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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.

Sensitivity of Risk Adjustment to Measurement Interval

Are widely used volatility-adjusted investment performance metrics, such as Sharpe ratio, robust to different measurement intervals? In the July 2014 version of their paper entitled “The Divergence of High- and Low-Frequency Estimation: Implications for Performance Measurement”, William Kinlaw, Mark Kritzman and David Turkington examine the sensitivity of such metrics to the length of the return interval used to measure it. They consider hedge fund performance, conventionally estimated as Sharpe ratio calculated from monthly returns and annualized by multiplying by the square root of 12. They also consider mutual fund performance, usually evaluated as excess return divided by excess volatility relative to an appropriate benchmark (information ratio). Finally, they consider Sharpe ratios of risk parity strategies, which periodically rebalance portfolio asset weights according to the inverse of their return standard deviations. Using monthly and longer-interval return data over available sample periods for each case, they find that: Keep Reading

Sources of Active Equity Mutual Fund Risk

Are the sources of active mutual fund risk mostly common (systematic) or unique (idiosyncratic)? In his July 2014 paper entitled “Components of Portfolio Variance: R2, SelectionShare and TimingShare”, Anders Ekholm decomposes mutual fund return variance (risk) into three sources: (1) passive systematic factor exposure (R-squared); (2) active security selection or stock picking (SelectionShare); and, (3) active systematic factor timing (TimingShare). He demonstrates estimation of these three components based on mutual fund returns (reflecting daily manager actions) rather than holdings (known only via quarterly snapshots). He employs the widely used four-factor (market, size, book-to-market, momentum) model of stock returns to define systematic risk. Using daily returns for a broad sample of actively managed U.S. equity mutual funds and for the four factors during 2000 through 2013, he finds that: Keep Reading

Estimating Snooping Bias for a Multi-parameter Strategy

A subscriber flagged an apparently very attractive exchange-traded fund (ETF) momentum-volatility-correlation strategy that, as presented, generates a optimal compound annual growth rate of 45.7% with modest maximum drawdown. The strategy chooses from among the following seven ETFs:

ProShares Ultra S&P500 (SSO)
SPDR EURO STOXX 50 (FEZ)
iShares MSCI Emerging Markets (EEM)
iShares Latin America 40 (ILF)
iShares MSCI Pacific ex-Japan (EPP)
Vanguard Extended Duration Treasuries Index ETF (EDV)
iShares 1-3 Year Treasury Bond (SHY)

The steps in the strategy are, at the end of each month:

  1. For the first six of the above ETFs, compute log returns over the last three months and standard deviation (volatility) of log returns over the past six months.
  2. Standardize these the monthly sets of past log returns and volatilities based on their respective means and standard deviations.
  3. Rank the six ETFs according to the sum of 0.75 times standardized past log return plus 0.25 times past standardized volatility.
  4. Buy the top-ranked ETF for the next month.
  5. However, if at the end of any month, the correlation of SSO and EDV monthly log returns over the past four months is greater than 0.75, instead buy SHY for the next month.

The developer describes this strategy as an adaptation of someone else’s strategy and notes that he has tested a number of systems. How material might the implied secondary and primary data snooping bias be in the performance of this system? To investigate, we examine the fragility of performance statistics to variation of each strategy parameter separately. As presented, the author substitutes other ETFs for the two with the shortest histories to extend the test period backward in time. We use only price histories as available for the specified ETFs, limited by EDV with inception January 2008. Using monthly adjusted closing prices for the above seven ETFs and for SPDR S&P 500 (SPY) during January 2008 through February 2014 (74 months), we find that: Keep Reading

When Rebalancing Works?

Under what conditions is periodic rebalancing a successful “volatility harvesting” strategy? In his February 2014 paper entitled “Disentangling Rebalancing Return”, Winfried Hallerbach analyzes the return from periodic portfolio rebalancing by decomposing its effects into a volatility return and a dispersion discount. He defines:

  • Rebalancing return as the difference in (geometric) growth rates between periodically rebalanced and buy-and-hold portfolios.
  • Volatility return as the difference in growth rates between a periodically rebalanced portfolio and the equally weighted average growth rate of its component assets.
  • Dispersion discount as the difference in growth rates between a buy-and-hold portfolio and the equally weighted average growth rate of portfolio assets.

