## Is Momentum Effect Result of Over- of Under-reaction? Wednesday, 25 November, 2015

**#3 - Sector Momentum – Rotational System
#14 - Momentum Effect in Stocks**

Authors: **Heidari**

Title: **Over or Under? Momentum, Idiosyncratic Volatility and Overreaction**

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2687480

Abstract:

Several studies have attributed the high excess returns of the momentum strategy in the equity market to investor behavioral biases. However, whether momentum effects occur because of investor underreaction or because of investor overreaction remains a question. Using a simple model to illustrate the linkage between idiosyncratic volatility and investor overreaction as well as the stock turnover as another measure of overreaction, I present evidence that supports the investor overreaction explanation as the source of momentum effects. Furthermore, I show that when investor overreaction is low, momentum effects are more due to industries (industry momentum) rather than stocks.

Notable quotations from the academic research paper:

"The existence of significantly positive excess returns from momentum strategies is well established in the literature. However, there is no consensus over what drives these returns. Finding a risk-based explanation for the momentum effects is a tremendously difficult task and momentum constitutes perhaps "the toughest challenge for rational theories of the cross-section of stock returns" (Nagel, 2001). As an alternative, behavioral theories of momentum effects have been suggested by a number of researchers.

The models in this behavioral literature can be divided into two camps: those that characterized price momentum as investor underreaction and those that view it as an investor overreaction to information.

The contributions of this paper are as follows. First, I provide a channel for the contribution of investor overreaction to the idiosyncratic volatility of stocks. Second, I present empirical evidence of the relationship between momentum effects, idiosyncratic volatility and stock turnover. I argue that these results are consistent with the overreaction explanation of momentum effects and also provide a clearer explanation for the connection between momentum and idiosyncratic volatility. Third, I shed some light on the relationship between stock momentum and industry momentum and show that the contribution of the industries in the momentum varies with the level of firm-specific information which is proxied by idiosyncratic volatility.

In this paper, I verify that the momentum effect is stronger among stocks with higher idiosyncratic volatility. I then examine an alternative null hypothesis that does not rely on mispricing or limits to arbitrage. I employ a simple model and show that idiosyncratic volatility is related to the investor overreaction. By introducing the relationship between idiosyncratic volatility and overreaction, I conclude that the higher momentum effect among stocks with higher idiosyncratic volatility is due to investor overreaction. I, therefore, provide support for the overreaction explanation of momentum effects.

In this study, I analyze the relationship between industry and stock momentum from a different perspective. I show that industry momentum contributes more to stock momentum when idiosyncratic volatility is low. Among stocks with high idiosyncratic volatility, most of the momentum returns are driven by stocks rather than industries. This is consistent with the overreaction explanation: when idiosyncratic volatility is low, it implies that investors' overreaction is lower, so momentum returns (which is lower than those of the higher idiosyncratic volatility stocks) are more due to industry momentum. When idiosyncratic volatility is high, there is higher investor overreaction to the stock level information and most of the momentum effect is solely individual security momentum rather than industry momentum."

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## Time-Varying Conditional Market Exposures of the Value Premium Thursday, 19 November, 2015

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

Authors: **Qiao**

Title: **Conditional Market Exposures of the Value Premium**

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2687528

Abstract:

Value strategies exhibit a large positive beta if contemporaneous market excess returns are positive, and a small beta if contemporaneous market excess returns are negative. Value also has a large positive beta after bear markets, but a small beta after bull markets. These facts hold for equity-value strategies in 21 countries, and to a lesser extent for three non-equity-value strategies. Betas conditional on contemporaneous market returns are able to capture expected return variation associated with the book-to-market ratio. These betas partially explain the value premium, and are related to a larger cash-flow risk of value strategies.

Notable quotations from the academic research paper:

"Value strategies exhibit asymmetric betas: a large and positive up-market beta when the contemporaneous market excess returns are positive, and a small or negative down-market beta when the contemporaneous market excess returns are zero or negative. Value strategies also exhibit time-varying betas: after a string of good market returns, or a bull market, value has a small negative bull-market beta. After a string of poor market returns, value has a large positive bear-market beta. Asymmetric betas and time-varying betas also exist for international equity-value strategies, and to a lesser extent, in three non-equity-value strategies.

