# 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.

**September 18, 2012** - Strategic Allocation, Volatility Effects

Risk-focused asset allocation strategies derive from evidence that forecasting asset return volatility is easier than forecasting average return. Is there a best risk-focused strategy? In his September 2012 paper entitled “A Small Survey of Quantitative Models that Discard Estimation of Expected Returns for Portfolio Construction”, Stefano Colucci compares asset allocation strategies that rely on forecasted asset risk metrics but not on forecasted average returns. Specifically, he compares future gross annualized return-risk ratios, Ulcer indexes, one-month maximum drawdowns and average monthly portfolio turnovers for the following asset allocation strategies:

- Minimum Variance (least volatile, or left-most, efficient portfolio per Modern Portfolio Theory).
- Minimum Expected Shortfall with weightings estimated by Monte Carlo simulation.
- Equal Risk Contribution (each asset weighted by the inverse of its forecasted maximum expected shortfall).
- Maximum Diversification (related to expected shortfall with weightings again estimated by numerical simulation).
- Risk Parity (each asset weighted by the inverse of its portfolio volatility contribution).
- Equal Weighting (requiring neither average return nor volatility forecasts) as a benchmark.

He reforms portfolios every 20 trading days (approximately monthly) and estimates future risk metrics based on a rolling historical window of 500 trading days (approximately two years). Using daily returns over recent periods for stock and bond indexes and individual stocks segregated into several asset selection universes, *he finds that:* Keep Reading

**September 6, 2012** - Volatility Effects

What is the best way to bet against beta in equity markets? In their August 2012 paper entitled “Beta-Arbitrage Strategies: When Do They Work, and Why?”, Tony Berrada, Reda Jurg Messikh, Gianluca Oderda and Olivier Pictet derive and test a dynamic low-beta portfolio strategy designed to maximize excess return relative to the market portfolio. They test the strategy on a broad sample of U.S. stocks, 18 developed country stock indexes and 10 equity sector indexes by varying the emphasis on low versus high beta each month based on beta dispersion in lagged rolling 60-month intervals. Using monthly total returns for U.S. stocks during July 1925 through December 2011, for developed country stock market indexes during January 1970 through November 2010 and for sector indexes during January 1995 through November 2010, *they find that:* Keep Reading

**August 10, 2012** - Equity Premium, Volatility Effects

How should investors view the predictability of stock market returns and volatility? In sections 5 and 6 of the July 2012 version of his draft chapter entitled “Equity Market Level”, Andrew Ang examines the predictability of the equity risk premium and equity market volatility. He also addresses the exploitability of any predictive power found. Using both theoretical arguments and empirical tests based on long-run data through December 2011, *he concludes that:* Keep Reading

**July 13, 2012** - Big Ideas, Volatility Effects

Does demand for high-beta stocks by money managers extinguish the risk-return relationship? In his May 2012 paper entitled “Agency-Based Asset Pricing and the Beta Anomaly”, David Blitz investigates whether a volatility preference among stock portfolio managers flattens any relationship between beta and expected returns, thereby invalidating the most widely used asset pricing models. Because institutional investors typically evaluate portfolio managers versus market returns and prohibit or limit leverage, these managers have an incentive (under a belief in reward-for-risk) to focus investments in high-beta stocks with high expected returns. He calculates beta of a stock by regressing its monthly returns (in excess of the risk-free rate) against stock market excess monthly returns over the prior 60 months. Using monthly returns and characteristics for a broad sample of U.S. common stocks during July 1926 through December 2010, along with various benchmark data, *he finds that:* Keep Reading

**July 10, 2012** - Strategic Allocation, Volatility Effects

Are popular exchange-traded products (ETP) such as VXX (iPath S&P 500 VIX Short Term Futures) and VXZ (iPath S&P 500 VIX Mid-Term Futures), designed to track specific S&P 500 VIX futures constant maturity index series, good hedges for stock portfolios? In their June 2012 paper entitled “Are VIX Futures ETPs Effective Hedges?”, Geng Deng, Craig McCann and Olivia Wang investigate whether these ETPs effectively hedge basic U.S. stock portfolios or exchange-traded funds (ETF) that leverage U.S. stock market indexes. Because the ETPs are only very recently available, they use the one-month (SPVXSP) and five-month (SPVXMP) S&P 500 VIX futures constant maturity indexes as proxies for them. They examine the hedging effectiveness of these indexes for five stock portfolios: 100% SPDR S&P 500 (SPY); 100% Vanguard Total Stock Market Index Fund (VTSMX); 80% VTSMX and 20% Vanguard Total Bond Market Index Fund (VBMFX); 60% VTSMX and 40% VBMFX; and, 40% VTSMX and 60% VBMFX. They also examine the hedging effectiveness of these indexes for three 2x-leveraged exchange-traded funds (ETF): ProShares Ultra S&P500 (SSO); ProShares Ultra QQQ (QLD); and, ProShares Ultra Dow30 (DDM). They compute optimal hedge ratios using consecutive (non-overlapping) 26-week lagged regressions of weekly total returns of each portfolio/ETF versus weekly returns of the hedging instrument. Using weekly data for all portfolio funds and VIX futures indexes since December 2005, and for leveraged ETFs since late July 2006, all through mid-April 2012, *they find that:* Keep Reading

