Once again, an interesting academic paper related to multiple equity factors:

Authors: Briere, Szafarz

Title: Factor Investing: The Rocky Road from Long Only to Long Short

Link: https://papers.ssrn.com/sol3/papers2.cfm?abstract_id=2908491

Abstract:

The performances of factor investing rely heavily on short sales, not only for building the initial long-short strategy, but also for regularly rebalancing the positions. Since short selling is subject to both legal restrictions and substantial costs, this paper examines how severely restrictions on short positions affect the financial attractiveness of factor investing. To fill the gap between unconstrained long-short allocations and restricted long-only portfolios, we consider two in-between strategies: the first imposes that only the market can be shorted, and the second is the so-called “130/30” scenario that caps total short exposure at 30%. The takeaways are twofold. First, any infringement to the long-short strategy can harm significantly the mean-variance performances of efficient factor-based portfolios. This is linked to the fact that the total short exposure of optimal long-short portfolios can reach figures around 400% and above. Second, the factor portfolios built originally by Fama and French (1992) with the purpose of developing asset pricing are impressively clear-sighted when it comes to portfolio management. Indeed, combining these portfolios generates mean-variance performances similar to those of optimized long-short portfolios, except for low levels of volatility.

Notable quotations from the academic research paper:

"A sizeable literature on portfolio management suggests that making short sales on a regular basis to rebalance portfolios is difficult. The aim of this paper is to assess the actual dependence of the mean-variance performances of factor investing on short selling restrictions.

In order to relax the necessity of short selling in factor investing, we proceed in two steps. First, we disentangle the long and short legs of the five historical factors. The ten resulting long-only factors provide additional flexibility in portfolio management. Second, short-selling restrictions, if any, are imposed separately on each of these ten factors. Last, we consider short-selling restrictions on the market index separately to reflect that shorting the market is much easier to implement (through derivative markets, for instance) than shorting any other factor.

Using as a benchmark the efficient frontier built from the Fama-French portfolios, we will examine the consequences on mean-variance performances of imposing five sets of short-selling-based restrictions.

Portfolios in group 1 (global long-only) exclude any short position whatsoever. Group 2 (longshort market + long-only factors) puts no restriction on exposure to market but excludes short positions in factors. The rationale is that easy access to index trading makes shorting the market easier and less costly than shorting factors, which are hardly tradable. Group 3 includes the typical 130/30 portfolios defined by the combination of a 130% long position and a 30% short one. Finally, in group 4, no position is constrained.

Figure 1 shows our five efficient frontiers. It reveals that the expected dominances are logically represented graphically. From definitions, we expect that the frontier corresponding to the global long-short case (group 4) dominates all the others, including the benchmark, since it allows running fully unconstrained optimization. Likewise, the global long-only case (group 1) is evidently more restrictive than both the cases of the long-short market + long-only factors (group 2) and 130/30 (group 3), which implies that the frontier associated with group 1 must be dominated by the two others. There is no clear dominance to be expected between the frontiers corresponding to groups 2 and 3, since on the one hand the exposure to market is unconstrained in group 2 but constrained by the 130/30 restriction in group 3, and the other factors can be shorted (to a certain extent) in group 3 but not at all in group 2. Hence, comparing the frontiers obtained for groups 2 and 3 can bring insights on the trade-off arising from shorting the market only versus shorting single-legged factors. 

The market portfolio is located below all our frontiers of interest; even the most restricted one (corresponding to group 1), which bans any short sale."

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An interesting academic paper related to multiple equity factors:

Authors: Blitz

Title: Are Exchange-Traded Funds Harvesting Factor Premiums?

Link: https://papers.ssrn.com/sol3/papers2.cfm?abstract_id=2912287

Abstract:

Some exchange-traded funds (ETFs) are specifically designed for harvesting factor premiums, such as the size, value, momentum and low-volatility premiums. Other ETFs, however, may implicitly go against these factors. This paper analyzes the factor exposures of US equity ETFs and finds that, indeed, for each factor there are not only funds which offer a large positive exposure, but also funds which offer a large negative exposure towards that factor. On aggregate, all factor exposures turn out to be close to zero, and plain market exposure is all that remains. This finding argues against the notion that factor premiums are rapidly being arbitraged away by ETF investors, and also against the related concern that factor strategies are becoming ‘overcrowded trades’.

