Volatility Effects

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: Keep Reading

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: Keep Reading

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: Keep Reading

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: Keep Reading

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: Keep Reading

Studies of leveraged exchange-traded funds (ETF), such as those summarized in “The Unintended Characteristics of Leveraged and Inverse ETFs” and “The Performance of Leveraged ETFs over Extended Holding Periods”, find that the frequent rebalancing actions necessary to maintain targeted leverage substantially affect long-term performance. A reader observed:

“I’ve read so many articles about how the leveraged ETFs are screwy, and they chew up both sides of the market due to their rebalancing, etc. So I’ve been shorting equal amounts of the long and short double ETFs. I’m short the QID and the QLD, short the TWM and UWM, short the UGL and the GLL, and short the DIG and DUG. I figure, if they are bad longs, they must be good shorts. My thinking is that in a STRONGLY trending market, the position may lose some ground, at least temporarily. But in a weakly trending market, or sideways, both will decay nicely. When I look back on the ones that are a few years old, they just melt away (one side more than the other).”

Does this reverse thinking work? To check, we examine the inception-to-date performance of paired short positions for Ultra S&P500 ProShares (SSO) / UltraShort S&P500 ProShares (SDS) and Ultra QQQ ProShares (QLD) / UltraShort QQQ ProShares (QID). Using daily adjusted closes for these 2X and -2X ETFs for the period 7/13/06 (the first date prices for all four are available) through 10/13/11 (about 63 months), we find that: Keep Reading

Can the forward-looking aspect of the S&P 500 Volatility Index (VIX) amplify technical analysis? In their September 2011 paper entitled “Using VIX Data to Enhance Technical Trading Signals”, James Kozyra and Camillo Lento apply nine simple technical trading rules (three each moving average crossovers, filters and trading range breakouts) to VIX to generate daily trading signals for the S&P 500 Index, the NASDAQ index and the Dow Jones Industrial Average. They reason that a relatively high (low) level of VIX indicates strong (weak) future stock index returns, so technical rules that separate daily levels of VIX into high and low regimes should aid trading. They compare results for VIX rule signals to those for signals generated by applying the rules to the indexes themselves. In all 27 cases (nine rules times three indexes), rule implementation assumes going long (short) an index on the day after buy (sell) signals. Estimated trading friction accounts for the bid-ask spread and a broker fee at the time of each trade. Using daily closes for VIX and the three indexes for January 1999 through July 2009, they find that: Keep Reading

In their September 2011 paper entitled “The Impact of Asymmetry on Expected Stock Returns: An Investigation of Alternative Risk Measures”. Stephen Huffman and Cliff Moll investigate the relation between various measures of lagged total, downside and upside risk and future daily stock returns. Specifically, they consider the following 12 alternative risk measured over rolling intervals of the past 100 trading days: standard deviation, semi-variance, semi-deviation, skewness, kurtosis, downside risk below zero, upside risk above zero, mean absolute deviation and lower partial moments for four investor types (extremely risk averse, risk averse, risk neutral and risk seeking). Using daily returns and quarterly market valuation and firm accounting data for a broad sample of U.S. stocks over the period 1988 through 2009, they find that: Keep Reading

What happens to the S&P 500 Implied Volatility Index (VIX) after days when it changes dramatically? To ensure that a trader could have identified the days selected in real time and to accommodate volatility regime changes, we define a dramatic change as an advance or decline of at least four standard deviations of the daily VIX changes over the preceding four years (1,008 trading days). Using daily closes for VIX from January 2, 1990 through August 10, 2011, we find that: Keep Reading

“Overview of Financial Market Regime Change” states that researchers often use return volatility to discriminate financial market regimes (intervals of persistent behavior). Investors often use some variation of simple moving average (SMA) crossovers to determine market regime. Do these perspectives intersect? To investigate, we examine realized volatility (standard deviation of daily returns) and frequency of days with extreme returns during bull and bear regimes as defined by the S&P 500 Index being above or below its 200-day SMA. We define extreme days based on standard deviations from the mean daily return over the prior 1000 trading days (about four years). These definitions avoid look-ahead bias. Using daily S&P 500 Index closes (excluding dividends) for January 1950 through July 2011 (with the first four years used only to set initial thresholds for extreme days), we find that: Keep Reading