Volatility Effects

Should investors believe in the superiority of stocks for the long run and bonds for the short run? In his December 2011 paper entitled “Stocks, Bonds, Risk, and the Holding Period: An International Perspective”, Javier Estrada examines how the absolute and relative risks of stocks and bonds evolve as investment horizon grows (time diversification). Considering both annual and cumulative returns and various measures of variability/risk, he focuses on the question of whether stocks become less risky than bonds for long holding periods. Using annual total returns for stocks and bonds in 19 countries during 1900 through 2009, he finds that: More…

Do economic announcements systematically remove uncertainty from financial markets and thus reliably lower implied volatility indexes? In their September 2010 paper entitled “The Impact of Macroeconomic Announcements on Implied Volatilities”, Roland Füss, Ferdinand Mager and Lu Zhao measure the reactions of the Chicago Board Options Exchange Volatility Index (VIX) and the DAX Volatility Index (VDAX) to U.S. and German macroeconomic announcements. They consider announcements of Gross Domestic Product (GDP), the Producer Price Index (PPI) and the Consumer Price Index (CPI). The measurement interval is apparently close-to-close from the day before to the day of announcement. Using monthly/quarterly macroeconomic announcement dates from January 2005 through December 2009 and contemporaneous daily data for VIX and VDAX (60 months), they find that: More…

Is risk avoidance by itself a good tactical asset allocation strategy? In their November 2011 paper entitled “A Risk Based Approach to Tactical Asset Allocation”, Dario Brandolini and Stefano Colucci propose a purely risk-based asset allocation framework designed to buffer effects of volatility clusters. Their critical allocation variable is expected shortfall, estimated each week to adjust the allocation for each asset in the portfolio separately. They test their framework on the following (U.S. dollar-denominated) indexes as proxies for portfolio assets: S&P 500 Index, TOPIX, DAX, MSCI UK, MSCI France, Italy Comit Globale, MSCI Canada, MSCI Emerging Markets, Reuters-Jefferies CRB and Merril Lynch U.S. Treasuries (7-10 years). They assume strategic allocations of 70% to equities (scaled by market according to GDP as measured every five years), 10% to commodities and 20% to U.S. Treasuries. They shift the allocation for each equities/commodities asset partially to a risk-free alternative (U.S. treasuries or cash) to the degree its one-month expected shortfall for the worst 5% of observations falls below a target of -6%. They assume rebalancing occurs simultaneously with signals and impose top-down annual total expense ratios of 2% for active reallocation and 0.6% for a comparable passive but diversified portfolio. Using daily total returns as available (mostly since the late 1980s) and capital gains only before then for the ten indexes during 1974 through 1999 for calibration and 2000 through most of August 2011 for out-of-sample testing, they find that: More…

An array of leveraged exchange-traded funds (ETF) track short-term (daily) changes in commodity and currency exchange indexes. Over longer holding periods, these ETFs tend to veer off track. The cumulative veer can be large. How do leveraged ETFs perform over a multi-year period? What factors contribute to their failure to track underlying indexes? To investigate, we consider a set of 12 ProShares 2X leveraged index ETFs (six matched long-short pairs), involving a commodity index, oil, gold, silver and the euro-dollar and yen-dollar exchange rates, with the start date of 12/9/08 determined by inception of the youngest of these funds (Ultra Yen). Using daily dividend-adjusted prices for these funds over the period 12/9/08 through 11/4/11 (almost three years), we find that: More…

Does the S&P 500 Implied Volatility Index (VIX) exhibit seasonality across calendar months? To check, we calculate the average daily VIX for each month and average the averages by calendar month. For comparison, we also calculate the average daily VIX range (high minus low) and the S&P 500 Index return by month and average by calendar month. Using daily closes of VIX since January 1990, daily VIX highs and lows since October 2003 and monthly closes of the S&P 500 Index since December 1989, all through October 2011, we find that: More…

Does the S&P 500 Implied Volatility Index (VIX) measured at a monthly interval usefully predict stock market returns? To check, we consider four relationships:

1. S&P 500 Depository Receipts (SPY) next-month return versus VIX monthly close.
2. SPY next-month return versus VIX monthly range, a measure of the volatility of implied volatility.
3. SPY next-month return versus product of VIX monthly change and SPY monthly return (to explore implications of VIX and SPY moving in opposite or same directions).
4. SPY next-month return versus monthly difference between SPY implied volatility (IV, measured by VIX) and realized volatility (RV, measured by the standard deviation of monthly SPY returns over the past 12 months), as a crude measure of the volatility risk premium.

