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The Efficient Market Theory has been challenged by the finding that relatively simple anomalies can be utilized to construct trading strategies, that are found to generate statistically significant higher returns than those of the market portfolio. There is also a second possibility where the Market efficiency is also challenged if some simple investment strategy generates a comparable return to that of the market but at a systematically lower level of risk. Well known strategies that challenge efficiency are Momentum, Size and Value, but a large amount of research has been made about volatility effect in stocks.

Low-risk stocks exhibit significantly higher risk-adjusted returns than the market portfolio, while high-risk stocks significantly underperform on a risk-adjusted basis. Authors Clarke, de Silva and Thorley have found that minimum variance portfolios, based on the 1000 largest US stocks over the years 1968-2005, achieve a volatility reduction of about 25%, while delivering comparable or even higher average returns than the benchmark market portfolio. This paper has even found that portfolios, which consist of stocks with the lowest historical volatility, are associated with Sharpe ratio improvements, that are even larger than those in the aforementioned minimum variance portfolios. Baker, Bradley and Wurgler in their work: Benchmarks as Limits to Arbitrage: Understanding the Low Volatility Anomaly, have proved that over the past 41 years, high volatility and high beta stocks have substantially underperformed low volatility and low beta stocks in U.S. markets. Clearly, there is a lot of evidence that the low-volatility effect is an anomaly that works and should be utilized in an investing strategy. Concentrating on long-term volatility, the aforementioned anomaly can be utilized by the investor to create decile portfolios that are based on a straightforward ranking of stocks on their historical return volatility. Afterward, the investor would simply long the decile with the stocks with the lowest volatility (moreover, he can short the decile of stocks with the highest volatility).

Going long on low-risk stocks and short on high-risk stocks produce a significant volatility spread. However, a long-short portfolio isn’t the only way to exploit this anomaly. A long-only strategy is much easier to implement than a long-short strategy. The investor could simply go long on low volatility stocks and enjoy the higher Sharpe ratio than common equity indices.

Fundamental reason

Firstly, in order to take full advantage of the attractive absolute returns of low-risk stocks, there is a need for leverage. However, in practice, either many investors are not allowed or they are simply unwilling to actually apply leverage, especially the leverage needed for exploiting the volatility effect. This results in the fact that the opportunity, which is presented by low-risk stocks, cannot be easily arbitraged away. Secondly, the volatility effect could be the result of an inefficient and decentralized investment approach. The problem of benchmark driven investing is that asset managers have an incentive to tilt towards high beta or high volatility stocks. This is a relatively simple way for every asset manager to generate returns above the average if he assumes that the CAPM at least partially holds. This results in overpriced high-risk stocks, while low-risk stocks may become under-priced, this is particularly consistent with the return patterns which were documented in this paper.

The volatility effect may also be caused by behavioral biases among private investors. Private investors will overpay for risky stocks which are perceived to be similar to lottery tickets because they are in the search for high returns in as short time as possible. Additionally, Li, Sullivan and García-Feijóo in their paper, The Low-Volatility Anomaly: Market Evidence on Systematic Risk versus Mispricing, have found out that the anomaly returns associated low-volatility stocks can be attributed to market mispricing or to compensation for higher systematic risk. Soe, in “The low-volatility effect: A comprehensive look”, claims that volatility-effect challenges the traditional equilibrium asset pricing theory that an asset’s expected return is directly proportional to its beta or systematic risk, or, in other words, higher-risk securities should be rewarded with higher expected returns while lower-risk assets receive lower expected returns. The evidence seems to be endless. Moreover, the volatility effect is similar in size compared to classic effects (momentum, size and value) and remains significant after Fama-French adjustments and double sorts. Last but not least, concentrating on long-term, past 3 years volatility implies a much lower portfolio turnover.

