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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.

Linear Factor Stock Return Models Misleading?

Does use of alphas from linear factor models to identify anomalies in U.S. stock returns mislead investors? In the February 2013 draft of their paper entitled “Using Maximum Drawdowns to Capture Tail Risk”, Wesley Gray and Jack Vogel investigate maximum drawdown (largest peak-to-trough loss over a time series of compounded returns) as a simple measure of tail risk missed by linear factor models. Specifically, they quantify maximum drawdowns for 11 widely cited U.S. stock return anomalies identified via one-factor (market), three-factor (plus size and book-to-market ratio) and four-factor (plus momentum) linear models. These anomalies are: financial distress; O-score (probability of bankruptcy); net stock issuance; composite stock issuance; total accruals; net operating assets; momentum; gross profitability; asset growth; return on assets; and, investment-to-assets ratio. They calculate alphas for each anomaly by using the specified linear model risk factors to adjust gross monthly returns from a portfolio that is long (short) the value-weighted or equal-weighted tenth of stocks that are “good” (“bad”) according to that anomaly, reforming the portfolio annually or monthly depending on anomaly input frequency. Using monthly returns and firm fundamentals for a broad sample of U.S. stocks, and contemporaneous stock return model factor returns, during July 1963 through December 2012, they find that: Keep Reading

Layers of Low Beta

Do low-beta equity strategies work differently for industries and countries compared to individual stocks? In their January 2013 paper entitled “The Low Risk Anomaly: A Decomposition into Micro and Macro Effects”, Malcolm Baker, Brendan Bradley and Ryan Taliaferro decompose the low-beta anomaly into individual stock (micro) and industry/country (macro) components. To study individual stock versus industry effects, they use a long sample (48 years) of data for U.S. stocks, with betas estimated over lagged 60-month intervals from monthly excess returns (relative to U.S. Treasury bills). To study individual stock versus country effects, they use a shorter sample (about 22.5 years) of data for developed market (including the U.S.) stocks, with betas estimated over lagged 60-week intervals from weekly excess returns. Their principal performance metrics are: (1) gross one-factor (excess market return) alpha; and, (2) the difference in gross alphas between the value-weighted lowest-beta and highest-beta fifths (quintiles) of assets, reformed monthly. They decompose effects for individual stocks and industries/countries via double-sorts. Using monthly returns, SIC codes and market capitalizations for U.S. common stocks during January 1963 through December 2011, and both weekly and monthly returns and market capitalizations for common stocks from 30 developed country stock markets as available during July 1989 through January 2012, they find that: Keep Reading

Country Stock Market Return-Risk Relationship

Do returns for country stock markets vary systematically with the return volatilities of those markets? In their December 2012 paper entitled “Are Investors Compensated for Bearing Market Volatility in a Country?”, Samuel Liang and John Wei investigate the relationships between monthly returns and both total and idiosyncratic volatilities for country stock markets. They measure total market volatility as the standard deviation of country market daily returns over the past month. They measure idiosyncratic market volatility in two ways: (1) standard deviation of three-factor (global market, size, book-to-market ratio) model monthly country stock market return residuals over the past three years; and, (2) standard deviation of one-factor (global market) model country stock market return residuals over the past month. They then relate monthly country market raw return, global one-factor alpha and global three-factor alpha to prior-month country market volatility. Using monthly returns and characteristics for 21 developed country stock markets (indexes) and the individual stocks within those markets, and contemporaneous global equity market risk factors, during 1975 through 2010, they find that: Keep Reading

Compounding Loss from High Beta?

How does volatility interact with market beta? In his 2012 paper entitled “Volatility and Compounding Effects on Beta and Returns”, William Trainor investigates the performance of stocks sorted on market beta overall and during intervals of low and high market volatility. He considers both ideal (theoretical) betas and betas estimated from lagged returns. He defines low (high) market volatility as below (above) the long-term annual average for a value-weighted index constructed from a broad sample of U.S. stocks (15.8%). Using both theoretical derivations and empirical monthly returns for sampled stocks during January 1926 through December 2009, he finds that: Keep Reading

News, VIX and Stock Market Returns

How does aggregate stock news sentiment relate to equity market return and volatility? In his October 2012 paper entitled “Time-Varying Relationship of News Sentiment, Implied Volatility and Stock Returns”, Lee Smales investigates relationships among aggregate unscheduled firm-specific news sentiment, changes in the S&P 500 Implied Volatility Index (VIX) and both contemporaneous and future S&P 500 Index returns. He measures daily aggregate unscheduled firm-specific news sentiment as an average of scores calculated by the RavenPack news analysis tool for articles with headlines specifying S&P 500 stocks published for the first time that day on the Dow Jones news wire and in the Wall Street Journal. Unscheduled means exclusion of scheduled news releases such as earnings and dividend announcements. Using daily aggregated news sentiment for S&P 500 firms and levels of the S&P 500 Index and VIX during January 2000 through December 2010, he finds that: Keep Reading

Option Straddles Around Earnings Announcements

Does market underestimation of stock price uncertainty around earnings announcements support a short-term straddle strategy (call option and put option with matched strike and expiration, profitable with large stock price moves)? In their January 2013 paper entitled “Anticipating Uncertainty: Straddles Around Earnings Announcements”, Yuhang Xing and Xiaoyan Zhang investigate the performance of short-term, near-the-money straddles during intervals around earnings announcements. Short-term means no more than 60 days to expiration. Near-the-money means moneyness in the range 0.95 to 1.05. They focus on a delta-neutral straddle constructed by appropriately weighting the call and put positions at initiation, but they also consider a simple one call-one put alternative. They examine several straddle holding periods starting at the close five, three or one trading day before scheduled earnings announcement date and ending at the close on or one day after earnings announcement date. They calculate option returns based on the mid-point of the daily closing bid and ask as a fair option price (and require it to be at least $0.125). Using daily stock returns and option prices (with data filtered to exclude implausible data), along with contemporaneous quarterly firm fundamentals, during January 1996 through December 2010, they find that: Keep Reading

Exploit Short-term VIX Reversion with VXX?

