Biased Betting Against Beta?

17.January 2019

A new research paper related mainly to:

#77 – Beta Factor in Stocks

Authors: Novy-Marx, Velikov

Title: Betting Against Betting Against Beta

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3300965

Abstract:

Frazzini and Pedersen’s (2014) Betting Against Beta (BAB) factor is based on the same basic idea as Black’s (1972) beta-arbitrage, but its astonishing performance has generated academic interest and made it highly influential with practitioners. This performance is driven by non-standard procedures used in its construction that effectively, but non-transparently, equal weight stock returns. For each dollar invested in BAB, the strategy commits on average $1.05 to stocks in the bottom 1% of total market capitalization. BAB earns positive returns after accounting for transaction costs, but earns these by tilting toward profitability and investment, exposures for which it is fairly compensated. Predictable biases resulting from the paper’s non-standard beta estimation procedure drive results presented as evidence supporting its underlying theory.

Notable quotations from the academic research paper:

" Frazzini and Pedersen’s (FP) Betting Against Beta (BAB, 2014) is an unmitigated academic success. Despite being widely read, and based on a fairly simple idea, BAB is not well understood. This is because the authors use three unconventional procedures to construct their factor. All three departures from standard factor construction contribute to the paper’s strong empirical results. None is important for understanding the underlying economics, and each obscures the mechanisms driving reported effects.

Two of these non-standard procedures drive BAB’s astonishing “paper” performance, which cannot be achieved in practice, while the other drives results FP present as evidence supporting their theory. The two responsible for driving performance can be summarized as follows:

Non-standard procedure #1, rank-weighted portfolio construction: Instead of simply sorting stocks when constructing the beta portfolios underlying BAB, FP use a “rank-weighting” procedure that assigns each stock to either the “high” portfolio or the “low” portfolio with a weight proportional to the cross-sectional deviation of the stock’s estimated beta rank from the median rank.

Non-standard procedure #2, hedging by leveraging: Instead of hedging the low beta-minus-high beta strategy underlying BAB by buying the market in proportion to the underlying strategy’s observed short market tilt, FP attempt to achieve market-neutrality by leveraging the low beta portfolio and deleveraging the high beta portfolio using these portfolios’ predicted betas, with the intention that the scaled portfolios’ betas are each equal to one and thus net to zero in the long/short strategy.

BAB equally weighted portfolio

FP’s first of these non-standard procedures, rank-weighting, drives BAB’s performance not by what it does, i.e., put more weight on stocks with extreme betas, but by what it does not do, i.e., weight stocks in proportion to their market capitalizations, as is standard in asset pricing. The procedure creates portfolios that are almost indistinguishable from simple, equal-weighted portfolios. Their second non-standard procedure, hedging with leverage, uses these same portfolios to hedge the low beta-minus-high beta strategy underlying BAB. That is, the rank-weighting procedure is a backdoor to equal-weighting the underlying beta portfolios, and the leveraging procedure is a backdoor to using equal-weighted portfolios for hedging.

BAB with costs

BAB achieves its high Sharpe ratio, and large, highly significant alpha relative to the common factor models, by hugely overweighting micro- and nano-cap stocks. For each dollar invested in BAB, the strategy commits on average $1.05 to stocks in the bottom 1% of total market capitalization. These stocks have limited capacity and are expensive to trade. As a result, while BAB’s “paper” performance is impressive, it is not something an investor can actually realize. Accounting for transaction costs reduces BAB’s profitability by almost 60%. While it still earns significant positive returns, it earns these by tilting toward profitability and investment, exposures for which it is fairly compensated."


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The Size Effect Has a Lottery-Style Payoff

11.January 2019

A new research paper related mainly to:

#25 – SIze Premium

Authors: McGee, Olmo

Title: The Size Premium As a Lottery

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3279645

Abstract:

We investigate empirically the dependence of the size effect on the top performing stocks in a cross-section of risky assets separated by industry. We propose a test for a lottery-style factor payoff based on a stochastic utility model for an under-diversified investor. The associated conditional logit model is used to rank different investment portfolios based on size and we assess the robustness of the ranking to the inclusion/exclusion of the best performing stocks in the cross-section. Our results show that the size effect has a lottery-style payoff and is spurious for most industries once we remove the single best returning stock in an industry from the sample each month. Analysis in an asset pricing framework shows that standard asset pricing models fail to correctly specify the size premium on risky assets when industry winners are excluded from the construction of the size factor. Our findings have implications for stock picking, investment management and risk factor analysis.

