Are Size and Book-Value Factors Really Significant ? Tuesday, 5 January, 2016

A new related paper has been added to:

#25 - Small Capitalization Stocks Premium Anomaly

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

Authors: Lambert, Hubner

Title: Size Matters, Book Value Does Not! The Fama-French Empirical CAPM Revisited

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2506690

Abstract:

The Fama and French (F&F) factors do not reliably estimate the size and book-to-market effects. Our paper shows that the former has been underestimated in the US market while the latter overestimated. We do so by replacing F&F's independent rankings by the conditional ones introduced by Lambert and Hubner (2013), over which we improve the sorting procedure. This new specification better reflects the properties of the individual risk premiums. We emphasize a much stronger size effect than conventionally documented. As a major related outcome, the alternative risk factors deliver less specification errors when used to price passive investment indices..

Notable quotations from the academic research paper:

"The paper revisits the size and book-to-market effect in the US market over the 1980-2007 sample period. It demonstrates a strong size but an insignificant book-to-market effect over the sample period. Our result challenges the Fama and French evidence of the presence of a stronger book-to-market than size effect in the US market. Fama and French’s size and book-to-market premiums are indeed shown to be respectively insignificant and positively significant over the analyzed period. Their evidence is partly supported in the standard construction methodology itself as more weight is attributed to the ranking according to the book-to-market dimensions (Fama and French, 1993).

We propose an alternative way to construct the empirical risk factors of Fama and French (1993) that avoids the contamination of the premiums from the correlation structure of the data. Our paper aims indeed at addressing some of the drawbacks identified in this heuristic approach to construct risk factors. Some attention has been drawn to the potential misevaluation of the size and book-to-market effect implied by the way the Fama and French methodology was constructed (Cremers et al., 2010; Huij and Verbeek, 2009; Brooks et al., 2008). The original Fama and French (F&F) method performs a 2x3 sort of US stocks on market capitalization and on book-to-market and forms six two-dimensional portfolios at the intersections of the two independent rankings. The premiums are defined as the spread between the average low- and high-scoring portfolios. Our main argument motivating the modifications brought to the original F&F method is that the independent sorting procedure underlying the formation of the six F&F two-dimensional portfolios distorts the way stocks are ranked into portfolios by placing disproportionate weights between the portfolios.

We follow the methodology of Lambert and Hübner (2013) and apply a generalized Fama and French technique to infer the size, book-to-market and momentum factors from the US stock market over the sample period of 1980-2007. The main innovations of our premiums reside in a monthly rebalancing of the portfolios (underlying the construction of the risk premiums) in order to capture the time-varying dimensions of risk, in a finer size classification and in a conditional sorting of stocks into portfolios. We consider three risk dimensions. The conditional sorting procedure answers the question whether there is still return variation related to the third risk criterion after having controlled for two other risk dimensions. It consists in performing a sequential sort in three stages. The first two sorts are performed on control risks, while we end by the risk dimension to be priced. As in Cremers, Petajusto and Zitzewitz (2010) and in Huij and Verbeek (2009), our paper demonstrates that the book-to-market premium of F&F is overvalued. We perform several asset pricing tests to check the validity and pricing power of our alternative premium specification. Compared to the Fama and French method, our factor construction method better captures the return spread associated with the source of risk to be priced. It maximizes the dispersion in the related source of risk while keeping minimal dispersion in correlated sources of risk. The conditional sorting and the finer size classification contribute to better balance the weights placed on the small/large value/growth portfolios. The great improvement of the new method lies in the reduction of the specification errors when pricing passive benchmark investment portfolios. Besides, without losing in significance, the modified technique is neater and leads to risk premiums that may not necessarily be used jointly in a regression-based model, unlike the original Fama and French factors whose risk exposures are highly sensitive to the inclusion of the other Fama and French risk factors in the regression.

