Information processing device, information processing program, and information processing method

Abstract

When constructing a portfolio, we assess the uncertainty regarding future portfolio returns. [Solution] The information processing device 100 includes a prediction interval calculation unit 110 that calculates the return of each portfolio based on a set of portfolios and the characteristic quantities and return history of the assets constituting the portfolio, performs conformal prediction based on the return of each portfolio, the characteristic quantities of the assets constituting the portfolio at a future point in time, and a prediction model that predicts the return of the portfolio at a future point in time, and calculates a prediction interval in which the return of the portfolio at a future point in time is included with a predetermined probability or higher, and a portfolio selection unit 120 that selects a certain portfolio from the set of portfolios based on an objective function that depends on the prediction interval calculated by the conformal prediction unit.

Description

[Technical Field]

[0001] The present invention relates to an information processing apparatus, an information processing program, and an information processing method. [Background technology]

[0002] Portfolio optimization is a fundamental problem in finance, and many approaches have been developed to help investors select the optimal portfolio. One representative approach is Markowitz's mean-variance portfolio theory. This theory uses variance as a risk indicator and optimizes the portfolio by considering the trade-off between mean and variance of asset returns (Non-Patent Documents 1-3). However, while variance increases with increasing returns, investors generally prefer higher returns, so variance does not always accurately reflect risk. Furthermore, while variance considers the overall distribution of returns, it may include results that do not reflect true risk from the investor's perspective.

[0003] To address these issues, quantile-based approaches have been proposed. For example, Non-Patent Document 4 proposes minimizing the conditional risk value (CVaR) using linear programming, and Non-Patent Document 5 proposes another portfolio selection method that incorporates return and risk quantiles. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Harry Markowitz. Portfolio selection. The Journal of Finance, 1952. [Non-Patent Document 2] Harry Markowitz. Portfolio selection: efficient diversification of investments. Yale university press, 1959.

Non-Patent Document 3

Non-Patent Document 4

Non-Patent Document 5

SUMMARY OF THE INVENTION

PROBLEMS TO BE SOLVED BY THE INVENTION

[0005] Conventional methods often rely on distribution information estimated from historical data. However, this alone may not be sufficient to adequately evaluate the uncertainty associated with future portfolio returns.

[0006] In view of such actual circumstances, the present invention aims to evaluate the uncertainty related to future portfolio returns when constructing a portfolio.

MEANS FOR SOLVING THE PROBLEMS

[0007] An information processing device according to one embodiment of the present invention comprises: a prediction interval calculation unit that calculates the return of each portfolio based on a set of portfolios, the characteristic quantities and return history of the assets constituting the portfolios, performs conformal prediction based on the return of each portfolio, the characteristic quantities of the assets constituting the portfolios at a future point in time, and a prediction model that predicts the return of the portfolios at a future point in time, and calculates a prediction interval in which the return of the portfolios at a future point in time is included with a predetermined probability or higher; and a portfolio selection unit that selects a certain portfolio from the set of portfolios based on an objective function that depends on the prediction interval calculated by the conformal prediction unit. [Effects of the Invention]

[0008] According to the present invention, when constructing a portfolio, it is possible to evaluate the uncertainty regarding future portfolio returns. [Brief explanation of the drawing]

[0009] [Figure 1] This graph shows experimental results for US stocks using the method according to the embodiment of the present invention and other methods. [Figure 2] This graph shows experimental results for Japanese stocks using the method according to the embodiment of the present invention and other methods. [Figure 3] This is a flowchart of portfolio selection based on conformal forecasting. [Figure 4] This is a block diagram showing an example of the functional configuration of a portfolio selection device. [Figure 5] This is a block diagram showing an example of a hardware configuration for a portfolio selection device. [Modes for carrying out the invention]

[0010] Embodiments of the present invention will be described below. However, the present invention is not limited to the embodiments described below.

