Equity Premium

How big is the return premium associated with stock illiquidity? In his March 2014 paper entitled “The Pricing of the Illiquidity Factor’s Systematic Risk”, Yakov Amihud specifies and measures an illiquidity premium. He defines illiquidity as the average daily ratio of absolute return to dollar volume over the past three months. He specifies the illiquidity premium as the average four-factor (market, size, book-to-market, momentum) alpha on a set of hedge portfolios that are long (short) the stocks that are most (least) illiquid. Specifically, each month he:

• Sorts stocks on illiquidity and deletes the 1% with highest illiquidities as unreliable.
• Ranks surviving stocks on standard deviation of daily returns (volatility) over the last three months into three segments (terciles).
• To avoid confounding volatility and illiquidity, ranks stocks within each volatility tercile into illiquidity quintiles (creating 15 volatility-illiquidity portfolios). This step effectively controls for size, which relates negatively to volatility.
• Skips two months (avoiding reversal/momentum effects) and calculates value-weighted returns for the 15 portfolios during the third month after formation based on market capitalizations at the end of the prior month.
• Calculates the monthly illiquidity return as the average difference in returns between highest and lowest illiquidity portfolios across the three volatility groups.
• Calculates illiquidity alpha by controlling monthly illiquidity returns for market, size, book-to-market and momentum factors over the past 36 months.

Using daily and monthly data for all NYSE and AMEX common stocks and monthly factor returns during 1950 through 2012, he finds that: Keep Reading

Is there a simple compromise between easy-to-implement market weights and more diversified equal sector and equal stock weights? In their December 2013 paper entitled “A Simple Diversified Portfolio Strategy”, Bernd Hanke and Garrett Quigley present a stock portfolio construction approach that blends market weights, equal stock weights and equal sector weights. The objectives of the approach (relative to market weights) are: (1) higher returns (by capturing more of the diversification premium); (2) lower risk (via increased diversification); and, (3) competitive capacity and rebalancing frictions (by limiting the tilt toward small, illiquid stocks). In testing this approach, they form and rebalance annually regional (U.S., European and Japanese) portfolios of relatively liquid stocks. They ignore rebalancing frictions. They define sectors via the broadest Global Industry Classification Standard level (ten sectors). Using total (dividend-reinvested) returns, market capitalizations and sector memberships for a broad sample of relatively liquid stocks during January 1992 through March 2013, they find that: Keep Reading

Do emerging markets still deserve their reputation as a portfolio-diversifying asset class? In the October 2013 version of their paper entitled “Emerging Equity Markets in a Globalizing World”, Geert Bekaert and Campbell Harvey examine whether, given the dramatic globalization of the past 20 years, it still make sense to classify country equity markets as “developed” or “emerging.” Using monthly returns as available for developed and emerging equity markets mostly during January 1988 through August 2013, they conclude that: Keep Reading

Are stocks so attractive over the long run that they crowd bonds and cash out of the optimal portfolio? In their September 2013 paper entitled “Optimal Portfolios for the Long Run”, David Blanchett, Michael Finke and Wade Pfau relate optimal portfolio equity allocation to investment horizon worldwide to determine whether stocks universally exhibit time diversification (whereby mean reversion of returns causes equity risk to decrease as investment horizon lengthens). In calculating optimal equity allocation, they employ a utility function to model how investors feel about the risk of good and bad outcomes (not volatility as measured by standard deviation of returns). They consider different levels of investor risk aversion on a scale of 1 to 20, with 20 extremely risk averse. They measure returns for both overlapping and independent investment intervals of 1 to 20 years. They constrain portfolios to long-only positions in three assets: government bills (cash), government bonds and stock indexes. Using annual real returns to local investors in bills, bonds and stock indexes for 20 countries during 1900 through 2012, they find that: Keep Reading

What initial retirement portfolio withdrawal rate is sustainable over long horizons when, as currently, bond yields are well below and stock market valuations well above historical averages? In their June 2013 paper entitled “Asset Valuations and Safe Portfolio Withdrawal Rates”, David Blanchett, Michael Finke and Wade Pfau apply predictions of bond yields and stock market returns to estimate whether various initial withdrawal rates succeed over different retirement periods. They define initial withdrawal rate as a percentage of portfolio balance at retirement, escalated by inflation each year thereafter. They simulate future bond yield as a linear function of current bond yield with noise, assuming a long-term average of 5% and bounds of 1% and 10%. They simulate future U.S. stock mark return as a linear function of Cyclically Adjusted Price-to-Earnings ratio (CAPE, or P/E10), the ratio of current stock market level to average earnings over the last ten years, assuming P/E10 has a long-term average of 16.4 with noise (implying average annual return 10% with standard deviation 20%). They simulate inflation as a function of bond yield, change in bond yield, P/E10 and change in P/E10 with noise. They assume an annual portfolio management fee of 0.5%. They run 10,000 Monte Carlo simulations for each of many initial withdrawal rate scenarios, with probability of success defined as the percentage of runs not exhausting the portfolio before the end of a specified retirement period. Using initial conditions of a government bond yield of 2% and a P/E10 of 22 as of mid-April 2013, they find that: Keep Reading

