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arXiv:2504.14345v2 [q-fin.PM] 19 Oct 2025

LLM-Enhanced Black-Litterman Portfolio Optimization
Youngbin Lee∗

Yejin Kim∗

Juhyeong Kim

youngandbin@elicer.com
Elice
AI Quant Lab, MODULABS
Seoul, Republic of Korea

yejin.kim.ds@meritz.com
Meritz Fire & Marine Insurance
AI Quant Lab, MODULABS
Seoul, Republic of Korea

juhyeong.kim@miraeasset.com
nonconvexopt@gmail.com
Mirae Asset Global Investments
AI Quant Lab, MODULABS
Seoul, Republic of Korea

Suin Kim

Yongjae Lee†

suin@elicer.com
Elice
Seoul, Republic of Korea

yongjaelee@unist.ac.kr
Ulsan National Institute of Science
and Technology
Ulsan, Republic of Korea

Abstract
The Black-Litterman model addresses the sensitivity issues of traditional mean-variance optimization by incorporating investor
views, but systematically generating these views remains a key
challenge. This study proposes and validates a systematic framework that translates return forecasts and predictive uncertainty
from Large Language Models (LLMs) into the core inputs for the
Black-Litterman model: investor views and their confidence levels. Through a backtest on S&P 500 constituents, we demonstrate
that portfolios driven by top-performing LLMs significantly outperform traditional baselines in both absolute and risk-adjusted
terms. Crucially, our analysis reveals that each LLM exhibits a distinct and consistent investment style which is the primary driver
of performance. We found that the selection of an LLM is therefore
not a search for a single best forecaster, but a strategic choice of
an investment style whose success is contingent on its alignment
with the prevailing market regime. The source code and data are
available at https://github.com/youngandbin/LLM-BLM.

CCS Concepts
• Computing methodologies → Natural language processing.

Keywords
Portfolio Optimization, Black-Litterman Model, Large Language
Models, Mean-Variance Optimization, Quantitative Investing, Deep
Learning in Finance
ACM Reference Format:
Youngbin Lee, Yejin Kim, Juhyeong Kim, Suin Kim, and Yongjae Lee. 2025.
LLM-Enhanced Black-Litterman Portfolio Optimization. In Proceedings of
∗ These authors contributed equally to this work.
† Corresponding author

CIKM’25 Workshop on FinAI, Seoul, Republic of Korea
© 2025 Copyright held by the owner/author(s). Publication rights licensed to ACM.
This is the author’s version of the work. It is posted here for your personal use. Not
for redistribution. The definitive Version of Record was published in Proceedings of
the 34th ACM International Conference on Information and Knowledge Management
(CIKM ’25), November 10–14, 2025, Seoul, Republic of Korea, https://doi.org/10.48550/
arXiv.2504.14345.

the 34th ACM International Conference on Information and Knowledge Management (CIKM ’25), November 10–14, 2025, Seoul, Republic of Korea. ACM,
New York, NY, USA, 14 pages. https://doi.org/10.48550/arXiv.2504.14345

1

Introduction

Portfolio optimization is a fundamental problem in finance, traditionally approached using mean-variance optimization [23]. However, a well-known limitation of mean-variance optimization is
its sensitivity to input parameters, such as expected returns and
covariance estimates. The Black-Litterman asset allocation model
[4] was introduced to mitigate these problems by incorporating investor views into expected returns through a Bayesian framework.
Unlike traditional mean-variance optimization, which relies purely
on historical data, the Black-Litterman model blends prior market
equilibrium returns with subjective investor views, weighted by
confidence levels. This approach not only stabilizes return estimates
but also allows for a more flexible and systematic integration of expert knowledge and quantitative signals. While theoretical research
has extended the framework to complex dynamic, multi-period settings [2], our study utilizes the conventional single-period model to
focus specifically on the novel challenge of generating views from
LLMs.
Although the Black-Litterman model remains widely used in
asset management industry, including Goldman Sachs, a key challenge lies in how to define and quantify these views in a systematic
and reliable manner. Traditionally, these views have been derived
from qualitative assessments or ad hoc quantitative models, limiting
scalability and objectivity.
This study proposes a systematic framework for integrating
LLM-generated views into the Black-Litterman model. Our contribution lies not in developing a new time-series forecasting model
with LLMs, but in establishing a structured methodology to
translate LLM predictions into actionable portfolio views.
This framework systematically incorporates not only the LLM’s
return predictions but also their inherent uncertainty, allowing for
a data-driven and scalable generation of views while mitigating human bias. Our experiments serve to illustrate how this framework
operates in practice, demonstrating that the final portfolio performance becomes contingent on the quality of the views generated
by the specific LLM employed.

CIKM’25 Workshop on FinAI, November 14, 2025, Seoul, Republic of Korea

The primary objective of this research is to empirically demonstrate our proposed framework. We apply it to generate portfolios
based on views from several state-of-the-art LLMs, using S&P 500
constituents as the asset universe. We use a dedicated validation
period to tune the Black-Litterman model’s key hyperparameter, 𝜏,
which governs the confidence in market equilibrium returns versus
LLM-generated views. The optimized portfolio is then backtested on
an unseen test period against traditional benchmarks. The analysis
focuses not on crowning a superior forecasting model, but on illustrating how the characteristics of different LLM-generated views,
when systematically integrated via our framework, lead to distinct
portfolio performance outcomes. Performance is assessed using
standard metrics such as the Sharpe ratio, providing a clear picture
of how each model’s predictive patterns translate into investment
results.

