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.

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Multi-year Performance of Leveraged ETFs

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

Achieving a Low-volatility Stock Portfolio Efficiently

How far can a fund manager squeeze turnover while still maintaining an effective low-volatility portfolio? In his June 2015 paper entitled “Low Turnover: a Virtue of Low Volatility”, Pim van Vliet investigates the lower limit of turnover for a low-volatility stock portfolio in two ways. First, he reviews 21 published analyses to relate turnover to volatility reduction while controlling for other factors. Second, he directly relates turnover and volatility reduction for an equally weighted portfolio that: (1) initially selects the 500 of 3,000 liquid global stocks with the lowest weekly volatility over the prior three years; and, (2) each subsequent month rebalances stocks that have at least doubled their baseline portfolio weight and sells stocks when they fall out of the top X% of the volatility ranking, with X varying from 20% (baseline) to 90%. He also models the costs of maintaining low-volatility stock portfolios. Using findings from 13 academic journal articles and working papers and weekly returns for the 3,000 most liquid global stocks during January 1989 through December 2013, he finds that: Keep Reading

Country Stock Market Factor Strategies

Do factors that predict returns in U.S. stock data also work on global stock markets at the country level? In the May 2015 version of their paper entitled “Do Quantitative Country Selection Strategies Really Work?”, Adam Zaremba and Przemysław Konieczka test 16 country stock market selection strategies based on relative market value, size, momentum, quality and volatility. For each of 16 factors across these categories, they sort country stock markets into fifths (quintiles) and measure the factor premium as return on the highest minus lowest quintiles. They consider equal, capitalization and liquidity (average turnover) weighting schemes within quintiles. They look at complementary large and small market subsamples, and complementary open (easy to invest) and closed market subsamples. Using monthly total returns adjusted for local dividend tax rates in U.S. dollars for 78 existing and discontinued country stock indexes (primarily MSCI) during 1999 through 2014, they find that: Keep Reading

Betting Against High Downside Risk?

Do low-volatility strategies work for all stocks? In their April 2015 paper entitled “Low Risk Anomalies?”, Paul Schneider, Christian Wagner and Josef Zechner examine relationships between low-beta/low-volatility stock anomalies and implied stock return skewness. They compute ex-ante (implied) skewness for each stock via a portfolio of associated options that is long (short) out-of-the-money calls (puts). The more investors are willing to pay for downside risk protection (puts), the more negative this measure becomes. Using stock and option price data for 5,509 U.S. stocks for which options are available during January 1996 through August 2014, they find that: Keep Reading

Momentum Risk Management Strategies

Which stock momentum return predictor works best? In his March 2015 paper entitled “Momentum Crash Management”, Mahdi Heidari compares the crash protection effectiveness of seven stock momentum return predictors, categorized into two groups: 

  1. Overall stock market statistics: prior-month market return; change in monthly market return; volatility of market returns (standard deviation of weekly returns for the past 52 weeks); cross-sectional dispersion of daily stock returns for the past month; and, market illiquidity (value-weighted average of the monthly averages of daily price impacts of trading for all stocks).
  2. Momentum return series statistics: volatility of momentum returns (standard deviation of monthly returns over the past six months); and monthly change in volatility of momentum returns.

He measures momentum conventionally by first ranking all stocks by their returns from 12 months ago to one month ago and then after the skip-month forming a hedge portfolio that is long (short) the value-weighted tenth of stocks with the highest (lowest) past returns. He next tests the power of the above seven variables to predict the resulting monthly momentum return series. Finally, he tests dynamic momentum risk management strategies that execute the conventional momentum strategy (go to cash) when each of the seven predictors is below (above) the 90 percentile of its values over the last five years. Using daily and monthly returns, daily trading volumes and shares outstanding for a broad sample of U.S. common stocks during January 1926 through December 2013, he finds that: Keep Reading

A Few Notes on The 3% Signal

In the introduction to his 2015 book entitled The 3% Signal: The Investing Technique that Will Change Your Life, author Jason Kelly states: “Ideas count for nothing; opinions are distractions. The only thing that matters is the price of an investment and whether it’s below a level indicating a good time to buy or above a level indicating a good time to sell. We can know that level and monitor prices on our own, no experts required, and react appropriately to what prices and the level tell us. Even better, we can automate the reaction because it’s purely mathematical. This is the essence of the 3 percent signal [3Sig]. …Used with common market indexes, this simple plan beats the stock market. …The performance advantage of the 3 percent signal can be yours after just four fifteen-minute calculations per year…” Based on his experience and analyses, he concludes that: Keep Reading

