# 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.

**October 4, 2013** - Momentum Investing, Strategic Allocation, Volatility Effects

Has Modern Portfolio Theory failed to deliver over the past decade because users employ long-term averages for expected returns, volatilities and correlations that do not respond to changing market environments? Do short-term estimates of these key inputs work better? In their May 2012 paper entitled “Adaptive Asset Allocation: A Primer”, Adam Butler, Michael Philbrick and Rodrigo Gordillo backtest a progression of strategies culminating in an Adaptive Asset Allocation (AAA) strategy that incorporates return predictability from relative momentum (last 120 trading days, about six months), volatility predictability from recent volatility (last 60 trading days) and pairwise correlation predictability from recent correlations (last 250 trading days). Their tests employ nine asset class indexes (U.S. stocks, European stocks, Japanese stocks, U.S. real estate investment trusts (REIT), International REITs, intermediate-term U.S. Treasuries, long-term U.S. Treasuries and commodities) and a spot gold price series. They reform portfolios monthly based on evolving return, volatility and correlation forecasts. They ignore trading frictions as negligible for “intelligent retail or institutional investors” via mutual funds or Exchange Traded Funds. Using daily returns for the nine indexes and spot gold) to test six strategies during January 1995 through March 2012, *they find that:* Keep Reading

**September 20, 2013** - Bonds, Volatility Effects

Do low-risk bonds, like low-risk stocks, tend to outperform their high-risk counterparts? In their September 2013 paper entitled “Low-Risk Anomalies in Global Fixed Income: Evidence from Major Broad Markets”, Raul Leote de Carvalho, Patrick Dugnolle, Xiao Lu and Pierre Moulin investigate whether low-risk beats high-risk for different measures of risk and different bond segments. They consider only measures of risk that account for the fact that the risk of a bond inherently decreases as it approaches maturity, emphasizing duration-times-yield (yield elasticity). They focus on corporate investment grade bonds denominated in dollars, euros, pounds or yen, but also consider government and high-yield corporate bonds worldwide. Each month, they rank a selected category of bonds by risk into fifths (quintile portfolios). For calculation of monthly quintile returns, they weight individual bond returns by market capitalization. They reinvest coupons the end of the month. They focus on quintile portfolio Sharpe ratios to test the risk-performance relationship. Using monthly risk data and returns for 85,442 individual bonds during January 1997 through December 2012 (192 months), *they find that:* Keep Reading

**September 5, 2013** - Volatility Effects

Some experts interpret stock market return volatility as an indicator of investor sentiment, with high (low) volatility indicating ascendancy of fear (greed). Volatility of volatility (VoV) would thus indicate uncertainty in investor sentiment. Does the risk associated with this uncertainty depress stock prices and thereby predict relatively high future stock market returns? To investigate, we consider two measures of U.S. stock market volatility: (1) realized volatility, calculated as the standard deviation of daily S&P 500 Index return over the last 21 trading days (annualized); and, (2) *implied* volatility as measured by the Chicago Board Options Exchange Market Volatility Index (VIX). For both, we calculate VoV as the standard deviation of volatility over the past 21 trading days and test the ability of VoV to predict SPDR S&P 500 (SPY) returns. To avoid overlap in volatility and VoV calculations, we focus on monthly return intervals. Using daily values of the S&P 500 Index since December 1989 and VIX since inception in January 1990, and monthly dividend-adjusted SPY closes since inception in January 1993, all through July 2013, *we find that:* Keep Reading

**August 12, 2013** - Volatility Effects

Does exceptional (idiosyncratic) stock volatility exploitably predict future returns? In her April 2013 paper entitled “Revisiting Idiosyncratic Volatility and Stock Returns”, Fatma Sonmez re-examines the relationship between idiosyncratic volatility and future stock returns. She defines idiosyncratic volatility as the standard deviation of daily residuals from monthly regressions of returns (in excess of the risk-free rate) for each stock versus Fama-French model factors. Using daily returns and contemporaneous market, size and book-to-market factors for U.S. listed stocks during 1963 through 2008, *she finds that:* Keep Reading

**June 13, 2013** - Volatility Effects

Does the market pay a premium to equity funds with relatively high “bad” (left tail) volatility? In their May 2013 paper entitled “Volatility vs. Tail Risk: Which One is Compensated in Equity Funds?”, James Xiong, Thomas Idzorek and Roger Ibbotson compare return premiums for conventional volatility (standard deviation of total returns) and tail risk (value-at-risk) across U.S. and non-U.S. equity mutual funds. Each month, they use the previous five years of monthly net total returns to sort funds into fifths (quintiles) based on volatility and on excess (relative to a normal distribution) value-at-risk for the worst 5% of returns. They estimate premiums for these two risk measures as the difference in average (arithmetic mean) returns between the riskiest and least risky quintiles in excess of the Treasury bill (T-bill) yield. Using monthly returns for the oldest share class for a broad sample of alive and dead open-end equity mutual funds (3,389 U.S. and 1,055 non-U.S.), and the contemporaneous T-bill yield, during January 1980 through September 2011, *they find that:* Keep Reading

**June 11, 2013** - Volatility Effects

Why does the widely cited and intuitive Capital Asset Pricing Model (CAPM) prediction that extra risk (beta) earns extra reward (rate of return) not work for stocks? In their May 2013 paper entitled “Explanations for the Volatility Effect: An Overview Based on the CAPM Assumptions”, David Blitz, Eric Falkenstein and Pim van Vliet organize research on potential explanations according to the following CAPM assumptions:

- Investors are unconstrained regarding leverage, short selling and solvency (regulatory capital requirements).
- Investors are risk-averse, focus on absolute return and care only about return mean and variance (such that returns are normally distributed).
- There is only one return measurement interval and therefore no compounding effect (ignoring the difference between arithmetic and geometric means).
- Investors have complete information and process it rationally.
- Investors have no liquidity constraints, transaction costs or taxes.