Asymmetric betas and time-varying betas are plausibly linked through mean-reversion of market returns. Value has a large positive beta in bear markets when market returns have been low. Because market returns tend to mean-revert, expected market returns are high when realized returns have been low. Therefore, value has a large positive beta when expected market returns are high. Value also has a small negative beta when expected market returns are low. Taken together, the time-varying betas combined with mean-reverting market returns translate into asymmetric contemporaneous betas.

Conditional market exposures shed light on the mechanism of value strategies. A decomposition of beta into its cash-flow and discount-rate components reveals asymmetric betas mostly come from cash-flow betas, consistent with the idea that value securities have higher cash-flow risk."

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## Deconstructing the Time-Series Momentum Strategy Wednesday, 11 November, 2015

**#118 - Time Series Momentum Effect**

Authors: **Kim, Tse, Wald**

Title: **Time Series Momentum and Volatility Scaling**

Link: http://world-finance-conference.com/papers_wfc2/468.pdf

Abstract:

Moskowitz, Ooi, and Pedersen (2012) show that time series momentum delivers a large and significant alpha for a diversified portfolio of various international futures contracts over the 1985 to 2009 period. Although we confirm these results with similar data, we find that their results are driven by the volatility-scaled returns (or the so-called risk parity approach to asset allocation) rather than by time series momentum. The alpha of time series momentum monthly returns drops from 1.27% with volatility-scaled weights to 0.41% without volatility scaling, which is significantly lower than the cross-sectional momentum alpha of 0.95%. Using volatility-scaled positions, the cumulative return of a time series momentum strategy is higher that that of the buy-and-hold strategy; however, timeseriesmomentuman buy-and-hold offer similar cumulative returns if they are not scaled by volatility. The superior performance of the time series momentum strategy also vanishes in the more recent post-crisis period of 2009 to 2013.

Notable quotations from the academic research paper:

"We revisit the findings of MOP (Moskowitz, Ooi, and Pedersen 2012 time series momentum strategy) using 55 futures contracts over the 1985to 2013 period. One special procedure used by MOP is that they scale the returns of the different futures contracts by a simple lagged estimate of volatility. In particular, an asset with a lower volatility will take a greater position size and have a higher weight in the portfolio. Using the same period as MOP, 1985-2009, and also volatility-scaling returns, we find similar results: A portfolio of 55 futures contracts based on the prior 12-month momentum offers an alpha of 1.27% per monthand the alphas of all the individual contracts (except one) are positive with an average of 1.31%. However, if we use unscaled equal-weighted returns, the portfolio alpha and the average individual alpha drop to 0.41% and 0.42%, respectively.

More specifically, MOP scale the volatility of each individual futures contract to correspond to the volatility of an average stock by effectively leveraging the positions. When we scale the futures contracts toa lower (higher) volatility, we obtain smaller (larger) alphas, and scaling the buy-and-hold strategy produces similar results. Thus the magnitude of the TSMOM strategy appears to be largely due to leveraging a strategy which happened to generate a positive alpha. Without volatility scaling, the monthly time series momentum returns underperform the cross-sectional momentum strategy.

Moreover, while we find a positive alpha when applying a TSMOM (time series momentum) strategy to individual contracts, the individual contract returns do not generally outperform a buy-and-hold futures strategy. Specifically, TSMOM offers higher profits than buy-and-hold for 29 (out of 55) contracts using unscaled returns, and 31 contracts using volatility-scaled returns.

MOP also show that time series momentum profits are larger than those from the cross-sectional momentum (XSMOM) strategy of Jegadeesh and Titman (1993). In contrast, examining the foreign exchange market only, Menkoff et al. (2012) find that the TSMOM strategy is less profitable than the XSMOM strategy. We note that when implementing the TSMOM, Menkoff et al. do not volatility-scale their results. In our study, we show that the alpha of the XSMOM, 0.95%, lies between the alphas obtained from the TSMOM using equal (non-volatility-scaled) and volatility-scaled weights. Therefore, the different weighting schemes may explain the conflicting conclusions of MOP and Menkoff et al.