Do returns for country stock markets vary systematically with the return volatilities of those markets? In their December 2012 paper entitled “Are Investors Compensated for Bearing Market Volatility in a Country?”, Samuel Liang and John Wei investigate the relationships between monthly returns and both total and idiosyncratic volatilities for country stock markets. They measure total market volatility as the standard deviation of country market daily returns over the past month. They measure idiosyncratic market volatility in two ways: (1) standard deviation of three-factor (global market, size, book-to-market ratio) model monthly country stock market return residuals over the past three years; and, (2) standard deviation of one-factor (global market) model country stock market return residuals over the past month. They then relate monthly country market raw return, global one-factor alpha and global three-factor alpha to prior-month country market volatility. Using monthly returns and characteristics for 21 developed country stock markets (indexes) and the individual stocks within those markets, and contemporaneous global equity market risk factors, during 1975 through 2010, they find that: Keep Reading

How might the capital gains tax rate affect stock market returns? First, a relatively low (high) rate might encourage (discourage) capital investment and stimulate (depress) economic growth, thereby persistently increasing (decreasing) corporate earnings and stock market returns. Second, an increase (decrease) in the rate might immediately drive lower (higher) portfolio allocations to stocks and thereby cause a temporary dip (spike) in stock market returns. To investigate, we relate the annual maximum capital gains tax rate in the U.S. to annual S&P 500 Index returns (capital gains only). When there there is a change in the tax rate during a year, we use the changed value. Using annual data for 1954 through 2012 (partial), we find that: Keep Reading

Are European stock market returns predictable? In their September 2012 paper entitled “Forecasting Returns: New European Evidence”, Steven Jordan, Andrew Vivian and Mark Wohar test the ability of fundamental, macroeconomic and technical variables to predict next-month returns in 14 developed and emerging European country stock markets both in-sample and out-of-sample. They consider four fundamental variables (using logarithms): dividend-price ratio; dividend yield; earnings-price ratio; and, dividend payout ratio (dividend-to-earnings). They consider two macroeconomic variables: the risk-free rate; and, variance of weekly stock market returns over the last 52 weeks. They consider two technical variables: monthly price pressure (ratio of number of rising stocks to number of falling stocks); and, monthly change in volume of all stocks. They test predictive power via simple linear regression, with a rolling historical window of 60 months for out-of-sample tests. They use the historical average as a benchmark forecast. To assess the economic value of forecasts, they examine whether portfolio allocations based on regression outputs beat those based on the historical average. Using monthly data for 14 European/Mediterranean stock market indexes during January 1995 (so out-of-sample tests begin in 2000) through December 2011, they find that: Keep Reading

Does a simple model based on the gap between the stock market earnings yield and an inflation-adjusted Treasury yield usefully predict the equity risk premium (ERP)? In their June 2012 paper entitled “Equities (Still) for the Long Run: A New Look at the Future Equity Premium”, Michael Crook and Brian Nick construct and test a model that compares an estimate of the future stock market earnings yield to real bond return expectations. They use the S&P 500 as a proxy for the stock market. They estimate the future stock market earnings yield as the inverse of Shiller’s cyclically adjust price-earnings ratio (P/E10). They use nominal Treasury yields with duration matched to forecast horizon and adjust this yield with inflation expectations from the Federal Reserve Bank of Cleveland. They apply simple inception-to-date linear regression to relate forecasted ERP to actual ERP. Using monthly S&P 500 Index total returns, Shiller’s P/E10 data, Treasury yields (10-year, 5-year and 2-year notes and bills) and the Cleveland Federal Reserve’s Index of Inflation (limiting the start of the sample period) during 1982 through April 2012, they find that: Keep Reading

Is price-to-earnings ratio cyclically adjusted via a 10-year average (CAPE, or P/E10) a good predictor of future stock market performance? In his October 2012 paper entitled “The Enhanced Risk Premium Factor Model & Expected Returns”, Javier Estrada examines three simple models that generate 10-year annualized stock market expected return (ER) based on P/E10 and the risk-free rate (R_f). Specifically, the three models hypothesize that ER is:

1. The product of a linear function of P/E10 and R_f:  ER = (a + b * P/E10) * R_f
2. The sum of independent linear functions of P/E10 and R_f:  ER = c + d * P/E10 + e * R_f
3. A simple linear function of P/E10:  ER = f + g * P/E10

…where parameters a, b, c, d, e, f and g derive from monthly regressions over a rolling historical window of 120 months. He assesses the performance of the models by comparing forecasted and actual future 10-year annualized stock market returns. He uses the S&P 500 as a proxy for the stock market. Using monthly S&P 500 earnings and 10-year Treasury note yields (as the risk-free rate) for December 1949 through December 2001 and monthly S&P 500 Index total returns from December 1959 through December 2011, he finds that: Keep Reading