You will be provided with a reference and some statements. Please determine whether each statement is 'supported', 'unsupported', or 'unknown' with respect to the reference. Please note:
First, assess whether the reference contains any valid content. If the reference contains no valid information, such as a 'page not found' message, then all statements should be considered 'unknown'.
If the reference is valid, for a given statement: if the facts or data it contains can be found entirely or partially within the reference, it is considered 'supported' (data accepts rounding); if all facts and data in the statement cannot be found in the reference, it is considered 'unsupported'.

You should return the result in a JSON list format, where each item in the list contains the statement's index and the judgment result, for example:
[
    {
        "idx": 1,
        "result": "supported"
    },
    {
        "idx": 2,
        "result": "unsupported"
    }
]

Below are the reference and statements:
<reference>
[2005.13665] Deep Learning for Portfolio Optimization

Abstract page for arXiv paper 2005.13665: Deep Learning for Portfolio Optimization

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Quantitative Finance > Portfolio Management

arXiv:2005.13665
(q-fin)

[Submitted on 27 May 2020 (
v1
), last revised 23 Jan 2021 (this version, v3)]

Title:
Deep Learning for Portfolio Optimization

Authors:
Zihao Zhang
,
Stefan Zohren
,
Stephen Roberts

View a PDF of the paper titled Deep Learning for Portfolio Optimization, by Zihao Zhang and 2 other authors

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Abstract:
We adopt deep learning models to directly optimise the portfolio Sharpe ratio. The framework we present circumvents the requirements for forecasting expected returns and allows us to directly optimise portfolio weights by updating model parameters. Instead of selecting individual assets, we trade Exchange-Traded Funds (ETFs) of market indices to form a portfolio. Indices of different asset classes show robust correlations and trading them substantially reduces the spectrum of available assets to choose from. We compare our method with a wide range of algorithms with results showing that our model obtains the best performance over the testing period, from 2011 to the end of April 2020, including the financial instabilities of the first quarter of 2020. A sensitivity analysis is included to understand the relevance of input features and we further study the performance of our approach under different cost rates and different risk levels via volatility scaling.

Comments:

12 pages, 6 figures

Subjects:

Portfolio Management (q-fin.PM)
; Machine Learning (cs.LG); Computational Finance (q-fin.CP)

Cite as:

arXiv:2005.13665
[q-fin.PM]

(or

arXiv:2005.13665v3
[q-fin.PM]
for this version)

https://doi.org/10.48550/arXiv.2005.13665

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arXiv-issued DOI via DataCite

Related DOI
:

https://doi.org/10.3905/jfds.2020.1.042

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DOI(s) linking to related resources

Submission history
From: Zihao Zhang [
view email
]

[v1]

Wed, 27 May 2020 21:28:43 UTC (1,238 KB)

[v2]

Thu, 9 Jul 2020 20:25:46 UTC (1,238 KB)

[v3]

Sat, 23 Jan 2021 18:19:33 UTC (1,238 KB)

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</reference>

<statements>
1. Zhang, Zohren & Roberts (2020, Journal of Financial Data Science): an LSTM directly maximizing Sharpe on a 4-ETF portfolio (VTI/AGG/DBC/VIX; 2011–Apr 2020) achieves annualized Sharpe of 1.858 (no vol scaling) / 1.962 (with 10% vol scaling), versus best fixed-allocation baseline ~1.23 / ~1.58; the MV baseline reached only 0.759 / 1.120. Outperformance held through the Q1 2020 COVID crash.
</statements>

Begin the assessment now. Output only the JSON list, without any conversational text or explanations.