Notable quotations from the academic research paper:

" Firms with small market capitalization tend to outperform larger companies. Investors are attracted to lottery-like assets with positively skewed returns because they o ffer a very large payoff with a small probability, which the investors overweight. This demand makes positively skewed securities overpriced and likely to earn low returns. In this article we test whether the size/market capitalization attribute, and associated factor-mimicking portfolios, receive a lottery-like payoff . The implications of this are that most small stocks do not payoff and the returns to a size strategy are driven by a small number of winners. This type of payo ff can be captured through diversi fication but leaves an under-diversifi ed investor exposed. The risk being that they will not include winning stocks and their resulting return expectation is negative.

To investigate the e ffect of winning stocks on the performance of investment portfolios based on the size we propose a conditional logit model for ranking di fferent investment portfolios based on size and assess the robustness of the ranking to the inclusion/exclusion of the best performing stocks in the cross-section. This parametric choice is embedded within a stochastic utility model for explaining the investment decisions of under-diversi fied size investors aiming to exploit the so-called size premium. under-diversifi ed individuals maximize their expected utility in each period by choosing the stock that is predicted to yield the highest return (highest positive skew). This choice is driven by market capitalization of the portfolio and modeled parametrically using the conditional logit model.

In order to obtain cross-sectional variation on the relationship between the size e ffect and portfolio performance we split the whole cross-section of stocks into di fferent industries and fi t the conditional logit model to each industry separately. We apply the conditional logit model at an industry-speci fic level across three ranked sorted portfolios based on market capitalization: a small, mid-size and big portfolio created from the stocks in each tercile of the cross-section of assets in a speci fic industry ranked by asset size. This exercise is repeated for 20 industries over the period January 1970 to November 2015. Our results reveal that the size e ffect vanishes once the top performing stocks in an industry are removed from the sample.

size lottery

Our empirical findings also highlight the role of industry momentum in determining the relationship between market capitalization and portfolio performance. Speci fically, market capitalization has signi ficantly better predictive ability for portfolio return performance in the months following a positive return in an industry than in the months following a negative industry return.

Given these findings, we investigate further the influence of the winning stocks in industry-speci fic size portfolios. In particular, we propose an alternative size portfolio that we denominate as the winner-weighted index, based on the forecast rank probabilities of stocks provided by the conditional logit model. Intuitively, those stocks that are predicted to be winners in the next period receive a larger allocation of wealth than those stocks that have a low probability of becoming winners. More formally, the allocation of wealth to each asset in the portfolio is determined by the forecast winning probabilities obtained from the conditional logit model and driven by asset size. The performance of this portfolio is compared against a cap-weighted index benchmark portfolio. The weights in the latter portfolio are also driven by market capitalization, however, in contrast to our winner-weighted index portfolio, smaller stocks within an industry receive a smaller allocation of wealth. We consider statistical and economic measures such as the Sharpe ratio, Sortino ratio, the certainty equivalent return of a mean-variance investor and portfolio turnover. We observe the existence of two regimes in portfolio performance. During positive industry momentum periods, the winner-weighted index outperforms the cap-weighted portfolio for 19 out of 20 industries, the exception being the utilities industry. This result is, however, reversed in periods of negative industry momentum for which the cap-weighted index outperforms the winner-weighted index in 18 out of 20 industries.

Our second objective is to explore the influence of winning stocks on the size portfolio pricing factor widely used in the empirical asset pricing literature. Our empirical results for both a top-minus-bottom trading portfolio and a long-only portfolio show that standard asset pricing models are not able to adequately capture the contribution of the size premium to the overall risk premium when the winning stocks are removed from the size factor portfolio. In contrast, we note that the factor loadings ( Beta's) associated to the size portfolio pricing factor in standard models are robust to the inclusion/exclusion of the winning stocks. The removal of winning stocks is a ffecting the risk premium rather than the covariance of portfolios with the risk factor."


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Quantpedia’s Solution for Bear Markets

6.January 2019

Dear readers,

Equity markets have once again entered a high volatility regime at the end of the year 2018. Risk of an economic slowdown increases and investors and traders are looking for  trading strategies which can perform well in such uncertain times.

