## Deep Learning Insights for Factor Investing Wednesday, 3 January, 2018

**Deep learning is a very popular area of research and is used in a lot of industries. We link to a new paper which gives interesting insights about equity factor investing:**

**Authors:** Messmer

**Title: **Deep Learning and the Cross-Section of Expected Returns

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3081555

**Abstract:**

Deep learning is an active area of research in machine learning. I train deep feedforward neural networks (DFN) based on a set of 68 firm characteristics (FC) to predict the US cross-section of stock returns. After applying a network optimization strategy, I find that DFN long-short portfolios can generate attractive risk-adjusted returns compared to a linear benchmark. These findings underscore the importance of non-linear relationships among FC and expected returns. The results are robust to size, weighting schemes and portfolio cutoff points. Moreover, I show that price related FC, namely, short-term reversal and the twelve-months momentum, are among the main drivers of the return predictions. The majority of FC play a minor role in the variation of these predictions.

**Notable quotations from the academic research paper:**

"This study includes cross-sectional stock data from the CRSP/Compustat database from 1970-2014. In total I use 68 published FC, constructed based on accounting and market data. The focus of the analysis lies solely on large and mid cap stocks, to prevent a potential contamination arising from economically unimportant small and micro-cap stocks.

Training a deep neural network for stock picking, is at least partly motivated by a recent important contribution to the open source software community. The so called ”Tensorflow” library provides a highly scalable and flexible machine learning framework, allowing an efficient usage of DL networks and is the core implementation of Google’s artificial intelligence (AI), unit which is under active development. Moreover, the US cross-section of returns is a relative data rich environment. In this application, roughly 2.1 million observations provide a fertile ground for these parameter rich networks.

On the other hand, it is hard to assess ex-ante if these methods are suitable for predicting stock returns, due to the inherently different statistical character they possess — for example, the signal-to-noise ratio of a stock return process is a tiny fraction compared to the processes typically encountered in computer science.

The main contribution of this work lies in the investigation if recent developments in artificial intelligence are of any use predicting cross-sectional stock returns. Applying artificial neural networks (ANN) in finance is not new. Hence, past attempts have to be distinguished. This study can be seen as an extension to earlier attempts of applying ANN to predict stock returns, with the difference of having access to additional regularization techniques, better computational resources and more data. Additionally, it is, to best of my knowledge, the first study which investigates the cross-section and its relation to a rich set of published FC by exploiting a purely data-driven algorithm without any prior assumption on the functional relation between FC and expected return spreads.

Precisely, this paper aims at answering the following main three research questions: First, how can one efficiently employ a DFN framework for the purpose of return predictions? Second, do DFN based predictions add additional economic value compared to a parsimonious linear approach utilizing the same information set? Third, which set of FC drive the prediction results and how far do they differ from recent findings in the literature of FC selection.

The first question is related to the selection problem of the optimal DFN design for this exercise. I address this question by stating the problem as an outer optimization problem. This computational intensive task is tackled by utilizing a random search algorithm as proposed in Bergstra and Bengio (2012) in combination with a one-dimensional grid search for learning rate tuning. The procedure reveals that many network designs fail to deliver reasonable numerical behavior. Despite a relatively high failure rate, I identify architectures which show promising improvements compared to the linear benchmarks based on a validation data set.

The short answer whether economically measurable improvements can be achieved, is yes. I find significant and robust factor alpha’s, which are consistently higher compared to the parsimonious linear benchmark. In many (but not in all) cases I document significant higher Sharpe Ratios (SR). No specification favors the linear model, irrespectively of which performance measure is considered. However, a naive strategy is sensitive to trading cost adjustments for both approaches. Nonetheless, I show that a simple rebalancing frequency adjustment leads to stark improvements. An explicit rebalancing optimization is not carried out and can be seen as a limitation of this work. Over the sample period, I document that DFN based portfolios perform much weaker during high volatility periods compared to times of calmer markets, a phenomena which is characteristical for momentum based strategies. Controlling for momentum exposure during these times, levels the alpha’s significantly into the positive domain.