[0011] <1 Introduction> As mentioned above, various methods exist for utilizing distribution information when selecting a portfolio. However, relying solely on historical data for distribution information may not lead to effective predictions. For example, due to the uncertainty of time series data, the average of past samples is often unsuitable for predicting future asset returns. Therefore, autoregressive (AR) models and machine learning models are sometimes used to predict asset returns such as stocks, currencies, and real estate. However, AR models and machine learning models have challenges in evaluating the uncertainty of predictions. For example, confidence intervals can be easily calculated for low-dimensional linear regression models, but general machine learning models involve high-dimensional parameters, making it difficult to apply conventional statistical inference. Furthermore, when there are dependencies between data, it is difficult to construct a reasonable prediction interval without making strong assumptions such as normality in the error term of the regression model.

[0012] A method called conformal prediction is known to address the problem of evaluating the uncertainty of machine learning models (Vladimir Vovk, Alex Gammerman, and Glenn Shafer. Algorithmic Learning in a Random World. Springer-Verlag, 2005 (Non-Patent Literature 6), Victor Chernozhukov, Kaspar Wüthrich, and Zhu Yinchu. Exact and robust conformal inference methods for predictive machine learning with dependent data. In Conference On Learning Theory (COLT), 2018. (Non-Patent Literature 7)). Using conformal prediction, it is possible to calculate effective prediction intervals independently of the model.

[0013] Conformal prediction is a method that provides distribution-free prediction intervals and confidence levels by using the "nonconformity" of the training data as an indicator, without making strong assumptions about the data. It guarantees a certain level of coverage even with finite samples and is applied in various fields of machine learning and statistics. Guaranteeing coverage means that, given a coverage of 1-α, the following relationship holds for a random variable W and the set of possible values ​​C^ for W:

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[0014] This confidence interval represents the uncertainty of future asset returns. A machine learning model (predictive model) learned from the data is used to construct a prediction confidence interval C^(data). The more accurate the prediction, the more accurate the estimation of C^(data). This allows for the evaluation of the prediction uncertainty of various machine learning models.

[0015] Embodiments of the present invention relate to a Conformal Predictive Portfolio Selection (CPPS) framework for estimating and utilizing distribution information of future asset returns. This approach predicts future portfolio returns, calculates corresponding prediction intervals, and then selects the optimal portfolio based on those intervals. This framework is flexible and can accommodate various predictive models, such as time series models including autoregressive (AR) models, random forests, and neural networks.

[0016] <2 Problem settings> Let T and K be positive integers ≥ 2. Let the time series of T+1 periods be denoted as 1, 2, ..., T, T+1. There are K financial assets, and each asset a ∈ [K] := {1, 2, ..., K} has a return Y in each period t ∈ [T+1]. a,t This generates a d-dimensional feature vector for each period t∈[T+1].

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[0017] The returns and features of K assets are as follows:

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[0018] The ratio of investments in K financial assets, i.e.

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[0019] dataset

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[0020] In portfolio optimization, investors typically consider both the uncertainty of asset returns and risk preferences. Merely maximizing R T+1 (w T+1 )is not necessarily desirable. This is because such an approach may mean taking excessive risks. In order to balance the trade-off between return and risk, many methods use risk measures such as variance and quantiles. Well-known examples include the aforementioned mean-variance portfolio, risk parity portfolio, and quantile-based portfolio.

[0021] Existing approaches rely on distributional information (mean, variance, quantiles), but this distributional information is unknown and needs to be estimated when constructing a portfolio. This estimation introduces uncertainty due to estimation errors and the possibility of distributional changes over time. In particular, since this embodiment focuses on the distributional information of future returns, various predictive models, including machine learning algorithms, can be used. However, these methods are more complex than more classical models such as linear regression, which can complicate the quantification of uncertainty. Therefore, a portfolio is constructed using prediction intervals that can more effectively evaluate the uncertainty of the distributional information estimator.

[0022] <2.1 Predictive Models> The focus is,

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[0023] The problem can be formalized as follows: Dataset

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[0024] <2.2 Conformal forecast of portfolio returns> Portfolios are constructed based on predictions generated by predictive models. Conformal predictions are used to assess the uncertainty of these predictions. Conformal predictions offer flexibility by not imposing constraints on the selection of predictive models and are effective if certain conditions, such as the rate of estimation error, are met.

[0025] Let α ∈ (0, 1) be the error level. (Dataset)

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[0026] <3 Portfolio Selection Based on Conformal Forecasts> In this embodiment, portfolio selection is performed using a forecast interval for future asset returns. While forecast asset returns provide insights into future performance, they often fail to reflect the associated uncertainties. In portfolio optimization, if investors are not risk-neutral, this uncertainty plays a crucial role in determining the optimal portfolio. Therefore, it is important to incorporate methods that consider the uncertainty of forecast portfolio returns.