2 Related Works
2.1 The Black-Litterman Model and the
Challenge of View Generation
The Black-Litterman model [4] offered a novel approach to portfolio
optimization by systematically blending market equilibrium returns
with investor-specific views. A key advantage of this model is that
it produces more intuitive and stable portfolios than traditional
mean-variance optimization [9, 24].
However, the practical application of the model has always been
limited by its most critical input: the generation of investor views.
Historically, these views were based on the subjective judgments
of human experts [11]. This process is difficult to scale and is prone
to cognitive biases, such as overconfidence and herding, which
are widely studied in behavioral finance [3, 14]. The challenge
of converting expert opinions into a quantitative format while
avoiding human error has led to a long search for a more systematic
and data-driven approach to view generation.
To address the subjectivity of human views, researchers turned to
machine learning, which has shown significant success in empirical
asset pricing [8]. Early approaches employed quantitative models to
forecast returns based on historical patterns, using techniques like
temporal relational ranking or multi-graph convolutional networks
[7, 28].
More sophisticated methods have been developed to systematically generate views. For instance, machine learning has been used
to systematically generate views based on established asset pricing
factors [16]. Other studies have integrated advanced deep learning architectures like Transformers and Generative Adversarial
Networks (GANs) to capture complex, non-linear market dynamics and refine predictions [35]. Beyond prediction, some research
has explored deep reinforcement learning to directly learn optimal
trading policies [12]. While these methods are a significant step
towards objectivity, they share a common limitation: they are primarily designed for structured inputs. This means that processing
unstructured information, such as natural language, requires extensive feature engineering. Consequently, their ability to adapt
to new information sources or changing market regimes remains
limited.

Lee et al.

2.2

LLMs in Finance

Recent advances in LLMs have created new opportunities in finance, particularly due to their ability to understand and reason
with unstructured text data. This has led to the development of specialized financial models like BloombergGPT [29] and open-source
initiatives like FinGPT [21]. As a result, LLMs are being applied to
a wide range of fianncial tasks, as surveyed by [20].
The application of LLMs in finance now extends far beyond simple text summarization. For example, studies have used LLMs to
generate qualitative evaluations for asset pricing models [5], analyze news sentiment for return forecasting [22], and create specialized financial asset representations to overcome the limitations of
general-purpose embeddings [18]. These diverse capabilities highlight the potential of LLMs to serve as powerful signal generators
for portfolio optimization [10, 34].
Another key application area is return forecasting. Studies have
explored using LLMs for return forecasting [13], with techniques
like retrieval-augmented generation (RAG) further improving prediction accuracy [30]. However, a critical gap remains: these studies
often focus on the accuracy of the forecast itself, rather than on the
crucial subsequent step of how to systematically integrate these
powerful, yet inherently uncertain, predictions into a robust portfolio construction framework. Simply using raw LLM outputs can
lead to unstable portfolios, as LLMs possess their own inherent
biases that can distort recommendations if left unchecked [19]. A
separate line of research even bypasses optimization frameworks
entirely, designing fully autonomous trading agents where the LLM
is the sole decision-maker [31, 33].
Our work bridges the gap between unstructured LLM insights
and structured portfolio optimization. We move beyond merely
generating forecasts and propose a systematic framework that
translates not only the return predictions from LLMs but also their
inherent uncertainty into the core inputs of the Black-Litterman
model. By quantifying this uncertainty, our approach automatically
calibrates the confidence in LLM-generated views, mitigating the
risk of overweighting biased or unstable predictions. To our knowledge, this is the first study to establish a structured methodology
for integrating both the predictive power and the predictive uncertainty of various LLMs into a proven portfolio optimization model,
thereby addressing the challenge of systematic view generation in
a novel and scalable manner.

3

Method

We first describe the financial dataset, then explain how LLMs are
prompted to generate predictive views. Finally, we formalize the
integration of these views and their underlying uncertainty into
the Black-Litterman portfolio optimization framework.

3.1

Data Description

We use historical stock price data from the largest 50 S&P 500 constituents by market capitalization as of March 26, 2025, sourced
from Yahoo Finance. The total dataset spans 13 months, from June
2024 to June 2025. To ensure a robust evaluation and avoid overfitting, we divide the data into two distinct periods:

LLM-Enhanced Black-Litterman Portfolio Optimization

CIKM’25 Workshop on FinAI, November 14, 2025, Seoul, Republic of Korea

Estimate parameters

Stock prices in

lookback period

Make Views 

LLM

BlackLitterman

Optimize portfolio

Invest

Stock prices in
evaluation period

Repeat steps at next rebalancing period

Figure 1: The Proposed Framework for Integrating LLM Views into Black-Litterman Model
• Validation Period (3 months): From June 2024 to August
2024. This period is used exclusively for tuning the hyperparameter 𝜏 of the Black-Litterman model.
• Test Period (10 months): From September 2024 to June
2025. This unseen data is used for the final performance
evaluation of the portfolios.
The portfolio is rebalanced every two weeks. At each rebalancing
date, the LLM is provided with the past two weeks of stock price
data and company metadata to generate return predictions for the
subsequent two weeks. This iterative process ensures that each
portfolio construction is based on the most recent information
available.

3.2

Large Language Models

We use LLMs to generate forward-looking views for the BlackLitterman model in an automated and scalable way. We detail this
process, covering the selection of specific LLMs, our structured
prompting technique for eliciting quantitative forecasts, and the
method for measuring the uncertainty of these predictions.
3.2.1 Selection of Large Language Models. To incorporate predictive views, we employ four state-of-the-art models. Crucially, the
knowledge cutoff for all selected models predates our entire evaluation period (Jun 2024–Jun 2025). This ensures that the models’
internal knowledge does not contain information about future stock
performance, thereby preventing any form of look-ahead bias. We
use instruction-tuned models to ensure consistency in the generated
return predictions, and use vLLM [17] for optimized inference.
Model

Size

Release

Developer

Gemma-7B [27]
Qwen-2-7B [32]
LLaMA-3.1-8B [6]
GPT-4o-mini [25]

7B
7B
8B
∼8B

Feb 2024
Jun 2024
Jul 2024
Jul 2024

Google DeepMind
Alibaba Cloud
Meta
OpenAI

Although the exact size of GPT-4o-mini has not been officially disclosed, [1]
estimate it to be within the 8 billion parameter range, making it comparable to
the open-source models used in our study.