The answer to the question which FC drive the predictions points unambiguously at price based information, predominantly **short-term reversal** (providing an explanation for the turnover intensity) and the** twelve-months momentum**. However, I study the impact purely by looking at prediction changes arising from variation in the input data. As a result, it can not be seen as a perfect measure, but a computational trivial way in gaining model insights at this stage.

"

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## Persistence in Cryptocurrencies Saturday, 30 December, 2017

**Cryptocurrencies are at the moment very popular, therefore we decided to point on a short research paper showing interesting cryptos' characteristic - persistence:**

**Authors:** Caporale, Gil-Alana, Plastun

**Title: **Persistence in the Cryptocurrency Market

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3084023

**Abstract:**

This paper examines persistence in the cryptocurrency market. Two different longmemory methods (R/S analysis and fractional integration) are used to analyse it in the case of the four main cryptocurrencies (BitCoin, LiteCoin, Ripple, Dash) over the sample period 2013-2017. The findings indicate that this market exhibits persistence (there is a positive correlation between its past and future values), and that its degree changes over time. Such predictability represents evidence of market inefficiency: trend trading strategies can be used to generate abnormal profits in the cryptocurrency market.

**Notable quotations from the academic research paper:**

"One of the key issues yet to be analysed is whether the dynamic behaviour of cryptocurrencies is predictable, which would be inconsistent with the Efficient Market Hypothesis. Long-memory techniques can be applied for this purpose.

The present study carries out a more comprehensive analysis by considering four main cryptocurrencies (the most liquid ones: BitCoin, LiteCoin, Ripple, Dash) and applying two different long-memory methods (R/S analysis and fractional integration) over the period 2013-2017 to investigate their stochastic properties. Moreover, it also examines the evolution of persistence over time (by looking at changes in the Hurst exponent). Any predictable patterns could of course be used as a basis for trading strategies aimed at making abnormal profits in the cryptocurrency market.

As can be seen, the series do not follow a random walk, and are persistent, which is inconsistent with market efficiency. The most efficient cryptocurrency is Bitcoin, which is the oldest and most commonly used, as well as the most liquid. Degree of persistence varies over the time, and fluctuates around its average.

"

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## Carry Trade Across Fixed and Floating Currency Regimes Wednesday, 20 December, 2017

**A new financial research paper related to:**

**Authors:** Accominotti, Cen, Chambers, Marsh

**Title: **Currency Regimes and the Carry Trade

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3077029

**Abstract:**

Carry trade returns vary across fixed and floating currency regimes. Over the last century, outsized carry returns occur exclusively in the floating regime, being zero in the fixed regime. The absence of skewness in floating carry returns rules out a skewness-based explanation for this result. Fixed-to-floating regime shifts deliver negative return shocks to the floating carry strategy, even when controlling for volatility risk. This result explains average excess returns to the floating and therefore the unconditional carry trades over the long-run. We rationalize these findings with a model allowing risk compensation in currency markets to depend on regime.

**Notable quotations from the academic research paper:**

"Our empirical analysis exploits a new database of daily bid and offered exchange rates in spot and forward markets spanning the interval 1919-present. The year 1919 marks the dawn of modern currency trading with the emergence of a continuously traded forward market in London. Consistent with the post-Bretton Woods evidence, we find that the carry trade earns significant average returns over the whole sample period. Our estimated Sharpe ratio of between 0.5 and 0.6 is still substantial and only slightly lower than the 0.7 to 0.8 for the post-Bretton Woods sample. This finding of outsized carry returns across the whole period is robust to differing portfolio weights and to the inclusion of transaction costs. We further exploit our data to examine the dependence of carry trade returns on currency regimes by conditioning the return to the carry trade on the exchange rate regime of each currency pair at the beginning of each period.1 We classify any currency pair into a floating (fixed) regime based on whether its exchange rate volatility is above (below) a certain threshold.