[0027] Conformal forecasting provides a formal method for measuring the uncertainty of a forecast. Conformal forecasting allows us to...

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[0028] Using the prediction interval as input, portfolio

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[0029] This framework is flexible and can incorporate various objectives in portfolio selection. Furthermore, the selection of predictive models and conformal prediction methods is not limited to a specific method; the appropriate method should be chosen according to the data generation process.

[0030] In conformal forecasting-based portfolio selection (CPPS), forecast intervals are calculated using conformal forecasts, and these intervals are used to construct portfolios based on those intervals. The CPPS method mainly consists of the following two steps. For each portfolio w∈W, the forecast interval is calculated using conformal forecasting, and the portfolio value is calculated. • Optimize the objective function, which depends on the prediction interval, to select a portfolio. The pseudocode for this procedure is shown in Algorithm 1. [Table 1]

[0031] Individual Asset Y a,T+1 The reason for calculating forecast intervals per portfolio rather than per asset is related to the need to capture the correlational structure of the time series of multiple assets. In principle, a multivariate conformal forecasting framework that comprehensively handles such correlations is required. To address this problem, in this embodiment, prior to conformal forecasting, the returns for each asset are integrated into the return for a single portfolio, thereby avoiding the complexities associated with multivariate time series analysis.

[0032] This method is attractive for two main reasons. First, while it is generally difficult to directly model high-dimensional time series data, this method requires only a univariate predictive model. Second, this method is easy to implement. That is, it relies on standard conformal prediction routines and a relatively simple algorithmic structure. In contrast, multivariate conformal prediction methods based on optimal transport involve more complex algorithms. The ease of implementation of this method plays a significant role in practical applications. Therefore, although this method requires computational resources when many portfolios must be considered, it remains practical and beneficial for implementation in real-world scenarios. In practice, the portfolio class W can be restricted to a finite set.

[0033] <3.1 HR-LR CPPS> As mentioned earlier, the CPPS framework does not require a specific prediction model or conformal prediction method, but a concrete example is given below to illustrate the procedure. Here, we present a CPPS that selects a portfolio that maximizes returns within a prediction interval determined by a specified error level α, while limiting risk.

[0034] Given a certain error level, one possible approach is to calculate the lowest return within the prediction interval at the specified error level, select multiple portfolios with high lowest returns, and then choose the portfolio with the highest return within the prediction interval. This method aims to guarantee worst-case performance by selecting a portfolio from those with high returns within a given error level. This is called a High-Return-from-Low-Risk (HR-LR) portfolio. The procedure and its corresponding pseudocode are also shown. For conformal prediction, the method proposed in Non-Patent Document 7 is used.

[0035] Let α∈(0, 1) be the error level, and H be R T+1 Let (w) be a hypothetical value. For simplicity, we assume that H is a discrete set such that H = {-0.3, -0.2, 0.0, 0.1, 0.2, 0.3}. For each w ∈ W, using conformal prediction,

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[0036] Next, let m≧1 be a positive integer. For each portfolio w∈W,

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[0037] <3.2 HR-LR CPPS using AR models> As a more concrete example, we present the CPPS framework using the AR model, a type of time series model, as the predictive model. This framework is also applicable to more general time series models. For conformal prediction, we apply the method proposed in Non-Patent Document 7.

[0038] Step 1: Data Expansion Hypothetical value H = {r (1) , r (2) ,..., r (H) Suppose} is given. For each w∈W and r∈H, the extended dataset

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[0039] Let π be a permutation of the set {1, 2, ..., T}. The dataset after permutation is

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[0040] Step 2: Training the predictive model Original Data D (r) Each dataset including

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[0041] Step 3: Conformal Prediction The p-value is defined as follows:

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[0042] [Table 3]

[0043] Step 4: Defining maximum return and minimum risk For each w,

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[0044] Step 5: HR-LR CPPS Finally, gather

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[0045] Thus, in the HR-LR method, we first search for a set of portfolios with a relatively large lower bound on the (1-α) prediction interval. This is for the purpose of managing downside risk. Specifically, for each candidate portfolio w,

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[0046] <3.3 Theoretical analysis> Next, following the results of Non-Patent Document 7, we demonstrate the validity of conformal prediction for dependent data. The unknown oracle score function S *is defined. The effectiveness of conformal prediction for dependent data depends on the score S defined by Equation (3) approximating the oracle score S * to what extent.