Table 1: Summary of LLMs used in this study.

3.2.2 Structured Prompting for Predictive Views. To elicit predictive views from the LLMs, we developed a structured prompting
strategy that combines a detailed system prompt with a concise
user prompt. This two-part structure is designed to guide the models toward generating quantitative, data-driven return forecasts
while minimizing narrative or qualitative output. The full prompt
structure is detailed in Appendix A.
The system prompt sets the context, defines the task, and specifies the output format. It instructs the model to act as a financial
analyst tasked with predicting the average daily return for a stock
over the upcoming two-week period. It outlines the required analytical steps: analyzing the provided time-series data, considering
the broader sector and market context, and incorporating companyspecific information. Crucially, it constrains the output to a single
floating-point number to ensure the response can be directly integrated into our quantitative framework.
The user prompt supplies the specific data for each stock at each
rebalancing date. It includes four key pieces of information:
• Stock Daily Returns: The stock’s own daily returns from the
past two weeks.
• Sector and Market Returns: The corresponding daily returns
for the stock’s GICS sector and the S&P 500 index.
• Company Information: Metadata including the ticker, company name, GICS sector, and sub-industry.

3.3

Integration with the Black-Litterman Model

The overall workflow for integrating the predictive views and their
uncertainty, generated by the LLMs, into the Black-Litterman framework is summarized in Figure 1. Our portfolio strategy adheres to
a two-week rebalancing cycle.
At each rebalancing date, we first utilize the stock price data
from the preceding two weeks (the lookback period). This data is
fed into the LLM using the structured prompting technique detailed
in Section 3.2.2 to generate predictive views for the subsequent twoweek period. These resulting views, along with their corresponding
confidence levels, are then integrated with the market equilibrium
returns within the Black-Litterman model.
The model combines these inputs to estimate the posterior expected returns. Based on this updated estimation, portfolio optimization is performed to determine the new optimal asset allocation weights. This portfolio is then invested (held) according to
these weights for the duration of the two-week evaluation period,

CIKM’25 Workshop on FinAI, November 14, 2025, Seoul, Republic of Korea

Lee et al.

at which point the cycle repeats. This entire process is executed
iteratively at every rebalancing date throughout the test period.
3.3.1 Overview of the Black-Litterman Model. The Black-Litterman
model is a portfolio optimization framework that combines market equilibrium returns derived from the Capital Asset Pricing
Model (CAPM) [26] with investor views to generate more stable
and intuitive asset allocations. Unlike traditional mean-variance
optimization, which is highly sensitive to input parameters, the
Black-Litterman model integrates external views by adjusting equilibrium returns in a Bayesian manner [15].
In the standard Black-Litterman framework, the equilibrium return vector 𝝅 is derived from market capitalization weights and
serves as a prior estimate of expected returns for each stocks. Views
on specific assets, denoted by a view vector q and the corresponding confidence matrix 𝛀, are incorporated to adjust 𝝅 and compute
the posterior expected returns 𝝁, which, along with the covariance
matrix 𝚺 of the stocks, are then used as input for portfolio optimization to get optimal weights w∗ for stocks [11], as detailed in
Appendix B.
That is, we solve for the posterior expected returns 𝝁 from the
Equation 1:
y = X𝝁 + 𝜺,
y=

 
𝝅
,
q

X=

𝜺 ∼ N (0, V)

 
I
,
P

V=


𝜏Σ
0

(1)
0
Ω


(2)

where 𝜏 is a hyperparameter to balance confidence between
the market equilibrium and the LLM-generated views. Σ is the
covariance matrix of stock returns.
Our framework defines the remaining components using LLM
outputs as described in Table 2.
3.3.2 Incorporating LLM-Generated Views. In this study, we extend
the Black-Litterman model by leveraging LLM-generated predictive
views instead of human-defined views. These views, extracted from
multiple queries to LLMs, represent the expected average daily
return for each asset and are incorporated into the model alongside
their confidence levels.
When calculating the posterior expected returns 𝝁, we can determine the equilibrium return vector 𝝅 and the covariance matrix 𝚺 of
the stocks from historical return data. To integrate LLM-generated
predictive views into the Black-Litterman model, we now define the
view expectation vector q, the picking matrix P, and the confidence
matrix 𝛀 based on the LLM output. This process is described in
Figure 1. By structuring the LLM outputs in this manner, we systematically integrate them into the Black-Litterman framework. The
resulting posterior expected returns are then used in the portfolio
optimization process.
View Vector (q ∈ R𝑘 ). The vector q contains the expected return
for each of the 𝑘 views. For each stock, the LLM is queried 𝑁 = 100
times, and the mean of these repeated responses constitutes the
view for that stock.
Picking matrix (P ∈ R𝑘 ×𝑛 ). In our framework, we formulate
one absolute view for each individual stock, rather than relative
views between assets. The picking matrix specifies which of the

Component
View vector

Symbol
q ∈ R𝑘

Description
A vector containing the specific expected return forecasts
for each of the k views.
Picking matrix
P ∈ R𝑘 ×𝑛 A matrix that maps the k views
to the corresponding n assets in
the portfolio.
Confidence matrix 𝛀 ∈ R𝑘 ×𝑘 A diagonal matrix quantifying
the level of uncertainty for each
of the k views.
Table 2: LLM-generated inputs for the Black-Litterman model

𝑛 stocks correspond to each of the 𝑘 views. Since we generate an
independent view for each of the 𝑛 stocks, the picking matrix P is
an identity matrix (𝑘 = 𝑛), linking each view directly to a single
asset.
Confidence Matrix (𝛀 ∈ R𝑘 ×𝑘 ). This diagonal matrix captures the
uncertainty of each view. The diagonal elements are populated with
the variance of the 𝑁 repeated predictions for each stock. A higher
variance signals greater uncertainty, automatically down-weighting
that view’s influence in the final blended return calculation.