We at Quantpedia can help with that!

I am really excited to give you an opportunity to work with a new filtering field in our Screener, which you can use to find  strategies that can be utilized as a hedge/diversification to equity market risk factor during bear markets.

Come and find your new hedge!

Team of Quantpedia.com
 

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ETFs Increase Correlation of International Equity Markets

4.January 2019

Everybody can see that international equity markets are highly correlated (and especially during past 10-15 years). A new interesting financial research paper shows that ETF arbitrage mechanism is one of the key channels through which U.S. shocks propagate to local economies leading to increased return correlation with the U.S. market:

Authors: Filippou, Gozluklu, Rozental

Title: ETF Arbitrage and International Correlation

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3287417

Abstract:

Assets under management of exchange-traded funds (ETF) have been growing significantly, yet the majority of ETF trades still occur on U.S. exchanges. We show that investment decisions of both institutional and retail investors when trading international country ETFs are mostly driven by shocks related to U.S. fundamentals, measured by VIX, rather than local country risks. Investors react only to negative news about local economies. When U.S. economic uncertainty increases, investors leave the country ETF market and switch to Cash ETF products. We demonstrate that ETF arbitrage mechanism is one of the key channels through which U.S. shocks propagate to local economies leading to increased return correlation with the U.S. market both in time-series and cross-sectional dimensions. We find that countries with stronger ETF price-discovery and lower limits to arbitrage tend to have a higher comovement with the U.S. market.

Notable quotations from the academic research paper:

"Signi ficant innovations in financial products made international investments increasingly possible. Over the recent years, exchange-traded funds experienced a double-digit growth in assets under management. Nevertheless, the short-run interdependence of trading across major international ETFs and its association with local and global risk aversion remain understudied. While the majority of earlier studies focuses on direct eff ects of ETFs on the underlying securities in the basket that it tracks, we examine the indirect e ffect of ETF trading as a transmission mechanism of U.S. market shocks to foreign country equity markets.

We provide a view that as the U.S. accommodates the largest share of ETF global trading volume, its market conditions directly impact the decisions of country ETF investors. We show that international ETF market participants trade based on shocks related to U.S. fundamentals rather than local ones, and propagate those shocks to local markets. The shock transmission is performed via ETF arbitrage. We argue that such arbitrage activity is one of the few mechanisms responsible for increasing correlation between the U.S. market and the rest of the world.

This high cross-country correlation limits the ability of investors to cheaply diversify U.S. risk via international ETF investments. In addition, ETFs often provide an easier access to less integrated emerging markets or to countries were direct investments are costly (e.g., Brazil). However, the transmission of U.S. shocks to those markets limits the diversi fication bene ts of emerging market strategies.

correlation

We fi rst test the hypothesis whether country ETF investors react to changes in the U.S. rather than local economic uncertainty, as measured by CBOE Volatility Index (VIX). To this end, we compute order imbalances of retail investors (e.g., Boehmer, Jones, and Zhang, 2017), and trades of di fferent size, capturing high frequency trading (HFT) and institutional trades. Focusing on a large cross-section of 41 countries, we find strong association between ETF order imbalances and U.S. VIX, indicating that international investment decisions are mainly driven by the latter measure, rather than its local counterparts. For example, an increase in the U.S. VIX results in a selling pressure in the country ETF market. Such result is robust to di fferent volatility regimes and is consistent across di fferent types of investors. Asymmetric response analysis confi rms that country ETF investors only react to positive changes in local VIX, which correspond to negative news in the local markets. Moreover, we observe that, when reacting to an increase in U.S. uncertainty, investors switch to safer assets such as cash equivalent ETFs. We also find that investors respond to changes in U.S. political uncertainty di fferently than to economic uncertainty – they leave the U.S. stock market and buy international country-level ETFs. However, they do not react to local political uncertainty and the economic eff ect of political risk is much smaller than of changes in U.S. VIX.

In order to access the impact of ETF arbitrage on correlation of country returns with the U.S. market, we regress daily innovations in such correlation on a proxy for ETF arbitrage during di fferent volatility regimes. We provide time-series evidence that during periods of high volatility in the U.S., an increase in the arbitrage activity by the authorized participant (AP) (as measured by net share creation/redemption) results in an increase in innovation in such daily correlation. We argue that during periods of high volatility in the U.S. market, it is harder for investors to distinguish between noise and fundamental component of the order flow. Consequently, based on wake-up call hypothesis investor may treat U.S. shocks as relevant to their own country and consume such shocks via ETF arbitrage.