**July 6, 2012** - Volatility Effects

Does the condition of S&P 500 Volatility Index (VIX) futures relative to spot VIX (contango or backwardation) predict exploitable VIX futures returns? In their June 2012 paper entitled “The VIX Futures Basis: Evidence and Trading Strategies”, David Simon and Jim Campasano investigate the predictability and exploitability of VIX futures returns based on whether VIX futures are in contango or backwardation. They focus on the two VIX futures contracts nearest to maturity, which are generally liquid with low bid-ask spreads. Their baseline trading strategy is to sell (buy) the nearest VIX futures with at least 10 trading days to maturity when in contango (backwardation) with daily roll greater than 0.10 (less than -0.10) points and hold for five trading days, hedged against changes in the level of spot VIX by (long) short positions in E-mini S&P 500 futures. Daily roll is the difference between the selected VIX futures price and spot VIX, divided by the number of trading days to maturity. Hedge ratios derive from historical regressions and are fixed for a given trade. Tests assume round-trip brokerage costs of $3 per futures contract, plus the full bid-ask spread for VIX futures and $12.50 for E-mini-S&P 500 futures (roughly $60 per complete trade). Using spot VIX levels, bid-ask data for VIX futures and prices for nearest E-mini S&P 500 futures during 2006 through 2011, *they find that:* Keep Reading

**May 31, 2012** - Strategic Allocation, Volatility Effects

Are there exchange-traded notes (ETN) based on S&P 500 Index implied volatility (VIX) futures, or combinations of such ETNs, that are attractive for absolute return and diversification? In the May 2012 version of their paper entitled “Volatility Exchange-Traded Notes: Curse or Cure?”, Carol Alexander and Dimitris Korovilas examine the behaviors of simple (first generation) and enhanced (second generation) ETNs constructed from VIX futures. They focus on: (1) roll return or yield, the loss (gain) of maintaining a position in VIX futures by continually rolling from a near to a far maturity contract when in contango (backwardation); and, (2) term structure convexity of VIX futures, the generally greater magnitude of roll return when rolling between contracts near to maturity versus between contracts far from maturity. To extend the sample period, they replicate recently available ETNs back to December 2005 using S&P constant-maturity VIX futures indexes and March 2004 using daily closes of VIX futures (debting respective annual ETN fees). Using daily closes for all VIX futures contracts, 30-day (VIX) and 93-day (VXV) S&P 500 implied volatility indexes as calculated by CBOE, S&P constant-maturity VIX futures indexes, one-month (VXX) and five-month (VXZ) constant-maturity VIX futures ETNs and two recently launched second-generation VIX futures ETNs (XVIX and XVZ) as available from late March 2004 through March 2012, *they find that:* Keep Reading

**May 29, 2012** - Volatility Effects

Is reward-for-risk or reward-for-not taking risk the rule among stocks? In their April 2012 paper entitled “Low Risk Stocks Outperform within All Observable Markets of the World”, Nardin Baker and Robert Haugen measure performance differences between low-volatility stocks and high-volatility stocks in developed and emerging equity markets worldwide. They define a stock’s lagged volatility as the standard deviation of its monthly total returns over the past 24 months. Each month beginning in 1990, they form ten (apparently) equally weighted portfolios in each country ranked by lagged volatility. They then calculate the differences in average annualized gross returns, standard deviations of annualized gross returns and annualized gross Sharpe ratio (estimated as the ratio of average return to volatility) between the portfolios with the lowest and highest lagged volatilities. Using monthly returns for broad samples of stocks in 21 developed and 12 emerging markets during 1988 through 2011 (288 months), *they find that:* Keep Reading

**May 29, 2012** - Volatility Effects

Should investors focus on relatively wild (high-volatility) or tame (low-volatility) stocks in emerging stock markets? In their April 2012 paper entitled “The Volatility Effect in Emerging Markets”, David Blitz, Juan Pang and Pim van Vliet examine the empirical relationship between risk and return in emerging equity markets. At the end of each month, they form equally-weighted quintile portfolios of emerging market stocks ranked separately on: (1) lagged volatility (standard deviation of total monthly returns in local currency over the past 36 months); and, (2) lagged beta (from regression of total monthly returns in U.S. dollars versus the appropriate S&P/IFCI country market index over the past 36 months). They make portfolios country-neutral by distributing each country’s stocks evenly across quintiles. They calculate annualized arithmetic and geometric average returns, volatilities and Sharpe ratios for the quintile portfolios based on their monthly total returns in U.S. dollars in excess of the one-month Treasury bill (T-bill) yield. Using monthly total returns in local currencies and U.S. dollars for stocks from 30 emerging markets (an average of about 1,000 stocks per year) during December 1988 through December 2010, along with the contemporaneous T-bill yield, *they find that:* Keep Reading

**May 14, 2012** - Currency Trading, Volatility Effects

Are there ways to enhance the currency carry trade (long currencies offering high interest rates and short those offering low rates)? In the May 2012 version of their paper entitled “Average Variance, Average Correlation and Currency Returns”, Gino Cenedese, Lucio Sarno and Ilias Tsiakas investigate the ability of components of the currency exchange market risk (variance of the average return for all exchange rates) to predict carry trade returns. Their baseline carry trade portfolio involves U.S. dollar nominal exchange rates, rebalanced monthly. They decompose the market variance into two components: average variance of individual exchange rate returns, and average correlation of exchange rate returns. They examine the effects of changes in these risk components on the entire future distribution of currency trade returns (via quantile breakdowns), focusing on the large losses in the left tail and large gains in the right tail. Using daily spot and forward exchange rates for 33 currencies relative to the U.S. dollar as available during 1976 through February 2009 (15 active exchange rates at the beginning and 22 at the end), *they find that:* Keep Reading