# 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.

**February 15, 2019** - Momentum Investing, Strategic Allocation, Volatility Effects

Subscribers asked whether risk parity might work better than equal weighting of winners within the Simple Asset Class ETF Momentum Strategy (SACEMS), which each month selects the best performers over a specified lookback interval from among the following eight asset class exchange-traded funds (ETF), plus cash:

PowerShares DB Commodity Index Tracking (DBC)

iShares MSCI Emerging Markets Index (EEM)

iShares MSCI EAFE Index (EFA)

SPDR Gold Shares (GLD)

iShares Russell 2000 Index (IWM)

SPDR S&P 500 (SPY)

iShares Barclays 20+ Year Treasury Bond (TLT)

Vanguard REIT ETF (VNQ)

3-month Treasury bills (Cash)

To investigate, we focus on the SACEMS Top 3 portfolio and compare equal weighting to risk parity weights. We calculate risk parity weights at the end of each month by:

- Calculating daily asset return volatilities over the last 63 trading days (about three months, as suggested). This step includes Cash, which has very low volatility.
- Picking the volatilities of the Top 3 momentum winners.
- Weighting each winner by the inverse of its volatility.
- Scaling winner weights such that the total of the three allocations is 100%. This step essentially puts the entire portfolio into Cash when any of the Top 3 is Cash.

We use gross compound annual growth rates (CAGR) and maximum drawdowns (MaxDD) to compare strategies. We check robustness by trying lookback intervals of one to 12 months for both momentum ranking and volatility estimation (increments of 21 trading days for the latter). Using monthly dividend-adjusted closing prices for asset class proxies and the yield for Cash during February 2006 (when all ETFs are first available) through December 2018, *we find that:* Keep Reading

**January 29, 2019** - Value Premium, Volatility Effects

Do investors systematically undervalue stocks that have relatively large book-to-market fluctuations? In their December 2018 paper entitled “The Value Uncertainty Premium”, Turan Bali, Luca Del Viva, Menna El Hefnawy and Lenos Trigeorgis test whether book-to-market volatility relates positively to future returns. They specify book-to-market volatility as standard deviation of daily estimated book-to-market ratios divided by their average over the past 12 months. They estimate book value using the most recent quarterly balance sheet plus analyst forecasts of net income minus expected dividends since that quarter. They lag all accounting data three months and analyst forecasts one month to avoid look-ahead bias. They then each month starting January 1986 rank stocks into tenths (deciles) by book-to-market volatility and reform a hedge portfolio that is long (short) the highest (lowest) decile. Using monthly and daily returns and firm accounting data for a broad sample of non-financial U.S. stocks and data for a large set of control variables during January 1985 through December 2016, *they find that:*

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**January 22, 2019** - Size Effect, Volatility Effects

Do unconventional portfolio construction techniques obscure how, and how well, betting against beta (BAB) works? In their November 2018 paper entitled “Betting Against Betting Against Beta”, Robert Novy-Marx and Mihail Velikov revisit the BAB factor, focusing on interpretation of three unconventional BAB construction techniques:

- Rank weighting of stocks – BAB employs rank weighting rather than equal or value weighting, with each stock in high and low estimated beta portfolios weighted proportionally to the difference between its estimated beta rank and the median rank.
- Hedging by leveraging – BAB seeks market neutrality by deleveraging (leveraging) the high (low) beta portfolio based on estimated betas rather than borrowing to buy the market portfolio to offset BAB’s short market tilt.
- Novel beta estimation – BAB measures stock betas by combining market correlations based on five years of overlapping 3-day returns with volatilities based on one year of daily returns, rather than using slope coefficients of daily stock returns versus daily market returns.

