## Beta Anomaly Is a Force Behind a Number of Equity Factors Thursday, 18 October, 2018

**A new financial research paper has been published and is related to:**

**#77 - Beta Factor in Stocks**

**Authors:** Liu

**Title:** Asset Pricing Anomalies and the Low-Risk Puzzle

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3258015

**Abstract:**

The original observation in Black, Jensen and Scholes (1972) that the security market line is too flat – the beta anomaly – is a driving force behind a number of well-documented cross-sectional asset pricing puzzles. I document that returns to a broad set of anomaly portfolios are negatively correlated with the contemporaneous market excess return. I show that this negative covariance implicitly embeds the beta anomaly in these cross-sectional return puzzles. Taking into account the exposure to the beta anomaly either attenuates or eliminates the economic and statistical significance of the risk-adjusted returns to a large set of asset pricing anomalies.

**Notable quotations from the academic research paper:**

"Defying both theory and intuition, low beta assets have consistently outperformed high beta assets, both over time and across various asset markets. This observation has come to be known as the beta anomaly. In this paper, I present evidence that the beta anomaly is embedded in a broad set of cross-sectional asset pricing puzzles.

I document that anomaly portfolio returns share a striking and peculiar pattern: returns are positive and peak in market downfalls, but are negative when the market rises. I verify that this negative covariance is empirically equivalent to the long portfolios holding stocks with lower betas relative to the short portfolios. Mitigating the exposure to the beta anomaly either attenuates or eliminates the economic and statistical significance of the risk-adjusted returns to numerous cross-sectional anomalies.

This paper analyzes a set of ten asset pricing puzzles representative of different types of cross-sectional return predictors documented in the literature. The sample includes anomalies that are operation-based (total accruals, return on assets, profitability, investment growth), return-based (momentum), risk-based (O-score, default probability, return volatility, idiosyncratic volatility), as well as issuance-related (composite equity issues). It is remarkable that portfolios formed on such a wide range of characteristics all have returns that are negatively correlated with the market.

The observed negative covariance has two immediate implications. First, to the extent that these anomaly portfolios hold "quality" stocks (profitable, high past return, mature, low probability of failure, etc.), the fact that they pay off in bad states of the world is consistent with flight to quality in market downturns. The negative covariance between "quality" stocks and the market points to the beta anomaly as an explanation for why "quality" stocks have high average returns. Second, the shared negative covariance with the market is suggestive of the data mining concern in the empirical asset pricing literature - the search for cross-sectional return predictability has led to different dimensions to slice the data, many of which somehow implicitly take advantage of the beta anomaly.

To show that the beta anomaly subsumes the risk-adjusted returns of the cross-sectional anomalies, I mitigate the long-short portfolios' exposure to the beta anomaly in two complementary ways.

First, I consider an alternative weighting scheme when aggregating returns to the portfolio level: I weight stocks in long legs using the ascending decile ranking of their pre-formation betas, and weight stocks in short legs using the descending decile beta rankings. This way of constructing portfolios keeps the original portfolio constituents while putting more weight on high beta stocks in the long leg, and more weight on low beta stocks in the short leg, relative to value-weighted portfolios.

The second approach complements the first by keeping the value-weighting scheme from the original portfolio construction, but removing stocks with low betas in the long leg, and stocks with high betas in the short leg.

Together these two approaches allow me to separate the effect of beta exposure from the eect of the anomaly characteristics on the long-short portfolios' alphas. **Both modified portfolio construction methods reduce or remove the exposure to the beta anomaly, and lead to reduced CAPM alphas for the anomaly trading strategies. In terms of economic magnitude, the reduction in trading profitability ranges from 27% up to a reversed sign.**"

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## It Is Hard to Profit by Buying Options and Betting on Higher Volatility Thursday, 11 October, 2018

**A new financial research paper has been published and is related to:**

**#20 - Volatility Risk Premium Effect**

**Authors:** Israelov, Tummala

**Title:** Being Right is Not Enough: Buying Options to Bet on Higher Realized Volatility

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3248500

**Abstract:**

Speculators who wish to bet on higher future volatility often purchase options to “go long volatility.” Should investors who buy options expect to profit when realized volatility increases? If so, under what conditions? To answer these questions, we conduct an analysis of the relationship between long volatility performance (buying options) and contemporaneous changes in volatility. We find that buying one-month S&P 500 options is only consistently profitable in the highest decile of changes in one-month volatility. Buying options consistently loses money in the lowest seven deciles of changes in volatility. We then study the trade entry and exit timing required to retain the profits from long option positions during significant volatility increases. We find similar results in global equity option markets.

**Notable quotations from the academic research paper:**

"During most of the mid-2010s, the S&P 500 Index’s volatility hovered near its historical lows. This calm environment has led many investors to ask whether low volatility presents an opportunity to obtain “cheap” portfolio downside protection by purchasing index options. Israelov and Nielsen (2015) show that the answer to this question is no. They show that the Volatility Risk Premium (VRP) also exists in low volatility environments, and therefore that portfolio protection is still expensive even in calm markets.