4

Experiment

We conduct an empirical backtest to evaluate the performance of
our proposed framework, which integrates LLM-generated views
into the Black-Litterman model (BLM). To structure our analysis,
we address the following key research questions:
RQ1 (Performance) How does the investment performance of portfolios constructed using our LLM-BLM framework compare
to traditional benchmarks like EW and MVO in terms of
absolute and risk-adjusted returns?
RQ2 (Style) Do different LLMs exhibit distinct and characterizable
‘investment styles’ in their predictive view distributions, and
if so, how do they differ in terms of bias, dispersion, and
conviction?
RQ3 (Attribution) What is the relationship between an LLM’s
overarching predictive sentiment and its portfolio performance, and how does this relationship depend on the market
regime?
The subsequent sections are structured to answer each of these
questions in turn. Our evaluation follows a two-stage process: first,
we optimize the model’s key hyperparameter, 𝜏, which was introduced in Equation 2. Second, we assess the final portfolio performance on an unseen test period to address our research questions.

4.1

Experimental Setup

To ensure a comprehensive analysis, we evaluate four distinct LLMenhanced Black–Litterman portfolios, each driven by views from a
different model: BLM-Gemma, BLM-Qwen, BLM-Llama, and BLM-GPT.
We compare their performance against three standard baselines:
• S&P 500 Index (Market): A market-capitalization-weighted
index that serves as the overall market benchmark.

LLM-Enhanced Black-Litterman Portfolio Optimization

CIKM’25 Workshop on FinAI, November 14, 2025, Seoul, Republic of Korea

Figure 2: Comparative Analysis of Cumulative Returns for BLM and Benchmark Portfolios. The results highlight the significant
outperformance of the BLM-Qwen and BLM-Llama strategies, which consistently generated higher returns compared to both
the market index and conventional quantitative models.
• Equally Weighted (EW): A simple yet robust baseline strategy that allocates equal capital to each asset, representing
naive diversification.
• Mean-Variance Optimization (MVO): The classic Markowitz
portfolio model, which relies solely on historical return and
covariance estimates and serves as a traditional quantitative
benchmark.
The performance of each strategy is measured using a comprehensive suite of standard financial metrics. These include return
indicators such as the Cumulative Annual Growth Rate (CAGR)
alongside both daily (mean) and annualized (mean ann.) average returns; corresponding volatility (std); risk-adjusted returns (Sharpe);
and key downside risk measures, including Maximum Drawdown
(MDD), 95% Value at Risk (VaR 95%), and 95% Conditional Value at
Risk (CVaR 95%).
Furthermore, to more realistically reflect the actual investment
environment, transaction costs are incorporated into the backtest.
Costs are calculated as 0.1% of the portfolio weight changes at
each rebalancing and are factored into the final performance. This
setup allows us to rigorously test the practical value of integrating
LLM-generated insights into a structured portfolio optimization
framework.

𝜏 on the validation dataset. This is a crucial step to find the optimal
balance between market priors and the specific characteristics of
each LLM’s views for our asset universe. We employ a two-step
process for this tuning.
4.2.1 Step 1: Heuristic Estimation of Initial 𝜏. First, we derive a
heuristic initial estimate for 𝜏, denoted as 𝜏init . This value is designed to dynamically ground our model’s confidence based on
the relative uncertainty between the LLM’s views and the market’s
historical volatility. We calculate 𝜏init by averaging the ratio of these
uncertainties across all rebalancing periods (𝑡) in the validation set
(𝑇𝑣𝑎𝑙 ):
∑︁ mean(𝛀𝑡 )
1
𝜏init =
(3)
|𝑇𝑣𝑎𝑙 | 𝑡 ∈𝑇 mean(𝚺𝑡 )
𝑣𝑎𝑙

where 𝛀𝑡 is the confidence matrix of the LLM views and 𝚺𝑡 is
the covariance matrix of asset returns at rebalancing period 𝑡. The
mean(·) function computes the mean of all elements in the given
matrix. This approach ensures our initial hyperparameter is directly informed by the relative uncertainties observed during the
validation period.
4.2.2 Step 2: Grid Search for Optimal 𝜏. Using 𝜏init as a center point,
we perform a grid search over a range of values, T , defined as:
T = {0.5𝜏init, 0.75𝜏init, 𝜏init, 1.25𝜏init, 1.5𝜏init }

4.2

Hyperparameter Tuning

The primary hyperparameter in our framework is 𝜏, which, as introduced in the variance-covariance matrix V in Equation (2), balances
the confidence between the market equilibrium prior and the LLMgenerated views. A higher value of 𝜏 indicates less confidence in the
prior (market equilibrium returns), thus placing more weight on the
LLM’s views. Instead of relying on a fixed, arbitrary value, we tune

For each 𝜏 ∈ T , we run a full backtest on the validation period
and calculate the resulting Sharpe ratio. The 𝜏 value that yields the
highest Sharpe ratio is selected as the optimal hyperparameter, 𝜏 ∗ .
The optimal hyperparameter, 𝜏 ∗ , found during the validation
phase is then used for the final evaluation. We run a single backtest
over the test period (Sep 2024-Jun 2025), rebalancing the portfolio
every two weeks using this fixed 𝜏 ∗ .

