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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.

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)
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

VIX Streaks

Does the S&P 500 implied volatility index (VIX) behave predictably after up or down streaks? To check, we look at next-day percentage changes in VIX after up and down streaks ranging from two to seven trading sessions. To test exploitability, we repeat the analysis on the much shorter sample available for the iPath S&P 500 VIX ST Futures ETN (VXX). Using daily closes of VIX from the beginning of January 1990 and VXX from the end of January 2009, both through mid-November 2012, we find that: Keep Reading

Front-running Leveraged ETFs at the End of the Day?

Does predictable end-of-day rebalancing behavior of leveraged exchange-traded funds (ETF) present trading opportunities? In their October 2012 paper entitled “Intraday Share Price Volatility and Leveraged ETF Rebalancing”, Arthur Rodier, Edgar Haryanto, Pauline Shum and Walid Hejazi examine: (1) the effects of leveraged ETF rebalancing activities on late-day market volatility; and, (2) the profitability of trading strategies designed to anticipate these rebalancing activities. For the former, they measure the average intraday volatility of 346 large-capitalization stocks within indexes tracked by many leveraged ETFs. For the latter, they consider intraday trades of ProShares Ultra S&P500 (SSO) and ProShares UltraShort S&P500 (SDS) according to whether anticipated late-day rebalancing pressure is likely to be bullish or bearish, respectively. Using intraday returns for the S&P 500 Index, 346 individual S&P 500 stocks, SSO and SDS during late June 2006 through mid-July 2011, they find that: Keep Reading

Volatility-based Equity Market Allocations

Do allocations aimed at managing volatility beat simple equal weighting as applied to the cheapest third of 32 country stock markets based on 10-year cyclically adjusted price-to-earnings ratio (CAPE, or P/E10). In their October 2012 paper entitled “Global CAPE Model Optimization”, Adam Butler, Michael Philbrick, Rodrigo Gordillo and Mebane Faber compare the following six volatility management strategies to EW for a low-P/E10 equity index portfolio:

  1. Equal Volatility: each selected index contributes equally to the volatility of a fully invested portfolio.
  2. Fixed Volatility Limit: allocates to each selected index up to a daily volatility limit of 1%, with any remaining funds going to cash.
  3. Portfolio Volatility Target: allocates equally to all selected indexes with a portfolio-level annualized volatility target of 10%, going to cash when above target (but not applying leverage when below).
  4. Risk Parity with Portfolio Volatility Target: a combination of strategies 1 and 3; allocates such that all indexes contribute equally to portfolio volatility with a portfolio-level annualized volatility target of 10%, going to cash when above target (but not applying leverage when below).
  5. Minimum Variance: minimum variance via a combination of low volatilities and low correlations per Modern Portfolio Theory, but always fully invested. 
  6. Minimum Variance with Portfolio Volatility Target: minimum variance allocations adjusted at the portfolio level to target 10% annualized portfolio volatility, going to cash when above target (but not applying leverage when below).

For all strategies, they estimate prescribed volatilities based on the last 60 days of returns, with monthly portfolio reformation. Using daily and monthly total returns for the 32 country stock indexes during April 1999 through August 2012, they find that: Keep Reading

Low-volatility Stock Performance by International Group

Do low-volatility stocks outperform high-volatility stocks around the globe? In their October 2012 paper entitled “Stock Return Volatility, Operating Performance and Stock Returns: International Evidence on Drivers of the ‘Low Volatility’ Anomaly”, Tanuj Dutt and Mark Humphery-Jenner investigate links among stock return volatility, stock returns and firm operating performance in emerging and developed markets outside North America. They focus on a 500-day moving variance of daily stock returns as a measure of volatility, but also consider 90-day, 180-day, 250-day and 1000-day alternatives. They assign stocks based on listing exchange to one of four market groups: Emerging Asia, Emerging EMEA, Latin America and Ex-U.S./Canada Developed. For each group each month, they rank stocks into quintiles (fifths) by return volatility and track value-weighted and equal-weighted average quintile returns for the balance of the month. Using daily prices for a broad sample of international stocks (excluding the smallest and least liquid, but still capturing over 90% of market capitalization) and associated firm operating performance data during 1990 through 2009, they find that: Keep Reading

Common Factor Exposures of Specialized Stock Indexes

How do specialized stock indexes relate to commonly used equity risk factors? In his February 2012 paper entitled “Evaluating Alternative Beta Strategies”, Xiaowei Kang examines risk exposures (betas), construction methodologies and historical performances of alternative stock indexes such as those based on value, low-volatility and diversification strategies. He considers five risk factors: (1) market, representing excess return of the market capitalization-weighted U.S. stock market; (2) size, representing return from a portfolio that is long small-cap stocks and short large-cap stocks; (3) value, representing return from a portfolio that is long high book-to-market stocks and short low book-to-market stocks; (4) momentum, representing return from a portfolio that is long past winning stocks and short past losing stocks; and, (5) volatility, representing return from a portfolio that is long high-volatility stocks and short low-volatility stocks. Using monthly returns for several specialized indexes and the specified risk factors as available through 2011, he finds that: Keep Reading

Betting Against Mutual Fund Beta

Does a low-beta strategy work for mutual funds? In his September 2012 paper entitled “Capitalizing on the Greatest Anomaly in Finance with Mutual Funds”, David Nanigian examines portfolios of funds sorted on lagged beta to determine whether mutual fund investors can capitalize on outperformance of low-beta assets. He calculates rolling betas for each mutual fund based on monthly returns over the prior 60 months (or less, as few as 24 months, when 60 months of returns are unavailable) or 12 months. He then ranks funds based on lagged betas into asset-weighted fifths each month and holds for one month, or each year and holds for one year. Using monthly net returns and total assets for a broad sample of U.S. equity open-end mutual funds, along with contemporaneous U.S. stock market returns, the risk-free rate and commonly applied risk factors, during December 1990 through April 2012, he finds that: Keep Reading

Daily, Overnight and Intraday VIX Tendencies

Does the S&P 500 options-implied volatility index (VIX) exhibit predictable daily, overnight and intraday tendencies? In their September 2012 paper entitled “What Makes the VIX Tick?”, Warren Bailey, Lin Zheng and Yinggang Zhou employ high-frequency data to investigate patterns in VIX behavior and measure relationships between VIX and various financial fundamentals, economic announcements and investor sentiment. Using data for VIX and other variables sampled at one-minute intervals (as appropriate) during January 2005 through June 2010, they find that: Keep Reading

Exploit VXX Deviation from Indicative Value?

The authors of the study summarized in “Exploit ETN Deviation from Indicative Value?” argue that deviations of prices for exchange-traded notes (ETN) from their indicative (immediate redemption) values may be useful as trading signals. How well does this mispricing concept work for the very liquid iPath S&P 500 VIX Short-term Futures ETN (VXX)? To check, we consider several mispricing thresholds and measure the short-term profitability of both long and short trades based on these thresholds. Using daily split-adjusted opening and closing prices and closing indicative values for VXX from inception at the end of January 2009 through mid-September 2012 (916 trading days), we find that: Keep Reading

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