Portfolio protection, however, is not the only rationale for purchasing options. A long option position allows a speculator to bet on rising volatility. Many proponents of long volatility exposure often advocate this trade in a low implied volatility market environment. Heightened levels of uncertainty, geopolitical risk, or merely a reversion to long-term volatility are some of the arguments put forth by those who expect volatility to spike.

A recommendation to buy options to capture a predicted increase in volatility is predicated on the assumption that investors profit from long options (or long volatility) positions when volatility increases. This paper tests that assumption.

Although it may seem unintuitive, we show that long volatility positions can lose money even when realized volatility rises. How can this be true? Because, long volatility investors must overcome the well-documented VRP – the difference between implied and realized volatility – just to break even. On average this VRP spread is around 3% in the S&P 500. Therefore, the VRP spread typically accrues to the volatility seller, paid by the long volatility investor. As such, long volatility investors enter their trade facing a significant head wind.

Exhibit 2 sorts the ex post VRP into deciles and reports the average within each decile. On average, equity index options have been richly priced, with an average VRP of 3.0%. The VRP was positive around 85% of the time. Correspondingly, Exhibit 2 shows that, on average, the VRP is positive in eight of the ten deciles, approximately flat in one decile, and negative in one decile. This result implies that long volatility positions in one-month equity index options have been profitable infrequently.

Exhibit 3 sorts the returns of the long option portfolios into deciles, and reports their average annualized return within each decile. Similar to Exhibit 2, Exhibit 3 shows that long option portfolios were infrequently profitable (28% of the time). Average returns were negative in seven of the ten deciles, flat in one decile, and profitable in two. Sorting on actual profitability reveals that there are relatively few profit opportunities.

Volatility mean-reverts over the long run. With equity volatility at historical lows in the mid-2010s, many market commentators suggested long volatility positions in order to bet on increases in volatility. But are bets on increasing volatility actually profitable when volatility increases?

Using our change in volatility measure, we document that over 30-day periods volatility increased 43% of the time in the S&P 500 between 1996 and 2016. Exhibit 4 reports the long option portfolio’s return properties conditional on only holding options during those 30-day periods in which volatility actually increased. For a more complete picture, the exhibit also reports return properties of the unconditional long option portfolio in which the investor does not attempt to time, as well as return properties conditional on periods in which volatility decreased. Having perfect foresight into whether equity markets become more volatile is profitable, but not reliably so. The conditional ex post VRP is -0.9% during periods in which volatility increased versus the 3.0% unconditional VRP. During periods when volatility increased, the average conditional delta-hedged long option annualized return is 1.1%, with a 0.6 Sharpe ratio. This is certainly better than the unconditional long option annualized return of -1.7%, with a -1.1 Sharpe ratio, and considerably better than the conditional long option annualized return of -3.9% and corresponding -3.9 Sharpe ratio during periods when volatility decreased. However, even when realized volatility increases, long option returns are only profitable about half the time. A small set of out-sized volatility increases is what led to positive conditional average long option returns. This suggests that even knowing with certainty that volatility will increase is not enough to reliably profit from a long volatility position. The investor is left with a coin flip in terms of the hit rate of holding a long option position in this scenario.

Then what condition is sufficient to reliably profit? We sort the ex post VRP into deciles by change in volatility and report the average in each decile in Exhibit 5. The ex post VRP is only negative in the tenth decile. It is also interesting that the first decile’s average VRP is more positive than the tenth decile’s is negative.

Exhibit 6 shows the distribution of the ex post VRP within each decile. The ex post VRP was positive more than 90% of the time in seven of the ten deciles, and positive more than 65% of the time in the eighth and ninth decile. The only decile in which the ex post VRP was consistently negative was the tenth decile. Correspondingly, large increases in volatility are the only time that we expect long option positions to be profitable.

Realized option returns are likely more interesting to option investors than the difference between implied and realized volatility. In that regard, we next sort long option returns into deciles by change in volatility, and report the average annualized return in each decile in Exhibit 7.

Average long option returns were negative in eight of the ten deciles. Exhibit 8 shows the distribution of long option returns in each decile. Long option returns were consistently negative in most deciles, positive slightly more than half the time in the ninth decile, and consistently positive (85% of the time) in the tenth decile.