Our paper more generally supports Lambert and Hübner’s (2013) previous evidence that a sequential sorting procedure could be more appropriate to take into consideration the contamination effects between the premiums. We show that the premiums constructed along this way deliver more consistent risk properties while reaching at least the same specification level as the F&F premiums. Given the critical stance of our paper, we have to go quite in depth into the origins of the improvements of the proposed sequential procedure, assorted with various methodological variations, over the original F&F method. The robustness checks deliver clear insights vis-à-vis the key drivers of alternative approach’s pricing performance. It is the replacement of an independent sort by a sequential one that seems to make the largest difference as expected."


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Upside and Downside Risks in Momentum Returns Tuesday, 29 December, 2015

A new related paper has been added to:

#13 - Short Term Reversal in Stocks
#14 - Momentum Effect in Stocks

#15 - Momentum Effect in Country Equity Indexes

Authors: Dobrynskaya

Title: Upside and Downside Risks in Momentum Returns

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2695001

Abstract:

I provide a novel risk-based explanation for the profitability of momentum strategies. I show that the past winners and the past losers are differently exposed to the upside and downside market risks. Winners systematically have higher relative downside market betas and lower relative upside market betas than losers. As a result, the winner-minus-loser momentum portfolios are exposed to extra downside market risk, but hedge against the upside market risk. Such asymmetry in the upside and downside risks is a mechanical consequence of rebalancing momentum portfolios. But it is unattractive for an investor because both positive relative downside betas and negative relative upside betas carry positive risk premiums according to the Downside-Risk CAPM. Hence, the high returns to momentum strategies are a mere compensation for their upside and downside risks. The Downside Risk-CAPM is a robust unifying explanation of returns to momentum portfolios, constructed for different geographical and asset markets, and it outperforms alternative multi-factor models.

Notable quotations from the academic research paper:

"I show that the downside risk alone does not fully explain the returns to the cross-section of momentum portfolios because the upside risk plays a significant role too and cannot be neglected. In fact, it is the difference in the downside and upside betas (beta asymmetry) which varies across momentum portfolios the greatest. For any cross-section of momentum portfolios considered, the difference in betas is monotonically increasing from past losers to past winners. As a result, the winner-minus-loser momentum portfolios are exposed to the downside risk, but hedge against the upside risk.

This finding is consistent with a recent study by Daniel and Moskowitz (2014), who show that the winner-minus-loser momentum portfolios tend to crash when the market rebounds after a decline. The momentum crashes occur during the market upturns because these portfolios appear to be long in the low-beta stocks and short in the high-beta stocks picked in the preceding formation period of the declining market. But if the formation period coincides with the growing market, on the contrary, the momentum portfolios appears to be long in the high-beta stocks and short in the low-beta stocks, what leads to their high exposure to the downside risk if the market turns down. Because the momentum portfolios are rebalanced periodically, and because the market changes its trend often, the momentum portfolios appear to have positive downside betas and negative upside betas mechanically. Recent studies by Barroso and Santa-Clara (2015) and Jacobs, Regele and Weber (2015) also show that past winner and loser portfolios have asymmetric return distributions and, as a result, the momentum portfolio returns exhibit significant negative skewness and high kurtosis. Such asymmetry in risks is not attractive for an investor and requires a risk premium.

In the cross-sectional tests, I show that the relative downside beta, which captures the extra downside risk and, hence, the downside-upside risk asymmetry, explains the returns to the momentum portfolios well, whereas the traditional beta has no explanatory power. The relative downside beta premium is approximately 3-4 percent per month, highly statistically significant and similar in magnitude to the estimates obtained for the stock and currency markets (Lettau et al., 2014; Dobrynskaya, 2014).

My findings are similar for all cross-sections of momentum portfolios in different geographical markets and asset classes. I study the US, Global, European, North-American and Asian-Pacific momentum portfolios of individual stocks, global momentum portfolios of country indices, currency momentum portfolios. I show that momentum is a global phenomenon indeed, and its upside-downside risk structure is similar around the world and in different asset markets. I confirm the findings of Asness, Moskowitz, and Pedersen (2013) that momentum strategies in different locations and asset markets share common risks. But the major contribution of this paper is to show that a microfounded theoretical asset-pricing model (namely, the Downside-Risk CAPM – DR-CAPM) previously used to explain stock and currency returns can also explain the momentum returns well."