CIKM’25 Workshop on FinAI, November 14, 2025, Seoul, Republic of Korea

4.3

RQ1: Portfolio Performance

Metric
EW
MVO BLM-Gemma BLM-Qwen BLM-Llama BLM-GPT
CAGR ↑
0.1907 0.0607
0.1590
0.2811
0.2751
0.0768
0.0010
0.0004
mean ↑
0.0008 0.0004
0.0007
0.0011
std ↓
0.0122 0.0179
0.0156
0.0152
0.0124
0.0132
Sharpe ↑
0.0563 0.0176
0.0402
0.0669
0.0774
0.0228
mean (ann.) ↑
0.1932 0.0994
0.1784
0.2763
0.2627
0.0958
std (ann.) ↓
0.1938 0.2841
0.2481
0.2413
0.1975
0.2093
Sharpe (ann.) ↑ 0.8937 0.2793
0.6386
1.0624
1.2286
0.3619
MDD ↑
−0.1688 −0.1620 −0.1551 −0.1375
-0.1383
−0.1649
VaR95% ↑
−0.0171 −0.0259
-0.0168
−0.0182
−0.0169
−0.0157
-0.0283
−0.0312
CVaR95% ↑
−0.0280−0.0448 −0.0372 −0.0320

Table 3: Out-of-sample Investment Performance of Portfolios

Table 3 and Figure 2 summarize the comparative performance
analysis of four proposed BLM-based models (BLM-Gemma, BLM-Qwen,
BLM-Llama, and BLM-GPT) against two traditional benchmarks: the
EW and MVO portfolios. The evaluation encompasses various metrics, including absolute returns, risk-adjusted returns, and downside
risk.
The analysis reveals a strong performance from the BLM-based
models, particularly BLM-Qwen and BLM-Llama. BLM-Qwen achieved
the highest CAGR of 0.2811, closely followed by BLM-Llama at
0.2751. Both significantly outperformed the traditional benchmarks,
EW (0.1907) and MVO (0.0607).
In terms of risk-adjusted returns, measured by the annualized
Sharpe Ratio, Sharpe (ann.), BLM-Llama delivered the top performance with a ratio of 1.2286. BLM-Qwen secured the second-highest
position at 1.0624. This indicates that both models generated superior excess returns per unit of risk, far exceeding the benchmarks
EW (0.8937) and MVO (0.2793).
Regarding volatility, std (ann.), the EW portfolio was the most
stable with a value of 0.1938, underscoring the benefits of simple diversification. However, BLM-Llama was a very close second
with a volatility of 0.1975, indicating effective risk management.
In downside risk, the BLM models also excelled. BLM-Qwen posted

Lee et al.

the lowest MDD at -0.1375, with BLM-Llama following closely at
-0.1383, both demonstrating significantly better capital preservation
than the benchmarks during downturns.
The other LLM-based strategies showed mixed results. The BLM-Gemma
model delivered a modest positive CAGR of 0.1590, while the BLM-GPT
model lagged with a CAGR of 0.0768, performing similarly to the
MVO benchmark in terms of returns.
In conclusion, the framework successfully translated LLM-generated
views into high-performing portfolios. The BLM-Qwen and BLM-Llama
models, in particular, demonstrated exceptional and distinct strengths:
BLM-Qwen excelled in generating the highest absolute returns (CAGR),
while BLM-Llama delivered the best risk-adjusted performance (Sharpe)
and showcased strong risk control. Both models decisively outperformed traditional benchmarks and other LLM strategies, highlighting the framework’s effectiveness.

4.4

RQ2: Investment Styles

To further investigate how LLMs formulated asset views, we analyzed the distribution of their individual return predictions. In our
setup, each LLM repeatedly generated predictions per stock at each
rebalancing point. Figure 3 displays a time-series of these distributions. Specifically, each individual boxplot on the chart represents
the entire population of views (𝑁 predictions × 𝑛 assets) generated
by a model for that single rebalancing period. This visualization
method reveals how the overall distribution of views—encompassing
both cross-sectional differences across assets and the inherent uncertainty within the predictions—evolves over time. The y-axis is
clipped to a range of -3% to 3% for clarity, and the summary statistics in Table 4 provide details on the aggregate distribution across
all periods.
The most striking characteristic is the distribution of views from
BLM-Llama. The boxplots and summary statistics reveal an exceptionally wide dispersion of predictions (Std: 0.6903) with extreme
outliers (Min: -57.99%, Max: 91.70%). This indicates that BLM-Llama
generated highly differentiated and high-conviction views, confidently identifying both strong positive and strong negative return

Figure 3: LLM-generated Views Over Time at Rebalancing Intervals. The figure visualizes the distribution of all generated
return forecasts for each LLM at every two-week rebalancing interval.

LLM-Enhanced Black-Litterman Portfolio Optimization

opportunities. Despite the extreme negative outliers, the overall distribution maintained the highest positive mean (0.1786), suggesting
its positive views were particularly impactful. This "sharp" differentiation between assets appears to be a key driver of its strong
portfolio performance.
In stark contrast, BLM-Gemma and BLM-Qwen represent two opposite poles of view generation. BLM-Gemma consistently exhibited a
strong pessimistic bias; its median view was almost always negative, a fact confirmed by its negative overall mean of -0.3847. This
persistent negative outlook on the market likely led to suboptimal
asset selection. Conversely, BLM-Qwen adopted a cautiously optimistic stance. Its views were the most tightly clustered around a
stable, slightly positive median, reflected in the lowest standard
deviation (0.2872) among all models. This suggests a consistent,
low-conviction strategy that avoids extreme bets.
The BLM-GPT model can be characterized as a middle ground.
Its view distribution was more dispersed than BLM-Qwen’s but less
biased than BLM-Gemma’s, with a moderately positive mean (0.1347)
and standard deviation (0.4805). Its predictions were less stable than
Qwen’s but avoided the persistent pessimism of Gemma.
In conclusion, these results clearly show that the "style" of view
generation is critical. The final portfolio outcomes are a direct reflection of the distinct characteristics of each model’s predictive distribution. BLM-Llama’s high-conviction differentiation, BLM-Qwen’s
stable and cautious optimism, and BLM-Gemma’s pervasive pessimism
are not just statistical artifacts but are the fundamental drivers that
explain their divergent investment performance.

