Cross-section of Inherent Stock Price Frictions

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

High Prices Mean Good Stocks?

Are stocks with high prices or low prices inherently better deals? In their October 2016 paper entitled “Nominal Stock Price Investing”, Ulrich Hammerich, Christian Fieberg and Thorsten Poddig examine the relationship between stock price and future stock performance in the German equity market. Specifically, they each month sort stocks by price and measure the difference in average total returns between the equally weighted tenth (decile) of stocks with the highest prices and the equally weighted decile with the lowest prices. Using monthly prices and total returns for a broad set of German stocks from the end of January 1990 through December 2013, they find that: Keep Reading

Enterprise Multiple Interactions with Other Stock Valuation Metrics

Enterprise multiple (EM) is the ratio of enterprise value (EV) to earnings before interest, taxes, depreciation and amortization (EBITDA), with EV market value of equity plus total debt and preferred stock value minus cash and short-term investments. What happens when EM disagrees with other stock valuation metrics? In their October 2016 paper entitled “Why Do Enterprise Multiples Predict Expected Stock Returns?”, Steve Crawford, Wesley Gray and Jack Vogel investigate how EM interacts with other stock valuation metrics. They first sort stocks into fifths (quintiles) ranked by EM and then re-sort EM quintiles into sub-quintiles based on each of 12 fundamental valuation metrics: (1) financial distress; (2) O-Score (probability of bankruptcy); (3) net stock issuance; (4) composite equity issuance; (5) total accruals; (6) net operating assets; (7) momentum; (8) gross profitability; (9) asset growth; (10) return on assets; (11) investment-to-assets ratio; and, (12) a combination metric derived by first ranking stocks based on each of the 11 individual metrics and then averaging ranks for each stock. There are thus 25 double-sort portfolios for each valuation metric. They then focus on two value-weighted hedge portfolios that concentrate disagreement/agreement between EM and other valuation metrics:

  • High-mispricing – long (short) stocks with low (high) EMs and high (low) fundamental valuations, representing extreme disagreement.
  • Low-mispricing – long (short) stocks with low (high) EMs and low (high) fundamental valuations, representing extreme agreement.

Portfolio reformations are at mid-year annually for all variables except momentum, for which reformations are monthly. They measure portfolio performance based on monthly return, market alpha, three-factor (market, size, book-to-market) alpha and four-factor (adding momentum) alpha. Using prices and firm fundamentals required to construct specified metrics for a broad sample of U.S. common stocks during July 1972 through December 2015, they find that: Keep Reading

Exploitable VIX Trends?

Does identification of trends in the CBOE Volatility Index (VIX) via simple moving averages (SMA) support effective timing of the U.S. stock market or VIX futures exchange-traded notes (ETN)? to investigate we consider timing four asset pairs:

  1. SPDR S&P 500 (SPY)ProShares Short S&P500 (SH) since SH inception on 6/21/06.
  2. SPY – iShares 1-3 Year Treasury Bond (SHY) since 6/21/06.
  3. VelocityShares Daily Inverse VIX ST ETN (XIV)iPath S&P 500 VIX ST Futures ETN (VXX) since XIV inception on 11/30/10.
  4. XIV – SHY since 11/30/10.

SPY and XIV are offensive assets, and SHY and VXX are defensive assets. We consider five individual SMAs to determine VIX trend: 200-day (SMA200); 100-day (SMA100); 50-day (SMA50); 20-day (SMA20); and, 10-day (SMA10). We also consider one “majority rules” combination wherein at least three of the five individual SMAs agree (SMA-Multi). When daily VIX is above (below) its SMA, expected stock market volatility is trending up (down), and we hold the defensive (offensive) asset of the above pairs. We assume a baseline 0.1% for asset switching frictions. Using daily values of the above assets as specified through most of September 2016 (10.3 years for SPY pairs and 5.8 years for XIV pairs), we find that: Keep Reading

Generalized Price-Dividend Ratio

Is there a straightforward way to incorporate current business/economic climate into equity market valuation ratios? In their September 2016 paper entitled “Generalized Financial Ratios to Predict the Monthly Equity Market Premium”, Andres Algaba and Kris Boudt introduce and test a generalized price-dividend ratio (GDPR) that takes into account recent business and discount rate conditions, as follows:


Where P is equity market (index) price, D is aggregate market dividend, the beta exponent for D accounts for changes in the kinds of companies dominating the market (those that retain versus those that pay out earnings) and the lambda multiplier for D accounts for variation in the discount rate used to evaluate dividend streams. The t subscripts indicate that all vary over time. They estimate beta and lambda via regressions using rolling historical windows of five or nine years (representing two views of business cycle length). They test the ability of GPDR to predict the U.S. equity market premium (ERP) using inception-to-date forecasting regressions, without and with a rule that switches to the historical average ERP when recent (last three and six months) GPDR predictions are poor. They use the historical average ERP as a benchmark. They employ the first nine years of data to estimate initial GPDR. They then use the next 20 years (1956-1975) for the first predictive regression, leaving 39 years for out-of-sample monthly ERP predictions (1976-2014). To assess the economic value of using GPDR to predict ERP, they consider a risk-averse, mean-variance optimizing investor who each month reallocates across equities and U.S. Treasury bills (T-bills). This investor employs a 5-year rolling window to estimate volatility, does not sell short and limits leverage to 1.5 with one-way trading friction 0.1%. Using monthly levels of the S&P 500 Index, monthly 12-month historical dividends and monthly 3-month T-bill yield as the risk-free rate during January 1947 through December 2014, they find that: Keep Reading

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