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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.

Gold Plus Low-volatility Stocks?

Does an allocation to gold truly protect a portfolio from downside risk? In their April 2023 paper entitled “The Golden Rule of Investing”, Pim van Vliet and Harald Lohre examine downside risks for portfolios of stocks (value-weighted U.S. stock market) and bonds (10-year U.S. Treasury notes) with and without gold (bullion) based on real returns and a 1-year investment horizon. They also investigate substitution of low-volatility stocks for the broad stock market in search of further downside risk protection. Using monthly returns for the specified assets and U.S. inflation data during 1975 (when gold becomes truly tradable) through 2022, they find that:

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Comprehensive Equity Factor Timing

Is timing of U.S. equity factors broadly and reliably attractive? In their March 2023 paper entitled “Timing the Factor Zoo”, Andreas Neuhierl, Otto Randl, Christoph Reschenhofer and Josef Zechner analyze effectiveness of 39 timing signals applied to 318 known factors. Factors include such categories as intangibles, investment, momentum, profitability, trading frictions and value/growth. Timing signals encompass momentum, volatility, valuation spread, characteristics spread, issuer-purchaser spread and reversal. Specifically, they:

  • Forecast monthly returns for each factor and each signal (12,402 timed factors).
  • Aggregate timing signals using partial least squares regression.
  • Construct multi-factor portfolios that are each month long (short) the fifth, or quintile, of factors with the highest (lowest) predicted returns.
  • Investigate composition of optimal factor timing portfolios, considering such properties such as turnover and style tilt.

Using monthly factor and signal data as available (different start dates) during 1926 through 2020, they find that: Keep Reading

Conditionally Substitute SSO for SPY in SACEVS and SACEMS?

A subscriber asked about boosting the performance of the Simple Asset Class ETF Value Strategy (SACEVS) and the Simple Asset Class ETF Momentum Strategy (SACEMS), and thereby the Combined Value-Momentum Strategy (SACEVS-SACEMS), by substituting ProShares Ultra S&P500 (SSO) for SPDR S&P 500 ETF Trust (SPY) in these strategies whenever:

  1. SPY is above its 200-day simple moving average (SMA200); and,
  2. The CBOE Volatility Index (VIX) SMA200 is below 18.

Substitution of SSO for SPY applies to portfolio holdings, but not SACEMS asset ranking calculations. To investigate, we test all versions of SACEVS, SACEMS and monthly rebalanced 50% SACEVS-50% SACEMS (50-50) combinations. We limit SPY SMA200 and VIX SMA200 conditions to month ends as signals for next-month actions (no intra-month changes). We consider baseline SACEVS and SACEMS (holding SPY as indicated) and versions of SACEVS and SACEMS that always hold SSO instead of SPY as benchmarks. We look at average gross monthly return, standard deviation of monthly returns, monthly gross reward/risk (average monthly return divided by standard deviation), gross compound annual growth rate (CAGR), maximum drawdown (MaxDD) and gross annual Sharpe ratio as key performance metrics. In Sharpe ratio calculations, we employ the average monthly yield on 3-month U.S. Treasury bills during a year as the risk-free rate for that year. Using daily unadjusted SPY and VIX values for SMA200 calculations since early September 2005 and monthly total returns for SSO since inception in June 2006 to modify SACEVS and SACEMS inputs, all through February 2023, we find that: Keep Reading

Validating Use of Wilder Volatility Stops to Time the U.S. Stock Market

Can investors reliably exploit the somewhat opaquely presented strategy summarized in “Using Wilder Volatility Stops to Time the U.S. Stock Market”, which employs Welles Wilder’s Average True Range (ATR) volatility metric to generate buy and sell signals for broad U.S. stock market indexes? To investigate, we each trading day for the SPDR S&P 500 ETF Trust (SPY):

  1. Compute true range as the greatest of: (a) daily high minus low; (b) absolute value of daily high minus previous close; and, (c) absolute value of daily low minus previous close.
  2. Calculate ATR as the simple average of the last five true ranges (including the current one).
  3. Generate a Wilder Volatility Stop (WVS) by multiplying ATR by a risk factor of 2.5.
  4. When out of SPY, buy when it closes above a dynamic trendline defined by a trend minimum plus current WVS (breakout). When in SPY, sell when it closes below a dynamic trendline defined by a trend maximum minus current WVS (breakdown).

We perform the above calculations using raw (not adjusted for dividends) daily SPY prices, but use dividend-adjusted prices to calculate returns. We assume any breakout/breakdown signal and associated SPY-cash switch occurs at the same close. We initially ignore SPY-cash switching frictions, but then test outcome sensitivity to different levels of frictions. We ignore return on cash due to frequency of switching. We further test outcome sensitivity to parameter choices and to an alternative definition of ATR. We use buy-and-hold SPY as a benchmark. Using daily raw and dividend-adjusted prices for SPY during January 1993 (inception) through most of February 2023, we find that: Keep Reading

Using Wilder Volatility Stops to Time the U.S. Stock Market

Can investors use volatility signals to identify short-term stock market trend changes? In his February 2023 paper entitled “Using Volatility to Add Alpha and Control Portfolio Risk”, John Rothe uses Welles Wilder’s Average True Range (ATR) volatility metric to generate buy and sell signals for broad U.S. stock market indexes. Specifically, he each trading day:

  1. Computes the true range of a broad equity exchange-traded fund (ETF) as the greatest of: (a) daily high minus low; (b) absolute value of daily high minus previous close; and, (c) absolute value of daily low minus previous close.
  2. Calculates ATR as the simple average of the last five true ranges (including the current one).
  3. Generates a Wilder Volatility Stop (WVS) by multiplying ATR by a factor of 2.5 as representative of investor volatility risk tolerance.
  4. When out of the asset, he buys when the asset closes above a dynamic trendline apparently defined by a trend minimum plus current WVS (breakout). When in the asset, he sells when the asset closes below a dynamic trendline apparently defined by a trend maximum minus current WVS (breakdown).