Based on mathematical analysis and empirical results using returns for a broad sample of U.S. stocks during January 1968 through December 2017, *they find that:* Keep Reading

**December 28, 2018** - Strategic Allocation, Volatility Effects

Are there advantages to using leveraged exchange-traded funds (ETF) to implement conventional asset class exposures? In their October 2018 paper entitled “A Portfolio of Leveraged Exchange Traded Funds”, William Trainor, Indudeep Chhachhi and Chris Brown investigate performance of diversified portfolios of 2X or 3X leveraged ETFs that limit exposures to those typically achieved with 1X ETFs. Specifically, when using 2X (3X) funds, allocations are only one half (one third) those for corresponding 1X ETFs. While this approach allows large allocations to a safe asset, it also exposes the portfolio to the higher expense ratios, internal financing costs, leverage decays and rebalancing frequencies of leveraged ETFs. The authors two strategic allocations:

- Actual ETFs during 2010-2017 (see the first table below) – 1X portfolio allocations are 30% U.S. large caps, 10% U.S. midcaps, 10% U.S. small caps, 10% non-U.S. developed market stocks, 10% emerging market stocks, 5% real estate investment trusts (REIT), 5% >20-year U.S. Treasuries, 5% 7-year to 10-year U.S. Treasuries and 15% aggregate corporate bonds. “Savings” from holding leveraged ETFs goes to the aggregate bond ETF, for which there are no leveraged counterparts. Rebalancing occurs whenever equities combined deviate from the specified overall levels by more than 10%.
- Simulated ETFs during 1946-2017 – 1X portfolio allocations are 50% S&P 500, 10% U.S. midcaps, 10% U.S. smallcaps, 15% >20-year U.S. Treasuries, 15% 7-year to 10-year U.S. Treasuries. An equal-weighted ladder of 1-year, 2-year, 5-year and 7-year U.S. Treasuries. “Savings” from holding leveraged ETFs goes to an equal-weighted ladder of 1-year, 2-year, 5-year, and 7-year treasury bonds. Rebalancing occurs whenever equities combined deviate from the specified overall level by more than 10%.

Using daily returns for specified ETFs since 2010 and data required to simulate specified ETFs since 1946, all through December 2017, *they find that:* Keep Reading

**December 10, 2018** - Equity Premium, Volatility Effects

Is there a distinct systematic asset risk, as measured by its market beta, associated with each return measurement interval (frequency, such as daily, monthly or annually)? In other words, is return measurement frequency a risk factor? In their October 2018 paper entitled “Measuring Horizon-Specific Systematic Risk via Spectral Betas”, Federico Bandi, Shomesh Chaudhuri, Andrew Lo and Andrea Tamoni introduce spectral beta, an asset’s market beta for a given return measurement frequency, as a way to assess this frequency as a source of systematic investment risk. They specify how to combine spectral betas into an overall beta and explore ways to interpret and exploit spectral betas. Using mathematical derivations and samples of monthly and daily returns for broad samples of U.S. stocks and stock portfolios, *they find that:* Keep Reading

**November 27, 2018** - Fundamental Valuation, Momentum Investing, Value Premium, Volatility Effects

What is the best way to construct equity multifactor portfolios? In the November 2018 revision of their paper entitled “Equity Multi-Factor Approaches: Sum of Factors vs. Multi-Factor Ranking”, Farouk Jivraj, David Haefliger, Zein Khan and Benedict Redmond compare two approaches for forming long-only equity multifactor portfolios. They first specify ranking rules for four equity factors: value, momentum, low volatility and quality. They then, each month:

- Sum of factor portfolios (SoF): For each factor, rank all stocks and form a factor portfolio of the equally weighted top 50 stocks (adjusted to prevent more than 20% exposure to any sector). Then form a multifactor portfolio by equally weighting the four factor portfolios.
- Multifactor ranking (MFR): Rank all stocks by each factor, average the ranks for each stock and form an equally weighted portfolio of those stocks with the highest average ranks, equal in number of stocks to the SoF portfolio (again adjusted to prevent more than 20% exposure to any sector).