Notable quotations from the academic research paper:

"This paper investigates if factor premiums, such as the size, value, momentum and low-volatility premiums, are systematically being harvested by investors in exchange-traded funds (ETFs).

Using a comprehensive sample of US equity ETFs, this paper finds that there are many funds which offer a large positive exposure to target factors such as size, value, momentum and low-volatility. At the same time, however, there are also many funds which offer a large negative exposure towards these factors. On aggregate, the exposures towards the size, value, momentum and low-volatility factors turn out to be very close to zero.

The take-away from these results is that despite a large variation in factor exposures across funds, the only thing that remains when everything is added up is plain market beta exposure. This finding argues against the notion that factor premiums are rapidly being arbitraged away by ETF investors.

It also argues against the related concern that factor strategies may have become ‘overcrowded trades’. Many investors are concerned about overcrowding of factor strategies, although the concept is not clearly defined. The general idea behind factor overcrowding is that so many investors are chasing the same factors that the long-term premiums associated with these factors disappear, that valuations of the stocks in factor portfolios increase, and that correlations among the stocks in factor portfolios increase as well, which might result in elevated crash risk. As, from a factor investing perspective, there seems to be just as much ETF money chasing stocks with the wrong factor characteristics as ETF money chasing stocks with the right factor characteristics, the ETF market does not seem to justify factor overcrowding concerns."

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A related paper to:

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

Authors: Blitz

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

Link: https://papers.ssrn.com/sol3/papers2.cfm?abstract_id=2898034

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.

Notable quotations from the academic research paper:

"There is a vast amount of evidence that low-volatility and low-beta stocks earn higher returns than predicted by the Capital Asset Pricing Model (CAPM). Blitz, Falkenstein, and van Vliet (2014) provide an extensive overview of the various explanations for this phenomenon that have been proposed in various streams of literature. One of the most popular explanations is that the anomaly results from limits to arbitrage, such as leverage, short-selling and benchmark constraints.

Leverage, short-selling and benchmark constraints may indeed prevent a lot of investors from exploiting the low-volatility anomaly, but such limits to arbitrage are much less of a concern for hedge funds, as these funds tend to be characterized by an absolute return objective and ample flexibility to apply leverage and shorting. Based on the limits to arbitrage explanation one would therefore expect hedge funds to be the smart money that actively takes advantage of the opportunity provided by low-volatility stocks. This paper empirically tests this hypothesis by regressing aggregate hedge fund returns on the return difference between low- and high-volatility stocks.

The main finding is 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 do not bet on, but against the low-volatility anomaly. This argues against limits to arbitrage such as leverage, short-selling and benchmark constraints being the main explanation for the low-volatility anomaly. The finding that the multi-trillion hedge fund industry is not arbitraging but contributing to the low-volatility anomaly also argues against the popular notion that the anomaly is disappearing or becoming an ‘overcrowded’ trade. The findings in this paper also have implications for the hedge fund performance evaluation literature, as the return difference between low- and high-volatility stocks turns out to be a stronger explanatory factor for hedge fund returns than many previously documented factors."

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A related paper to:

#26 – Value (Book-to-Market) Anomaly

Authors: Folkinshteyn, Meric, Meric

Title: Value and Growth Stock Price Behavior During Stock Market Declines

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2814956

Abstract:

Using data for five major stock market declines during the 1987-2008 period, this paper provides evidence that value stocks are generally less sensitive to major stock market declines than growth stocks, controlling for beta, firm size, and industry group. Further analysis using several hundred different significant market move events between 1980 and 2015 confirms the observation that value stocks tend to outperform both the market average and growth stocks during market declines. The implication for investment practitioners is that following a value strategy does not lead one to assume greater sensitivity to unfavorable market conditions.

Notable quotations from the academic research paper:

"We conduct our study using data for five major stock market declines during the 1987-2008 period and several hundred stock market declines during the 1980-2015 period. For our core analysis, we selected a representative sample of five of the largest consecutive days of market decline in the S&P 500 index.

We use a combination of three ratios: dividend to price (dividend yield), market to book, and earnings to price (earnings yield). We classify a stock as a 'growth stock' if it pays no dividends, has an above-median market to book ratio, and a below-median earnings yield. We classify a stock as a 'value stock' if it pays dividends, has a below-median market to book ratio, and an above-median earnings yield.

