Maximizing Ex Ante Information Ratio for a 150/50 Portfolio

Summary

The document asks how to optimize a 150/50 portfolio against the S&P 500 by maximizing its expected excess return relative to tracking error. It contrasts this with a market-neutral portfolio, where the benchmark return is zero and portfolio variance can be calculated from asset weights and a covariance matrix. The author proposes representing the benchmark as a short position and asks whether including it in the covariance calculation yields tracking error.

The text presents the optimization question but supplies no answer, derivation, empirical evidence, or recommended method. It therefore identifies the key modeling issue—benchmark-relative risk—but does not establish whether the proposed augmented portfolio formulation is appropriate. Readers would need to derive tracking error from the covariance of active returns and account for the portfolio’s leverage and constraints before applying an optimizer.

Key ideas

• The document asks how to maximize expected excess return relative to tracking error for a 150/50 portfolio.
• It distinguishes benchmark-relative optimization from market-neutral optimization.
• It proposes treating the benchmark as a short position in an augmented covariance calculation.
• The document does not provide an answer or validate the proposed formulation.

Tags

# What is the correct method to maximize information ratio ex ante of a 150/50 portfolio against the S&P500


# What is the correct method to maximize information ratio ex ante of a 150/50 portfolio against the S&P500












I have no problem forecasting and minimize ex ante information ratio for a market neutral portfolio, because the benchmark is just zero and you are just minimizing portfolio variance while maximizing return, using some optimization software and wT x cov x w to calculate variance.

But how do I change the formulation when I am trying to maximize information ratio, aka the sharpe ratio of excess returns relative to tracking error? How do I calculate tracking error from the covariance matrix?

I have tried adding the index to the weights at weight -100 and then add index to the covariance matrix, but would wT x cov x w then output tracking error?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.