Other papers

**Sullivan, Li: Why Low-Volatility Stocks Outperform: Market Evidence on Systematic Risk Versus Mispricing**

**- Abstract**

We explore whether the well publicized anomalous returns associated low-volatility stocks can be attributed to market mispricing or to compensation for higher systematic risk. Our results, conducted over a 46 year study period (1962-2008), indicate that the high returns related to low-volatility portfolios cannot be viewed as compensation for systematic factor risk. Instead, the excess returns are more likely to be driven by market mispricing as perhaps associated with an imperfection such as some investor irrationality connected with volatility.

**Baker, Bradley, Wurgler: Benchmarks as Limits to Arbitrage: Understanding the Low Volatility Anomaly**

**- Abstract**

Over the past 41 years, high volatility and high beta stocks havesubstantially underperformed low volatility and low beta stocks in U.S.markets. We propose an explanation that combines the average investor’spreference for risk and the typical institutional investor’smandate to maximize the ratio of excess returns and tracking errorrelative to a fixed benchmark (the information ratio) without resortingto leverage. Models of delegated asset management show that suchmandates discourage arbitrage activity in both high alpha, low betastocks and low alpha, high beta stocks. This explanation is consistentwith several aspects of the low volatility anomaly including why it hasstrengthened in recent years even as institutional investors have becomemore dominant.

**Baker, Haugen: Low Risk Stocks Outperform within All Observable Markets of the World**

**- Abstract**

This article provides global evidence supporting the Low Volatility Anomaly: that low risk stocks consistently provide higher returns than high risk stocks. This study covers 33 different markets during the time period from 1990-2011. (Two previous studies by Haugen & Heins (1972) and Haugen & Baker (1991) show the same negative payoff to risk in time periods 1926-1970 and 1970-1990.) The procedure for our study is intentionally simple, transparent and easily replicable. Our samples include non-survivors. We look at an international universe of stocks beginning with the first month of 1990 until December 2011; we compute the volatility of total return for each company in each country over the previous 24 months. Stocks in each country are ranked by volatility and formed into deciles. In the total universe and in each individual country low risk stocks outperform, the relationship with respect to Sharpe ratios is even more impressive. We believe this anomaly is caused primarily by agency issues, namely the compensation structures and internal stock selection processes at asset management firms which lead institutional investors on average to hold more volatile stocks. The article also addresses the implications for how corporate finance managers make capital investment decision in light of this evidence. The evidence presented here dethrones both CAPM and the Efficient Market Hypothesis.

**Soe: THE LOW-VOLATILITY EFFECT: A COMPREHENSIVE LOOK**

**- Abstract**

Among the long-standing anomalies in modern investment theory, perhaps none are as puzzling and compelling as the low-volatility effect. It challenges the traditional equilibrium asset pricing theory that an asset’s expected return is directly proportional to its beta or systematic risk, or, in other words, higher-risk securities should be rewarded with higher expected returns while lower-risk assets receive lower expected returns.

**Dutt, Humphery-Jenner: Stock Return Volatility, Operating Performance and Stock Returns: International Evidence on Drivers of the ‘Low Volatility’ Anomaly**

**- Abstract**

This study highlights the link between stock return volatility, operating performance, and stock returns. Prior studies suggest that there is a ‘low volatility’ anomaly, where firms with a low stock return volatility out-perform firms with a high stock return volatility. This paper confirms that low volatility stocks earn higher returns than high volatility stocks in emerging markets and developed markets outside of North America. We also show that low volatility stocks have higher operating returns and this might explain why low volatility stocks earn higher stock returns. These results provide a partial explanation for the ‘low volatility effect’ that is independent from the existence of market anomalies or per se inefficiencies that might otherwise drive a low volatility effect. We emphasize the importance of controlling for stock return volatility when analyzing operating performance and stock performance.

