Calculating the Logarithmic Return from Open to Close

Summary

The document defines an open-to-close logarithmic return as the natural logarithm of the closing price divided by the opening price. By the logarithm quotient identity, this is equivalent to subtracting the log of the open from the log of the close. The measure expresses the price change over that interval in log terms and is identified as potentially useful to arbitrageurs.

The page gives only the formula and a pointer to further reading; it does not explain how to use the measure in an arbitrage strategy or present empirical evidence. It also does not discuss practical choices such as price adjustments, sampling frequency, or handling zero and invalid prices. As a result, the note supports understanding the calculation itself but cannot establish that any particular trading use will be effective.

Key ideas

• The open-to-close log return is the natural logarithm of close divided by open.
• The same value is obtained by subtracting the logarithm of the open from the logarithm of the close.
• The document suggests the measure may be useful in arbitrage analysis.
• It provides no trading rules, empirical results, or implementation caveats beyond the formula.

Tags

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