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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.

Country Stock Market Return-Risk Relationship

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

Capital Gains Tax Rate and Stock Market Returns

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

Forecasting Stock Market Returns in Europe

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

Predicting the Equity Risk Premium

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

Future Stock Market Returns and P/E10

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 (Rf). Specifically, the three models hypothesize that ER is:

  1. The product of a linear function of P/E10 and Rf:  ER = (a + b * P/E10) * Rf
  2. The sum of independent linear functions of P/E10 and Rf:  ER = c + d * P/E10 + e * Rf
  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

Benefits of Investing in Emerging Equity Markets

How can positions in emerging equity markets benefit investment portfolios? In their October 2012 paper entitled “How Large are the Benefits of Emerging Market Equities?”, Mitchell Conover, Gerald Jensen and Robert Johnson examine the returns of emerging equity markets with focus on: (1) performance measures that account for return distribution risk and abnormalities; (2) performance by region; and, (3) effects of global economic/monetary environment on returns and diversification power. Using monthly local-currency and dollar-denominated stock index returns and annual GDP estimates for 20 emerging markets as available, along with monthly returns for MSCI developed market MSCI indexes (including MSCI World and MSCI USA) for comparison, during January 1976 through December 2010, they find that: Keep Reading

Risk-adjusted Equity Market Horse Race

Which equity markets worldwide offer the best reward-to-risk ratios? In their October 2012 paper entitled “Risk-Adjusted Performances of World Equity Indices”, Yigit Atilgan and Ozgur Demirtas investigate whether 52 developed and emerging market equity indexes compensate investors equally based on reward-to-risk ratios. They consider three reward-to-risk ratios: (1) conventional Sharpe ratio based on monthly return and standard deviation of daily returns over the past 100 trading days; (2) Sharpe ratio substituting non-parametric value at risk (VAR) (magnitude of minimum daily return over past 100 trading days) for standard deviation of returns; and, (3) Sharpe ratio substituting parametric VAR (accounting for return distribution skewness and kurtosis) for standard deviation of returns. The latter two variations of the Sharpe ratio emphasize downside risk and return distribution non-normalities. Using daily returns and monthly total returns in local currencies for 28 developed and 24 emerging market value-weighted indexes, and associated risk-free rates, during January 1973 through December 2011 (38 years), they find that: Keep Reading

Predicting Stock Market Returns and Volatility

How should investors view the predictability of stock market returns and volatility? In sections 5 and 6 of the July 2012 version of his draft chapter entitled “Equity Market Level”, Andrew Ang examines the predictability of the equity risk premium and equity market volatility. He also addresses the exploitability of any predictive power found. Using both theoretical arguments and empirical tests based on long-run data through December 2011, he concludes that: Keep Reading

Persistent Usefulness of Emerging Markets in Equity Diversification

How does consideration of return distribution tails (not just linear correlations) affect assessment of global equity diversification benefits? In their May 2012 paper entitled “Is the Potential for International Diversification Disappearing? A Dynamic Copula Approach”, Peter Christoffersen, Vihang Errunza, Kris Jacobs and Hugues Langlois examine the evolution of equity market diversification benefits based on a methodology that accommodates non-linearity in the relationship between return streams. They focus on differences between developed and emerging markets. Using weekly returns in U.S. dollar for 16 developed markets during January 1973 through mid-June 2009, 13 emerging markets during late January 1989 through July 2008 and 17 emerging markets during July 1995 through mid-June 2009, they find that: Keep Reading

Risk-based Allocation to Frontier Equity Markets

What is the best way to include the least developed (frontier) stock markets for portfolio diversification? In his December 2011 paper entitled “Frontier Markets: Punching Below their Weight? A Risk Parity Perspective on Asset Allocation”, Jorge Chan-Lau compares the diversification effects of frontier markets within a world equity portfolio based on risk parity and market capitalization weighting approaches. Risk parity equalizes risk contributions across equity classes by assigning the same risk budget to each asset based on co-movement between the asset’s returns and the portfolio returns. The asset allocation comparison assumes five major equity classes: U.S., European including the UK, East Asia and Far East, emerging markets and frontier markets. Co-movement of asset and portfolio returns derive from weekly return measurements over five-year rolling historical windows. Using weekly returns in U.S. dollars for each equity class based on corresponding Morgan Stanley Capital Indexes during June 2002 through November 2011, he finds that: Keep Reading

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