Our research makes several important contributions to the literature. We document a consistent pattern of lower than average sensitivity of value stocks to most stock market declines, in excess of that predicted by beta. We also document that growth stocks have a greater sensitivity to most major stock market declines. We find that the decline of 2008 was distinct from the other major stock market declines in our study, wherein equities across the value-growth continuum were evenly affected. Further analysis using several hundred different significant market move events between 1980 and 2015 confirms the observation that value stocks tend to outperform both the market average and growth stocks during stock market declines."

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An amazing academic paper about multiple equity factor models and about the way how to pick the best one:

Authors: Cooper, Maio, Philip

Title: Multifactor Models and the APT: Evidence from a Broad Cross-Section of Stock Returns

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2883765

Abstract:

We seek to describe the broad cross-section of average stock returns. We follow the APT literature and estimate the common factor structure among a large cross-section containing 278 decile portfolios (associated with 28 market anomalies). Our statistical model contains seven common factors (with an economic meaning) and prices well both the original portfolio returns and an efficient combination of these portfolios. This model clearly outperforms the empirical workhorses in the literature when it comes to pricing this broad cross-section. Augmenting the empirical models with new factor-mimicking portfolios, based on APT principles, significantly improves their performance.

Notable quotations from the academic research paper:

"The traditional workhorse in the empirical asset pricing literature the three-factor model of Fama and French (1993, 1996) (FF3 henceforth) fails to explain the new market anomalies. Moreover, the four-factor model of Carhart (1997) (C4) does a good job in capturing price momentum, but also struggles in terms of explaining some of the profitability- and investment-based anomalies. In response to this gap, we have witnessed the emergence of new multifactor models containing (different versions of) investment and profitability factors, in particular the five-factor model of Fama and French (2015, 2016b) (FF5) and the four-factor model of Hou, Xue, and Zhang (2015, 2016) (HXZ4). However, several dimensions of the broad cross-section of stock returns are still not explained by the new factor models. In particular, the five-factor model does not account for momentum (including industry momentum), while both of these models do not capture several profitability and investment-based (in particular, several forms of accruals) anomalies.

Following such evidence, several questions naturally emerge in the empirical asset pricing literature: How many factors do we need, and what are these factors, to describe well the broad cross-section of stock returns? To which dimensions of the cross-section of stock returns are these factors more correlated? To what extent (and how) can we improve the current multifactor models proposed in the literature in order to achieve a better description of large-scale cross-sectional risk premia? This paper attempts at providing answers to these questions. In order to achieve this goal, we adopt the general framework of the Arbitrage Pricing Theory (APT).

We follow part of the relatively small empirical APT literature in terms of estimating common stock return factors by applying asymptotical principal components analysis (APCA) to a large cross-section of stock returns. We employ a total of 28 anomalies or portfolio sorts for a total of 278 decile portfolios. The estimation results show that there are seven common factors that are statistically significant over our sample period (1972 to 2013). These seven factors cumulatively explain around 91% of the cross-sectional variations in the 278 portfolio returns. The first common factor basically captures the average anomaly and thus resembles a market factor. The other six factors capture different dimensions of the large cross-section of market anomalies. In particular, the second, third, and four factors are strongly correlated with value-growth, investment, profitability, and momentum-based anomalies. This is consistent with the role of the seven-factor model in terms of describing well this cross-section of 278 equity portfolios. This statistical model is thus a benchmark for this specific cross-section of stock returns, against which the existent models are compared.

We conduct cross-sectional asset pricing tests of our APT model by using the 278 equity portfolios as testing assets. The results confirm that the seven-factor model explains about 60% of the cross-sectional variation in the risk premia associated with the 278 portfolios. Moreover, most factor risk price estimates are statistically significant. Across categories of anomalies, the APT does a better job in pricing value-growth and intangibles, compared to the group of investment-based anomalies. Moreover, the model prices perfectly an efficient combination of the original portfolios as indicated by the GLS cross-sectional R2 estimates around 100%. This result confirms that the statistical model is a successful APT.