**Feijoo, Kochard, Sullivan, Wang: Low-Volatility Cycles: The Influence of Valuation and Momentum on Low-Volatility Portfolios**

**- Abstract**

Research showing that the lowest risk stocks tend to outperform the highest risk stocks over time has led to rapid growth in so-called low-risk equity investing in recent years. We provide evidence that both extends and contrasts with existing research on low-risk investing. First, we demonstrate that the low-risk anomaly might more accurately be referred to as the high-risk anomaly due to the fact that the anomalous returns are found primarily among those stocks in the highest risk quintile. Next, we demonstrate that the historical performance of low risk investing is strikingly cyclical and driven to a large degree by swings in the relative valuation levels of low risk versus high risk stocks and also by varying appetite for momentum driven investing. Furthermore, the current valuation cycle nears historically high levels, which, combined with high exposure to momentum, indicates greater uncertainty in low-risk investing future outcomes.

**Chow, Hsu, Kuo, Li: A Survey of Low Volatility Strategies**

**- Abstract**

This paper replicates various low volatility strategies and examines their historical performance using U.S., global developed markets, and emerging markets data. In our sample, low volatility strategies outperformed their corresponding cap-weighted market indexes due to exposure to the value, betting against beta (BAB), and duration factors. The reduction in volatility is driven by a substantial reduction in the portfolios’ market beta. Different approaches to constructing low volatility portfolios, whether optimization or heuristic based, result in similar factor exposures and therefore similar long-term risk-return performance. For long-term investors, low volatility strategies can contribute to a considerably more diversified equity portfolio which earns equity returns from multiple premium sources instead of market beta alone. While the lower risk and higher return seem persistent and robust across geographies and over time, we identify flaws with naïve constructions of low volatility portfolios. First, naïve low volatility strategies tend to have very high turnover and low liquidity, which can erode returns significantly. They also have very concentrated country/industry allocations, which neither provide sensible economic exposures nor find theoretical support in the more recent literature on the within-country/industry low volatility effect. Additionally, there is concern that low volatility stocks could become expensive, a development which would eliminate their performance advantage. This highlights the potential danger of a portfolio construction methodology that is unaware of the fundamentals of the constituent stocks — after all, low volatility investing is useful only if it comes with superior risk-adjusted performance. That many naïve low volatility portfolios are no longer value portfolios today bodes poorly for their prospective returns. More thoughtful portfolio construction research is necessary to produce low volatility portfolios that are more likely to repeat the historical outperformance with reasonable economic exposure and adequate investability.

**Jordan, Riley: The Long and Short of the Vol Anomaly**

**- Abstract**

On average, stocks with high prior-period volatility underperform those with low prior-period volatility, but that comparison is misleading. As we show, high volatility is an indicator of both positive and negative future abnormal performance. Among high volatility stocks, those with low short interest actually experience extraordinary positive returns, while those with high short interest experience equally extraordinary negative returns. The fact that publicly available information on aggregate short selling can be used to predict positive and negative abnormal returns of great magnitude points to a large-scale market inefficiency. Further, based on the evidence in this study, the current “low vol” investing fad has little or no real foundation.

**Huang, Lou, Polk: The Booms and Busts of Beta Arbitrage**

**- Abstract**

Historically, low-beta stocks deliver high average returns and low risk relative to high-beta stocks, offering a potentially profitable investment opportunity for professional money managers to “arbitrage” away. We argue that beta-arbitrage activity instead generates booms and busts in the strategy’s abnormal trading profits. In times of relatively little activity, the beta-arbitrage strategy exhibits delayed correction, taking up to three years for abnormal returns to be realized. In stark contrast, in times of relatively-high activity, short-run abnormal re turns are much larger and then revert in the long run. Importantly, we document a novel positive-feedback channel operating through firm-level leverage that facilitates these boom and bust cycles. Namely, when arbitrage activity is relatively high and beta-arbitrage stocks are relatively more levered, the cross-sectional spread in betas widens, resulting in stocks remaining in beta-arbitrage positions significantly longer. Our findings are exclusively in stocks with relatively low limits to arbitrage (large, liquid stocks with low idiosyncratic risk), consistent with excessive arbitrage activity destabilizing prices.

