Volatility Effects

Is the market beta of a stock stable across measurement frequencies and measurement intervals? In their October 2014 paper entitled “Which Is the Right ‘Market Beta’?: 1,385 US Companies and 147 Betas/Company in a Single Date”, Jose Paulo Carelli, Pablo Fernandez, Isabel Fernandez Acín and Alberto Ortiz present calculations of 147 betas relative to the S&P 500 Index for each of the S&P 1500 stocks with at least five years of return data on March 31, 2014. They calculate different betas based on monthly, weekly or daily returns over past intervals of one to five years. They then look at the dispersion of each stock’s beta and beta ranking across calculation methods (see the chart below for an example). In assessing dispersion, they focus on the difference between maximum and minimum values by stock. Using daily, weekly and monthly returns for 1,385 stocks and the S&P 500 Index during April 2009 through March 2014, they find that: Keep Reading

S&P 500 Index options data imply expected S&P 500 Index volatility (VIX) over the next month. In turn, VIX futures options data imply expected volatility of VIX (VVIX) over the next month. Does VVIX predict stock index option and VIX option returns? In their September 2014 paper entitled “Volatility-of-Volatility Risk”, Darien Huang and Ivan Shaliastovich investigate whether VVIX represents a time-varying risk affecting: (1) S&P 500 Index option returns above and beyond the risk represented by VIX; and (2) VIX futures option returns. They measure risk effects via returns on S&P 500 Index options hedged daily by shorting the S&P 500 Index and VIX futures options hedged daily by shorting VIX futures. Using monthly S&P 500 Index returns, VIX futures returns, VIX, VVIX, S&P 500 Index option prices and VIX option prices during February 2006 through June 2013, they find that: Keep Reading

Is the return on CBOE S&P 500 Volatility Index (VIX) futures predictable? In his preliminary paper entitled “The Expected Return of Fear”, Ing-Haw Cheng investigates whether the relationship between VIX futures prices and VIX level predicts the return on VIX futures. He focuses on monthly returns to a continuously-invested position in the nearest available VIX futures contract. He considers several different explanations for the behavior of VIX futures prices. Using VIX futures daily settlement prices during March 2004 through July 2014 (125 months), he finds that: Keep Reading

Are there times when investors should avoid low-volatility stocks? In their August 2014 paper entitled “Tactical Timing of Low Volatility Equity Strategies”, Sanne De Boer and James Norman investigate which factors predict the performance of low-volatility stocks relative to a capitalization-weighted index globally since 1980. They focus on two concerns: (1) will low-volatility stocks perform poorly when they are relatively expensive compared to the rest of the market; and, (2) will low-volatility stocks, which tend to pay high dividends, underperform when interest rates rise. Their low-volatility portfolio is a capitalization-weighted collection of country sectors processed quarterly in three steps designed to achieve a balance of low risk and sufficient diversification. They do not account for quarterly portfolio reformation frictions in return calculations. Using weekly data for all country sectors included in the MSCI Developed Markets Index during January 1975 through March 2014, they find that: Keep Reading

What is the best way to harvest asset mispricings derived from aggregate overreaction/underreaction by naive investors? In his July 2014 presentation package entitled “Betting On ‘Dumb Volatility’ with ‘Smart Beta'”, Claude Erb examines strategies for exploiting the “dumb volatility” arguably generated by naive investors who buy high and sell low, temporarily driving prices materially above and below fair values. These strategies generally involve periodically rebalancing portfolios to equal weights or some version of fair value weights (smart beta). Using monthly returns for a variety of indexes and funds during December 2004 through June 2014 (since the advent of smart beta research), he finds that: Keep Reading

Are widely used volatility-adjusted investment performance metrics, such as Sharpe ratio, robust to different measurement intervals? In the July 2014 version of their paper entitled “The Divergence of High- and Low-Frequency Estimation: Implications for Performance Measurement”, William Kinlaw, Mark Kritzman and David Turkington examine the sensitivity of such metrics to the length of the return interval used to measure it. They consider hedge fund performance, conventionally estimated as Sharpe ratio calculated from monthly returns and annualized by multiplying by the square root of 12. They also consider mutual fund performance, usually evaluated as excess return divided by excess volatility relative to an appropriate benchmark (information ratio). Finally, they consider Sharpe ratios of risk parity strategies, which periodically rebalance portfolio asset weights according to the inverse of their return standard deviations. Using monthly and longer-interval return data over available sample periods for each case, they find that: Keep Reading