[0047] When using the AR model together with block permutation Π, under certain regularity conditions, the following proposition holds for the sequence. Each term converges to 0 when t→∞ (Non-Patent Document 7). [Mathematical formula] The following proposition holds for the sequence. Each term converges to 0 when t→∞ (Non-Patent Document 7). ·With a probability of at least 1-γ1, the randomization distribution [Mathematical formula] satisfies [Mathematical formula] and F(x)=P(S * (Z)<x). When this holds, it is said that [Mathematical formula] has almost ergodic property with respect to F(x). ·With a probability of at least 1-γ2, the estimation error is small. -The mean squared error satisfies [Mathematical formula] . -The pointwise error at π=identity is small, that is [Mathematical formula] . -The density of S * (Z) is uniformly bounded by a constant D. Here, for the number of permutations, |Π|=T. Therefore, the confidence interval derived from conformal prediction has a coverage of approximately 1-α.

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[0048] <4 Experiments> Next, we will verify the empirical performance of the CPPS framework. In particular, we will focus on HR-LR CPPS and conduct an empirical study using equity data from the US and Japanese markets. Specifically, we will use HR-LR CPPS together with the AR(3) model and a neural network to calculate the prediction interval. In the neural network approach, we will use a feedforward network with 100 hidden units to calculate R for each w∈W. T (w), R T-1 (w), R T-3 (w) is the input, R T+1 (w) is predicted. For each market, three stocks shown in Tables 1 and 2 are used. [Table 4]

[0049] The stock price data covers the period from January 1, 2009 to December 31, 2019, and returns are calculated on a monthly basis. Data from January 2009 to December 2011 is used solely for parameter training, and portfolio performance is tested using data from January 2012 to December 2018. Parameter estimates are updated sequentially from January 2012 onward.

[0050] <4.1 Alternative method> We will construct a portfolio using the following methods and compare it with the proposed method. • Sample mean over the past year (Mean) t [1]) • Sample mean over the past 3 years (Mean) t [3]) • AR(1) regression model using samples from the past 3 years (AR t (1)) • AR(2) regression model using samples from the past 3 years (AR t (2)) • AR(3) regression model using samples from the past 3 years (AR t (3)) • Uniform investment strategy: Allocating 1 / K to each asset.

[0051] <4.2 Experimental Results> We will implement each method using data from January 1, 2008 to December 31, 2019, and report the cumulative returns. Figures 1 and 2 show the cumulative returns of various portfolio strategies for US stocks and Japanese stocks, respectively. In the figures, HR-LR CPPS with AR(3) is denoted as "Conformal (AR)", and HR-LR CPPS with a neural network is denoted as "Conformal (NN)".

[0052] Figure 1, which shows the case for US stocks, confirms that Conformal (AR) and Conformal (NN) demonstrate better performance in terms of cumulative return compared to other methods. Notably, these two approaches also show greater stability, avoiding the sharp declines in portfolio value seen with other methods such as Uniform and AR(3).

[0053] Figure 2, which shows the case of Japanese stocks, also confirms that the methods according to the embodiments of the present invention exhibit good performance. Conformal (AR) achieved the highest cumulative return, followed closely by Conformal (NN). Both methods effectively mitigate the impact of extreme portfolio losses, as indicated by their smoother upward trajectories. Mean shows significant volatility. t This is in contrast to [1] and AR(2).

[0054] Overall, these results clearly demonstrate the robustness of the HR-LR CPPS framework for balancing risk and return. By introducing forecast intervals that capture uncertainty, the method of this embodiment adapts to changing data distributions and maintains stable performance, especially during market downturns. This adaptability surpasses that of conventional methods that rely primarily on point estimates (Mean t Unlike [3] and AR(1)), this stems from the fact that predictive uncertainty is taken into account when constructing the portfolio.