**de Carvalho, Zakaria, Xiao, Moulin: Low Risk Anomaly Everywhere – Evidence from Equity Sectors**

**- Abstract**

We give strong empirical evidence of a risk anomaly in equity sectors in a number of regions and countries of developed and emerging markets, with the lowest risk stocks in each activity sector generating higher returns than would be expected given their levels of risk, and the converse outcome for the riskier stocks. We believe this evidence is a likely consequence of the fact that equity analyst and active fund managers tend to specialize in particular sectors and to mainly select stocks from those sectors. Additionally, constraints restricting the deviation of sector weights in active portfolios against their market capitalization benchmarks are often used by active fund managers, in particular by quantitative managers which tend to go as far as being sector neutral. As a consequence, we find that sector-neutral, low-risk approaches appear more efficient at generating alpha than non-sector neutral approaches, with the latter showing strong sector allocation towards financials, utilities and consumer staples than sector neutral, at least when applied to developed countries in a global universe. We also discuss some properties of low-risk investing such as tail risk, turnover and liquidity.

**Falkenstein: Requisite Assumptions for the Persistence of the Low Volatility Anomaly**

**- Abstract**

Common explanations of the low volatility anomaly involve biases or frictions that cause investors to overpay for high volatility assets, giving them a negative alpha within the CAPM model, yet currently all such mechanisms are either heuristic or partial equilibrium. This paper shows that leverage constraints of Frazzini and Pedersen (2014) alone cannot explain this result if there also exist rational investors. If 3 non-standard assumptions are added — hybrid relative utility, delusional subset of investors, residual systematic risk across beta — then we can capture several facts existing models cannot simultaneously capture: a positive return to the market, positive holdings by rational investors to negative CAPM-alpha stocks, and a negative Security Market Line. New data relevant to these assumptions are presented.

**Wang: Institutional Holding, Low Beta and Idiosyncratic Volatility Anomalies**

**- Abstract**

Institutional investors subject to benchmarking, short-selling and leverage constraints have asymmetric effects on both low beta and low volatility anomalies documented by previous studies. Specifically, institutional investors prefer high-beta stocks to low-beta stocks to minimize the tracking error and utilize the embedded leverage of high beta stocks, leading to low-beta anomaly. They can act as the supply source of security lending to the short-sellers, mitigating the overpricing induced negative effect on expected returns from idiosyncratic volatility. Using size effect adjusted institutional ownership as a proxy for institutional limits to arbitrage, I confirm that mandated and financial constrained institutional investors contribute positively to the low beta anomaly but mitigate the low IVOL anomaly using sorting and Fama-MacBeth regressions. I distinguish the highly correlated low beta and low volatility anomalies and find a significantly positive risk premium for institutional holding. A strong January reversal effect of idiosyncratic volatility on expected return is also documented.

**Baker, Wugler: The Risk Anomaly Tradeoff of Leverage**

**- Abstract**

The “low risk anomaly” refers to the empirical pattern that apparently high-risk equities do not earn commensurately high returns. In this paper, we consider the possibility that the risk anomaly represents mispricing, not a misspecification of risk, and develop the implications for corporate capital structure. The risk anomaly generates a simple tradeoff model: Starting at zero leverage, the overall cost of capital initially falls as leverage increases equity risk. As debt becomes risky, however, the marginal benefit of increasing equity risk declines. The optimum is reached at lower leverage for firms with high asset risk. Consistent with a risk anomaly tradeoff, firms with low-risk assets choose higher leverage. In addition, leverage is inversely related to systematic risk, holding constant total risk; a large number of firms maintain small or zero leverage despite high marginal tax rates; and many others maintain high leverage despite little tax benefit.

**Schneider, Wagner, Zechner: Low Risk Anomalies?**

**- Abstract**

This paper shows theoretically and empirically that beta- and volatility-based low risk anomalies are driven by return skewness. The empirical patterns concisely match the predictions of our model that endogenizes the role of skewness for equity returns through credit risk. We show that ex-ante skewness predicts equity returns and that the prevalence of low risk anomalies depends on the skewness of the firms’ underlying return distributions. Betting against beta or volatility is profitable for firms with high downside risk but generates losses among firms with less negative or positive ex-ante skewness. Since skewness is directly connected to default risk, our results also provide new insights for the distress puzzle.

