Volatility Effects

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

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

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

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

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

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

Does adjusting leverage based on lagged strategy volatility protect an industry momentum strategy from crashes? In their September 2016 paper entitled “Risk-Managed Industry Momentum and Momentum Crashes”, Klaus Grobys, Joni Ruotsalainen and Janne Aijo investigate the profitability of risk-managed industry momentum strategies. Their asset universe consists of the 49 Fama-French value-weighted industry portfolios. They focus on a conventional momentum strategy that each month takes equally weighted long positions in past winners (top eight industries) and short positions in past losers (bottom eight industries) based on cumulative returns from 12 months ago to one month ago (12-2). They also analyze 6-2 and 12-7 variations to determine whether more recent or older past returns drive results. For risk management, they forecast next-month momentum strategy volatility based on past strategy volatility calculated based on daily returns over the past one, three or six months. They apply the volatility forecasts to determine the portfolio leverage required to target constant 12% annualized volatility. Using monthly and daily returns for the 49 industries during July 1926 through September 2014, they find that: Keep Reading

Does identification of trends in the CBOE Volatility Index (VIX) via simple moving averages (SMA) support effective timing of the U.S. stock market or VIX futures exchange-traded notes (ETN)? to investigate we consider timing four asset pairs:

1. SPDR S&P 500 (SPY) – ProShares Short S&P500 (SH) since SH inception on 6/21/06.
2. SPY – iShares 1-3 Year Treasury Bond (SHY) since 6/21/06.
3. VelocityShares Daily Inverse VIX ST ETN (XIV) – iPath S&P 500 VIX ST Futures ETN (VXX) since XIV inception on 11/30/10.
4. XIV – SHY since 11/30/10.

SPY and XIV are offensive assets, and SHY and VXX are defensive assets. We consider five individual SMAs to determine VIX trend: 200-day (SMA200); 100-day (SMA100); 50-day (SMA50); 20-day (SMA20); and, 10-day (SMA10). We also consider one “majority rules” combination wherein at least three of the five individual SMAs agree (SMA-Multi). When daily VIX is above (below) its SMA, expected stock market volatility is trending up (down), and we hold the defensive (offensive) asset of the above pairs. We assume a baseline 0.1% for asset switching frictions. Using daily values of the above assets as specified through most of September 2016 (10.3 years for SPY pairs and 5.8 years for XIV pairs), we find that: Keep Reading

Is the term structure of CBOE Volatility Index (VIX) futures useful for timing the underlying stock index? In the February 2012 version of his paper entitled “The Relationship between VIX Futures Term Structure and S&P500 Returns”, Athanasios Fassas relates the VIX futures term structure to both contemporaneous and future S&P500 Index returns. He measures the VIX futures term structure as the slope of a best-fit line for VIX (spot value) and closing prices for available VIX futures as a function of time to maturity. He rolls futures such that no contract in the calculation is within two weeks of maturity. He tests relationships between change in VIX futures term structure and S&P 500 Index return via regressions run at frequencies of one day, one week, two weeks, one month and two months, with the sample winnowed in each case so that measurements do not overlap. Using daily closing prices of spot VIX and the six nearest VIX futures with at least two weeks to maturity during late March 2004 through July 2010, he finds that: Keep Reading

Do investors exploiting common stock return anomalies risk extraordinarily large drawdowns during market crashes? In their May 2016 paper entitled “Can Exposure to Aggregate Tail Risk Explain Size, Book-to-Market, and Idiosyncratic Volatility Anomalies?”, Sofiane Aboura and Eser Arisoy investigate whether portfolios based on the size, book-to-market ratio and idiosyncratic volatility effects bear elevated stock market tail risk. They measure market tail risk as change in VIX Tail Hedge Index (VXTH), which hedges extreme drops in the S&P 500 Index by holding the index and one-month far out-of-the-money (30-delta) call options on the CBOE Volatility Index (VIX). They test sensitivity of size and book-to-market factors to overall risk and tail risk by adding change in VIX (market volatility risk factor) and change in VXTH (market tail risk factor) to the Fama-French three-factor (market, size, book-to-market) model of stock returns. They consider two equal subperiods, one containing the 2008 financial crisis, to check robustness of findings. Using monthly values of VIX and VXTH, factor model returns and U.S. Treasury bill yields during January 2007 through February 2016 (110 months), they find that: Keep Reading