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Time-Series vs. Cross-Sectional Implementation of Momentum, Value and Carry Strategies Thursday, 17 December, 2015

A new related paper has been added to:

#28 - Value and Momentum across Asset Classes

Authors: Baz, Granger, Harvey, Le Roux, Rattray

Title: Dissecting Investment Strategies in the Cross Section and Time Series

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2695101

Abstract:

We contrast the time-series and cross-sectional performance of three popular investment strategies: carry, momentum and value. While considerable research has examined the performance of these strategies in either a directional or cross-asset settings, we offer some insights on the market conditions that favor the application of a particular setting.

Notable quotations from the academic research paper:

"In quantitative cash equity strategies, momentum is almost always traded across assets (relative value) whereas in futures trading, momentum is typically applied directionally. Why? Our goal is to better understand the performance of three popular strategies, carry, momentum and value in di fferent implementations: time-series vs. cross-sectional.

We fi ll this gap by providing an analysis of both the time-series and cross-section using a broad number of asset classes: equity, fixed income, currencies and commodities. We measure the relative performance of directional vs. cross-asset strategies as well as strategies that combine the information in each dimension. We show that these strategies are largely pro fitable over our sample - and the best performance is when these strategies are combined.

Contrasting Table 1 Panel A and Table 5 Panel A, we have quite di fferent results for the three styles: value works well in the cross-section, poorly in time-series; carry works about equally well in both cross-section and time-series and momentum works well in time-series, but poorly in the cross-section.

At a basic level, assuming linear signals, cross sectional portfolio weights are equal to time series weights minus the cross sectional average. This average can be thought of as a global factor. Therefore, we can think of a cross sectional portfolio as a time series portfolio hedged for the global factor. Pursuing this line of reasoning, time series momentum will outperform cross sectional momentum to the extent that the global factor is trending. Alternatively, to the extent that the value indicator trades reversion to the mean, time series value investing will do better than cross sectional value investing when the global factor returns are negatively autocorrelated.

So how do we interpret the results from our data exploration? As stated above, momentum outperformance seems to go hand in hand with value underperformance in the time series versus the cross section. Although this result is difficult to interpret, we can off er three possible explanations.

The fi rst is that momentum, unlike value, takes the price movements themselves as being informative and, as in such, may be better placed to assimilate any truly novel information about the global factor which may not be captured by the valuation model. In other words, the momentum model may account unwittingly for the factors omitted by the valuation model. This distinction between value and momentum is most prominent in the more correlated asset classes of equities and bonds.

In FX and commodities where a global factor is much less apparent the performance di erences between the cross section and time series is much less. This makes sense, because in moving from time series to cross sectional portfolios we are essentially hedging out a single global factor. If this factor explains less, there will be less to hedge out and less di fference between the portfolios (in either direction). This is exactly what we observe. Although this explanation may have merits, it does not help us understand why value performs better than momentum in the cross section.

Another explanation is that major global factors have exhibited very strong trends which have by de finition hurt reversion based value predictors. It may even be claimed that the central purpose of stimulative public policies recently was to boost wealth e ffects by supporting a sustained rally in stocks and bonds, that in turn favored momentum over value in both asset classes.

A third explanation for time series versus cross sectional performance is the correlations of the signals, and how they compare to the correlations of the underlying markets. All else being equal, a cross sectional approach has more to gain when asset correlations are very high, as the above-mentioned global factor will dominate, and hedging this out will increase diversi cation by boosting exposure to a wider range of other factors. However, if signals are also highly correlated, a cross sectional approach will hedge out most of the (presumably informative) signals as well, potentially canceling out any gain from the diversi cation. Conversely if asset correlations are high, but signal
correlations low, we will likely lose very little of the information in the signals by forcing them to be cross-sectional as their information already mostly relates to the non-global factors. This could potentially explain the outperformance of time series momentum against time series value in bonds and equities. Although both asset classes are internally highly correlated, the momentum signals on them are even more correlated, so moving to a cross-sectional framework will potentially hedge out more of the alpha from the signals than noise from the market. Correlations of value signals are notably smaller.