**Baker, Wurgler: Do Strict Capital Requirements Raise the Cost of Capital? Bank Regulation, Capital Structure, and the Low Risk Anomaly**

**- Abstract**

Traditional capital structure theory predicts that reducing banks’ leverage reduces the risk and cost of equity but does not change the weighted average cost of capital, and thus the rates for borrowers. We confirm that the equity of better-capitalized banks has lower beta and idiosyncratic risk. However, over the last 40 years, lower risk banks have not had lower costs of equity (lower stock returns), consistent with a stock market anomaly previously documented in other samples. A calibration suggests that a binding ten percentage-point increase in Tier 1 capital to risk-weighted assets could double banks’ risk premia over Treasury bills.

**Cannon: The Idiosyncratic Volatility Puzzle: A Behavioral Explanation**

**- Abstract**

In this study, I propose an alternative explanation for the idiosyncratic volatility puzzle. I postulate that the negative coefficient observed between idiosyncratic volatility and future returns is driven by investor sentiment. The results obtained from these analyses support the idea that the idiosyncratic volatility puzzle can be explained by investor sentiment. In periods of high investor sentiment, investors are optimistic in choosing stocks. Such effects lead investors to flock to assets with high idiosyncratic volatility, creating the negative relationship with return. Furthermore, in periods of lowest investor sentiment, results indicate a natural, positive relationship between idiosyncratic volatility and future returns, supporting standard risk-return theory.

**Ilmanen: Do Financial Markets Reward Buying or Selling Insurance and Lottery Tickets?**

**- Abstract**

Selling financial investments with insurance or lottery characteristics should earn positive longrun premiums if investors like positive skewness enough to overpay for these characteristics. The empirical evidence is unambiguous: Selling insurance and selling lottery tickets have delivered positive long-run rewards in a wide range of investment contexts. Conversely, buying financial catastrophe insurance and holding speculative lottery-like investments have delivered poor longrun rewards. Thus, bearing small risks is often well rewarded, bearing large risks not.

**Van Vliet: Low Turnover: A Virtue of Low Volatility**

**- Abstract**

Excessive trading can be linked to human behavior. One explanation for unnecessary turnover is the well-documented overconfidence bias. Another explanation is a misalignment of interest between asset managers and asset owners: trading sends a positive signal to superiors and clients. To actively get exposure to low-volatility stocks requires a certain amount of trading. Using a meta-study combining 21 previous analyses we find a weak concave relation between turnover and the achieved risk reduction. In general 30% annualized turnover should be enough to reduce portfolio volatility by 25% compared to a market-weighted index, and low-volatility stocks are also relatively cheap to trade. Thus long-term investors can get efficient exposure to the low-volatility effect, at moderate trading levels.

**Stefano, Lamperiere, Bevaratos, Simon, Laloux, Potters, Bouchaud: Deconstructing the Low-Vol Anomaly**

**- Abstract**

We study several aspects of the so-called low-vol and low-beta anomalies, some already documented (such as the universality of the effect over different geographical zones), others hitherto not clearly discussed in the literature. Our most significant message is that the low-vol anomaly is the result of two independent effects. One is the striking negative correlation between past realized volatility and dividend yield. Second is the fact that ex-dividend returns themselves are weakly dependent on the volatility level, leading to better risk-adjusted returns for low-vol stocks. This effect is further amplified by compounding. We find that the low-vol strategy is not associated to short term reversals, nor does it qualify as a Risk-Premium strategy, since its overall skewness is slightly positive. For practical purposes, the strong dividend bias and the resulting correlation with other valuation metrics (such as Earnings to Price or Book to Price) does make the low-vol strategies to some extent redundant, at least for equities.