**Our first finding is** that carry trade returns vary with exchange rate regimes. Average excess returns of the unconditional carry trade are entirely driven by returns to the carry strategy conditioned on the sample of currency pairs in the floating exchange rate regime. We term this strategy the floating carry trade. In comparison, the carry strategy conditioned on the sample of currency pairs in the fixed exchange rate regime (the fixed carry trade) generates zero returns on average. Moreover, the exchange rate of a floating currency pair tends to move according to a random walk without drift as the average spot return is close to zero and statistically insignificant. In contrast, the exchange rate of a fixed currency pair tends to move as predicted by the uncovered interest parity (UIP). **Although the carry component of fixed carry trade returns is substantial at 2-3%, these gains are exactly offset by losses from spot rate depreciation when fixed exchange rate regimes collapse.**

There are three other results related to our main finding regarding the regime-dependence of carry returns.

First, we find that the skewness of returns to the floating and fixed carry trade strategies in our long sample differ from the consensus view regarding skewness in the literature. In the post-Bretton Woods period, outsized carry returns display negative skewness and we confirm this result in our own sample. However, when we examine skewness of floating and fixed carry returns separately in our long sample, only the unprofitable fixed carry trade displays negative return skewness due to losses arising from the collapse of currency pegs. In contrast, the return skewness of the profitable floating carry trade is not significantly different from zero.

Second, we further explore the indirect relationship between floating carry returns and the fixed regime. We find that the more that either currency in a floating pair is in a pegged relationship with other currencies, the worse is the performance of the floating carry trade strategy.

Last, we ascertain that the variation of carry trade returns is not only related to the time-series but also the cross-section of exchange rate regimes across currency pairs.

**Our second main finding is that** the collapse of currency pegs has spill-over effects on floating currency pairs, thereby causing significant losses to carry traders. The January 2015 abandonment by the Swiss National Bank of its cap on the value of the franc against the euro is an example of such a collapse. The breakdown of this particular fixed exchange rate coincides with poor carry trade returns when investment currencies such as the Australian and New Zealand dollars depreciate against the pound sterling, while funding currencies such as the Japanese yen and Swiss franc appreciate. Our regression analysis verifies that this example is representative of the relationship between fixed-to-floating regime changes and negative returns to the floating carry trade.

"

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## FX Momentum Explained via Dispersion Risk Monday, 11 December, 2017

**A new financial research paper related to FX Momentum strategies:**

**Authors:** Eriksen

**Title: **Cross-Sectional Return Dispersion and Currency Momentum

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3001681

**Abstract:**

This paper studies the relation between global foreign exchange (FX) return dispersion risk and the cross-section of currency momentum returns. We find robust empirical evidence that FX return dispersion is a priced risk factor and that it contains information beyond traditional factors. Currencies with high past returns (winners) load positively on dispersion innovations, whereas currencies with low past returns (losers) load negatively. Intuitively, investors demand a premium for holding past winners as they perform poorly in periods with unexpectedly low cross-sectional dispersion, while past losers provide insurance against periods with disappearing dispersion.

**Notable quotations from the academic research paper:**

"In this paper, we offer a risk-based explanation of currency momentum profits by showing empirically that the high returns to winner currencies can be understood as compensation for dispersion risk, which, in our setting, is defined as innovations to the cross-sectional deviation in currency market excess returns. More precisely, we find that winner currencies load positively on innovations to cross-sectional FX dispersion and perform poorly in periods with unexpectedly low cross-sectional dispersion, periods in which loser currencies provide insurance by delivering positive returns. That is, the high return to winner currencies can be understood as compensation to momentum investors for the risk of disappearing dispersion.

Our main sample of currencies comprises up to 48 countries as in Menkhoff et al. (2012) and our main results are based on momentum portfolio constructed by sorting currencies into five portfolios based on their past excess returns. Investing in the portfolio of winner currencies and shorting the portfolio of loser currencies yields large unconditional excess returns of 5.73% and 5.84% per annum for one- and three-month formation periods, respectively, after adjusting for transaction costs through bid and ask quotes.

This high return is hard to explain using traditional risk factor, but can be rationalized using dispersion risk. We construct our measure of dispersion risk as the cross-sectional deviation across five carry trade portfolios formed by sorting individual currencies into five portfolios based on their previous period’s forward discount. Using this factor, we show that the observed heterogeneity in average net excess returns across currency momentum portfolios can be explained by their different exposures to FX dispersion innovations.