The volatility scale used by MOP is similar to the so-called risk parity approach to asset allocation. A risk parity portfolio is an equally weighted portfolio, where the weights refer to risk (proxied by standard deviation in MOP) rather than dollar amount invested in each asset (Kazemi, 2012). Risk parity balances a portfolio by increasing (decreasing) the weights of low (high) risk assets and using leverageto attain higher portfolio returns.

We also examine the results for several sub-periods: pre and post-2001, and following the financial crisis, 2009-2013. The choice of 2001 is based on a potential structural break in commodity futures markets around the passage of the Commodity Futures Modernization Act (CFMA) in December 2000. We show that the superior performance of TSMOM is concentrated in the pre-2001 period. When we use more recent periods, we find that the performance of TSMOM is worse than that of a buy-and-hold strategy. These results are consistent with the increase in market quality documented for the equity market by Chordia, Roll, and Subrahmanyam (2011)."

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## Deconstructing the Low-Volatility Anomaly Thursday, 5 November, 2015

**#6- Volatility Effect in Stocks - Long-Short Version**

**#7- Volatility Effect in Stocks - Long-Only Version**

Authors: **Stefano, Lamperiere, Bevaratos, Simon, Laloux, Potters, Bouchaud**

Title: **Deconstructing the Low-Vol Anomaly**

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2670076

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.

Notable quotations from the academic research paper:

"Our main results are as follows:

We do confirm once again the strength and persistence of the low-vol and low-beta effect on a pool of 9 different countries; in fact we find that the P&L of the two anomalies are very strongly correlated ( ≈ 0.9) suggesting that these two anomalies are in fact one and the same. However, since the market neutral low-vol/low-beta strategy has (by construction) a long dollar bias, it is sensitive to the financing rate.

We find that the low-vol anomaly has nothing to do with short-term (one month) stock reversal – at variance with some claims in the literature, as it entirely survives lagging the measure of past volatilities by one month or more. The low-vol effect is therefore a persistent, long-term effect.

We find that, as expected, low-vol (low-beta) portfolios have strong sector exposures. However, the performance of these strategies remains strong even when sector neutrality is strictly enforced. The low-vol effect is therefore not a sector effect.

We find that a large proportion of the low-vol performance is in fact eked out from dividends. This is our central result, that follows from the strong negative correlation between volatility and dividend yields which (oddly) does not seem to be clearly documented in the literature. However, the low-vol anomaly persists for ex-dividend returns which are found to be roughly independent of the volatility level. Therefore risk-adjusted exdividend returns are themselves higher for low-vol stocks, which is in itself an “anomaly”.

We find that the skewness of low-vol portfolios is small but systematically positive, suggesting that the low-vol excess returns cannot be identified with a hidden risk-premium.

The P&L of the low-vol strategy is ∼ −0.5 correlated with the Small-Minus-Big (Size) Fama-French factor, ∼ 0.2 correlated with the High-Minus-Low (Value) factor and ∼ 0.5 correlated with the Earning-to-Price factor, which is expected since earnings and dividends are themselves strongly correlated. Once these factors are controlled for, the residual performance of low-vol becomes insignificant. This result ties with Novy-Marx’s observations: profitability measures explain to a large degree the low-vol (low-beta) effect.

We find that part of the low-vol effect can be explained by compounding, i.e. the mere fact that a stock having plummeted −20% must make +25% to recoup the losses. Although significant, this mechanism is only part of the story.

By analyzing the holding of mutual funds, we find that (at least in the U.S.) these mutual funds are indeed systematically over-exposed to high vol/small cap stocks and underexposed to low-vol/large cap stocks, in agreement with the leverage constraint and/or bonus incentives stories alluded to above. A similar observation was made in Ref. [13] concerning the behaviour of Japanese institutional investors.