**Schneider, Wagner, Zechner: Low Risk Anomalies?**

**- Abstract**

This paper shows theoretically and empirically that beta- and volatility-based low risk anomalies are driven by return skewness. The empirical patterns concisely match the predictions of our model that endogenizes the role of skewness for stock returns through default risk. With increasing downside risk, the standard capital asset pricing model (CAPM) increasingly overestimates expected equity returns relative to firms’ true (skew-adjusted) market risk. Empirically, the profitability of betting against beta/volatility increases with firms’ downside risk, and the risk-adjusted return differential of betting against beta/volatility among low skew firms compared to high skew firms is economically large. Our results suggest that the returns to betting against beta or volatility do not necessarily pose asset pricing puzzles but rather that such strategies collect premia that compensate for skew risk. Since skewness is directly connected to default risk, our results also provide insights for the distress puzzle.

**Blitz: The Value of Low Volatility**

**- Abstract**

The evidence for the existence of a distinct low-volatility effect is mounting. However, implicit exposures to the Fama-French value factor (HML) seem to explain the performance of straightforward U.S. low-volatility strategies since 1963. In this paper I show that the value effect can neither explain the performance of large-cap low-volatility strategies pre-1963, nor post 1984, when the Fama-French value factor itself ceased to be effective in the large-cap segment of the market. Moreover, the performance of small-cap low-volatility strategies cannot be explained by the value effect during any period. Fama-MacBeth regressions support the existence of a low-volatility effect for every subsample. Based on these results and various other arguments I conclude that there exists a distinct low-volatility effect which cannot be explained by the value effect. The combined evidence even appears to be stronger for the low-volatility effect than for the value effect.

**Blitz, Vidojevic: The Profitability of Low Volatility**

**- Abstract**

Low-risk stocks exhibit higher returns than predicted by established asset pricing models, but this anomaly seems to be explained by the new Fama-French five-factor model, which includes a profitability factor. We argue that this conclusion is premature given the lack of empirical evidence for a positive relation between risk and return. We find that exposure to market beta in the cross-section is not rewarded with a positive premium, regardless of whether we control for the new factors in the five-factor model. We also observe stronger mispricing for volatility than for beta, which suggests that the low-volatility anomaly is the dominant phenomenon. We conclude that the low-risk anomaly is not explained by the five-factor model.

**Driessen, Kuiper, Beilo: Does Interest Rate Exposure Explain the Low Volatility Anomaly?**

**- Abstract**

We show that part of the outperformance of low volatility stocks can be explained by a premium for interest rate exposure. Low volatile portfolios have a positive exposure to interest rates, whereas the more volatile stocks have a negative exposure. Incorporating an interest rate premium explains part of the anomaly. Depending on the methodology chosen the reduction of unexplained excess return is between 20% and 80%. Our results provide evidence that interest rate risk is priced differently in the bond and equity market. Our results imply a strong implicit exposure of low volatility portfolios to bonds.

**Andricopoulos: Leverage As A Weapon of Mass Shareholder-Value Destruction; Another Look at the Low-Beta Anomaly**

**- Abstract**

The ‘low-beta’ or ‘low-volatility anomaly’ is one of the most researched in the field of ‘alternative beta’. Despite strong published evidence going back to the 1970s that high beta/volatility stocks underperform relative to expectations generated by the Capital Asset Pricing Model (CAPM), the anomaly still persists. The explanations given for this are all behavioural; that investor biases lead to overpricing of high volatility stocks. This paper shows that investor biases cannot be the explanation for the anomaly. Instead, it is proposed that the anomaly stems from a destruction of shareholder value. The strong implication is that the more market leverage a firm has, the more shareholder value is destroyed. Although the prevailing view for a long time has been that adding debt is good for shareholders, making balance sheets more ‘efficient’, there is in fact a considerable volume of evidence that the opposite is true; evidence which has been incorrectly interpreted for many years. Some possible mechanisms for this shareholder-value destruction are proposed.

