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Abstract:
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This study evaluated the effectiveness of the Black-Litterman model in optimizing sectoral
portfolios in the United States, with the objective of outperforming the S&P 500
index return over the long term. The methodology involved constrained (wi ≥ 0) and
unconstrained (–1 ≤ wi ≤ 1) portfolios, utilizing ETFs as proxies for the 10 S&P 500
sectors. Historical adjusted price data were sourced from Yahoo Finance, covering
the period from 2005 to 2022, with training conducted up to 2021 and testing in 2022.
Equilibrium returns were computed as π = δΣw, and the covariance matrix was estimated
using the Exponentially Weighted Covariance (EWC) method with λ = 0.94,
without initial subjective views (Q = 0). Efficient frontier optimization was performed
using the PyPortfolioOpt library, and performance was assessed through historical and
dynamic backtesting, comparing the results to the S&P 500 using metrics such as the
Sharpe ratio, Value at Risk (VaR), and Maximum Drawdown. The findings indicated that
the MaxSharpe portfolio outperformed the S&P 500, achieving a cumulative return of
245% compared to 173% over 10 years, with a Sharpe ratio of 0.7818 and a drawdown
of -19%, making it ideal for moderate investors or those focused on retirement. The
LongShort portfolio, with an average annual return of 13%, was suitable for aggressive
profiles but exhibited high volatility (-39.90% in 2022) and a drawdown of -29%, highlighting
vulnerabilities in adverse scenarios. The absence of subjective views limited
adaptability, suggesting that future integration with views or artificial intelligence could
refine the results. This work concluded that the Black-Litterman model is effective for
long-term sectoral optimization, delivering superior returns and improved risk control
when properly calibrated. |
