Volatility Effects

Are higher even moments of asset return distributions useful predictors of future returns? In the September 2015 version of her paper entitled “A Low-Risk Strategy based on Higher Moments in Currency Markets”, Claudia Zunft explores an adaptive currency trading strategy that exploits the predictive power of higher even moments of forward currency exchange rate returns. The strategy is each month long (short) the equally weighted fifth, or quintile, of currencies with the lowest (highest) higher even return moments relative to recent past levels. For each currency, she first computes 13 even daily return moments over the last month (versus the U.S. dollar) ranging from 4 to 100 and then subtracts from these moments their respective average monthly values over lookback intervals of 12, 24, 36, 48 and 60 months and inception-to-date. From the resulting 78 combinations of moments and lookback intervals, she each month selects the combination with the highest average excess portfolio return over the last three months. For comparison, she also tests long-short quintile carry trade (high interest rate currencies minus low interest rate currencies) and momentum (high prior-month return currencies minus low prior month currencies) portfolios. Using bid, ask and mid-quote spot and forward contract (maturities up to a year) exchange rates versus the U.S. dollar for 20 of the most liquid developed and emerging market currencies as reliably available during December 1989 through October 2014, she finds that: Keep Reading

Is there a “trick” to good results for risk parity backtests? In their April 2014 brief research paper entitled “The Risks of Risk Parity”, the Brandes Institute examines the sustainability of a critical performance driver for the risk parity asset allocation approach. This approach weights asset classes such that their expected contributions to overall portfolio risk (volatility) are equal, generally by shifting conventional portfolio weights substantially from equities to bonds. Using hypothetical portfolio performance during 1994 through 2013 and bond yield data during 1871 through 2013, they find that: Keep Reading

How can investors best exploit research showing that low-beta (high-beta) stocks tend to outperform (underperform)? In their August 2015 paper entitled “Low-Beta Investment Strategies”, Olaf Kornz and Laura-Chloe Kuntz test 32 “zero-cost” (long-short) strategies designed to exploit the beta anomaly as applied to S&P 500 stocks. The strategies derive from three choices: (1) length of the rolling window used to calculate stock and market index betas (one, three, six or 12 months of daily returns); (2) portfolio holding period (12 months or three months); and, (3) portfolio tilt method (four alternatives). The four portfolio tilt alternatives are:

• Long Low-Beta/Short Index – long the equally weighted 50 stocks with the lowest betas, offset by a short position in the S&P 500 Index. 
• Long-Short Low-High Beta Equal Weight – equal dollar values for a long side of the equally weighted 50 stocks with the lowest betas and a short side of the equally weighted 50 stocks with highest betas, plus a small position in the market to offset any long-short beta mismatch.
• Long-Short Low-High Beta Matched – a long side of the equally weighted 50 stocks with the lowest betas and a short side of the equally weighted 50 stocks with highest betas, in different dollar amounts determined to produce a portfolio beta of one.
• Short High-Beta/Long Index – short the equally weighted 50 stocks with the highest betas, offset by a long position in the S&P 500 Index.

Portfolio tilt alternatives also include positions in 1-month U.S. Treasury bill futures to satisfy an exact zero-cost assumption. The authors form portfolios monthly, such that there are 12 (four) overlapping portfolios with 12-month (3-month) holding periods. They also test the ability of the betas of aggregate high-beta stocks and aggregate low-beta stocks to predict market returns. Using daily returns for the S&P 500 index and its component stocks during September 1988 through October 2014, they find that: Keep Reading

What indicator works best to mitigate stock momentum strategy crashes? In his March 2015 paper entitled “Momentum Crash Management”, Mahdi Heidari compares performances of seven indicators for avoiding conventional stock momentum strategy crashes: (1) prior-month market return; (2) change in prior-month market return: (3) market volatility (standard deviation of 52 weekly returns); (4) dispersion (variance) of daily returns across all stocks; (5) market illiquidity (aggregate impact of trading on price); (6) momentum volatility (standard deviation of momentum strategy returns the past six months); and, (7) change in momentum volatility. The conventional strategy is each month long (short) the value-weighted tenth of stocks with the highest (lowest) returns from 12 months ago to one month ago. For each of the competing indicators, he invests in the conventional momentum strategy (cash) when the indicator is below (within) the top 10% of its values over the past five years. He uses portfolio turnover to compare implementation costs. Using data for a broad sample of relatively liquid U.S. stocks during January 1926 through December 2013, he finds that: Keep Reading

Is implied volatility of implied volatility, interpretable as a measure of changes in investor fear level, a useful indicator of future stock market returns or VIX futures returns? To investigate, we examine relationships between the CBOE VVIX Index, a measure of the expected volatility of the 30-day forward level of the S&P 500 Implied Volatility Index (VIX) derived from prices of VIX options, and future returns for SPDR S&P 500 (SPY)and iPath S&P 500 VIX Short-Term Futures (VXX). Using daily levels of VVIX and daily adjusted closes for SPY and VXX as available during January 2007 (VVIX inception) through mid-August 2015, we find that: Keep Reading

Does the S&P 500 implied volatility index (VIX) exhibit systematic behaviors by day of the week, around turn-of-the-month (TOTM) or around options expiration (OE)? If so, are the behaviors exploitable? Using daily closing levels of VIX since January 1990, daily opening levels of VIX since January 1992 and daily reverse split-adjusted opening and closing levels of iPath S&P 500 VIX Short-Term Futures ETN (VXX) since February 2009, all through early July 2015, we find that: Keep Reading