__Overall, the results for long option returns are similar to those found for the ex post VRP. To consistently profit from a long volatility position on the basis of forecasting changes in volatility, you would have had to predict a 10% probability outcome. The average, annualized long option return in this decile was 6.6% and the average return across the other nine deciles was -2.7%.__

__Due to these considerations, tactical long volatility traders face a steep uphill battle. Managers who are able to successfully implement this strategy should be given credit for demonstrating exceptional skill (or congratulated for their good luck). However, some amount of healthy skepticism is likely warranted for those who claim to consistently have such exceptional skill.__"

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## Three New Academic Research Papers Related to Momentum in Stocks Friday, 5 October, 2018

**Related to:**

**#14 - Momentum Effect in Stocks**

**Author:** Muller, Muller

**Title:** The Remarkable Relevance of Characteristics for Momentum Profits

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3240609

**Abstract:**

This paper provides a comprehensive analysis of a large set of momentum enhancing strategies for global equity markets. Our findings reveal the relevance of characteristics in enhancing and explaining momentum after accounting for possible interrelations with idiosyncratic volatility and extreme past returns. Out of a set of eighteen stock characteristics, we find particularly age, book-to-market, maximum daily return, R², information diffusion, and 52-week high price to matter for momentum profits. Overall, and consistent with behavioral explanation attempts, momentum appears to work best for hard-to-value firms with high information uncertainty. There are however substantial cross-country differences with regard to which characteristics truly enhance momentum. Our results imply that the link between idiosyncratic volatility, extreme past returns, and momentum profits itself is unable to comprehensively explain enhanced momentum returns and corroborate the heterogeneity of stock markets around the globe.

**Author:** Abhyankar, Filippou, Garcia-Ares, Haykir

**Title:** Overcoming Arbitrage Limits: Option Trading and Momentum Returns

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3206873

**Abstract:**

Returns to cross-sectional momentum in the U.S. equity market, over 1996-2016, are fifty percent lower and statistically insignificant relative to the previous two decades. The decline is linked to larger arbitrage capital flows, lower stock trading costs, and greater investor awareness after publication. During this period stocks with traded options rose to more than seventy percent of all listed stocks. We find strong evidence that the reduction in momentum profits is also related to stock option trading that offers alternate avenues for short sales and information flows that contribute to more efficient stock pricing.

**Author:** Avramov, Hore

**Title:** Cross-Sectional Factor Dynamics and Momentum Returns

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3033349

**Abstract:**

This paper proposes and implements an inter-temporal model wherein aggregate consumption and asset-specific dividend growths jointly move with two mean-reverting state variables. Consumption beta varies through time and cross sectionally due to variation in half-lives and stationary volatilities of the dividend signals. Winner (Loser) stocks exhibit high (low) half-lives and stationary volatilities, and thus exhibit high (low) consumption beta commanding high (low) risk-premium. The model also rationalizes the "momentum crashes" phenomenon discussed in Daniel and Moskowitz (2014). High half-lives of dividend signals in Winners keep their consumption betas low long after recovering from a prolonged economic downturn, while low half-lives in Losers make their consumption betas grow rather quickly. Thus, coming out of a recession, the long Winner/short Loser strategy reduces in consumption beta and, hence, risk-premia.

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## VVIX Index Predicts Value/Growth Return Spread Thursday, 27 September, 2018

**A new financial research paper has been published and is related value/growth style returns:**

**#26 - Value (Book-to-Market) Anomaly**

**Author:** Krause

**Title:** Risk and Uncertainty in Style Rotation

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3209491

**Abstract:**

The effectiveness of the VIX index as a leading indicator of style returns has been examined in the finance literature, finding that increases in this “fear index” lead to outperformance of “value” vs “growth” stocks, although the effect has attenuated over time. This study introduces the concept of “uncertainty” as an additional indicator of returns to value, as measured by the CBOE® VVIX (“volatility of volatility”), that that may be considered as a proxy for “uncertainty” in the Knightian sense. Increases in uncertainty (the VVIX index) lead to negative short-term returns to value. Additional macroeconomic variables provide additional incremental information regarding these phenomena.

**Notable quotations from the academic research paper:**

"this study examines the effectiveness of the two CBOE® volatility indices as leading indicators of style returns (value vs. growth), and the results of the analysis indicate that the CBOE® VVIX index provides significant incremental information regarding the interaction of returns, volatility, and uncertainty on a lead-lag basis. The initial analysis of the VIX index relative to style returns is consistent with Boscaljon et al. (2011) since it finds largely insignificant short-term effects of the VIX index on returns to value.

However, innovations in the VVIX index indicate significant negative returns to value. The inclusion of several macroeconomic variables provides additional explanatory information since the VIX index indicates positive returns to value under certain conditions. The main contribution to the literature of this paper is the introduction of the additional concept of “uncertainty” into the returns to value analysis using highly liquid ETFs. The availability of these products, and their recent exponential growth, provides an opportunity to examine the relation of expected volatility and uncertainty to growth and value using similar, easily tradable and low-cost instruments.

In order to further explore the returns to value from uncertainty as proxied by the VVIX index, in Table 5, changes in the VVIX index are included in the estimations of Equation 2 as a potentially further explanatory, independent variable. In this estimation, there is one indication of the potential returns to value from volatility in conjunction with uncertainty. In Panel A, for the large-cap ETFs, the results for five-day returns to value are significantly positive for changes in the VIX index (volatility) at the five percent level, although some other coefficients (10- and 20- day) are significant at the ten percent level. Additionally, the coefficients are significant and negative for changes in the VVIX index (uncertainty) over five- to thirty-day time periods (the 20-day coefficient is marginally significant) at the five percent level.

"

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