Next, we compare our APT model to some of most popular multifactor models existent in the literature in terms of pricing the 278 portfolios. The models include the already mentioned FF3, C4, HXZ4, FF5, in addition to a restricted version of FF5 that excludes HML (FF4), and the four-factor model of Pastor and Stambaugh (2003) (which includes a stock liquidity factor). The results show that only C4 and HXZ4 offer an economically significant explanatory power for the broad cross-section of stock returns, while the fit of both FF5 and FF4 is quite small. Moreover, the performance of all the six empirical factor models clearly lags behind the fit of the seven-factor APT, suggesting that these models have a large room for improvement in terms of describing large-scale cross-sectional risk premia.

In light of such evidence, we define and estimate new empirical multifactor models to better describe the broad cross-section of anomalies. All these models contain seven factors, to be consistent with our benchmark APT, and represent augmented versions of C4, HXZ4, FF5, and FF4, the best performing empirical models. The new factors in each of these models represent factor-mimicking portfolios (spreads among extreme portfolio deciles) associated with selected anomalies. These anomalies are those for which the original factors in each model do a worse job in terms of describing the time-series variation in the corresponding decile portfolio returns. Thus, our criteria for selecting the new factors relies on the APT restriction that the risk factors should explain well the time-series variation in the returns of the testing assets. The results show that adding the new factors improves all four empirical models, and helps especially the performance of both FF5 and FF4 in terms of explaining the large cross-section of stock returns. Moreover, the augmented models do a very good job in explaining an efficient combination of the original portfolios, thus, showing that they represent valid APTs. Therefore, the performance of the augmented empirical models is quite similar to that of our benchmark APT. Overall, our results indicate that there is a significant room for improving the existing empirical multifactor models in terms of explaining the large cross-section of stock returns in a way that is consistent with the APT."

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A short but interesting academic paper about differences in a well-known CBOE PutWrite and BuyWrite Indexes:

Author: Israelov

Title: PutWrite versus BuyWrite: Yes, Put-Call Parity Holds Here Too

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2894610

Abstract:

The CBOE PutWrite Index has outperformed the BuyWrite Index by approximately 1.1 percent per year between 1986 and 2015. That is pretty impressive. But troubling. Yes – troubling – because the theory of put-call parity tells us that such outperformance should be almost impossible via a compelling no-arbitrage restriction. This paper explains the mystery of this outperformance, which has implications for portfolio construction.

Notable quotations from the academic research paper:

"Writing equity index covered calls is an effective approach to jointly earning the equity and volatility risk premium. So too is writing naked equity index put options. Which approach is better? Many investors compare the historical performance of the two approaches for the answer, potentially leading to the conclusion that put-writing is preferable to covered calls. On the surface, it appears that writing put options would be the preferred approach. The CBOE PutWrite Index (PUT) has outperformed the BuyWrite Index (BXM) by approximately 1.1 percent per year between 1986 and 2015. That is pretty impressive. But troubling. Yes – troubling – because the theory of put-call parity tells us that such outperformance should be almost impossible via a compelling no-arbitrage restriction.

The primary reason behind the performance difference in the PutWrite and BuyWrite Indices is due to a construction difference during just four hours per month. A quirky difference in their portfolio construction results in the PutWrite Index missing out on approximately four hours per month of S&P 500 Index return relative to the BuyWrite Index.

Each month on the morning of option expiration, both the BuyWrite’s call option and the PutWrite’s put option expire and settle at the same time at the Special Open Quotation (SOQ). At this time, option expiration fully divests the PutWrite Index of its equity exposure. Until it re-establishes a short put option position, it is a zero beta portfolio. In contrast, at the same time, the BuyWrite portfolio becomes a beta one portfolio with the expiration of its call option, because it is fully invested in the S&P 500 Index with no corresponding short call option position. It remains a beta one portfolio until it re-establishes its short call option position.

So, over this four-hour window, the BuyWrite Index is over-exposed to the S&P 500 relative to its longterm average exposure. Similarly, the PutWrite Index is under-exposed to the S&P 500 relative to its long-term average exposure.

As an example, on average, between 2004 and 2015, the S&P 500 Index was down 23 basis points on option expiration mornings. The equity returns over this four hour period 12 times per year suggests 2.7% of annual underperformance for the BuyWrite Index relative to the PutWrite Index. Adding back in the intercept (annualized) provides a combined effect of 2.0% of annualized expiration-date underperformance. This is very close to the 2.1% the BuyWrite Index underperformed the PutWrite Index over the same 2004 to 2015 period."

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