While all of the above explanations have appeal, the readers should note that value is traditionally traded in the cross section while momentum is traded in time series. So it would seem that traders have generally come to the "correct conclusions".

By combining simple signals in carry, momentum and value across less than 100 liquid futures, forwards and swap markets we are able to achieve a remarkably stable strategy over 25 years with a Sharpe ratio of close to 2, returning an approximately eight-fold increase on a hypothetical 15% volatility investment. This can be considered a genuine return, as the strategy has very low funding costs. Is this too good to be true? Why is not every investor trading these styles in combination?

We tried our hand at six possible explanations.

Selection bias is a partial answer. Why did we choose these styles and not others? Because, by and large, they have worked consistently over time and across asset classes. However, in defense of our results, not many styles make sense across such diverse asset classes; so the selection pool is not large.

What about potential over- tting? There was no fi tting in this exercise, although some potentially creeps in from experience. Why do our value predictors look back much further than the momentum predictor? Because momentum has worked better at medium frequencies, whereas value is clearly a long-term game. How obvious would this have been 25 years ago?

Survivorship and selection bias of assets is also a problem. Toxic emerging markets may be excluded. This study excluded Argentina but included the likes of Russia, Greece, Indonesia. This kind of bias will likely favor value and carry through the removal of markets where turmoil has caused major assets to exit.

Momentum suff ers from another potential bias. Back in 1990, many markets we would include now were much smaller. The ones that make it into our study have likely grown over this time, often via a strong long-term up-trend. By adding data for markets which are now big, but were once small, we likely give a positive bias to momentum predictors.

Another, perhaps more appealing explanation for the performance is simply that few firms have the appetite and patience to trade something so simple. It is easy to forget the arguments in 1999 that value had been replaced by growth, in 2008 that carry was toxic, and in 2011-13 that momentum was finished. These are long-term signals whose performance oscillates over time, with each style experiencing negative performances for at least three years. It is difficult to stick with underperforming strategies this long."


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An Analysis of Expected Returns of Trend-Following Strategies Friday, 11 December, 2015

Author: Nilsson

Title: Trend Following - Expected Returns

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2689861

Abstract:

This paper describes how to create ex-ante expectation for generalized trend-following rules. This report first study the effect of trend-following rules applied to random data with varying degrees of drift and autocorrelation. There is a positive relationship between drift, autocorrelation and the theoretically extractable Sharpe ratio for a trend following strategy. Drift is more important, since it is theoretically unbounded, but strong auto-correlation can create positive returns in the absence of long term drift. The realized Sharpe ratio of a trend strategy is proportional to the absolute drift and auto-correlation of a market above a threshold. From a practical perspective, this means that anyone engaging in trend following strategies, should expect to generate positive returns if the drift is strong enough or if there is enough autocorrelation. Conversely, when there is no drift or auto-correlation, trend-following is not profitable. There is a strong preference for slower strategies under drift and transaction costs. Returns are compared to actual markets and indices of active traders (managed futures) and a high correlation is detected to the results in this paper. Trend-following should never be applied to a single market on a stand-alone basis. That said, even portfolios of trend following strategies have low expected Sharpe, especially so when the systems generated correlated trades. In the end, trend-following does not necessarily need uncorrelated markets, but rather uncorrelated system-market returns. A nuance that is often lost.

Notable quotations from the academic research paper:

"In this report, the author has derived and verified the importance of auto-correlation and risk-adjusted drift for simple trend based strategies. After having reviewed the facts, auto-correlation for actual markets is close to zero (at least over the last 15 years) and most markets have a low drift. Thus, any return generated from medium to long-term trend following strategies is mostly due to market drift, rather than auto-correlation.

Trend-following, on a stand-alone basis, is a low Sharpe strategy, with an expected per-market Sharpe of approximately 0.15, depending on the drift of the underlying market. From there, the author performs an analysis in terms of market / system-market correlation which allows a predication of the expected Sharpe ratio for portfolios of strategies.

Trend following depends, not only on having a low market correlation, but is more dependent on having a low correlation between trading-systems. To some extent, this is one of the reasons for why trend-following is sometimes referred to as a portfolio effect. Most successful trend-following results have been recorded in diversified portfolios, rather than for single market traders.