We also explain cross-country variation in return correlation with the U.S. market. According to Ben-David, Franzoni, and Moussawi (2018), non-fundamental shocks must be reversed over time. This suggests that if all shocks transmitted from ETF market to local economies were non-fundamental, ETF arbitrage would not contribute towards increased correlation. In contrast, if the price deviation from the NAV is due to faster incorporation of fundamental information in ETF market, then arbitrage should a ffect returns of underlying index, and such e ffect should not be reverted. If such fundamental information is common both to U.S. and local market, one should observe a higher correlation between them.

Consistent with the literature, we argue that ETF transmits both fundamental and noise shocks to the underlying economies. We show that countries that have a higher degree of price discovery in their ETFs have on average a higher correlation with the U.S. market. In these markets fundamental information gets incorporated into ETF prices faster than in the Net Asset Value (NAV), and therefore, market makers closely follow and learn from changes in ETF prices. This is the case when derivative securities price the underlying assets, rather than the other way around. In addition, in order for fundamental shocks to get transmitted to underlying markets, the authorised participants (AP) must engage in arbitrage activity. We find that the lower the limits to ETF arbitrage the higher is the correlation between a country and the U.S. market. Neither the international trade channel nor the business cycles alter this result."


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FOMC Equity Drift Occurs in Periods of High Uncertainty

27.December 2018

A new research paper related mainly to:

#75 – Federal Open Market Committee Meeting Effect in Stocks

Authors: Martello, Ribeiro

Title: Pre-FOMC Announcement Relief

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3286745

Abstract:

We show that the pre-FOMC announcement drift in equity returns occurs mostly in periods of high market uncertainty or risk premium. Specifically, this abnormal return is explained by a significant reduction in the risk premium (implied volatility and variance risk premium) prior to the announcement, but only when the risk premium is high, e.g., when it is above its median. Likewise, the magnitude of the FOMC Cycle and other related patterns varies with uncertainty and risk premium. Market uncertainty measures are persistent and are not related to policy uncertainty or expectations. Markets become only marginally stressed in the days prior to the announcement and changes in uncertainty appear to be of lower frequency. We also explain why recent studies suggest that the pre-FOMC drift might have disappeared in the past decade, as this moderation is due to time variation that was also present in older data. Additionally, CAPM only works on FOMC dates when the risk premium is high, e.g., implied vol above its prior median level. The results are robust to different samples and measures of risk premium and uncertainty.

Notable quotations from the academic research paper:

"We show that pre-announcement return drift is associated with significant declines in risk (premium) during times of high risk (premium). Implied volatility and the variance risk premium decrease in the hours before the announcement in an almost perfect mirror image of the increase in market prices. Moreover, we show that the magnitude of the return drift and the decline in risk depends on the level of market implied volatility, or other related variables, days or even weeks prior to the announcement.

Just to exemplify, the average pre-FOMC drift when implied volatility is above its prior median is 109 basis points (bps), while it is only 9.7 bps when it is below its median. In the bottom 20% of implied volatilities, the drift is close to zero or even negative, depending on the specification. Lucca and Moench [2015] also showed the importance of the VIX in their analysis, but here we show that this and other market uncertainty variables are actually essential for a better understanding of the pre-announcement return drift and all FOMC announcement related patterns. Figure 2 replicates a figure in Lucca and Moench [2015] that shows stock market performance around FOMC releases. Here we show that the pre-announcement drift is much stronger in periods of high risk premium and uncertainty.

We also provide clear evidence of investor relief, i.e., a decline in implied volatility or other risk measures, hours before the announcement using intraday information. Panel B of Figure 2 also shows that uncertainty is going down as a mirror image of the realized return. The magnitude of this pre-announcement investor relief also depends on the level of market uncertainty, as it tends to go down more when it is high. Considering the squared value of the VIX as our priced risk proxy, we show that, during high volatility periods, implied variance declines by 103.5 bps in anticipation of the announcement, while during low volatility periods, it rises by insignificant 0.3 bps. Hence, high volatility periods present both higher realized equity returns and greater resolution of market uncertainty hours before pre-scheduled announcements.

