**Volatility Managed Portfolios**

Alan Moreira and Tyler Muir (Yale University)

*June 18, 2016*

Managed portfolios that take less risk when volatility is high produce large alphas, substantially increase factor Sharpe ratios, and produce large utility gains for mean-variance investors. We document this for the market, value, momentum, profitability, return on equity, and investment factors in equities, as well as the currency carry trade. Volatility timing increases Sharpe ratios because changes in factors’ volatilities are not fully offset by proportional changes in expected returns. Our strategy is contrary to conventional wisdom because it takes relatively less risk in recessions and crises yet still earns high average returns. This rules out typical risk-based explanations and is a challenge to structural models of time-varying expected returns.

**Abnormal Stock Market Returns Around Peaks in VIX: The Evidence of Investor Overreaction?**

Valeriy Zakamulin (University of Agder)

*May 1, 2016*

Even though the VIX index was intended to be a measure of future volatility of the stock market, researchers argue that in reality VIX measures the investor sentiment. Anecdotal evidence suggests that peaks in VIX coincide with stock market bottoms followed by rallies, yet so far there have been no scientific evidence confirming this casual observation. In this paper we perform an event study of abnormal stock market returns around peaks in VIX and discuss our findings within the framework of behavioral finance theory. First of all, we detect peaks in VIX using formal turning-point identification procedures and provide detailed descriptive statistics of periods of rising and falling VIX. The results of our event study reveal strong evidence of the presence of abnormal stock market returns around peaks in VIX. We argue that the pattern of abnormal returns can be attributed to investor overreaction to bad news with subsequent correction. To validate our conjecture, we test whether the abnormal returns around peaks in VIX satisfy the two properties of overreaction. We find that the results of these empirical tests are consistent with the overreaction hypothesis. To further confirm the idea that the VIX index reflects the investor sentiment, we test the predictions of behavioral finance theory which postulates that investor sentiment affects various types of stocks to different degrees. In agreement with the theoretical predictions, we find evidence that over the event window around a peak in VIX the prices of large and value stocks undergo a relatively small downward correction, while the prices of more speculative small and growth stocks are corrected down to a higher degree. Our additional tests suggest that these cross-sectional differences cannot be explained by a set of standard risk factors.

**Can Exposure to Aggregate Tail Risk Explain Size, Book-to-Market, and Idiosyncratic Volatility Anomalies?**

Sofiane Aboura and Yakup Eser Arisoy (Université Paris)

*May 9, 2016*

We examine the impact of aggregate tail risk on return dynamics of size, book-to-market ratio, and idiosyncratic volatility sorted portfolios. Using changes in VIX Tail Hedge Index (ΔVXTH) as a proxy for aggregate tail risk, and controlling for market, size, book-to-market, and aggregate volatility risk, we document significant portfolio return exposures to tail risk. In particular, portfolios that contain small, value and volatile stocks exhibit consistently positive and statistically significant tail risk betas, whereas portfolios of big, growth and non-volatile stocks exhibit negative tail risk betas. We posit that due to their positive tail risk exposures, tail risk-averse investors demand extra compensation to hold small, value, and high idiosyncratic volatility stocks. Our results offer a tail risk-based explanation to size, value, and idiosyncratic volatility anomalies.

**Volatility Weighting Applied to Momentum Strategies**

Johannes Paulus Du Plessis and Winfried G. Hallerbach (Robeco Asset Mgt.)

*April 27, 2015*

We consider two forms of volatility weighting (own volatility and underlying asset volatility) applied to cross-sectional and time-series momentum strategies. We present some simple theoretical results for the Sharpe ratios of weighted strategies and show empirical results for momentum strategies applied to US industry portfolios. We find that both the timing effect and the stabilizing effect of volatility weighting are relevant for the improvement in Sharpe ratios. We also introduce a dispersion weighting scheme which treats cross-sectional dispersion as (partially) forecastable volatility. Although dispersion weighting improves the Sharpe ratio, it seems to be less effective than volatility weighting.

**Volatility Derivatives and Downside Risk**

Yueh-Neng Lin (National Chung Hsing University)

August 19, 2016

The challenge in long volatility strategies is to minimize the cost of carrying such insurance due to negative roll yields and negative volatility risk premia. This study proposes a hedging strategy for volatility as an asset class that provides substantial protection against market crashes, while still participating upside preservation. The results show (i) timely hedging strategy removes the extreme negative tail risk and reduces the negative skewness in exchange for slightly fewer instances of large positive returns; (ii) dynamic allocation effectively mitigates the negative cost-of-carry problem; (iii) using volatility contracts as extreme downside hedges can be a viable alternative to buying out-of-the-money S&P 500 index puts; and (iv) the significant volatility-hedged return is a form of compensation for investable higher-moment equity risk factors.

**Tail protection for long investors: Trend convexity at work**

Tung-Lam Dao (Capital Fund Management), et al

*May 9, 2016*

The performance of trend following strategies can be ascribed to the difference between long-term and short-term realized variance. We revisit this general result and show that it holds for various definitions of trend strategies. This explains the positive convexity of the aggregate performance of Commodity Trading Advisors (CTAs) which — when adequately measured — turns out to be much stronger than anticipated. We also highlight interesting connections with so-called Risk Parity portfolios. Finally, we propose a new portfolio of strangle options that provides a pure exposure to the long-term variance of the underlying, offering yet another viewpoint on the link between trend and volatility.

**A Theory for Measures of Tail Risk**

Fangda Liu (China Institute for Actuarial Science) and Ruodu Wang (U. of Waterloo)

*September 28, 2016*

The notion of “tail risk” has been a crucial consideration in modern risk management. To achieve a comprehensive understanding of the tail risk, we carry out an axiomatic study for risk measures which quantify the tail risk, that is, the behavior of a risk beyond a certain quantile. Such risk measures are referred to as tail risk measures in this paper. The two popular classes of regulatory risk measures in banking and insurance, the Value-at-Risk (VaR) and the Expected Shortfall (ES), are prominent, yet elementary, examples of tail risk measures. We establish a connection between a tail risk measure and a corresponding law-invariant risk measure, called its generator, and investigate their joint properties. A tail risk measure inherits many properties from its generator, but not subadditivity or convexity; nevertheless, a tail risk measure is coherent if and only if its generator is coherent. We explore further relevant issues on tail risk measures, such as bounds, distortion risk measures, risk aggregation, elicitability, and dual representations. In particular, there is no elicitable tail convex risk measure rather than the essential supremum, and under a continuity condition, the only elicitable and positively homogeneous monetary tail risk measures are the VaRs.

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