4.5

RQ3: Performance Attribution to Predictive
Sentiment

Figure 4 visualizes the cumulative returns of each portfolio model,
with the background color illustrating the proportion of positive
views among all generated predictions at each rebalancing point.
The color scale ranges from pessimistic (red, a low proportion of
positive views) to optimistic (green, a high proportion). This analysis reveals a direct link between a model’s overarching market
sentiment and its investment performance, contingent on the market conditions of the test period.
(1) Alignment of Optimism with Market Trend in Top
Performers: The top-performing models, BLM-Llama and
BLM-Qwen, both demonstrate a clear synchronization between a consistently optimistic market outlook and strong
portfolio returns. Their backgrounds remain predominantly
green, indicating a high proportion of positive views. During
the observed test period, which featured a generally upward
market trend (as indicated by the S&P500 benchmark), this
stable, bullish conviction proved to be the correct strategic
stance. It allowed the models to effectively participate in
market updrafts and generate significant alpha.
(2) Misaligned Sentiment in Underperformers: In stark contrast, BLM-Gemma’s underperformance is clearly linked to a
persistent pessimistic bias. Its background is dominated by
red and yellow shades, signifying a low proportion of positive
views. This consistently bearish outlook was fundamentally
misaligned with the market’s overall upward trajectory during the period, causing the model to miss key appreciation

CIKM’25 Workshop on FinAI, November 14, 2025, Seoul, Republic of Korea

opportunities and leading to a decline in cumulative return.
Separately, BLM-GPT’s mediocre performance appears driven
by an unstable market view. Its frequent vacillation between
bullish and bearish sentiment suggests an inability to commit to the prevailing market trend, resulting in performance
that failed to meaningfully outperform the benchmarks.
(3) Alignment with Market Regime as the Key Differentiator: In summary, this visual analysis confirms that a model’s
performance is critically linked to how well its overarching
sentiment aligns with the market regime of the test period.
The success of BLM-Llama and BLM-Qwen was rooted in their
stable, optimistic view-generation process, which was the
appropriate stance for the generally bullish environment
observed. Conversely, BLM-Gemma’s failure can be attributed
to its pervasive pessimism being out of sync with the market,
while BLM-GPT’s middling results were a product of its inconsistent outlook. This highlights that for this framework to
succeed, the underlying LLM must generate a consistent and,
crucially, correctly calibrated conviction about the overall
market direction for a given period.

5

Conclusion

This study proposed and validated a systematic framework for
translating LLM predictions and their inherent uncertainty into
actionable views for the Black-Litterman model. Our empirical
backtest demonstrated that this approach generates portfolios, particularly from BLM-Llama and BLM-Qwen, that significantly outperform traditional benchmarks. Crucially, our analysis revealed that
performance is a direct consequence of each LLM’s distinct view
generation ‘style’—such as BLM-Llama’s high-conviction differentiation versus BLM-Qwen’s stable optimism. The key implication is that
the choice of an LLM is akin to selecting an investment manager
with a specific bias, whose success is contingent on its alignment
with the prevailing market regime. Future research could extend
this work by incorporating financial text into the view generation
process or by developing methods to dynamically select models
based on expected market conditions.

Acknowledgments
This research was supported by Brian Impact Foundation, a nonprofit organization dedicated to the advancement of science and
technology for all.

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CIKM’25 Workshop on FinAI, November 14, 2025, Seoul, Republic of Korea

CIKM’25 Workshop on FinAI, November 14, 2025, Seoul, Republic of Korea

A

Prompt Design Details

To clarify the temporal context for the return prediction task, we
include an explicit reference date in the system prompt. This date
represents the point in time at which the LLM is expected to provide
its analysis—positioned between the past time series data and the
future return period. By anchoring the prediction task to a specific
date, we help the model better interpret the directionality of the
input data and generate temporally coherent forecasts.
To ensure consistent and parseable responses from the LLMs, we
adopt a structured output format using the JSON schema supported
by the chat completions API endpoint. This approach standardizes
the outputs across all LLMs and ensures that each model provides
consistently structured responses across repeated queries, reducing
the likelihood of formatting errors and facilitating reliable downstream processing.
To enhance the models’ numerical sensitivity, all daily return
inputs are scaled by 100 (i.e., presented in percentage terms). For
instance, a daily return of -0.0036 is provided as -0.36. This scaling prevents issues arising from the small magnitude of raw daily
returns, which can be difficult for LLMs to differentiate and process effectively. This approach is analogous to using basis points
in finance to handle small numerical values. By providing a rich,
multi-faceted data context and clear instructions, the prompts enable the LLMs to generate informed, quantitative views for portfolio
construction.

B

Portfolio Optimization

In this study, we implement two distinct portfolio optimization
approaches: one based on the views generated by LLMs and the
other using traditional mean-variance optimization as a baseline.
The objective is to compare the performance of LLM-based portfolios against a benchmark portfolio optimized using conventional
techniques.

B.1

LLM-Enhanced Black-Litterman Portfolio

The first approach utilizes the posterior returns derived from the
views generated by the LLMs and covariance matrix 𝚺. The portfolio
optimization problem is formulated as a mean-variance optimization problem, where the goal is to maximize the expected return of
the portfolio while minimizing its risk.
The optimization problem is expressed as:


min w𝑇 Σw − 𝜆 · w𝑇 r
w

where:

Lee et al.

