SSAAM: Sentiment Signal-based Asset Allocation Method with Causality Information

This study used pseudo-log-likelihood scores (PLLs) to create polarity indices. PLLs are scores based on probabilistic language models proposed by Salazar et al.[3]. Because masked language models (MLMs) are pre-trained by predicting words in both directions, they cannot be handled by conventional probabilistic language models. However, PLLs can determine the naturalness of sentences at a high level because they are represented by the sum of the log-likelihoods of the conditional probabilities when each word is masked and predicted. Token $\psi_{t}$ is replaced by [MASK], and the past and present tokens $\textbf{$\Psi$}_{\backslash t}=[\psi_{1},\psi_{2},...,\psi_{t}]$ are predicted. $t$ represents time. $\Theta$ is the model parameter. $P_{MLM}(\cdot)$ denotes the probability of each sentence token. The MLM selects BERT (Devlin et al.[4]).

After pre-processing, score the financial news text with PLLs one sentence at a time. Quartile ranges¹¹1Arranging the data in decreasing order, the data in the 1/4 are called the 1st quartile, the data in the 2/4 are called the 2nd quartile, and the data in the 3/4 are called the 3rd quartile. (3rd quartile - 1st quartile) is called the quartile range. were calculated for data that scored one sentence at a time. The figure below illustrates the polarity classification method.

Aggregate the scores chronologically according to the title column of financial news.

In this study, we used VAR-LiNGAM to demonstrate the precedence. VAR-LiNGAM is a statistical causal inference model proposed by Hyvärinen et al.[5]. The causal graph inferred by VAR-LiNGAM is as follows:

where $\textbf{x}(t)$ is the vector of the variables at time $t$ and $\tau$ is the time delay. $T$ represents the maturity date. In addition, $\textbf{B}_{\tau}$ is a coefficient matrix that represents the causal relationship between the variables $\textbf{x}(t-\tau)$. $\textbf{e}(t)$ denotes the disturbance term. VAR-LiNGAM was implemented using the following procedure: First, a VAR (Vector Auto-Regressive) model is applied to the causal relationships among variables from the lag time to the current time. Second, for the causal relationships among variables at the current time, LiNGAM inference is performed using the residuals of the VAR model. This study confirms whether financial news is preferred to stock portfolios.

Binary segmentation search (Bai[6]; Fryzlewicz[7]) is a greedy sequential algorithm. The notation of the algorithm follows Truong et al.[8]. This operation is greedy in the sense that it seeks the change point with the lowest sum of costs. Next, the signal was divided into two at the position of the first change point, and the same operation was repeated for the obtained partial signal until the stop reference was reached. The binary segmentation search is expressed in Algorithm 1. We define a signal $y=\{y_{s}\}^{S}_{s=1}$ that follows a multivariate non-stationary stochastic process. This process involves $S$ samples. $L$ refers to the list of change points. Let $s$ denote the value of a change point. $G$ refers to an ordered list of change points to be computed. If signal $y$ is given, the $(b-a)$-sample long sub-signal $\{y_{s}\}^{b}_{s=a+1},(1\leq a<b\leq S)$ is simply denoted $y_{a,b}$. Hats represent the calculated values. Other notations are noted in the algorithm’s comment.

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The entropy value at risk (EVaR) is a coherent risk measure that is the upper bound between the value at risk (VaR) and conditional value at risk (CVaR) derived from Chernoff’s inequality (Ahmadi-Javid[9]; Ahmadi-Javid[10]). EVaR has the advantage of being computationally tractable compared to other risk measures, such as CVaR, when incorporated into stochastic optimization problems (Ahmadi-Javid[10]). EVaR is defined as follows.

$X$ is a random variable. $M_{X}$ is the moment-generating function. $\alpha$ denotes the significance level. $z$ are variables. A general convex programming framework for the EVaR is proposed by Cajas[11]. In this study, we switch between the following two optimization strategies depending on the regime classified in Section II-C.

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  Minimize risk optimization: A convex optimization problem with constraints imposed to minimize EVaR given a level of expected $\mu$ ($\widehat{\mu})$.

