# 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.

**January 3, 2012** - Strategic Allocation, Volatility Effects

Are the relatively placid financial markets of the American Century evolving to a high-volatility regime in a more evenly competitive world? In his December 2011 paper entitled “Adaptive Markets and the New World Order”, Andrew Lo examines the implications of the Adaptive Markets Hypothesis (AMH), wherein “markets are not always efficient, but they are usually highly competitive and adaptive, varying in their *degree* of efficiency as the economic environment and investor population change over time.” He believes that investors can prepare for occasional failures of market efficiency by viewing financial markets and institutions from the perspective of evolutionary biology. Applying this perspective to markets since 1926, *he concludes that:* Keep Reading

**December 30, 2011** - Momentum Investing, Volatility Effects

A subscriber suggested applying a simple momentum trading strategy to a set of leveraged equity style (size, value-growth) exchanged-traded funds (ETF), including leveraged long and leveraged short counterparts to exploit both positive and negative markets. It seems plausible that leverage may make funds react quickly and strongly to business cycle shifts that affect style performance. However, the costs of maintaining leverage are countervailing. We test a set of 12 ProShares 2X and -2x leveraged sector ETFs, all of which have trading data back at least as far as April 2007:

ProShares Ultra Russell1000 Value (UVG)

ProShares Ultra Russell1000 Growth (UKF)

ProShares Ultra Russell MidCap Value (UVU)

ProShares Ultra Russell MidCap Growth (UKW)

ProShares Ultra Russell2000 Value (UVT)

ProShares Ultra Russell2000 Growth (UKK)

ProShares UltraShort Russell1000 Value (SJF)

ProShares UltraShort Russell1000 Growth (SFK)

ProShares UltraShort Russell MidCap Val (SJL)

ProShares UltraShort Russell MCap Growth (SDK)

ProShares UltraShort Russell2000 Value (SJH)

ProShares UltraShort Russell2000 Growth (SKK)

As in “Simple Sector ETF Momentum Strategy Performance” and “Doing Momentum with Style (ETFs)”, we consider a basic momentum strategy that allocates all funds at the end of each month to the ETF with the highest total return over the past six months (6-1). Using monthly adjusted closing prices for the 12 leveraged style ETFs and S&P Depository Receipts (SPY) over the period April 2007 through November 2011 (only 56 months), *we find that:* Keep Reading

**December 22, 2011** - Momentum Investing, Volatility Effects

A subscriber suggested applying simple momentum trading strategies to a set of leveraged equity style (size, value-growth) funds. It seems plausible that leverage may make funds react quickly and strongly to business cycle shifts that affect style performance. However, the costs of maintaining leverage are countervailing. Historical data for leveraged style funds is very limited, so we test instead a set of seven ProFunds 1.5X leveraged sector mutual funds, all of which have trading data back at least as far as December 2000:

ProFunds UltraSector Oil & Gas Inv (ENPIX)

ProFunds UltraSector Financials Inv (FNPIX)

ProFunds UltraSector Health Care Inv (HCPIX)

ProFunds Real Estate UltraSector Inv (REPIX)

ProFunds Telecom UltraSector Inv (TCPIX)

ProFunds Technology UltraSector Inv (TEPIX)

ProFunds Utilities UltraSector Inv (UTPIX)

As in “Simple Sector ETF Momentum Strategy Performance” and “Doing Momentum with Style (ETFs)”, we consider a basic momentum strategy that allocates all funds at the end of each month to the mutual fund with the highest total return over the past six months (6-1). We also consider a more cautious strategy that allocates all funds at the end of each month either to the mutual fund with the highest total return over the past six months or to cash depending on whether the S&P 500 Index is above or below its 10-month simple moving average (6-1;SMA10). Using monthly adjusted closing prices for the seven leveraged sector funds, the S&P 500 index, 3-month Treasury bills (T-bills) and S&P Depository Receipts (SPY) over the period December 2000 through November 2011 (132 months), *we find that:* Keep Reading

**December 21, 2011** - Bonds, Equity Premium, Strategic Allocation, Volatility Effects

Should investors believe in the superiority of stocks for the long run and bonds for the short run? In his December 2011 paper entitled “Stocks, Bonds, Risk, and the Holding Period: An International Perspective”, Javier Estrada examines how the absolute and relative risks of stocks and bonds evolve as investment horizon grows (time diversification). Considering both annual and cumulative returns and various measures of variability/risk, he focuses on the question of whether stocks become less risky than bonds for long holding periods. Using annual total returns for stocks and bonds in 19 countries during 1900 through 2009, *he finds that:* Keep Reading

**December 9, 2011** - Volatility Effects

Is risk avoidance by itself a good tactical asset allocation strategy? In their November 2011 paper entitled “A Risk Based Approach to Tactical Asset Allocation”, Dario Brandolini and Stefano Colucci propose a purely risk-based asset allocation framework designed to buffer effects of volatility clusters. Their critical allocation variable is expected shortfall, estimated each week to adjust the allocation for each asset in the portfolio separately. They test their framework on the following (U.S. dollar-denominated) indexes as proxies for portfolio assets: S&P 500 Index, TOPIX, DAX, MSCI UK, MSCI France, Italy Comit Globale, MSCI Canada, MSCI Emerging Markets, Reuters-Jefferies CRB and Merril Lynch U.S. Treasuries (7-10 years). They assume strategic allocations of 70% to equities (scaled by market according to GDP as measured every five years), 10% to commodities and 20% to U.S. Treasuries. They shift the allocation for each equities/commodities asset partially to a risk-free alternative (U.S. treasuries or cash) to the degree its one-month expected shortfall for the worst 5% of observations falls below a target of -6%. They assume rebalancing occurs simultaneously with signals and impose top-down annual total expense ratios of 2% for active reallocation and 0.6% for a comparable passive but diversified portfolio. Using daily total returns as available (mostly since the late 1980s) and capital gains only before then for the ten indexes during 1974 through 1999 for calibration and 2000 through most of August 2011 for out-of-sample testing, *they find that:* Keep Reading