Has (hypothetical) equity factor investing worked as well in recent years as indicated in past studies? In his July 2015 paper entitled “Factor Investing Revisited”, David Blitz updates his prior study quantifying the performance of allocations to U.S. stocks based on three factor premiums: (1) value (high book-to-market ratio); (2) momentum (high return from 12 months ago to one month ago); and, (3) low-volatility (low standard deviation of total returns over the last 36 months). He considers two additional factor allocations: (4) operating profitability (high return on equity); and, (5) investment (low asset growth). He specifies each factor portfolio as the 30% of U.S. stocks with market capitalizations above the NYSE median that have the highest expected returns, reformed monthly for momentum and low-volatility and annually for the other factors. He considers both equal-weighted and value-weighted portfolios for each factor. He also summarizes recent research on the role of small-capitalization stocks, factor timing, long-only versus long-short portfolios, applicability to international stocks and applicability to other asset classes. Using value, momentum, profitability and investment factor portfolio returns from Kenneth French’s library and low-volatility portfolio returns as constructed from a broad sample of U.S. stocks during July 1963 through December 2014, he finds that: Keep Reading

Can traders use S&P 500 Implied Volatility Index (VIX) options to exploit predictability in behaviors of underlying VIX futures. In his June 2015 paper entitled “Trading the VIX Futures Roll and Volatility Premiums with VIX Options”, David Simon examines VIX option trading strategies that:

1. Buy VIX calls when VIX futures are in backwardation (difference between the front VIX futures and VIX, divided by the number of business days until expiration of the VIX futures, is greater than +0.1 VIX futures point).
2. Buy VIX puts when VIX futures are in contango (difference between the front VIX futures and VIX, divided by the number of business days until expiration of the VIX futures, is less than -0.1 VIX futures point).
3. Buy VIX puts when the VIX options-futures volatility premium (spread between VIX option implied volatility and lagged 10-trading day VIX futures volatility adjusted for number of trading days to expiration) is greater than 10%.

He measures trade returns for a holding period of five trading days, with entry and exit at bid-ask midpoints. An ancillary analysis relevant to strategy profitability looks at hedged returns on VIX options to determine whether they are overpriced: (1) generally; and, (2) for the top 25% of VIX options-futures volatility premiums. Using daily data for VIX options data and for VIX futures (nearest contract with at least 10 trading days to expiration) during January 2007 through March 2014, he finds that: Keep Reading

What volatility weighting scheme best exploits equity return volatility persistence based on net outcome? In the June 2015 version of his paper entitled “Dynamic Volatility Weighting in the Presence of Transaction Costs”, Valeriy Zakamulin examines a volatility weighting strategy with features that allow suppression of rebalancing frictions. The idea behind volatility weighting is to construct a portfolio that targets a specified (benchmark) volatility based on predictability (persistence) of asset volatility. Specifically, he compares three strategies:

1. The theoretically (frictionless and with perfectly predictable asset volatility) optimal strategy, which weights an asset according to the ratio of benchmark variance (square of standard deviation of returns) to predicted asset variance.
2. An optimized modified volatility weighting strategy, which includes two parameters to suppress trading: (1) a tuning parameter to control the aggressiveness of response to a change in predicted asset volatility; and, (2) a no-transaction buffer around targeted asset weight.
3. Conventional volatility targeting, which weights an asset according to the ratio of benchmark volatility (standard deviation of returns) to predicted asset volatility.

For all three strategies, he sets benchmark volatility at an annualized 20%. He forecasts annual asset volatility from an exponentially weighted moving average of daily returns over a rolling window of the past year. He considers daily, 5-day and 21-day volatility forecast revision frequencies. He considers four levels of trading frictions (0.0%, 0.1%, 0.25% and 0.5%) and optimizes modified strategy tuning and buffer parameters for each level. He employs the six Fama-French portfolios formed on size and
book-to-market ratio as test assets. Using daily returns for these six style series and for the aggregate U.S. stock market during January 1989 through December 2014, he finds that: Keep Reading

There are many leveraged exchange-traded funds (ETF) designed to track multiples of short-term (daily) changes in popular indexes. Over longer holding periods, these ETFs tend to veer off track. The cumulative tracking error can be large. How well do leveraged ETFs track benchmarks over a multi-year period? What return metric drives the degree to which they fail to achieve targeted leverage? To investigate, we consider two sets of the oldest leveraged ETFs:

• 34 ProShares +2X and -2X leveraged equity index ETFs (17 matched long-short pairs), with start date 3/14/07 (limited by the youngest fund), which track U.S. broad market and sector indexes.
• 10 ProShares +3X and -3X leveraged equity index ETFs (five matched long-short pairs), with start date 2/11/10, which track U.S. broad stock market indexes only.

We measure actual average daily tracking by comparing the average daily return of each leveraged ETF to the average daily return of a +1X ETF that tracks the same index. We measure longer-term (monthly) tracking by comparing the monthly Sharpe ratio of each leveraged ETF to that of a +1X ETF that tracks the same index. Using daily and monthly adjusted closing prices for the above funds and +1X counterparts through May 2015 and the contemporaneous monthly U.S. Treasury bill yield as the risk-free rate for Sharpe ratio calculations, we find that: Keep Reading