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  Maximize return optimization: A convex optimization problem imposed to maximize expected return given a level of expected $EVaR$ ($\widehat{EVaR}$).

where $q$, $z$ and $u$ are the variables, $K_{exp}$ is the exponential cone, and $T$ is the number of observations. $w$ is defined as a vector of weights for $N$ assets, $r$ is a matrix of returns, and $\mu$ is the mean vector of assets.

This study calculates the signal for portfolio rebalancing and tactical asset allocation to actively go for an alpha based on the assumption that financial news precedes the equity portfolio. Two types of data were used.

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  Stock Data: We used the daily stock data provided by Yahoo!Finance²²2https://finance.yahoo.com/. The stocks used are the components of the NYSE FANG+ Index: Facebook, Apple, Amazon, Netflix, Google, Microsoft, Alibaba, Baidu, NVIDIA, and Tesla were selected. For this data, adjusted closing prices are used. The time period for this data is January 2015 through December 2019.

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  Financial News Data: We used the daily historical financial news archive provided by Kaggle³³3https://www.kaggle.com/, a data analysis platform. This data represents the historical news archive of U.S. stocks listed on the NYSE/NASDAQ for the past 12 years. This data was confirmed to contain information on ten stock data issues. This data consists of 9 columns and 221,513 rows. The title and release date columns were used in this study. The time period for this data is January 2015 through December 2019.

The polarity index is presented in section II-A. The financial news data were pre-processed once before creating the polarity index. Both financial news and stock data are in daily units; however, to match the period, if there are blanks in either , lines containing blanks are dropped. Once the polarity index is created in Section II-A, the next step is to create a stock portfolio by adding the adjusted closing prices of 10 stocks. The investment ratio for the portfolio is set uniformly for all stocks. Next, we use VAR-LiNGAM in Section II-B to perform causal inference. The causal inference results are as follows: Python library ruptures (Truong et al.[8]) was used.

The values in Table II refer to the elements of the adjacency matrix. The lower limit was set to 0.05. The results in the table show that the polarity index has a leading edge in the equity portfolio. The Python library LiNGAM (Hyvärinen et al.[5]) was used.

In this study, the following rebalancing timings were merged and backtested. Python library vector (Polakow[12]) and Riskfolio-Lib (Cajas[13]) was used for backtesting. In addition to EVaR optimization, CVaR optimization and the mean-variance model were used as optimization algorithms and comparative methods, respectively. In this study, the number of regimes was set to 5 and 10. The rebalancing times were 30, 90, and 180 days. The backtesting methodology was as follows. In this study, CPD-EVaR++ was positioned as the proposed strategy, and CPD-EVaR+ was the runner-up strategy.

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  CPD-EVaR++ (proposed): Changepoint rebalancing using risk minimization and return maximization EVaR optimization + regular intervals rebalancing strategy

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  CPD-EVaR+: Changepoint rebalancing using risk minimization and no-restrictions EVaR optimization + regular intervals rebalancing strategy

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  EVaR: EVaR optimization regular intervals rebalancing strategy

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  CVaR: CVaR optimization regular intervals rebalancing strategy

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  MV: Mean-Variance optimization regular intervals rebalancing strategy

The binary determination of whether the polarity index within each regime shows an upward or downward trend is made by examining the divided regimes. MinRiskOpt (Section $\ref{Portfolio optimization}-(\ref{MinRisk})$) is assigned to an upward trend, and MaxReturnOpt (Section $\ref{Portfolio optimization}-(\ref{MaxRet})$) is assigned to a downward trend.

The following metrics were employed to assess the portfolio performance.

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  Total Return (TR): TR refers to the total return earned from investing in an investment product within a given period. TR formula is as follows: TR = Valuation Amount + Cumulative Distribution Amount Received + Cumulative Amount Sold - Cumulative Amount Bought. This study does not incorporate tax amounts and trading commissions.

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  Maximum Drawdown (MDD): MDD refers to the rate of decline from the maximum asset. MDD formula is as follows: MDD = (Trough Value - Peak Value) / Peak Value.