[0055] It should be noted that the alternative methods discussed here are relatively simple. More sophisticated approaches exist, but they can introduce further complexity and reduce the transparency of direct comparisons. Using a simple baseline is appropriate for demonstrating performance.

[0056] In summary, we have described a flexible framework for portfolio selection that generates forecast intervals using conformal forecasting. Conformal forecasting allows for the calculation of VaR and VoR, which can then be used to make investment decisions.

[0057] For example, when selecting a portfolio based on conformal prediction, first, a set of portfolios, i.e., a set of investment ratios π, is defined. Then, a machine learning model (predictive model) is used to predict the portfolio return that will be realized under a given investment ratio π∈π. In this case, the portfolio is determined first, and then conformal prediction is performed. This allows us to obtain a confidence interval that contains future portfolio returns with a high probability. From this confidence interval, an index corresponding to VaR or VoR is calculated, and the portfolio is selected based on that index.

[0058] As a concrete example, we described HR-LR CPPS, which selects the highest return from the lowest-risk portfolio. Empirical analysis using US and Japanese equity data suggests that HR-LR CPPS can avoid significant losses and maintain relatively stable gains, demonstrating the practical application of conformal forecasting in overcoming the inherent uncertainties of financial data. Overall, these findings highlight the value of forecast intervals in portfolio construction and support the broader applicability of this methodology to real-world investment scenarios.

[0059] Figure 3 shows the flow of Conformal Prediction-Based Portfolio Selection (CPPS), and Figure 4 shows the portfolio selection device 100 (or information processing device) that performs CPPS. The portfolio selection device 100 comprises a prediction interval calculation unit 110 and a portfolio selection unit 120.

[0060] The prediction interval calculation unit 110 obtains a set of portfolios W := {w(1), w(2), ..., w(K)} from the first database DB1. The prediction interval calculation unit 110 further obtains a historical dataset D := {(X a,t ,Y a,t The return of each portfolio is obtained from the second database DB2, where t=1,2,...,T and a=1,2,...,K. The prediction interval calculation unit 110 then calculates the return of each portfolio based on the portfolio set W and the historical dataset D.

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[0061] The prediction interval calculation unit 110 obtains a prediction model for predicting portfolio returns from the fourth database DB4. There are no restrictions on the prediction model, but examples include AR models, random forests, and neural networks. Based on the obtained prediction model, the prediction interval calculation unit 110 calculates the predicted return Y of the assets constituting the portfolio. a,T+1Calculate.

[0062] The prediction interval calculation unit 110 calculates the feature quantities {X} of each asset at a future time point T+1. 1,T+1 , X 2,T+1 ,...,X K,T+1 The} is obtained from the third database DB3. The prediction interval calculation unit 110 calculates the predicted value Y a,T+1 The returns of each portfolio calculated in step ST1, and the feature quantities of each asset at future time point T+1 {X} 1,T+1 , X 2,T+1 ,...,X K,T+1 Based on this, conformal forecasts are made, and the return R at a future point in time for each portfolio is calculated. T+1 Calculate the prediction interval in which (w) is included with a predetermined probability or higher (Step ST2).

[0063] Next, the portfolio selection unit 120 selects a portfolio from the set of portfolios W based on an objective function that depends on the prediction interval of each portfolio calculated by the prediction interval calculation unit 110 (step ST3).

[0064] Figure 4 shows an example of the computer hardware configuration of the portfolio selection device 100. This device includes a CPU 191, a communication device 192, a display device 193, an input device 194, a drive device 195, an auxiliary storage device 196, and a memory device 197, which are interconnected by a bus 199.

[0065] The program that implements the functions of the portfolio selection device 100 is provided on a recording medium 198 such as a CD-ROM. When the recording medium 198 on which the program is recorded is set in the drive device 195, the program is installed from the recording medium 198 to the auxiliary storage device 196 via the drive device 195. Alternatively, the program installation does not necessarily have to be done via the recording medium 198, but can also be done via a computer network. The auxiliary storage device 196 stores the installed program as well as necessary files and data.