Does the tendency of stock market volatility measures to persist offer an exploitable short-term reversion to mean? In other words, can traders win on average by speculating that market volatility spikes will soon reverse? To check, we first test for short-term reversion of the implied volatility of the S&P 500 Index (VIX) over its available history. We then test for exploitability of any discovered reversion via the investable iPath S&P 500 VIX Short-Term Futures ETN (VXX), which seeks to replicate the return on short-term VIX futures. Using daily closes of VIX for January 1990 through December 2012 (5,794 trading days) and daily adjusted closes of VXX for February 2009 through December 2012 (987 trading days), we find that: Keep Reading

Asset Allocation Combining Momentum, Volatility, Correlation and Crash Protection

Does combining different portfolio performance enhancement concepts actually improve outcome? In their December 2012 paper entitled “Generalized Momentum and Flexible Asset Allocation (FAA): An Heuristic Approach”, Wouter Keller and Hugo van Putten investigate the effects of combining momentum, volatility and correlation selection criteria to form an equally weighted portfolio of the three best funds from a set of mutual fund proxies for seven asset classes, as follows:

  1. To follow trend, rank funds from highest to lowest lagged total return (relative momentum).
  2. To suppress volatility, rank funds from lowest to highest volatility (standard deviation of daily returns).
  3. To enhance diversification, rank funds from lowest to highest average pairwise correlation of daily returns.
  4. To avoid drawdown, replace with cash any selected fund that has a negative lagged return (intrinsic or absolute momentum). 

Their seven asset class proxies are index mutual funds for U.S. stocks (VTSMX), developed market stocks outside the U.S. and Canada (FDIVX), emerging market stocks (VEIEX), mid-term U.S. Treasuries (VBMFX), short-term U.S. Treasuries (VFISX), commodities (QRAAX) and real estate (VGSIX). They use a default lagged measurement interval of four months for all four selection criteria. Their method of combining rankings for relative momentum, volatility and correlation is simple weighted average (with default weightings of 1, 0.5 and 0.5, respectively). They assume momentum calculations occur at the end of each month, with portfolio changes at the beginning of the next month. Using daily closing prices in U.S. dollars for the seven mutual funds from mid-1997 through mid-December 2012, they find that: Keep Reading

Testing Volatility-Based Allocation with ETFs

A subscriber suggested review of Empiritrage’s Volatility-Based Allocation (VBA). This strategy applies two monthly signals to an equally weighted portfolio of asset class total return proxies to determine whether to be in each proxy or cash, as follows:

  • Step 1: If the 10-day simple moving average (SMA) of the S&P 500 Volatility Index (VIX) is above its 30-day SMA (risk off), substitute the risk-free asset for all asset class proxies.
  • Step 2: If the 10-day simple moving average (SMA) of VIX is below its 30-day SMA (risk on), invest in each asset class proxy for which the respective two-month SMA is above the 12-month SMA, and otherwise in the risk-free asset.

Empiritrage’s simulation of VBA employs equal allocations each month to each of five asset class proxies (U.S. stocks, non-U.S. developed market stocks, emerging market stocks, real estate and long-term U.S. government bonds) or to U.S. Treasury bills (T-bills) as signaled, ignoring trading frictions, during March 1986 through August 2012. They find that VBA “dominates” an allocation based only on individual asset class proxy SMAs. However, indexes do not account for the costs of maintaining tradable assets, and the costs of switching between risk assets and cash may be material. For another perspective, we replicate VBA (with switching frictions) using the following exchange-traded funds (ETF) and estimated return on cash:

SPDR S&P 500 (SPY)
iShares MSCI EAFE Index (EFA)
iShares MSCI Emerging Markets Index (EEM)
SPDR Dow Jones REIT (RWR)
iShares Barclays 20+ Year Treasury Bond (TLT)
3-month Treasury bills (risk-free rate)

Using daily closes for VIX since March 2003 and monthly closes for the ETFs and risk-free rate since April 2003 (limited by inception of EEM), we find that: Keep Reading

A Few Notes on Antifragile

Nassim Taleb introduces his 2012 book, Antifragile, Things That Gain from Disorder, as “…my central work. I’ve had only one master idea, each time taken to the next step, the last step–this book–being more like a big jump. I am reconnected to my ‘practical self,’ my soul of a practitioner, as this is a merger of my entire history as practitioner and ‘volatility specialist’ combined with my intellectual and philosophical interests in randomness and uncertainty… …the relationship of this book to The Black Swan would be as follows:…Antifragile would be the main volume and The Black Swan its backup of sorts, and a theoretical one, perhaps even its junior appendix. Why? Because The Black Swan (and its predecessor, Fooled by Randomness) were written to convince us of a dire situation, and worked hard at it; this one starts from the position that one does not need convincing that (a) Black Swans dominate society and history (and people, because of ex post rationalization, think themselves capable of understanding them); (b) as a consequence, we don’t quite know what’s going on, particularly under severe nonlinearities…” For investors, key points are: Keep Reading

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