Are the sources of active mutual fund risk mostly common (systematic) or unique (idiosyncratic)? In his July 2014 paper entitled “Components of Portfolio Variance: R2, SelectionShare and TimingShare”, Anders Ekholm decomposes mutual fund return variance (risk) into three sources: (1) passive systematic factor exposure (R-squared); (2) active security selection or stock picking (SelectionShare); and, (3) active systematic factor timing (TimingShare). He demonstrates estimation of these three components based on mutual fund returns (reflecting daily manager actions) rather than holdings (known only via quarterly snapshots). He employs the widely used four-factor (market, size, book-to-market, momentum) model of stock returns to define systematic risk. Using daily returns for a broad sample of actively managed U.S. equity mutual funds and for the four factors during 2000 through 2013, he finds that: Keep Reading

A subscriber flagged an apparently very attractive exchange-traded fund (ETF) momentum-volatility-correlation strategy that, as presented, generates a optimal compound annual growth rate of 45.7% with modest maximum drawdown. The strategy chooses from among the following seven ETFs:

ProShares Ultra S&P500 (SSO)
SPDR EURO STOXX 50 (FEZ)
iShares MSCI Emerging Markets (EEM)
iShares Latin America 40 (ILF)
iShares MSCI Pacific ex-Japan (EPP)
Vanguard Extended Duration Treasuries Index ETF (EDV)
iShares 1-3 Year Treasury Bond (SHY)

The steps in the strategy are, at the end of each month:

1. For the first six of the above ETFs, compute log returns over the last three months and standard deviation (volatility) of log returns over the past six months.
2. Standardize these the monthly sets of past log returns and volatilities based on their respective means and standard deviations.
3. Rank the six ETFs according to the sum of 0.75 times standardized past log return plus 0.25 times past standardized volatility.
4. Buy the top-ranked ETF for the next month.
5. However, if at the end of any month, the correlation of SSO and EDV monthly log returns over the past four months is greater than 0.75, instead buy SHY for the next month.

The developer describes this strategy as an adaptation of someone else’s strategy and notes that he has tested a number of systems. How material might the implied secondary and primary data snooping bias be in the performance of this system? To investigate, we examine the fragility of performance statistics to variation of each strategy parameter separately. As presented, the author substitutes other ETFs for the two with the shortest histories to extend the test period backward in time. We use only price histories as available for the specified ETFs, limited by EDV with inception January 2008. Using monthly adjusted closing prices for the above seven ETFs and for SPDR S&P 500 (SPY) during January 2008 through February 2014 (74 months), we find that: Keep Reading

Under what conditions is periodic rebalancing a successful “volatility harvesting” strategy? In his February 2014 paper entitled “Disentangling Rebalancing Return”, Winfried Hallerbach analyzes the return from periodic portfolio rebalancing by decomposing its effects into a volatility return and a dispersion discount. He defines:

• Rebalancing return as the difference in (geometric) growth rates between periodically rebalanced and buy-and-hold portfolios.
• Volatility return as the difference in growth rates between a periodically rebalanced portfolio and the equally weighted average growth rate of its component assets.
• Dispersion discount as the difference in growth rates between a buy-and-hold portfolio and the equally weighted average growth rate of portfolio assets.

Based on mathematical derivations with some approximations, he concludes that: Keep Reading

What drives the performance of risk parity asset allocation, and on what asset classes does it therefore work best? In their January 2014 paper entitled “Inter-Temporal Risk Parity: A Constant Volatility Framework for Equities and Other Asset Classes”, Romain Perchet, Raul Leote de Carvalho, Thomas Heckel and Pierre Moulin employ simulations and backtests to explore the conditions/asset classes for which a periodically rebalanced risk parity asset allocation enhances portfolio performance. Specifically, they examine contemporaneous interactions between risk parity performance and each of return-volatility relationship, return volatility clustering and fatness of return distribution tails (kurtosis). They then compare different ways of predicting volatility for risk parity implementation. Finally, they backtest volatility prediction/risk parity allocation effectiveness separately for stock, commodity, high-yield corporate bond, investment-grade corporate bond and government bond indexes (each versus the risk-free asset). They optimize volatility prediction model parameters annually based on an expanding window of historical data. They forecast volatility based on one-year rolling historical daily return data. Using daily total returns in U.S. dollars for the S&P 500 Index during 1980 through 2012 and for the Russell 1000, MSCI Emerging Market, S&P Commodities, U.S. High Yield Bond, U.S. Corporate Investment Grade Bond and U.S. 10-Year Government Bond indexes and the 3-month U.S. Dollar LIBOR rate (as the risk-free rate) during January 1988 through December 2012, they find that: Keep Reading