Based on mathematical derivations with some approximations, he concludes that: Keep Reading

When (for What) Risk Parity Works

What drives the performance of risk parity asset allocation, and on what asset classes does it therefore work best? In their January 2014 paper entitled “Inter-Temporal Risk Parity: A Constant Volatility Framework for Equities and Other Asset Classes”, Romain Perchet, Raul Leote de Carvalho, Thomas Heckel and Pierre Moulin employ simulations and backtests to explore the conditions/asset classes for which a periodically rebalanced risk parity asset allocation enhances portfolio performance. Specifically, they examine contemporaneous interactions between risk parity performance and each of return-volatility relationship, return volatility clustering and fatness of return distribution tails (kurtosis). They then compare different ways of predicting volatility for risk parity implementation. Finally, they backtest volatility prediction/risk parity allocation effectiveness separately for stock, commodity, high-yield corporate bond, investment-grade corporate bond and government bond indexes (each versus the risk-free asset). They optimize volatility prediction model parameters annually based on an expanding window of historical data. They forecast volatility based on one-year rolling historical daily return dataUsing daily total returns in U.S. dollars for the S&P 500 Index during 1980 through 2012 and for the Russell 1000, MSCI Emerging Market, S&P Commodities, U.S. High Yield Bond, U.S. Corporate Investment Grade Bond and U.S. 10-Year Government Bond indexes and the 3-month U.S. Dollar LIBOR rate (as the risk-free rate) during January 1988 through December 2012, they find that: Keep Reading

Realized/Implied Return Variance Ratio as a Trading Signal

Is it possible to predict serial correlation (autocorrelation) of stock returns, and thereby enhance reversal and momentum strategies. In the January 2014 version of his paper entitled “The Information Content of Option Prices Regarding Future Stock Return Serial Correlation”, Scott Murray investigates the relationship between the variance ratio (the ratio of realized to implied stock return variance, a measure of the variance risk premium) to stock return serial correlation. He calculates realized variance at the end of each month from daily log stock returns over the prior three months. He calculates implied variance at the end of each month as the square of the volatility implied by at-the-money 0.5 delta call and put options one month from expiration. He first measures the power of the variance ratio to predict stock return serial correlation. He then tests the effectiveness of this predictive power to enhance reversal and momentum stock trading. Using the specified return and option data for all U.S. stocks with listed options during January 1996 through December 2012, he finds that: Keep Reading

Unexpected Market Volatility as a Market Return Predictor

Do upside (downside) market volatility surprises scare investors out of (draw investors into) the stock market? In the November 2013 version of his paper entitled “Dynamic Asset Allocation Strategies Based on Unexpected Volatility”, Valeriy Zakamulin investigates the ability of unexpected stock market volatility to predict future market returns. He calculates stock market index volatility for a month using daily returns. He then regresses monthly volatility versus next-month volatility to predict next-month volatility. Unexpected volatility is the series of differences between predicted and actual monthly volatility. He tests the ability of unexpected volatility to predict stock market returns via regression tests and two market timing strategies. One strategy dynamically weights positions in a stock index and cash (the risk-free asset) depending on the prior-month difference between actual and past average unexpected index volatility. The other strategy holds a 100% stock index (cash) position when the prior-month difference between actual and average past unexpected index volatility is negative (positive). His initial volatility prediction uses the first 240 months of data, and subsequent predictions use inception-to-date data. He ignores trading frictions involved in strategy implementation. Using daily and monthly (approximated) total returns of the S&P 500 Index and the Dow Jones Industrial Average (DJIA), along with the U.S. Treasury bill (T-bill) yield as the return on cash, during January 1950 through December 2012, he finds that: Keep Reading

Diversifying and Pair Trading with Volatility Futures

Are implied volatility futures good diversifiers of underlying indexes? Do implied volatility futures for different indexes represent a reliable pair trading opportunity? In their November 2013 paper entitled “Investment Strategies with VIX and VSTOXX Futures”, Silvia Stanescu and Radu Tunaru update the case for hedging conventional stock and stock-bond portfolios with near-term implied volatility futures for the S&P 500 Index (VIX) and the Euro STOXX 50 Index (VSTOXX). For this analysis, they use data for the U.S. and European stock market indexes, associated implied volatility futures and U.S. and European aggregate bond indexes from March 2004 for U.S. assets (VIX futures inception) and from May 2009 for European assets (VSTOXX futures inception), both through February 2012. They also investigate a statistical arbitrage (pair trading) strategy exploiting a regression-based prediction of the trend in the gap between VIX and VSTOXX during the last six months of 2012. Using daily data for the specified indexes and implied volatility futures contracts, they find that: Keep Reading

Stock Return-Implied Volatility Two-way Feedback

Is there exploitable feedback between stock returns and behaviors of associated options due to concentration of informed traders in one market or the other? In the October 2013 version of their paper entitled “The Joint Cross Section of Stocks and Options”, Byeong-Je An, Andrew Ang, Turan Baliand and Nusret Cakici investigate lead-lag relationships between stock returns and changes in associated option-implied volatilities. In case there is some asymmetry, they examine call option and put option implied volatilities separately. They focus on near-term options with delta of 0.5 and expiration in 30 days. Using daily stock returns and associated call and put option implied volatilities (available from OptionMetrics), firm fundamentals and risk adjustment factors during January 1996 through December 2011, they find that: Keep Reading

Agile Portfolio Theory?

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

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