# 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

**August 6, 2015** - Short Selling, Volatility Effects

“Shorting Leveraged ETF Pairs” looks at shorting leveraged long/short pairs of exchange-traded funds (ETF) and letting the short positions “melt away” over long holding periods. Findings suggest that the approach may be profitable, with most of the gain coming when market volatility is high. What about more active strategies of continually renewed short positions? To investigate, we consider monthly renewal of short positions in the ProShares Ultra S&P500 (SSO) / ProShares UltraShort S&P500 (SDS) 2X/-2X pair and the ProShares UltraPro S&P500 (UPRO) / ProShares UltraPro Short S&P500 (SPXU) 3X/-3X pair. Using monthly adjusted closes for these ETFs and for the S&P 500 Volatility Index (VIX) from respective inceptions through June 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 16, 2015** - Volatility Effects

“Identifying VXX/XIV Tendencies” finds that the Volatility Risk Premium (VRP), estimated as the difference between the current level of the S&P 500 implied volatility index (VIX) and the annualized standard deviation of S&P 500 Index daily returns over the previous 21 trading days (multiplying by the square root of 250 to annualize), may be a useful predictor of iPath S&P 500 VIX Short-term Futures ETN (VXX) and VelocityShares Daily Inverse VIX Short-term ETN (XIV) returns. Is there a way to exploit this predictive power? To investigate, we compare performance data for:

- Buying and holding XIV.
- Timing XIV to avoid times when VRP is low.
- Timing XIV and VXX to exploit both high and low VRP conditions.

Using daily closes for XIV, VXX, VIX and the S&P 500 Index from XIV inception (end of November 2010) through most of June 2015, *we find that:* Keep Reading

**July 15, 2015** - Commodity Futures, Volatility Effects

“Identifying VXX/XIV Tendencies” finds that S&P 500 implied volatility index (VIX) futures roll return, as measured by the percentage difference in settlement price between the nearest and next nearest VIX futures, may be a useful predictor of iPath S&P 500 VIX Short-term Futures ETN (VXX) and VelocityShares Daily Inverse VIX Short-term ETN (XIV) returns. Is there a way to exploit this predictive power? To investigate, we compare performance data for:

- Buying and holding XIV.
- Timing XIV to avoid times when the roll return is positive.
- Timing XIV and VXX to exploit both negative and positive roll return conditions.

Using daily closing prices for XIV and VXX and daily settlement prices for VIX futures from XIV inception (end of November 2010) through most of June 2015, *we find that:* Keep Reading

**July 14, 2015** - Commodity Futures, Volatility Effects

A subscriber inquired about strategies for trading exchange-traded notes (ETN) constructed from near-term S&P 500 Volatility Index (VIX) futures: iPath S&P 500 VIX Short-Term Futures ETN (VXX) and VelocityShares Daily Inverse VIX Short-Term (XIV), available since 1/30/09 and 11/30/10, respectively. The managers of these securities buy and sell VIX futures daily to maintain a constant maturity of one month (long for VXX and short for XIV), continually rolling partial positions from the nearest term contract to the next nearest. We consider four potential predictors of the price behavior of these securities:

- The level of VIX, in case a high (low) level indicates a future decrease (increase) in VIX that might affect VXX and XIV.
- The change in VIX, in case there is some predictable reversion or momentum for VIX that might affect VXX and XIV.
- The term structure of VIX futures (roll return) underlying VXX and XIV, as measured by the percentage difference in settlement price between the nearest and next nearest VIX futures, indicating a price headwind or tailwind for a fund manager continually rolling from one to the other. Roll return is usually negative (contango), but occasionally positive (backwardation).
- The Volatility Risk Premium (VRP), estimated as the difference between VIX and the annualized standard deviation of daily S&P 500 Index returns over the past 21 trading days (multiplying by the square root of 250 to annualize), in case this difference between expectations and recent experience indicates the direction of future change in VIX.

We identify predictive power by relating daily VXX and XIV returns over the next 21 trading days to daily values of each indicator. Using daily levels of VIX, settlement prices for VIX futures contracts, levels of the S&P 500 Index and split-adjusted prices for VXX and XIV from inceptions of the ETNs through most of June 2015, *we find 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