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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.

Simple, Practical Test of VRP as IEF Return Predictor

“Equity Market and Treasuries Variance Risk Premiums as Return Predictors” reports a finding, among others, that the variance risk premium for 10-year U.S. Treasury notes (T-note) predicts near-term returns for those notes (as manifested via futures). However, the methods used to calculate the variance risk premium are complex. Is there a simple way to exploit the predictive power found? To investigate, we test whether a simple measure of the volatility risk premium (VRP) for T-notes predicts returns for the iShares 7-10 Year Treasury Bond (IEF) exchange-traded fund. Specifically we:

  • Calculate daily realized volatility of IEF as the standard deviation of daily total returns over the past 21 trading days, multiplied by the square root of 252 to annualize.
  • Use daily closes of CBOE/CBOT 10-year U.S. Treasury Note Volatility Index (TYVIX) as annualized implied volatility.
  • Calculate the daily T-note VRP as TYVIX minus IEF realized volatility.

VRP here differs from that in the referenced research in three ways: (1) it is a volatility premium rather than a variance premium based on standard deviation rather than the square of standard deviation; (2) it is implied volatility minus expected realized volatility, rather than the reverse, and so should be mostly positive; and, (3) estimation of expected realized volatility is much simpler. When TYVIX has daily closes on non-market days, we ignore those closes. When TYVIX does not have daily closes on market days, we reuse the most recent value of TYVIX. These exceptions are rare. Using daily IEF dividend-adjusted prices since December 2002 and daily closes of TYVIX since January 2003 (earliest available), both through January 2017, we find that: Keep Reading

Equity Market and Treasuries Variance Risk Premiums as Return Predictors

Do bonds, like equity markets, offer a variance risk premium (VRP)? If so, does the bond VRP predict bond returns? In their January 2017 paper entitled “Variance Risk Premia on Stocks and Bonds”, Philippe Mueller, Petar Sabtchevsky, Andrea Vedolin and Paul Whelan examine and compare the equity VRP (EVRP) via the S&P 500 Index and U.S. Treasuries VRP (TVRP) via 5-year, 10-year and 30-year U.S. Treasuries. They specify VRP generally as the difference between the variance indicated by past values of variance (realized) and that indicated by current option prices (implied). Their VRP calculation involves:

  • To forecast daily realized variances at a one-month horizon, they first calculate high-frequency returns from intra-day price data of rolling futures series for each of 5-year, 10-year and 30-year Treasury notes and bonds and for the S&P 500 Index. They then apply a fairly complex regression model that manipulates squared inception-to-date returns (at least one year) and accounts for the effect of return jumps. 
  • To calculate daily implied variances for Treasuries at a one-month horizon, they employ end-of-day prices on cross-sections of options on Treasury futures. For the S&P 500 Index, they use the square of VIX.
  • To calculate daily EVRP and TVRPs with one-month horizons, subtract respective implied variances from forecasted realized variances.

When relating VRPs to future returns for both Treasuries and the S&P 500 Index, they calculate returns from fully collateralized futures positions. Using the specified futures, index and options data during July 1990 through December 2014, they find that: Keep Reading

Suppressing Unrelated Risks from Stock Factor Portfolios

Does suppressing unrelated risks from stock factor portfolios improve performance? In their January 2017 paper entitled “Diversify and Purify Factor Premiums in Equity Markets”, Raul Leote de Carvalho, Lu Xiao, François Soupé and Patrick Dugnolle investigate how to improve the capture of four types of stock factor premiums: value (12 measures); quality (16 measures); low-risk (two measures); and, momentum (10 measures). They standardize the different factor measurement scales based on respective medians and standard deviations, and they discard outliers. Their baseline factors portfolios employ constant leverage (CL) by each month taking 100% long (100% short) positions in stocks with factor values associated with the highest (lowest) expected returns. They strip unrelated risks from baseline portfolios by:

  • SN – imposing sector neutrality by segregating stocks into 10 sectors before ranking them for assignment to long and short sides of the factor portfolio. 
  • CV – replacing constant leverage by each month weighting each stock in the portfolio to target a specified volatility based on its actual volatility over the past three years.
  • HB – hedging the market beta of the portfolio each month based on market betas of individual stocks calculated over the past three years by taking positions in the capitalization-weighted market portfolio and cash.
  • HS – hedging the size beta of the portfolio each month based on size betas of individual stocks calculated over the past three years by taking positions in the equal-weighted market portfolio and the capitalization-weighted market portfolio.

They examine effects of combining measures within factor types, combining types of factors and excluding short sides of factor portfolios. They also look at U.S., Europe and Japan separately. Their portfolio performance metric is the information ratio, annualized average return divided by annualized standard deviation of returns. Using data for stocks in the MSCI World Index since January 1997, in the S&P 500 Index since January 1990, in the STOXX Europe 600 Index since January 1992 and in the Japan Topix 500 Index since August 1993, all through November 2016, they find that: Keep Reading

Intraday and Intraweek VIX Behaviors

Does the S&P 500 implied volatility index (VIX) exhibit reliable intraday and day-of-week patterns? In their December 2016 paper entitled “The Intraday Properties of the VIX and the VXO”, Adrian Fernandez-Perez, Bart Frijns, Alireza Tourani-Rad and Robert Webb investigate daily and intraday properties of VIX and its predecessor, the S&P 100 implied volatility index (VXO). VIX maintains constant 30-day maturity at a one-minute frequency, while VXO maintains a constant 30-day maturity on a daily basis. Using one-minute levels of VIX and VXO from 9:30 until 16:15 EST and of the S&P 500 Index from 9:30 to 16:00 EST during September 22, 2003 (introduction of VIX) through December 31, 2013, they find that: Keep Reading

How Much to Risk?