They consider variations in number of stocks selected for individual factor portfolios from 25 to 200, with comparable adjustments to the MFR portfolio. They assume trading frictions of 0.05% of turnover. Using monthly data required to rank the specified factors for a broad sample of U.S. common stocks and monthly returns for those stocks and the S&P 500 Total Return Index (S&P 500 TR) during January 2003 through July 2016, *they find that:* Keep Reading

**November 21, 2018** - Volatility Effects

Are there long-term positions in leveraged index exchange-traded funds (ETF) that beat buying and holding the underlying index? In his October 2018 paper entitled “Leveraged ETF Pairs: An Empirical Evaluation of Portfolio Performance”, Stanley Peterburgsky examines the performance of simple strategies involving leveraged and inverse leveraged ETFs. Specifically, he tests whether the following leveraged ETF portfolios are likely to outperform underlying total return indexes:

- A long position in SSO or UPRO, compared to the S&P 500 Index.
- 1/3 short UPRO (URTY) and 2/3 short SPXU (SRTY), compared to the S&P 500 (Russell 2000) Index.
- 1/4 short SSO (UWM) and 3/4 short SDS (TWM), compared to the S&P 500 (Russell 2000) Index.
- Short SH (RWM), compared to the S&P 500 (Russell 2000) Index.

All short positions have matching long positions in 1-month U.S. Treasury bills that drive some trading. For example, at the end of each trading day, if the UPRO/SRTY portfolio value is less than 90% (more than 110%) of the short balance, the strategy buys (shorts additional) shares of UPRO and SPXU in equal proportions to restore long-short balance. In addition, strategies 2 and 3 require occasional rebalancing of ETF pairs. Baseline strategies allows pair members to drift up to 20% apart before rebalancing. Sensitivity tests evaluate effects of tightening the rebalancing threshold to 10%. Key performance metrics are average annualized return, average annualized standard deviation of daily returns and average annualized Sharpe ratio. Using daily total returns for the specified leveraged ETFs and underlying indexes during 2010 (2/9/2010 for Russell 2000-based funds) through 2016, *he finds that:*

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**October 15, 2018** - Equity Premium, Momentum Investing, Sentiment Indicators, Size Effect, Value Premium, Volatility Effects

Quantitative investing involves disciplined rule-based approaches to help investors structure optimal portfolios that balance return and risk. How has such investing evolved? In their June 2018 paper entitled “The Current State of Quantitative Equity Investing”, Ying Becker and Marc Reinganum summarize key developments in the history of quantitative equity investing. Based on the body of research, *they conclude that:* Keep Reading

**August 30, 2018** - Volatility Effects

Does focusing on downside risk (volatility or beta) consistently produce more accurate forecasts of asset returns? In their July 2018 paper entitled “Tail Risk in the Cross Section of Alternative Risk Premium Strategies”, Bernd Scherer and Nick Baltas investigate how well downside risk explains cross-sectional returns of 260 risk factor strategies spanning asset classes and investment styles from six global investment banks. Their main model is a two-pass regression that distinguishes between conventional market beta and market downside beta. For corroboration, they consider four other indicators of downside risk (return skewness, correlation of tail returns with equity market returns, TED spread and economic policy uncertainty as measured by relative VIX level). Using weekly data risk factor returns and downside risk indicators during February 2008 through January 2018, *they find that:* Keep Reading

**July 10, 2018** - Momentum Investing, Volatility Effects

A betting against beta (BAB) portfolio is long low-beta assets and short high-beta assets, with each side leveraged to a beta of one. Do strong past stock market returns (when investors tend to overweight high-beta stocks) predict an increase in BAB returns? In his June 2018 paper entitled “Time-Varying Leverage Demand and Predictability of Betting-Against-Beta”, Esben Hedegaard tests the prediction that BAB performs better in times and in countries after high past stock market returns in three ways: (1) regression of BAB returns versus past market returns; (2) sorts of BAB returns into fifths (quintiles) based on past market returns; and, (3) a timing strategy that is long BAB half the time and short BAB half the time based on detrended inception-to-date past market returns, scaled to 10% annualized volatility for comparability. Using daily and monthly data, including monthly BAB returns, for U.S. common stocks and the U.S. stock market since 1931 and for 23 other countries from as early as 1988, all through January 2018, *he finds that:* Keep Reading