Based on a review of research on potential explanation for the empirical failure of CAPM, *they find that:* Keep Reading

**May 30, 2013** - Commodity Futures, Momentum Investing, Value Premium, Volatility Effects

Can commodities still be useful for portfolio diversification, despite their recent poor aggregate return, high volatility and elevated return correlations with other asset classes? In the May 2013 version of their paper entitled “Strategic Allocation to Commodity Factor Premiums”, David Blitz and Wilma de Groot examine the performance and diversification power of the commodity market portfolio and of alternative commodity momentum, carry and low-risk (low-volatility) portfolios. They define the commodity market portfolio as the S&P GSCI (production-weighted aggregation of six energy, seven metal and 11 agricultural commodities). The commodity long-only (long-short) momentum portfolio is each month long the equally weighted 30% of commodities with the highest returns over the past 12 months (and short the 30% of commodities with the lowest returns). The commodity long-only (long-short) carry portfolio is each month long the equally weighted 30% of commodities with the highest annualized ratios of nearest to next-nearest futures contract price (and short the 30% of commodities with the lowest ratios). The commodity long-only (long-short) low-risk portfolio is each month long the equally weighted 30% of commodities with the lowest daily volatilities over the past three years (and short the 30% of commodities with the highest volatilities). They also consider a combination that equally weights the commodity momentum, carry and low-risk portfolios. For comparison to U.S. stocks, they use returns of long-only, equally weighted “big-momentum” and “big-value” (comparable to commodity carry) stock portfolios from Kenneth French, and a similarly constructed “big-low-risk” stock portfolio. For comparison with bonds, they use the total return of the JP Morgan U.S. government bond index. For all return series and allocation strategies, they ignore trading frictions. Using daily and monthly futures index levels and contract prices for the 24 commodities in the S&P GSCI as available during January 1979 through June 2012, along with contemporaneous returns for a broad sample of U.S. stocks, *they find that:* Keep Reading

**May 23, 2013** - Strategic Allocation, Volatility Effects

Market volatility tends to rise as returns fall. Does adding a proxy for intermediate-term U.S. equity market volatility to a diversified portfolio improve its performance? To check, we add iPath S&P 500 VIX Mid-Term Futures (VXZ) to the following mix of asset class proxies (the same used in “Simple Asset Class ETF Momentum Strategy”):

PowerShares DB Commodity Index Tracking (DBC)

iShares MSCI Emerging Markets Index (EEM)

iShares MSCI EAFE Index (EFA)

SPDR Gold Shares (GLD)

iShares Russell 1000 Index (IWB)

iShares Russell 2000 Index (IWM)

SPDR Dow Jones REIT (RWR)

iShares Barclays 20+ Year Treasury Bond (TLT)

3-month Treasury bills (Cash)

First, per the findings of “Asset Class Diversification Effectiveness Factors”, we measure the average monthly return for VXZ and the average pairwise correlation of VXZ monthly returns with the monthly returns of the above assets. Then, we compare cumulative returns and basic monthly return statistics for equally weighted (EW), monthly rebalanced portfolios with and without VXZ. We ignore rebalancing frictions, which would be about the same for the alternative portfolios. Using adjusted monthly returns for VXZ and the above nine asset class proxies from March 2009 (first return available for VXZ) through April 2013 (only 50 monthly returns), *we find that:* Keep Reading

**May 23, 2013** - Strategic Allocation, Volatility Effects

Market volatility tends to rise as returns fall. Does adding a proxy for short-term U.S. equity market volatility to a diversified portfolio improve its performance? To check, we add iPath S&P 500 VIX Short Term Futures (VXX) to the following mix of asset class proxies (the same used in “Simple Asset Class ETF Momentum Strategy”):

PowerShares DB Commodity Index Tracking (DBC)

iShares MSCI Emerging Markets Index (EEM)

iShares MSCI EAFE Index (EFA)

SPDR Gold Shares (GLD)

iShares Russell 1000 Index (IWB)

iShares Russell 2000 Index (IWM)

SPDR Dow Jones REIT (RWR)

iShares Barclays 20+ Year Treasury Bond (TLT)

3-month Treasury bills (Cash)

First, per the findings of “Asset Class Diversification Effectiveness Factors”, we measure the average monthly return for VXX and the average pairwise correlation of VXX monthly returns with the monthly returns of the above assets. Then, we compare cumulative returns and basic monthly return statistics for equally weighted (EW), monthly rebalanced portfolios with and without VXX. We ignore rebalancing frictions, which would be about the same for the alternative portfolios. Using adjusted monthly returns for VXX and the above nine asset class proxies from February 2009 (first return available for VXX) through April 2013 (only 51 monthly returns), *we find that:* Keep Reading

**May 20, 2013** - Volatility Effects

Should investors regard any of the exchange-traded products (ETP) based on S&P 500 Index option-implied volatility (VIX) futures as long-term holdings? In the May 2013 draft of his paper entitled “Trading Volatility: At What Cost?”, Robert Whaley describes these ETPs and evaluates them as buy-and-hold investments. VIX ETPs are based on VIX futures indexes with daily rebalancing, subject to management fees and expenses including commissions and trading fees, licensing fees and (for some ETPs) foregone interest income. Many of the ETPs are exchange-traded notes (ETN), secured not by underlying assets but rather only by the good faith and collateral of the issuer. Using daily price and trading data for VIX futures (starting March 2004) and options (starting February 2006) and for 30 ETPs based on VIX futures (starting January 2009) through March 2012, *he finds that:* Keep Reading