How should investors balance expected return and expected risk in allocating between risky and risk-free assets? In their short December 2016 paper entitled “Optimal Trade Sizing in a Game with Favourable Odds: The Stock Market”, Victor Haghani and Andrew Morton apply a simple rule of thumb related to mean-variance optimization to estimate the optimal allocation to risky assets. They also note several implications of this rule. Based on assumptions about investor motivation and straightforward mathematics, they conclude that: Keep Reading

Market Volatility as Crisis Predictor

Do equity market volatility behaviors predict financial crises? In their October 2016 paper entitled “Learning from History: Volatility and Financial Crises”, Jon Danielsson, Marcela Valenzuela and Ilknur Zer investigate linkages among  stock market volatility, risk-taking and financial market crises over the very long run. Their volatility measurement methodology is:

  1. Measure volatility annually as standard deviation of 12 monthly returns (July through June).
  2. Determine the volatility trend via an annually iterated Hodrick-Prescott filter applied to historical volatility data (focusing on smoothing factor 5000, but considering other values).
  3. Calculate relatively high and low volatility as deviations of volatility above and below trend, respectively (see the chart below).

Their stock market return sample covers 60 countries and spans 211 years, with an average 62 years per country (with U.S. and UK the longest subsamples). They discard a few extreme observations and adjust returns for inflation using local consumer prices indexes. Their crisis measurement is a binary indicator of whether one of 262 identified banking crises occurs in a given year and country. They focus on five-year regressions to assess volatility-crisis relationships, but consider other intervals. They consider Gross Domestic Product per capita, inflation, change in government debt and institutional quality (political freedom) as control variables. Using monthly data as specified and available during 1800 through 2010, they find that: Keep Reading

VIX and VXX Behaviors Around Holidays

Does the S&P 500 implied volatility index (VIX) exhibit predictable behaviors around holidays? If so, is the predictability exploitable? To check, we look at percentage changes in VIX from three trading days before to three trading days after the following annual holidays: New Year’s Day, Super Bowl, Good Friday, Memorial Day, 4th of July, Labor Day, Thanksgiving and Christmas. To test exploitability, we employ iPath S&P 500 VIX ST Futures ETN (VXX), exchange-traded notes that hold short-term VIX futures. Using daily closes of VIX and VXX from their respective inceptions (January 1990 and February 2009) through November 2016 (214 and 62 holidays), we find that: Keep Reading

Betting Against Beta with Risk Management

Does a simple volatility-based risk management approach substantially enhance performance of a Betting-Against-Beta (BAB) strategy (long stocks with low market beta and short stocks with high market beta)? In their November 2016 paper entitled “Managing the Risk of the ‘Betting-Against-Beta’ Anomaly: Does It Pay to Bet Against Beta?”, Pedro Barroso and Paulo Maio examine a BAB risk management strategy that each month weights assets by a volatility target (12% annualized) divided by daily realized strategy volatility over the previous 21 trading days. For comparison, they apply this risk management approach also to other factor strategies based on their respective daily returns. Using daily and monthly BAB returns from AQR and momentum and factor model returns from Kenneth French covering a broad sample of U.S. stocks during July 1963 through December 2015, they find that: Keep Reading

Testing Lagged Volatility-Size Effect Relationship Robustness with ETFs

Is the finding in “Expected Stock Market Volatility and the Size Effect” that the size effect concentrates in intervals after months of very high stock market volatility robustly evident from liquid exchange-traded funds (ETF)? To investigate, we define the size effect as the difference in returns between iShares Russell 2000 (IWM) and iShares Russell 1000 (IWB) at a monthly frequency and use the CBOE Volatility Index (VIX) as expected market volatility. To check robustness of cited research, we consider:

  • Thresholds for high VIX ranging from above average to two standard deviations above average.
  • Out-of-sample identification of high monthly VIX values using either inception-to-date (ITD) or rolling 120-month (Rolling120) historical windows of monthly VIX closes.
  • Lags between VIX measurements and size effect returns ranging from zero to two months.

We focus on differences in average monthly IWM-IWB returns, standard deviations of IWM-IWB monthly returns and IWM-IWB monthly reward-to-risk ratio (average return divided by standard deviation of returns) for months after high versus not-high values of VIX. Using monthly levels of VIX during January 1990 (inception) through September 2016 and monthly total returns for IWM and IWB during May 2000 (inception) through September 2016, we find that: Keep Reading

Expected Stock Market Volatility and the Size Effect

Is the size effect (small stocks tend to outperform large stocks) related to level of market risk as indicated by expected stock market volatility? In their September 2016 paper entitled “High Risk Episodes and the Equity Size Premium”, Naresh Bansal, Robert Connolly and Chris Stivers investigate the relationship between the size effect and two measures of expected stock market volatility: (1) during 1960 through 1989, realized volatility (RV) calculated from daily stock market returns over the prior 66 trading days; and, (2) during 1990 through 2014, the CBOE Volatility Index (VIX). To measure the size effect, they focus on Fama-French SMB factor portfolio monthly returns (return of the tenth, or decile, of stocks with the smallest market capitalizations minus the return of the decile of stocks with the largest market capitalizations). They also study return differences between each of the next three smallest deciles and the return of the largest decile. They consider both value weighting and equal weighting of stock deciles. They insert a skip-month between the volatility measurement interval and size effect return measurement intervals of 1, 3, 6 or 12 months. Using the specified monthly and daily data, they find that: Keep Reading

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