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Reddits WallStreetBets (WSB) community has come to prominence in light of its notable role in affecting the stock prices of what are now referred to as meme stocks. Yet very little is known about the reliability of the highly speculative investment advice disseminated on WSB. This paper analyses WSB data spanning from January 2019 to April 2021 in order to assess how successful an investment strategy relying on the communitys recommendations could have been. We detect buy and sell advice and identify the communitys most popular stocks, based on which we define a WSB portfolio. Our evaluation shows that this portfolio has grown approx. 200% over the last three years and approx. 480% over the last year, significantly outperforming the S&P500. The average short-term accuracy of buy and sell signals, in contrast, is not found to be significantly better than randomly or equally distributed buy decisions within the same time frame. However, we present a technique for estimating whether posts are proactive as opposed to reactive and show that by focusing on a subset of more promising buy signals, a trader could have made investments yielding higher returns than the broader market or the strategy of trusting all posted buy signals. Lastly, the analysis is also conducted specifically for the period before 2021 in order to factor out the effects of the GameStop hype of January 2021 - the results confirm the conclusions and suggest that the 2021 hype merely amplified pre-existing characteristics.
We propose a novel approach that allows to calculate Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most important feature is the ability to take into account lead-lag relations on different scales, without knowing them in advance. We also present results obtained with this approach while working on Tokyo Stock Exchange intraday quotations. We show that individual sectors and subsectors tend to form important market components which may follow each other with small but significant delays. These components may be recognized by analysing eigenvectors of complex correlation matrix for Nikkei 225 stocks. Interestingly, sectorial components are also found in eigenvectors corresponding to the bulk eigenvalues, traditionally treated as noise.
In this paper we aim to compare Kurepa trees and Aronszajn trees. Moreover, we analyze the affect of large cardinal assumptions on this comparison. Using the the method of walks on ordinals, we will show it is consistent with ZFC that there is a Kurepa tree and every Kurepa tree contains a Souslin subtree, if there is an inaccessible cardinal. This is stronger than Komjaths theorem that asserts the same consistency from two inaccessible cardinals. We will show that our large cardinal assumption is optimal, i.e. if every Kurepa tree has an Aronszajn subtree then $omega_2$ is inaccessible in the constructible universe textsc{L}. Moreover, we prove it is consistent with ZFC that there is a Kurepa tree $T$ such that if $U subset T$ is a Kurepa tree with the inherited order from $T$, then $U$ has an Aronszajn subtree. This theorem uses no large cardinal assumption. Our last theorem immediately implies the following: assume $textrm{MA}_{omega_2}$ holds and $omega_2$ is not a Mahlo cardinal in $textsc{L}$. Then there is a Kurepa tree with the property that every Kurepa subset has an Aronszajn subtree. Our work entails proving a new lemma about Todorcevics $rho$ function which might be useful in other contexts.
We propose three different data-driven approaches for pricing European-style call options using supervised machine-learning algorithms. These approaches yield models that give a range of fair prices instead of a single price point. The performance of the models are tested on two stock market indices: NIFTY$50$ and BANKNIFTY from the Indian equity market. Although neither historical nor implied volatility is used as an input, the results show that the trained models have been able to capture the option pricing mechanism better than or similar to the Black-Scholes formula for all the experiments. Our choice of scale free I/O allows us to train models using combined data of multiple different assets from a financial market. This not only allows the models to achieve far better generalization and predictive capability, but also solves the problem of paucity of data, the primary limitation of using machine learning techniques. We also illustrate the performance of the trained models in the period leading up to the 2020 Stock Market Crash (Jan 2019 to April 2020).
In the IEEE Investment ranking challenge 2018, participants were asked to build a model which would identify the best performing stocks based on their returns over a forward six months window. Anonymized financial predictors and semi-annual returns were provided for a group of anonymized stocks from 1996 to 2017, which were divided into 42 non-overlapping six months period. The second half of 2017 was used as an out-of-sample test of the models performance. Metrics used were Spearmans Rank Correlation Coefficient and Normalized Discounted Cumulative Gain (NDCG) of the top 20% of a models predicted rankings. The top six participants were invited to describe their approach. The solutions used were varied and were based on selecting a subset of data to train, combination of deep and shallow neural networks, different boosting algorithms, different models with different sets of features, linear support vector machine, combination of convoltional neural network (CNN) and Long short term memory (LSTM).
We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the no-arbitrage condition characterization and the existence of an optimal portfolio in a (generically incomplete) discrete-time financial market model with finite time horizon. In contrast to the existing literature, we propose to consider a probability space which is not necessarily complete.