For VIX calculations, we “de-annualize” by dividing by the square root of 12. For VIX range and change calculations, we use raw VIX numbers. Using monthly high, lows and closes of VIX and monthly dividend-adjusted closes of SPY from January 1993 through September 2011, we find that: More…

Should investors strategically diversify across widely known equity market anomalies? In the October 2011 version of his paper entitled “Strategic Allocation to Premiums in the Equity Market”, David Blitz investigates whether investors should treat anomaly portfolios (size, value, momentum and low-volatility) as diversifying asset classes and how they can implement such a strategy.  To ensure implementation is practicable, he focuses on long-only, big-cap portfolios. To account for the trading frictions associated with anomaly portfolio maintenance and for time variation of anomaly premiums, he assumes future (expected) market and anomaly premiums lower than historical values, as follows: 3% equity market premium; 0% expected incremental size and low-volatility premiums; and, 1% expected incremental value and momentum premiums. He assumes future volatilities, correlations and market betas as observed in historical data and constrains weights of all anomaly portfolios to a maximum 40%. He considers both equal-weighted and value-weighted individual anomaly portfolios, and both mean-variance optimized and equal-weighted combinations of market and anomaly portfolios. Using portfolios constructed by Kenneth French to quantify equity market/anomaly premiums during July 1963 through December 2009 (consisting of approximately 800 of largest, most liquid U.S. stocks), he finds that: More…

An upward (downward) trend in implied volatilities with option maturity indicates that investors expect volatility to increase (decrease) over time. Do such expectations reliably predict future stock options prices? In his October 2011 paper entitled “Volatility Term Structure and the Cross-Section of Option Returns”, Aurelio Vasquez investigates whether the implied volatility term structure (measured as slope of implied volatilities across at-the-money options with receding expiration dates) predicts future option returns. Specifically, each month he ranks stocks into deciles by volatility term structure slope and then calculates future returns for extreme deciles from five option trading strategies: (1) naked calls; (2)naked puts; (3) straddles; (4) delta-hedged calls; and, (5) delta-hedged puts. He calculates returns relative to the initial prices of the options traded. Using monthly closing bid and ask prices for at-the-money options (moneyness between 0.95 and 1.05) on a broad sample of U.S. stocks, and associated firm characteristics, during January 1996 through June 2007 (260 stocks per month on average), he finds that: More…

Is selling insurance against stock market volatility reliably profitable? In the December 2010 version of his paper entitled “Variance Trading and Market Price of Variance Risk”, Oleg Bondarenko examines payoffs from synthesized variance swap contracts, derived from the difference between realized and contract-specified variances over a given interval, during a 20-years period. He constructs the hypothetical swap contracts from observed prices of S&P 500 Index futures and options on these futures. Using daily prices for these futures and options from January 1990 through December 2009, he finds that: More…

Experts and pundits sometimes cite a very high (low) Chicago Board Options Exchange (CBOE) Volatility Index (VIX), the options-implied volatility of the S&P 500 Index, as an indication of investor panic (complacency) and therefore of a pending U.S. stock market advance (decline). However, a more nuanced conventional wisdom has evolved in recent years that considers both very high VIX and very low VIX as favorable for future stock market returns. Do data support belief in either the original or evolved conventional wisdom? To check, we relate the level of VIX to S&P 500 Index returns over future horizons of 5, 10, 21 and 63 trading days. Using daily and monthly closes for VIX and for the S&P 500 Index over the period January 1990 through (most of) October 2011 (about 262 months), we find that: More…