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def estimate_covariance(returns, method='shrinkage'):
"""Estimate covariance with Ledoit-Wolf shrinkage."""
if method == 'shrinkage':
cov = LedoitWolf().fit(returns).covariance_
else:
cov = returns.cov().values
return cov
Sigma = estimate_covariance(asset_returns)Platform
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Why do we use Ledoit-Wolf shrinkage for covariance estimation?
Sample covariance is noisy with limited data. Shrinkage pulls extreme estimates toward a structured target.
"Developed mean-variance portfolio optimizer using CVXPY, implementing Ledoit-Wolf shrinkage for covariance estimation and generating efficient frontiers across 50+ asset universes"
Each project includes 2-3 resume bullets
Discover how markets move in recurring patterns by analyzing return data as geometric structure. Use vectors, matrices, and dimensionality analysis to see regimes as clusters in reduced space.
Build a complete portfolio optimization tool using CVXPY. Construct efficient frontiers, handle real-world constraints, implement robustness techniques, and produce a defensible allocation decision.
Design a single trade by choosing optimal parameters using single-variable calculus. At every step, you control one variable, analyze a function, and justify decisions mathematically.
Make a real quant decision: evaluate a trading strategy using expected value, break-even analysis, Monte Carlo simulation, and stress testing. Determine whether to trade or not trade—and justify your verdict.
Apply multivariable calculus to analyze how a two-asset portfolio responds to market movements. Compute partial derivatives, gradients, directional derivatives, and the Hessian to understand risk exposure and build Taylor approximations.
Price options using Monte Carlo simulation and variance reduction techniques.
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