**November 10, 2011** - Commodity Futures, Currency Trading, Gold, Volatility Effects

An array of leveraged exchange-traded funds (ETF) track short-term (daily) changes in commodity and currency exchange indexes. Over longer holding periods, these ETFs tend to veer off track. The cumulative veer can be large. How do leveraged ETFs perform over a multi-year period? What factors contribute to their failure to track underlying indexes? To investigate, we consider a set of 12 ProShares 2X leveraged index ETFs (six matched long-short pairs), involving a commodity index, oil, gold, silver and the euro-dollar and yen-dollar exchange rates, with the start date of 12/9/08 determined by inception of the youngest of these funds (Ultra Yen). Using daily dividend-adjusted prices for these funds over the period 12/9/08 through 11/4/11 (almost three years), *we find that:* Keep Reading

**November 1, 2011** - Volatility Effects

Does the S&P 500 Implied Volatility Index (VIX) measured at a monthly interval usefully predict stock market returns? To check, we consider four relationships:

- S&P 500 Depository Receipts (SPY) next-month return versus VIX monthly close.
- SPY next-month return versus VIX monthly range, a measure of the volatility of implied volatility.
- SPY next-month return versus product of VIX monthly change and SPY monthly return (to explore implications of VIX and SPY moving in opposite or same directions).
- SPY next-month return versus monthly difference between SPY implied volatility (IV, measured by VIX) and realized volatility (RV, measured by the standard deviation of monthly SPY returns over the past 12 months), as a crude measure of the volatility risk premium.

For VIX calculations, we “de-annualize” by dividing by the square root of 12. For VIX range and change calculations, we use raw VIX numbers. Using monthly high, lows and closes of VIX and monthly dividend-adjusted closes of SPY from January 1993 through September 2011, *we find that:* Keep Reading

**October 31, 2011** - Momentum Investing, Size Effect, Strategic Allocation, Value Premium, Volatility Effects

Should investors strategically diversify across widely known equity market anomalies? In the October 2011 version of his paper entitled “Strategic Allocation to Premiums in the Equity Market”, David Blitz investigates whether investors should treat anomaly portfolios (size, value, momentum and low-volatility) as diversifying asset classes and how they can implement such a strategy. To ensure implementation is practicable, he focuses on long-only, big-cap portfolios. To account for the trading frictions associated with anomaly portfolio maintenance and for time variation of anomaly premiums, he assumes future (expected) market and anomaly premiums lower than historical values, as follows: 3% equity market premium; 0% expected incremental size and low-volatility premiums; and, 1% expected incremental value and momentum premiums. He assumes future volatilities, correlations and market betas as observed in historical data and constrains weights of all anomaly portfolios to a maximum 40%. He considers both equal-weighted and value-weighted individual anomaly portfolios, and both mean-variance optimized and equal-weighted combinations of market and anomaly portfolios. Using portfolios constructed by Kenneth French to quantify equity market/anomaly premiums during July 1963 through December 2009 (consisting of approximately 800 of largest, most liquid U.S. stocks), *he finds that:* Keep Reading

**October 26, 2011** - Equity Options, Volatility Effects

An upward (downward) trend in implied volatilities with option maturity indicates that investors expect volatility to increase (decrease) over time. Do such expectations reliably predict future stock options prices? In his October 2011 paper entitled “Volatility Term Structure and the Cross-Section of Option Returns”, Aurelio Vasquez investigates whether the implied volatility term structure (measured as slope of implied volatilities across at-the-money options with receding expiration dates) predicts future option returns. Specifically, each month he ranks stocks into deciles by volatility term structure slope and then calculates future returns for extreme deciles from five option trading strategies: (1) naked calls; (2)naked puts; (3) straddles; (4) delta-hedged calls; and, (5) delta-hedged puts. He calculates returns relative to the initial prices of the options traded. Using monthly closing bid and ask prices for at-the-money options (moneyness between 0.95 and 1.05) on a broad sample of U.S. stocks, and associated firm characteristics, during January 1996 through June 2007 (260 stocks per month on average), *he finds that:* Keep Reading

**October 25, 2011** - Volatility Effects

Is selling insurance against stock market volatility reliably profitable? In the December 2010 version of his paper entitled “Variance Trading and Market Price of Variance Risk”, Oleg Bondarenko examines payoffs from synthesized variance swap contracts, derived from the diﬀerence between realized and contract-specified variances over a given interval, during a 20-years period. He constructs the hypothetical swap contracts from observed prices of S&P 500 Index futures and options on these futures. Using daily prices for these futures and options from January 1990 through December 2009, *he finds that:* Keep Reading