This report rests on the assumption that it is correct to approximate the result and correlation for other trend strategies with a long term momentum strategy. This is not always the case as there are trend strategies that are not perfectly correlated to the tested strategies.

When compared to actual hedge fund results, this report finds that two (Barclay and Credit Suisse) out of three indices tested, mirrors the results of a correlation driven reduction in the realized Sharpe. Larger managers, in more concentrated indices (Newedge CTA), have managed to generate better results. As a first approximation, attributing this to higher concentration to liquid markets (equities and fixed income) as well as potentially having access to diversifying strategies seems prudent.

For traders that using trend-following strategies, it would seem prudent to continue to look for uncorrelated markets/trading systems while trying to explicitly understand why a market would have a persistent auto-correlation and/or a high risk adjusted drift.

A more extreme version would be to build a large number of uncorrelated systems and apply them to a set of markets. There, despite having a long expected Sharpe ratio for each system, it is still possible to create diversifying return streams. This may no longer be a trend-following strategy though."


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A Liquidity-Based Explanation of FX Carry Strategy Wednesday, 2 December, 2015

#5 - FX Carry Trade

Authors: Jung, Lee

Title: A Liquidity-Based Resolution of the Uncovered Interest Parity Puzzle

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2685534

Abstract:

A new monetary theory is set out to resolve the "Uncovered Interest Parity (UIP)" Puzzle. It explores the possibility that liquidity properties of money and nominal bonds can account for the puzzle. A key concept in our model is that nominal bonds carry liquidity premia due to their medium of exchange role as either collateral or means of payment. In this framework no-arbitrage ensures a positive comovement of real return on money and nominal bonds. Thus, when inflation in one country becomes relatively lower, i.e., real return on this currency is relatively higher, its nominal bonds should also yield higher real return. We show that their nominal returns can also become higher under the economic environment where collateral pledgeability and/or liquidity of nominal bonds and/or collateralized credit based transactions are relatively bigger. Since a currency with lower inflation is expected to appreciate, the high interest currency does indeed appreciate in this case, i.e., the UIP puzzle is no longer an anomaly in our model. Our liquidity based theory can in fact help understanding many empirical observations that risk based explanations find difficult to reconcile with.

Notable quotations from the academic research paper:

"The vast majority of the literature on UIP puzzle is empirical, and very few theoretical attempts have been made to tackle the puzzle. Even among the theoretical literature, no consensus seems to have been reached. For instance, most prevailing theories revolve around the idea that the failure of the UIP has a close connection with the way the risk premium behaves. Nevertheless, many recent studies have become critical of these risk-based explanations. To that end, we take an alternative approach in this paper that the UIP violation might be attributed to endogenous liquidity properties of money and bonds.

In our microfounded monetary model of international asset pricing, the UIP does not have to hold uniformly. In particular, the negative relationship between anticipated inflation and nominal bond yield is shown to be sufficient for the UIP deviation. Crucially, our framework implies that nominal bonds must exhibit relatively high enough liquidity premia in order to guarantee the sufficient condition. We show in the model that the sufficiently higher liquidity premia of bonds can be indeed achieved when the portion of collaterlized-credit-transaction-based pairwise meetings is large and/or the pledgeability of bonds as collateral is high and/or exogenous illiquidity discount on bonds as a direct means of payment is low.

One may question if our framework where bonds exhibit as high liquidity premia as money is empirically substantive. One can then address potential concerns. First, not every nominal bonds, especially those issued by emerging economies, are same as the U.S. Treasury bonds. Second, the bond liquidity is surely time-varying, e.g., extreme dry-up of bond liquidity during the recent liquidity crunch episode.

Very interestingly, these two issues are precisely what leads to the non-uniform UIP deviation in our framework. Put it differently, our model implies that the sufficient condition for the UIP deviation cannot be met whenever bonds are not liquid enough. This bond illiquidity is one of the defining characteristics of emerging market bonds and the liquidity crisis. Thus, our model predicts that the UIP should be confined to emerging economies and the liquidity crunch period. These two predictions are well supported by prominent empirical studies."


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