**de Carvalho, Xiao, Soupe, Dugnolle: Diversify and Purify Factor Premiums in Equity Markets**

**- Abstract**

In this paper we consider the question of how to improve the efficacy of strategies designed to capture factor premiums in equity markets and, in particular, from the value, quality, low risk and momentum factors. We consider a number of portfolio construction approaches designed to capture factor premiums with the appropriate levels of risk controls aiming at increasing information ratios. We show that information ratios can be increased by targeting constant volatility over time, hedging market beta and hedging exposures to the size factor, i.e. neutralizing biases in the market capitalization of stocks used in factor strategies. With regards to the neutralization of sector exposures, we find this to be of importance in particular for the value and low risk factors. Finally, we look at the added value of shorting stocks in factor strategies. We find that with few exceptions the contributions to performance from the short leg are inferior to those from the long leg. Thus, long-only strategies can be efficient alternatives to capture these factor premiums. Finally, we find that factor premiums tend to have fatter tails than what could be expected from a Gaussian distribution of returns, but that skewness is not significantly negative in most cases.

**Blitz: Are Hedge Funds on the Other Side of the Low-Volatility Trade?**

**- Abstract**

The low-volatility anomaly is often attributed to limits to arbitrage, such as leverage, short-selling and benchmark constraints. One would therefore expect hedge funds, which are typically not hindered by these constraints, to be the smart money that is able to benefit from the anomaly. This paper finds that the return difference between low- and high-volatility stocks is indeed a highly significant explanatory factor for aggregate hedge fund returns, but with the opposite sign, i.e. hedge funds tend to bet not on, but against the low-volatility anomaly. This finding has several important implications. First, it implies that limits to arbitrage are not the key driver of the low-volatility anomaly. Second, it argues against the notion that the anomaly may be disappearing or may have turned into an ‘overcrowded’ trade. A final implication is that the return difference between low- and high-volatility stocks should be recognized as a key explanatory factor for hedge fund returns.

**Berghorn, Vogl, Schultz, Otto: Trend Momentum II: Driving Forces of Low Volatility and Momentum**

**- Abstract**

In discussions and critiques on the validity of the Efficient Market Hypothesis, there are two important research focuses: statistical analyses showing that the basic assumption of statistical independence in price series is violated and empirical findings that show that significant market anomalies exist. In this work, we combine both viewpoints by analyzing two important mathematical factor anomalies: low volatility and momentum. By applying an explicit trend model, we show that both anomalies require trending. Additionally, we show that the trend model used exhibits log-normal trend characteristics. Furthermore, the model allows us to describe how low volatility uses implicitly asymmetric trend characteristics while momentum directly exploits trends. Using Mandelbrot’s model of fractional Brownian Motions, we can finally link statistical analyses (measuring the Hurst exponent and persistence in returns) to the empirically observed momentum factor. Experimentally, the Hurst exponent in itself allows for a momentum strategy, and it can also be utilized to significantly improve low volatility strategies. In contrast to Mandelbrot’s approach, we offer a non-stationary view that allows us to describe both investment strategies using the trend model.

**Ilmanen, Israel, Moskowitz, Thapar, Wang: Factor Premia and Factor Timing: A Century of Evidence**

**- Abstract**

We examine four prominent factor premia – value, momentum, carry, and defensive – over a century from six asset classes. First, we verify their existence with a mass of out-of-sample evidence across time and asset markets. We find a 30% drop in estimated premia out of sample, which we show is more likely due to overfitting than informed trading. Second, probing for potential underlying sources of the premia, we find little reliable relation to macroeconomic risks, liquidity, sentiment, or crash risks, despite adding five decades of global economic events. Finally, we find significant time-variation in factor premia that are mildly predictable when imposing theoretical restrictions on timing models. However, significant profitability eludes a host of timing strategies once proper data lags and transactions costs are accounted for. The results offer support for time-varying risk premia models with important implications for theory seeking to explain the sources of factor returns.