Volatility Effects

The conventional wisdom is that annualized stock market volatility declines with investment horizon because of the moderating effect of mean reversion in returns. In the May 2009 version of their paper entitled “Are Stocks Really Less Volatile in the Long Run?” Lubos Pastor and Robert Stambaugh challenge this view by focusing on the reasonable expectations of investors dealing with uncertainty rather than data in hindsight. Using annual real (inflation-adjusted) returns and return predictors for the period 1802-2007 (206 years), they conclude that: Keep Reading

Is beta a useful risk management or leveraging tool for investors? Two May 2009 articles, “Beta = 1 Does a Better Job than Calculated Betas” by Pablo Fernandez and Vicente Bermejo and “Betas Used by Professors: A Survey with 2,500 Answers” by Pablo Fernandez, address this question by testing the reliability of beta measurements over time, across calculation methods and across data sources. Focusing on betas for the Dow Jones industrial stocks relative to the S&P 500 index, these articles conclude that: Keep Reading

Does the gap between the (sentiment-driven?) options-implied volatility and the (data-driven) expected volatility of the broad equity market predict future stock returns? In the May 2009 version of his paper entitled “Variance Risk Premia, Asset Predictability Puzzles, and Macroeconomic Uncertainty”, Hao Zhou examines the predictive power of this gap based on several ways to derive expected volatility from realized volatility. Using monthly values of the Chicago Board of Options Exchange Volatility Index (VIX) to calculate implied volatility and high-frequency intraday S&P 500 Index levels to calculate realized volatility over the period 1990-2008, along with contemporaneous data for traditional market predictors, he concludes that: Keep Reading

The intended characteristics of leveraged and inverse exchange-traded funds (ETF) are obvious. Do they have unintended characteristics that may make them unsuitable for some investors? In their April 2009 paper entitled “The Dynamics of Leveraged and Inverse-Exchange Traded Funds”, Minder Cheng and Ananth Madhavan investigate the dynamics, market impacts, unusual features and investor suitability of leveraged (2x and 3x long exposure) and inverse (-1x, -2x and -3x short exposure) ETFs. Using daily returns for many leveraged and inverse ETFs, they conclude that: Keep Reading

How closely do leveraged exchange-traded funds (ETF) track their nominal, short-term design leverages over extended holding periods? In their February 2009 paper entitled “Long Term Performance of Leveraged ETFs”, Lei Lu, Jun Wang and Ge Zhang measure the realized leverages for several Ultra (2x) and UltraShort (-2x) ETFs from the ProShares family. Using daily returns for Diamond Trust Series 1 (DIA), S&P Depository Receipts (SPY), PowerShares QQQ (QQQQ) and iShares Russell 2000 Index (IWM), and for their corresponding 2x and -2x ProShares leveraged ETF pairs, from inception of the leveraged funds through December 15, 2008, they conclude that: Keep Reading

Correlations among asset returns vary over time, introducing risk to the benefits of diversification. Intervals of extraordinarily high correlation amplify marketwide volatility and are disruptive to asset allocation policies. Does the risk of such correlation shocks explain the volatility risk premium associated with marketwide (equity index) options? In the July 2008 version of their paper entitled “The Price of Correlation Risk: Evidence from Equity Options”, Joost Driessen, Pascal Maenhout and Grigory Vilkov examine how correlation shocks affect the returns of options for a broad stock index and of options for its individual component stocks. Using daily returns for the S&P 100 index, its components and associated options over the period 1996-2003, they conclude that: Keep Reading

Why does the volatility of the stock market as implied by the prices of equity index options generally exceed actual (realized) volatility, thereby indicating large returns for sellers of index options? Is the reward of selling such options commensurate with the risk? In the June 2008 version of his paper entitled “The Volatility Premium”, Bjorn Eraker models the volatility risk premium based on the long-run effects of small (normal diffusion) and large (non-normal jumps) shocks to volatility. Using daily returns for the S&P 500 index and daily levels of the CBOE Volatility Index (VIX) over the period 1990-2007, he concludes that: Keep Reading

Does the volatility risk premium, the difference between options-implied volatility and future realized (actual) volatility, vary systematically with the four most widely used equity risk factors (market, size, book-to-market and momentum)? In other words, might the four factors point to pockets of underpriced or overpriced options? In their November 2008 paper entitled “Implied and Realized Volatility in the Cross-Section of Equity Options”, Manuel Ammann, David Skovmand and Michael Verhofen investigate the factor dependence of the volatility premium for U.S. equities. Using a sample of all U.S. equity at-the-money call options 91 days from expiration over the period January 1996 through April 2006, along with associated stock price and firm fundamentals data, they conclude that: Keep Reading

Are stock pickers more likely to out-pick the market by focusing on stocks that resist market efficiency? In their December 2008 paper entitled “When is Stock-Picking Likely to be Successful? Evidence from Mutual Funds”, Ying Duan, Gang Hu and David McLean examine changes in quarterly holdings of mutual funds to measure how the stock-picking performance of fund managers varies with stock idiosyncratic volatility (volatility that indicates risk factors different from those of the overall stock market). Using quarterly mutual fund stock holdings data and monthly stock return data for the period 1980-2003, they conclude that: Keep Reading

Standard deviation is likely the most widely used measure of investment risk, but quadratic dispersion from the mean not be the most intuitive measure. There is evidence that investors confuse standard deviation with mean absolute deviation, and they may further misinterpret standard deviation due to its “normal” association with the Gaussian distribution (inapplicable for some financial data series). Would some other baggage-free measure of risk make more sense to investors? In his November 2008 paper entitled “The Gain-Loss Spread: A New and Intuitive Measure of Risk”, Javier Estrada proposes the gain-loss spread (GLS) as an intuitive and useful measure of investment risk. GLS is the difference between the expected gain (probability of gain times average gain) and the expected loss (probability of loss times average loss). Using monthly return data for 49 country indexes (22 developed and 27 emerging) and 57 industry indexes from initial availability through December 2007, he concludes that: Keep Reading