FOMC return patterns"


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Are Equity Markets Manipulated?

13.December 2018

We present two interesting research papers written by Bruce Knuteson. He contemplates why the cyclically adjusted price to earnings ratio of the S&P 500 index has been oddly high for the past two decades. He states that persistently strong equity market in US (and therefore also its high valuation in a comparison to history) and also in other developed countries can be an outcome of intraday trading pattern of several huge quant equity long-short funds which aggressively buy in the morning and sell in the afternoon to expand their trading book (or alternatively to simply manipulate market – push prices of stocks in their portfolio up).

Authors: Bruce Knuteson

Title: Information, Impact, Ignorance, Illegality, Investing, and Inequality

Link: https://arxiv.org/pdf/1612.06855.pdf

Abstract:

We note a simple mechanism that may at least partially resolve several outstanding economic puzzles, including why the cyclically adjusted price to ear nings ratio of the S&P 500 index has been oddly high for the past two decades, why gains to capital have outpaced gains to wages, and the persistence of the equity premium.

Notable quotations from the academic research paper:

"In United States equity markets, bid-ask spreads early in the trading day are typically larger than spreads later in the trading day. The price impact of aggressive trades early in the trading day is therefore typically larger than the price impact of equally sized aggressive trades later in the day.

Market makers make wider markets early in the trading day. The market, viewed as an information aggregator, respects the information content of aggressive orders early in the day more than the information content of equally sized aggressive orders later in the day. A repeated sequence of intraday round trips – e.g., buying in the morning and selling in the afternoon, repeated over many days – can therefore be expected to result in net price impact in the direction of the morning trade.

If some market participant (M) performs the same round trip each day – e.g., aggressively buying in the morning and selling in the afternoon – M’s trading will, on average, nudge the market’s midprice in the direction of his morning trading. If M has a large, slowly varying portfolio, the mark to market gains resulting from M’s daily intraday round trip trades can exceed the cost M incurs by crossing the spread twice each day.

In light of the above, it is striking that the returns to the S&P 500 index over the fifteen years spanning 1993 to 2007, inclusive, all came at the start of the trading day. Indeed, Figure 1 of Ref. [M. J. Cooper,  M. T. Cliff,  and H. Gulen (2008), Return Differences Between Trading and Non-trading Hours:  Like Night and Day, URL http://ssrn.com/abstract=1004081] is so striking it calls for a simple explanation. We propose such an explanation. We propose some market participant M, tending to trade in one direction early in the trading day and in the other direction later in the day, has had a much larger long-term effect on United States equity prices than has so far been widely appreciated.

day vs night return"

And:

Authors: Bruce Knuteson

Title: How to Increase Global Wealth Inequality for Fun and Profit

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3282845

Abstract:

We point out a simple equities trading strategy that allows a sufficiently large, market-neutral, quantitative hedge fund to achieve outsized returns while simultaneously contributing significantly to increasing global wealth inequality. Overnight and intraday return distributions in major equity indices in the United States, Canada, France, Germany, and Japan suggest a few such firms have been implementing this strategy successfully for more than twenty-five years.

Notable quotations from the academic research paper:

"The Strategy is very simple: construct a large, suitably leveraged, market-neutral equity portfolio and then systematically expand it in the morning and contract it in the afternoon, day after day. The Strategy works because your trading will, on average, move prices in a direction that nets you mark-to-market gains. Bid-ask spreads are wider and depths are thinner near market open than near market close, so aggressive trades early in the trading day move prices more than equally sized aggressive trades later in the day. An intraday round trip (e.g., aggressively buying in the morning and selling in the afternoon) thus nudges the market's midprice in the direction of your morning trading. A reasonable level of daily round-trip trading combined with a suciently large portfolio will therefore produce expected mark-to-market gains exceeding the expected cost of your daily round-trip trading.

Figure 1, which shows cumulative overnight and intraday returns over the past 25 years in six major stock market indices: the S&P 500 index and the NASDAQ Composite index in the United States, Canada's TSX 60, France's CAC 40, Germany's DAX, and Japan's Nikkei 225 [20]. The return pattern in the S&P 500 index was rst pointed out over a decade ago. Similar return patterns have been identi ed in major indices of other developed countries. The only plausible explanation so far advanced for the highly suspicious return patterns in Figure 1 is someone using the Strategy.

day vs. night in other countries

"


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