Our key empirical results are as follows: i) We show that dispersion risk is priced in the cross-section of currency momentum portfolios, ii) has a significant positive price of risk, and iii) that dispersion risk is able to account for a substantial part of the heterogeneity is average momentum net excess returns.

The cross-sectional R2 exceeds 96% for one month momentum portfolios and is about 66% for three-month momentum portfolios.Moreover, we find that sorting individual currencies, where currency excess returns are signed according to their previous periods’ excess return (referred to as conditional excess returns), into five portfolios based on their ex ante exposure to dispersion innovations yields a monotonically increasing pattern of average excess returns, corroborating the fact that investors require a higher premium for investing in currencies that are more exposed to negative dispersion shocks.

"

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## Equity Market is Efficient - But on a Long Term Monday, 4 December, 2017

**A new financial research paper sheds some light on a long debate abour market efficiency:**

**Authors:** Bouchaud, Ciliberti, Lamperiere, Majewski, Seager, Ronia

**Title: **Black Was Right: Price Is Within a Factor 2 of Value

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3070850

**Abstract:**

We provide further evidence that markets trend on the medium term (months) and mean-revert on the long term (several years). Our results bolster Black’s intuition that prices tend to be off roughly by a factor of 2, and take years to equilibrate. The story behind these results fits well with the existence of two types of behaviour in financial markets: “chartists”, who act as trend followers, and “fundamentalists”, who set in when the price is clearly out of line. Mean-reversion is a self-correcting mechanism, tempering (albeit only weakly) the exuberance of financial markets.

**Notable quotations from the academic research paper:**

"In his remarkably insightful 1986 piece called “Noise”, Fisher Black famously wrote: __ An efficient market is one in which price is within a factor 2 of value, i.e. the price is more than half of value and less than twice value.__ He went on saying:

*The factor of 2 is arbitrary, of course. Intuitively, though, it seems reasonable to me, in the light of sources of uncertainty about value and the strength of the forces tending to cause price to return to value. By this definition, I think almost all markets are efficient almost all of the time*.As far as we are concerned, we always believed that Black was essentially right, precisely for the argument he sketched: humans are pretty much clueless about the “fundamental” value of anything traded on markets, except perhaps in relative terms. The myth that “informed” traders step in and arbitrage away any small discrepancies between value and prices does not make much sense. The wisdom of crowds is too easily distracted by trends and panic.

In Black’s view, prices evolve pretty much unbridled in response to uninformed supply and demand flows, until the difference with value is strong enough for some mean-reversion forces to drive prices back to more reasonable levels. If Black’s uncertainty band was – say – 0.1%, the efficient market theory (EMT) would be a very accurate representation of reality for most purposes. But if Black’s uncertainty band = 50% or so, as Black imagined, EMT would only make sense on time scale longer than the mean-reversion time TMR. For stock indices with volatility of 20%/year one finds TMR **6 years**.

The dynamics of prices within Black’s uncertainty band is in fact not random but exhibits trends: in the absence of strong fundamental anchoring forces, investors tend to under-react to news and/or take cues from past price changes themselves. This induces positive autocorrelation of returns that have been documented in virtually all financial markets. The picture that emerges, and that we test in the present study, is therefore the following: market returns are positively correlated on time scales <<TMR and negatively correlated on long time scales ~ TMR, before eventually following the (very) long term fate of fundamental value – presumably a biased geometric random walk with a non-stationary drift.

We test this idea on a large set of instruments: indexes, bonds, FX and commodity futures since 1960 (using daily data) and spot prices since 1800 (using monthly data). Our results confirm, and make more precise, Black’s intuition. We find in particular that mean-reversion forces start cancelling trend following forces after a time around 2 years, and mean-reversion appears to peak for channel widths of Black’s uncertainty band on the order of 50 to 100%, which corresponds to Black’s “factor 2”.

In a way, our results are very intuitive: mean-reversion comes as a mitigating force against trend following that allows markets to become efficient on the very long run, as anticipated by many authors. However, even highly liquid markets only equilibrate on time scales of years – and not seconds, as market efficient enthusiasts would claim.

"

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