System Prompt
You are providing analysis on {{DATE}}. Predict the average daily
return for the next two weeks based on the information provided
about a stock’s past performance.
You will receive the following inputs:
• Daily Returns: The stock’s daily returns, a time-series
from the past two weeks.
• Company Sector: The company’s GICS sector classification.
• Sector Returns: The company sector’s daily returns, a
time-series from the past two weeks.
• Market Returns: The S&P 500’s daily returns, a timeseries from the past two weeks.
• Company Information:
– Ticker: The stock symbol.
– Company Name: The name of the company.
– GICS Sector: The Global Industry Classification Standard sector.
– GICS Sub-Industry: The sub-industry classification.
# Steps
(1) Analyze the Time-Series Data: Review the historical
daily returns to identify patterns, trends, or anomalies that
may affect future performance.
(2) Consider Sector Performance: Analyze how the market
and the sector’s performance might influence the stock’s
future returns.
(3) Incorporate Company Information: Use the details
from the GICS sector and sub-industry, along with the
company symbol and name, to contextualize the predicted
performance within its industry.
(4) Predict Future Returns: Estimate the average daily returns for the next two weeks based on the analysis of
available data.
# Output Format
Return a single float value that represents the predicted average daily return for the stock over the
next two weeks, without any additional commentary or explanation.
# Notes
• Ensure the prediction considers the quantified data from
the time-series.
• Make calculations based on statistical trends from daily
returns data.
• Pay attention to the trends within both the stock’s daily
returns and the market’s return data.
• Consider the relevance of the company’s sector to refine
your predictions.
• Make calculations without additional interpretation or
commentary.

• w is the vector of portfolio weights,
• r is the vector of expected returns (posterior returns) from
the LLM views,
• Σ is the covariance matrix of returns,
• 𝜆 is the risk aversion parameter, which determines the tradeoff between return and risk.

Figure 5: The structure of the system prompt used to elicit
return forecasts from the LLMs.

In this formulation, w𝑇 r represents the portfolio return, and
w𝑇 Σw represents the portfolio risk (variance). The objective is to
maximize portfolio return while minimizing the risk, adjusted by
the risk aversion parameter 𝜆, which we set as 0.1. The optimization
is subject to the constraints:

Í
• The sum of the portfolio weights equals 1 ( 𝑤𝑖 = 1),
• No shorting is allowed, meaning each weight is non-negative
(𝑤𝑖 ≥ 0 for all 𝑖).

LLM-Enhanced Black-Litterman Portfolio Optimization

User Prompt
Daily Returns: [-1.17, -0.92, -2.31, -0.36, -3.02,
2.53, 0.1, -0.23, 0.45]

CIKM’25 Workshop on FinAI, November 14, 2025, Seoul, Republic of Korea

cautious and stable view generation process, while BLM-Gemma is
notable for its negative mean, confirming a persistent pessimistic
bias. These underlying statistical properties are the root cause of
the performance differences analyzed in the main text.

Company Sector: Information Technology
Sector Returns: [-0.14, -0.38, -1.88, 0.03, -1.1, 2.38,
-0.41, 0.17, -0.31]
Market Returns: [0.09, -0.39, -1.61, -0.04, -0.67,
2.05, -0.56, 0.4, -0.01]
Company Information:
Ticker: AAPL
Company Name: Apple Inc.
GICS sector: Information Technology
GICS sub-industry: Technology Hardware, Storage
& Peripherals

Table 4: Summary Statistics of LLM-Generated Views
Metric

BLM-Gemma

BLM-Qwen

BLM-Llama

BLM-GPT

Count

100000

Mean
Std
Min
25%
Median
75%
Max

−0.3847
0.9711
−22.3000
−1.1200
−0.6600
0.3200
4.8100

100000

100000

100000

0.1007
0.2872
−4.7500
0.0100
0.0300
0.1200
3.1400

0.1786
0.6903
−57.9913
0.0075
0.0270
0.2000
91.6982

0.1347
0.4805
−6.9250
−0.0244
0.1000
0.3190
6.1140

Figure 6: An example user prompt providing data for Apple
Inc. (AAPL) on a specific rebalancing date.
The optimal portfolio weights are obtained by minimizing the objective function.

B.2

Baseline Portfolio

For comparison, MVO is optimized using the traditional meanvariance framework, which is based on historical returns and the
covariance matrix of asset returns. The mean-variance optimization
problem aims to maximize the expected return while minimizing
the portfolio’s risk.
The optimization problem is formulated as:


min w𝑇 Σw − 𝜆 · w𝑇 r
w

where:
• w𝑇 Σw represents the portfolio risk (variance),
• w𝑇 r represents the portfolio return,
The portfolio risk (variance) and portfolio return are defined
similarly in both optimization problems, with w𝑇 Σw representing
risk and w𝑇 r representing return. The optimization problem is
subject to the same constraints:
Í
• The sum of the portfolio weights equals 1 ( 𝑤𝑖 = 1),
• No shorting is allowed, meaning each weight is non-negative
(𝑤𝑖 ≥ 0 for all 𝑖).
The result of this optimization provides the portfolio weights for
the baseline portfolio.