Our overall conclusion is that, while the low-vol (/low-beta) effect is indeed compelling in equity markets, it is not a real diversifier in a factor driven portfolio that already has exposure to Value type strategies, in particular Earning-to-

Price and Dividend-to-Price. Furthermore, the strong observed dividend bias makes us believe that the effect is probably not as convincing in other asset classes such as bonds."

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## Influence of Correlations on Time-Series Momentum Strategies Wednesday, 28 October, 2015

**#118 - Time Series Momentum Effect**

Authors: **Baltas**

Title: **Trend-Following, Risk-Parity and the Influence of Correlations**

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2673124

Abstract:

Trend-following strategies take long positions in assets with positive past returns and short positions in assets with negative past returns. They are typically constructed using futures contracts across all asset classes, with weights that are inversely proportional to volatility, and have historically exhibited great diversification features especially during dramatic market downturns. However, following an impressive performance in 2008, the trend-following strategy has failed to generate strong returns in the post-crisis period, 2009-2013. This period has been characterised by a large degree of co-movement even across asset classes, with the investable universe being roughly split into the so-called Risk-On and Risk-Off subclasses. We examine whether the inverse-volatility weighting scheme, which effectively ignores pairwise correlations, can turn out to be suboptimal in an environment of increasing correlations. By extending the conventionally long-only risk-parity (equal risk contribution) allocation, we construct a long-short trend-following strategy that makes use of risk-parity principles. Not only do we significantly enhance the performance of the strategy, but we also show that this enhancement is mainly driven by the performance of the more sophisticated weighting scheme in extreme average correlation regimes.

Notable quotations from the academic research paper:

"More generally and more aggressively, following the recent financial crisis in 2008, assets from different asset classes (and not just commodities) have started exhibiting stronger co-movement patterns, with the diversification benefits being dramatically diminished.In an environment of increased asset co-movement, the volatility-parity weighting scheme can be deemed a suboptimal choice. By ignoring the covariation between assets, volatility-parity fails to allocate equal amount of risk to each portfolio constituent. This is the reason why volatility-parity is also often called as naïve risk-parity (Bhansali, Davis, Rennison, Hsu and Li, 2012). Following these observations, one possible reason for the recent lacklustre performance of trend-following can be the suboptimal weighting scheme that ignores pairwise correlations (see e.g. Baltas and Kosowski, 2015). Our aim is to address this particular feature of the strategy and construct a portfolio that formally accounts for pairwise correlations.

At this stage, it is important to stress that the profitability of a trend-following strategy depends on two factors: (i) the existence of serial-correlation in the return series and (ii) the efficient combination of assets from various asset classes. It is obvious that the first factor is of utmost importance for the profitability of the strategy; non-existence of persistent price trends cannot be alleviated by a more robust weighting scheme. By amending the volatility-parity scheme in a way that accounts for pairwise correlations, we can only address any inefficiency in the risk allocation between portfolio constituents.

In principle, an optimal allocation to risk that would also account for correlations would optimally over-weight assets, which correlate less with the rest of the universe and under-weight assets that correlate more with the rest of the universe in an effort to improve the overall portfolio diversification. This is the principle of the risk-parity portfolio construction methodology (also known as the Equal Risk Contribution scheme). That is, to equate the contribution to risk from each portfolio constituent, after accounting for any pairwise correlation dynamics.

The empirical question is whether this more sophisticated scheme can overcome the limitations of volatility-parity and consequently hedge against drawdowns experienced in high-pairwise-correlation states. Our findings show that the trend-following portfolio that employs risk-parity principles constitutes a genuine improvement to the traditional volatility-parity variant of the strategy. The Sharpe ratio of the strategy increases from 1.31 to 1.48 over the entire sample period (April 1988 – December 2013), but most importantly it more than doubles over the post-crisis period (January 2009 – December 2013) from 0.31 to 0.78. The improvement is both economically and statistically significant. A correlation event study shows that the improvement is mainly driven by the superior performance of the risk-parity variant of the strategy in extreme average correlation conditions."

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