Betting Against Lottery Stocks

Do lottery traders create the low-volatility (betting-against-beta) effect by overpricing high-beta stocks? In the December 2014 version of their paper entitled “Betting against Beta or Demand for Lottery”, Turan Bali, Stephen Brown, Scott Murray and Yi Tang investigate whether demand for lottery-like stocks drives the empirically low (high) abnormal returns of stocks with high (low) betas. They measure lottery demand for a stock as the average of its five highest daily returns over the past month. They measure beta for a stock as the slope from a regression of its daily excess (relative to the risk-free rate) stock returns versus daily excess stock market returns over the past 12 months. They hypothesize that lottery traders drive current prices of stocks with high lottery demand upward, thereby depressing their expected returns. They further hypothesize that stocks with high lottery demand tend to be high-beta stocks. Using daily and monthly returns and characteristics for a broad sample of U.S. common stocks (excluding those priced under $5), associated firm accounting data and relevant financial variables during July 1963 through December 2012 (594 months), they find that: Keep Reading

Dissecting the Equity Market Variance Risk Premium

Is there a more precise way to measure the premium available to investors willing to bear volatility risk than overall return variance? In their January 2015 paper entitled “Downside Variance Risk Premium”, Bruno Feunou, Mohammad Jahan-Parvar and Cedric Okou investigate the usefulness of  (1) decomposing the variance risk premium (the difference between option-implied and realized variance) into upside and downside components and (2) defining the difference between these components as the skewness risk premium. They use high-frequency (5-minute) S&P 500 Index squared positive (negative) returns plus squared overnight positive (negative) returns to calculate realized upside (downside) variance. They sum upside and downside components to obtain total realized variance. They derive option-implied volatility from the most liquid out-of-the-money S&P 500 Index put and call options. Using intraday S&P 500 Index returns, daily S&P 500 Index option data and monthly yields for 3-month U.S. Treasury bills as the risk-free rate during September 1996 through December 2010, they find that:

Keep Reading

Interaction of Calendar Effects with Other Anomalies

Do stock return anomalies exhibit January and month-of-quarter (first, second or third, excluding January) effects? In his February 2015 paper entitled “Seasonalities in Anomalies”, Vincent Bogousslavsky investigates whether the following 11 widely cited U.S. stock return anomalies exhibit these effects:

  1. Market capitalization (size) – market capitalization last month.
  2. Book-to-market – book equity (excluding stocks with negative values) divided by market capitalization last December.
  3. Gross profitability – revenue minus cost of goods sold divided by total assets.
  4. Asset growth – Annual change in total assets.
  5. Accruals – change in working capital minus depreciation, divided by average total assets the last two years.
  6. Net stock issuance – growth rate of split-adjusted shares outstanding at fiscal year end.
  7. Change in turnover – difference between turnover last month and average turnover the prior six months.
  8. Illiquidity – average illiquidity the previous year.
  9. Idiosyncratic volatility – standard deviation of residuals from regression of daily excess returns on market, size and book-to-market factors.
  10. Momentum – past six-month return, skipping the last month.
  11. 12-month effect – average return in month t−k*12, for k = 6, 7, 8, 9, 10.

Each month, he sorts stocks into tenths (deciles) based on each anomaly variable and forms portfolios that are long (short) the decile with the highest (lowest) values of the variable. He updates all accounting inputs annually at the end of June based on data for the previous fiscal year. Using accounting data and monthly returns for a broad sample of U.S. common stocks during January 1964 to December 2013, he finds that: Keep Reading

VIX-VXX Seasonality

Does the S&P 500 Implied Volatility Index (VIX) exhibit exploitable seasonality? To check, we calculate average monthly change in VIX and and average iPath S&P 500 VIX Short-Term Futures ETN (VXX) monthly return by calendar month. Using monthly closes of VIX since January 1990 and monthly reverse split-adjusted closes for VXX since January 2009, both through December 2014, we find that: Keep Reading

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