B.3

B.3.2 Analysis of Forecasting Errors. Table 5 presents an analysis
of the forecasting accuracy for the views generated by each LLM
and for the traditional estimate used by the MVO benchmark. The
table quantifies the prediction error by comparing the expected
returns—either generated by an LLM or, in the case of MVO, estimated from the historical average of past returns—against the
actual realized returns of the subsequent period. This error is measured using three standard metrics where lower values are better:
Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and
Mean Absolute Error (MAE).
The results reveal a strong correspondence between a model’s
forecasting accuracy and its ultimate portfolio performance, as detailed in Table 3. BLM-Qwen and BLM-Llama, which demonstrated
the highest predictive accuracy by achieving the lowest errors
across all three metrics, also generated the portfolios with the best
absolute and risk-adjusted returns (CAGR and Sharpe Ratio respectively). This provides direct evidence that their outperformance was
rooted in a superior underlying ability to forecast market returns.
Conversely, the MVO benchmark, relying on naive historical averages, exhibited high prediction errors and correspondingly poor
investment results. Interestingly, while BLM-Gemma also showed
high forecasting errors—even worse than MVO’s—its final portfolio outperformed both MVO and BLM-GPT in terms of CAGR. This
suggests that within the Black-Litterman framework, the nature of
the views can be as important as their raw accuracy; the consistent
(though pessimistic) bias of Gemma may have provided a more
stable, albeit flawed, signal for the optimizer to work with.

Detailed Model-Level Statistics

B.3.1 View Statistics. Table 4 provides the summary statistics for
the entire population of raw views generated by each LLM throughout the test period. These statistics reveal the distinct predictive
"styles" of the models that were discussed in the main analysis. For
instance, BLM-Llama is characterized by the highest mean return but
also the largest standard deviation and the widest min-max range,
indicating a high-conviction, high-dispersion approach. In contrast,
BLM-Qwen shows the lowest standard deviation, reflecting a more

Table 5: Comparison of Prediction Errors
Metric

MVO

BLM-Gemma

BLM-Qwen

BLM-Llama

BLM-GPT

MSE ↓
RMSE ↓
MAE ↓

0.9376
0.9683
0.6989

1.2373
1.1123
0.8608

0.5125
0.7159
0.5168

0.5288
0.7272
0.5281

0.6505
0.8066
0.5702

CIKM’25 Workshop on FinAI, November 14, 2025, Seoul, Republic of Korea

B.4

Analysis of Portfolio Allocation Dynamics

Figures 7 and 8 illustrate the temporal evolution of portfolio allocations for the LLM-driven and baseline strategies, respectively.
Figure 7 details the asset weights at each rebalancing date for
the portfolios constructed using our proposed framework. The

Lee et al.

allocations shown are dynamically adjusted based on the predictive
views generated by each respective LLM. For comparison, Figure 8
displays the allocations for the baseline portfolios. These include
the static, uniformly distributed EW strategy and the MVO portfolio,
whose weights are derived solely from historical data.

LLM-Enhanced Black-Litterman Portfolio Optimization

CIKM’25 Workshop on FinAI, November 14, 2025, Seoul, Republic of Korea

Figure 7: Time-series of Asset Allocation Weights for BLM Portfolios

CIKM’25 Workshop on FinAI, November 14, 2025, Seoul, Republic of Korea

Figure 8: Time-series of Asset Allocation Weights for Baseline Portfolios

Lee et al.
</reference>

<statements>
1. A hybrid is feasible and already exists in several published forms: Black-Litterman or inverse-optimization backbones combined with machine-learning or LLM views
2. The LLM-Enhanced Black-Litterman framework translates not only LLM return forecasts but also their inherent uncertainty into Black-Litterman view-confidence inputs, automatically calibrating tau so that biased or unstable predictions are down-weighted
3. The paper states that simply using raw LLM outputs can lead to unstable portfolios and that LLM selection is a strategic choice of investment style whose success depends on alignment with the prevailing market regime
4. In its 10-month out-of-sample test from September 2024 to June 2025, BLM-Qwen achieved a CAGR of 0.2811 and BLM-Llama 0.2751, both above equal-weight at 0.1907 and mean-variance optimization at 0.0607, while BLM-Qwen posted the lowest maximum drawdown at -0.1375
5. BLM-Gemma delivered a modest positive CAGR of 0.1590 and BLM-GPT lagged at 0.0768, performing similarly to mean-variance optimization in returns
6. The authors also note that a consistent but pessimistic bias can sometimes provide a more stable signal for the optimizer than raw accuracy alone
7. The evidence supports hybrid frameworks, but not a symmetric merger of all three families: LLM and decomposition-ensemble models are used as view-generation layers inside Black-Litterman rather than as standalone allocators
8. The hybrids that appear strongest assign each component a specific job: a data-driven view layer supplied by LLMs or decomposition-ensemble forecasts
9. LLM-Enhanced Black-Litterman | LLM forecasts and forecast uncertainty as Black-Litterman views with calibrated confidence | Subjective human views and unstable raw LLM outputs | 50 S&P 500 constituents, 10-month test, style-dependent performance
10. The LLM-Enhanced Black-Litterman architecture is the clearest example of using machine learning as a view layer rather than as the allocator
11. Its contribution is not a new time-series forecasting model but a structured methodology to translate LLM predictions and their uncertainty into Black-Litterman inputs
12. This matters because Black-Litterman’s historical weakness is subjective human views, which are difficult to scale and prone to cognitive biases such as overconfidence and herding
13. The framework quantifies predictive uncertainty and automatically calibrates confidence, mitigating the risk of overweighting biased or unstable predictions
14. A separate line of research bypasses optimization frameworks entirely and uses LLMs as autonomous trading agents; the Black-Litterman hybrid deliberately keeps the optimization backbone
15. LLM and decomposition-ensemble hybrids report strong results, but over limited test periods and short holding horizons
16. The most defensible framework combines a stable equilibrium or regularized mean-variance backbone, machine-learning or LLM-generated views with explicit uncertainty calibration
17. What would change the judgment is not another backtest with a higher Sharpe ratio, but long-sample out-of-sample results after realistic costs, robustness across market regimes and holding horizons, transparent attribution that survives auditability, and deployment evidence showing that learned or hybrid allocators displace regularized mean-variance and Black-Litterman workflows in live robo-advisor or institutional asset-allocation settings.
</statements>

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