He focuses on SPDR S&P 500 ETF Trust (SPY) during 2000-2010 (beginning of 2000 through 2009) but also looks at both Invesco QQQ Trust (QQQ) and iShares Russell 2000 ETF (IWM). In an appendix, he provides similar results for 2010-2020. He assume trades occur at the same closes as breakout and breakdown signals. He ignores effects of dividends and trading frictions. He uses buy-and-hold SPY as the benchmark for the strategy applied to SPY. Using daily raw (not dividend-adjusted) data for SPY, QQQ and IWM during January 2000 through December 2019, he finds that: Keep Reading

Can Investors Capture Academic Equity Factor Premiums via Mutual Funds?

Do factor investing (smart beta) mutual funds capture for investors the premiums found in academic factor research? In their November 2022 paper entitled “Factor Investing Funds: Replicability of Academic Factors and After-Cost Performance”, Martijn Cremers, Yuekun Liu and Timothy Riley analyze the performance of funds seeking to capture of published (long-side) factor premiums. They group factor investing funds into four styles: dividend, volatility, momentum and q-factor (profitability and investment). They separately measure how closely fund holdings adhere to the long sides of academic factor specifications. They measure fund outperformance (alpha) relative to the market factor via the Capital Asset Pricing Model (CAPM) and via a multi-factor model (CPZ6) that accounts for the market factor and for granular size/value interactions. Using monthly returns for 233 hand-selected factor investing mutual funds and for the academic research factors during January 2006 (16 funds available) through September 2020 (207 funds available), they find that:

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Risk Metric That Combines Drawdown and Recovery Time

Is portfolio downside risk better manageable by combining drawdown and recovery into a single “submergence” metric? In their February 2023 paper entitled “Submergence = Drawdown Plus Recovery”, Dane Rook, Dan Golosovker and Ashby Monk present submergence density as a new risk metric to help investors analyze asset/portfolio drawdown and recovery jointly. They define submergence (s) of an asset/portfolio as percentage of current value below its past highwater mark. They define submergence density (d) during a given sample period as the κ-root of the sum of measurement interval submergences each raised to the κ-power during the sample period, as follows:

When κ=1,  submergence density is arithmetic average drawdown. When κ=∞ (or a very high number), submergence density is maximum drawdown. They use κ = 5 in examples to represent typical investor drawdown sensitivity. They define submergence risk-adjusted return as excess return (relative to the risk-free rate) minus a fraction (Θ) of submergence density, using the range 0.2 to 0.5 as reasonable for Θ. They apply submergence to several market indexes and discuss portfolio diversification and rebalancing in the context of reducing submergence overlaps. Using monthly excess returns for U.S. stocks, corporate bonds and Treasuries (S&P 500 Index, ICE BoA Corporate Bond Index and Bloomberg Treasuries Index, respectively) during 1979 through 2022, they find that:

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Interaction of Short-term Reversal and Liquidity

Are there different patterns of short-term stock return reversal based on stock liquidity (measured by size, volatility or turnover)? In their January 2023 paper entitled “Reversals and the Returns to Liquidity Provision”, Wei Dai, Mamdouh Medhat, Robert Novy-Marx and Savina Rizova examine interactions between short-term reversal returns and stock liquidity metrics. They select reversal candidates from the fifth (quintile) of stocks with the highest (winners) and lowest (losers) industry-relative returns over the last 1, 5 or 21 trading days, excluding 3-day returns around earnings announcements. They separately sort stocks into quintiles by size (market capitalization), volatility (standard deviation of daily returns over the last 63 days) or turnover (average percentage of shares outstanding traded daily over the last 63 days). While the sample includes all NYSE, AMEX and NASDAQ common stocks, quintile breakpoints come from NYSE stocks only. Finally, they look at returns to value-weighted intersections of reversal candidate quintiles and size, volatility or turnover quintiles. Using the specified inputs for all listed U.S. common stocks, measured monthly, during January 1973 through December 2021, they find that:

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Human Passions and Asset Volatility

How should investors think about, and perhaps exploit, asset return volatility? In his December 2022 paper entitled “A Stylized History of Volatility”, Emanuel Derman reviews how generations of financial modelers have quantified volatility and ultimately created tradable volatility-based assets. He also discusses some general modeling considerations. Based on the body of research and his experience, he concludes that: Keep Reading

Equity Factor Performance Before and After the End of 2000

Do the widely used U.S. stock return factors exhibit long-term trend changes and shorter-term cyclic behaviors? In his November 2022 paper entitled “Trends and Cycles of Style Factors in the 20th and 21st Centuries”, Andrew Ang applies various methods to compare trends and cycles for equity value, size, quality, momentum and low volatility factors, with focus on a breakpoint at the end of 2000. He measures size using market capitalization, value using book-to-market ratio, quality using operating profitability, momentum using return from 12 months ago to one month ago and low volatility using idiosyncratic volatility relative to the Fama-French 3-factor (market, size, book-to-market) model of stock returns. He each month for each factor sorts stocks into tenths, or deciles, and computes gross monthly factor return from a portfolio that is long (short) the average return of the two deciles with the highest (lowest) expected returns. As a benchmark, he uses the value-weighted market return in excess of the U.S. Treasury bill yield. Using market and factor return data from the Kenneth French data library during July 1963 through August 2022, he finds that:

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