# Volatility Effects

Reward goes with risk, and volatility represents risk. Therefore, volatility means reward; investors/traders get paid for riding roller coasters. Right? These blog entries relate to volatility effects.

**August 28, 2015** - Volatility Effects

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

**July 28, 2015** - Calendar Effects, Volatility Effects

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

**July 22, 2015** - Momentum Investing, Value Premium, Volatility Effects

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

**July 21, 2015** - Commodity Futures, Volatility Effects

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:

- 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).
- 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).
- 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

**July 10, 2015** - Volatility Effects

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:

- 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.
- 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.
- 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

**June 23, 2015** - Volatility Effects

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

**June 17, 2015** - Volatility Effects

How far can a fund manager squeeze turnover while still maintaining an effective low-volatility portfolio? In his June 2015 paper entitled “Low Turnover: a Virtue of Low Volatility”, Pim van Vliet investigates the lower limit of turnover for a low-volatility stock portfolio in two ways. First, he reviews 21 published analyses to relate turnover to volatility reduction while controlling for other factors. Second, he directly relates turnover and volatility reduction for an equally weighted portfolio that: (1) initially selects the 500 of 3,000 liquid global stocks with the lowest weekly volatility over the prior three years; and, (2) each subsequent month rebalances stocks that have at least doubled their baseline portfolio weight and sells stocks when they fall out of the top X% of the volatility ranking, with X varying from 20% (baseline) to 90%. He also models the costs of maintaining low-volatility stock portfolios. Using findings from 13 academic journal articles and working papers and weekly returns for the 3,000 most liquid global stocks during January 1989 through December 2013, *he finds that:* Keep Reading

**June 2, 2015** - Momentum Investing, Size Effect, Value Premium, Volatility Effects

Do factors that predict returns in U.S. stock data also work on global stock markets at the country level? In the May 2015 version of their paper entitled “Do Quantitative Country Selection Strategies Really Work?”, Adam Zaremba and Przemysław Konieczka test 16 country stock market selection strategies based on relative market value, size, momentum, quality and volatility. For each of 16 factors across these categories, they sort country stock markets into fifths (quintiles) and measure the factor premium as return on the highest minus lowest quintiles. They consider equal, capitalization and liquidity (average turnover) weighting schemes within quintiles. They look at complementary large and small market subsamples, and complementary open (easy to invest) and closed market subsamples. Using monthly total returns adjusted for local dividend tax rates in U.S. dollars for 78 existing and discontinued country stock indexes (primarily MSCI) during 1999 through 2014, *they find that:* Keep Reading

**April 28, 2015** - Equity Options, Volatility Effects

Do low-volatility strategies work for all stocks? In their April 2015 paper entitled “Low Risk Anomalies?”, Paul Schneider, Christian Wagner and Josef Zechner examine relationships between low-beta/low-volatility stock anomalies and implied stock return skewness. They compute ex-ante (implied) skewness for each stock via a portfolio of associated options that is long (short) out-of-the-money calls (puts). The more investors are willing to pay for downside risk protection (puts), the more negative this measure becomes. Using stock and option price data for 5,509 U.S. stocks for which options are available during January 1996 through August 2014, *they find that:* Keep Reading

**April 10, 2015** - Momentum Investing, Volatility Effects

Which stock momentum return predictor works best? In his March 2015 paper entitled “Momentum Crash Management”, Mahdi Heidari compares the crash protection effectiveness of seven stock momentum return predictors, categorized into two groups:

- Overall stock market statistics: prior-month market return; change in monthly market return; volatility of market returns (standard deviation of weekly returns for the past 52 weeks); cross-sectional dispersion of daily stock returns for the past month; and, market illiquidity (value-weighted average of the monthly averages of daily price impacts of trading for all stocks).
- Momentum return series statistics: volatility of momentum returns (standard deviation of monthly returns over the past six months); and monthly change in volatility of momentum returns.

He measures momentum conventionally by first ranking all stocks by their returns from 12 months ago to one month ago and then after the skip-month forming a hedge portfolio that is long (short) the value-weighted tenth of stocks with the highest (lowest) past returns. He next tests the power of the above seven variables to predict the resulting monthly momentum return series. Finally, he tests dynamic momentum risk management strategies that execute the conventional momentum strategy (go to cash) when each of the seven predictors is below (above) the 90 percentile of its values over the last five years. Using daily and monthly returns, daily trading volumes and shares outstanding for a broad sample of U.S. common stocks during January 1926 through December 2013, *he finds that:* Keep Reading