[0066] The memory device 197 reads and stores a program from the auxiliary storage device 196 when a program startup command is received. The CPU 191 implements the functions of the portfolio selection device 100 according to the program stored in the memory device 197. The communication device 192 is used as a communication interface for connecting to other computers via a network. The display device 193 displays a GUI (Graphical User Interface) or the like, generated by a program. The input devices 194 include a keyboard, mouse, and touch panel.

[0067] <Other> Portfolio Return R T+1 (w T+1 The prediction of ) can be made using any predictive model, regardless of whether it is a statistical or machine learning prediction method, such as linear regression, random forest, neural network, or time series model (AR model, MA model, ARIMA model, etc.).

[0068] The objective function can be anything that maximizes the return while imposing constraints on statistics such as VaR and variance. Examples include mean-variance portfolios, risk parity portfolios, and quantile risk-based portfolios.

[0069] Embodiments of the present invention can be applied to applications other than portfolios. For example, the following: • Selection of marketing strategies (ad distribution, coupon distribution, email distribution, etc.): An algorithm that selects the appropriate strategy when multiple strategies are available. • Product Recommendation: An algorithm that recommends the most appropriate product to a customer when multiple products are available. • Automated trading: How to buy and sell assets at each given time. Marketing strategies and product recommendations are generally considered to fall under the category of causal inference.

[0070] The embodiments described so far have aspects not only as a portfolio selection device (or information processing device), but also as a portfolio selection method (or information processing method) and a portfolio selection program (information processing program).

[0071] In the embodiments and figures described herein, one or more of the components, steps, functions, means, or methods may be combined into a single component, step, function, means, or method, or they may be integrated into several components, steps, functions, means, or methods. The algorithms described in the embodiments and figures described herein may be implemented as software or in hardware. Furthermore, many of the operations described as sequential processes may be executed in parallel or simultaneously. One or more of the various methods and operations described may be partially or completely implemented by programming (e.g., instructions and / or data) that can be stored in computer-readable storage media and / or processor-readable storage media, and may be executed by one or more processors or devices. In the claims and this specification, a singular reference to an element includes a reference to one or more elements unless otherwise specified. Although embodiments of the present invention have been described above, the present invention is not limited to the embodiments described above, and various modifications and changes are possible based on the technical concept of the present invention. [Explanation of Symbols]

[0072] 100 Portfolio Selection Device 110 Prediction interval calculation unit 120 Portfolio Selection Section

Claims

1. A prediction interval calculation unit calculates the return of each portfolio based on a set of portfolios and the characteristic quantities and return history of the assets constituting the portfolios, performs conformal prediction based on the return of each portfolio, the characteristic quantities of the assets constituting the portfolios at a future point in time, and a prediction model that predicts the return of the portfolios at a future point in time, and calculates a prediction interval in which the return of the portfolios at a future point in time is included with a predetermined probability or higher. A portfolio selection unit selects a portfolio from the set of portfolios based on an objective function that depends on the prediction interval calculated by the conformal prediction unit. An information processing device equipped with the following features.

2. The information processing apparatus according to claim 1, wherein the prediction model is a time series model.

3. A prediction interval calculation step involves calculating the return of each portfolio based on a set of portfolios, the characteristics and return history of the assets constituting the portfolios, performing conformal predictions based on the return of each portfolio, the characteristics of the assets constituting the portfolios at future points in time, and a prediction model that predicts the return of the portfolios at future points in time, and calculating a prediction interval in which the return of the portfolios at future points in time is included with a predetermined probability or higher, A portfolio selection step in which a portfolio is selected from the set of portfolios based on an objective function that depends on the prediction interval calculated by the conformal prediction unit. An information processing program that causes a computer to execute something.

4. An information processing method performed by an information processing device comprising a prediction interval calculation unit and a portfolio selection unit, The prediction interval calculation unit calculates the return of each portfolio based on a set of portfolios and the characteristic quantities and return history of the assets constituting the portfolios, performs conformal prediction based on the return of each portfolio, the characteristic quantities of the assets constituting the portfolios at a future point in time, and a prediction model that predicts the return of the portfolios at a future point in time, and calculates a prediction interval in which the return of the portfolios at a future point in time is included with a predetermined probability or higher, The portfolio selection step involves the portfolio selection unit selecting a portfolio from the set of portfolios based on an objective function that depends on the prediction interval calculated by the conformal prediction unit. Information processing methods including

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