# 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, 2023** - Technical Trading, Volatility Effects

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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**January 6, 2023** - Big Ideas, Volatility Effects

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

**January 3, 2023** - Fundamental Valuation, Momentum Investing, Size Effect, Value Premium, Volatility Effects

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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**December 22, 2022** - Equity Premium, Strategic Allocation, Volatility Effects

A subscriber requested evaluation of a strategy that seeks to exploit U.S stock market reversion after dips by temporarily applying margin. Specifically, the strategy:

- At all times holds the U.S. stock market.
- When the stock market closes down more than 7% from its high over the past year, augments stock market holdings by applying 50% margin.
- Closes each margin position after two months.

To investigate, we assume:

- The S&P 500 Index represents the U.S. stock market for calculating drawdown over the past year (252 trading days).
- SPDR S&P 500 (SPY) represents the market from a portfolio perspective.
- We start a margin augmentation at the same daily close as the drawdown signal by slightly anticipating the drawdown at the close.
- 50% margin is set at the opening of each augmentation and there is no rebalancing to maintain 50% margin during the two months (42 trading days) it is open.
- If S&P 500 Index drawdown over the past year is still greater than 7% after ending a margin augmentation, we start a new margin augmentation at the next close.
- Baseline margin interest is U.S. Treasury bill (T-bill) yield plus 1%, debited daily.
- Baseline one-way trading frictions for starting and ending margin augmentations are 0.1% of margin account value.
- There are no tax implications of trading.

We use buying and holding SPY without margin augmentation as a benchmark. Using daily levels of the S&P 500 Index, daily dividend-adjusted SPY prices and daily T-bill yields from the end of January 1993 (limited by SPY) through November 2022, *we find that:* Keep Reading

**October 10, 2022** - Equity Premium, Volatility Effects

Market commentators sometimes cite a high Chicago Board Options Exchange (CBOE) Volatility Index (VIX), the options-implied volatility of the S&P 500 Index as an indicator of investor sentiment and therefore a contrarian signal for the stock market. Specifically, a relatively high (low) VIX indicates panic (complacency) and therefore pending stock market strength (weakness). Does evidence support such conventional wisdom? To check, we relate the level of VIX to S&P 500 Index returns over the next 5, 10, 21, 63 and 126 trading days. Using daily closes for VIX and the S&P 500 Index during January 1990 (limited by the VIX series) through September 2022, *we find that: Keep Reading *

**September 23, 2022** - Strategic Allocation, Volatility Effects

The body of research indicates that low-volatility/low-beta stock investing suppresses exposure to overall equity market risk. Does it work equally well for different sources of such risk? In his September 2022 paper entitled “Macro Risk of Low-Volatility Portfolios”, David Blitz examines the separate exposures of low-volatility portfolios to interest rate, implied volatility, liquidity, commodity, sentiment, macroeconomic and climate (CO_{2} emissions) risk factors. Specifically, he compares the contemporaneous interactions with these risks of the MSCI USA Minimum Volatility Index (based on minimum variance optimization), the S&P 500 Low Volatility Index (the 100 inverse volatility-weighted stocks in the S&P 500 with the lowest volatilities over the past one year) and the S&P 500 Index as the market benchmark. He measures risk factor-index interactions via univariate regressions of monthly excess returns versus monthly risk factor values. He also considers risk factor interactions with ten (decile) equally weighted portfolios of the 1,000 largest U.S. stocks at each point in time sorted by preceding 36-month volatilities. Using monthly total returns for the indexes/portfolios in U.S. dollars in excess of the risk-free rate and monthly risk factor values during January 1991 through December 2021, *he finds that:*

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**September 22, 2022** - Equity Premium, Momentum Investing, Size Effect, Value Premium, Volatility Effects

Are equity multifactor strategies, as implemented by exchange-traded funds (ETF), attractive? To investigate, we consider seven ETFs, all currently available:

- iShares Edge MSCI Multifactor USA (LRGF) – holds large and mid-cap U.S. stocks with focus on quality, value, size and momentum, while maintaining a level of risk similar to that of the market. The benchmark is iShares Russell 1000 (IWB).
- iShares Edge MSCI Multifactor International (INTF) – holds global developed market ex U.S. large and mid-cap stocks based on quality, value, size and momentum, while maintaining a level of risk similar to that of the market. The benchmark is iShares MSCI ACWI ex US (ACWX).
- Goldman Sachs ActiveBeta U.S. Large Cap Equity (GSLC) – holds large U.S. stocks based on good value, strong momentum, high quality and low volatility. The benchmark is SPDR S&P 500 (SPY).
- John Hancock Multifactor Large Cap (JHML) – holds large U.S. stocks based on smaller capitalization, lower relative price and higher profitability, which academic research links to higher expected returns. The benchmark is SPY.
- John Hancock Multifactor Mid Cap (JHMM) – holds mid-cap U.S. stocks based on smaller capitalization, lower relative price and higher profitability, which academic research links to higher expected returns. The benchmark is SPDR S&P MidCap 400 (MDY).
- JPMorgan Diversified Return U.S. Equity (JPUS) – holds U.S. stocks based on value, quality and momentum via a risk-weighting process that lowers exposure to historically volatile sectors and stocks. The benchmark is SPY.
- Xtrackers Russell 1000 Comprehensive Factor (DEUS) – seeks to track, before fees and expenses, the Russell 1000 Comprehensive Factor Index, which seeks exposure to quality, value, momentum, low volatility and size factors. The benchmark is IWB.

We focus on monthly return statistics, along with compound annual growth rates (CAGR) and maximum drawdowns (MaxDD). Using monthly returns for the seven equity multifactor ETFs and benchmarks as available through August 2022, *we find that:* Keep Reading

**September 7, 2022** - Volatility Effects

How have different asset classes recently interacted with the CBOE Volatility Index (VIX)? To investigate, we consider relationships between VIX and the exchange-traded fund (ETF) asset class proxies used in the Simple Asset Class ETF Momentum Strategy (SACEMS) or the Simple Asset Class ETF Value Strategy (SACEVS) at a monthly measurement frequency. We consider both overall relationships and relationships across ranges of VIX. Using end-of-month levels of VIX since January 1990 and dividend-adjusted monthly closing prices for the asset class proxies as available since July 2002, all through July 2022, *we find that:* Keep Reading

**August 29, 2022** - Strategic Allocation, Volatility Effects

One concern about simple momentum strategies is data snooping bias impounded in selection of the lookback interval(s) used to measure asset momentum. To circumvent this concern, we consider the following argument:

- The CBOE Volatility Index (VIX) broadly indicates the level of financial markets distress and thereby the tendency of investors to act complacently (when VIX is low) or to act in panic (when VIX is high).
- Complacency translates to resistance in changing market outlook (long memory and lookback intervals), while panic translates to rapid changes of mind (short memory and short lookback intervals).
- The inverse of VIX is therefore indicative of the actual aggregate current lookback interval affecting investor actions.

We test this argument by:

- Setting a range for VIX using monthly historical closes from January 1990 through July 2002, before the sample period used for any tests of the Simple Asset Class ETF Momentum Strategy (SACEMS).
- Applying buffer factors to the bottom and top of this actual inverse VIX range to recognize that it could break above or below the historical range in the future.
- Segmenting the buffer-extended inverse VIX range into 12 equal increments and mapping these increments by rounding into momentum lookback intervals of 1 month (lowest segment) to 12 months (highest segment).
- Applying this same method to future end-of-month inverse VIX levels to select the SACEMS lookback interval for the next month.

We test the top one (Top 1), the equally weighted top two (EW Top 2) and the equally weighted top three (EW Top 3) SACEMS portfolios. We focus on compound annual growth rate (CAGR), maximum drawdown based on monthly measurements, annual returns and Sharpe ratio as key performance statistics. To calculate excess annual returns for the Sharpe ratio, we use average monthly yield on 3-month Treasury bills during a year as the risk-free rate for that year. Benchmarks are these same statistics for tracked SACEMS. Using monthly levels of VIX since inception in January 1990 and monthly dividend-adjusted prices of SACEMS assets since February 2006 (initial availability of a commodities ETF), all through July 2022, *we find that:* Keep Reading

**August 24, 2022** - Volatility Effects

A subscriber asked about frequency, magnitude and duration of bear market rallies. To investigate, we employ the S&P 500 Index and consider three ways to define a bear market:

- From the day the index is first down over 20% from a prior peak until the day it closes no more than 20% down (< -20% Drawdown).
- From the day the index is first down over 30% from a prior peak until the day it closes nor more than 30% down (< -30% Drawdown).
- From the day the index crosses below its 200-day simple moving average until the day it crosses back above this moving average (SMA200).

Based on bear market statistics for these three definitions, we then look at ways to characterize bear market rallies. Using daily S&P 500 Index closes from the end of December 1927 through mid-August 2022, *we find that:* Keep Reading