Calculating Portfolio Returns from Asset Log Returns

Summary

The document asks whether portfolio weights can be applied directly to asset log returns to calculate realized portfolio returns. The setting is weekly data: volatility forecasts come from GARCH models, and the resulting estimates feed a mean-variance allocation that produces asset weights. The author is weighing a log-return calculation against solving the allocation problem with simple returns.

The text raises the distinction between modeling in log-return space and measuring the return of a weighted portfolio, but provides no answer or derivation. It notes that a cited paper compares portfolios built using simple and log returns and discusses transforming log returns to simple returns, while the questioner suspects the difference may be small at weekly frequency. That expectation is not supported by evidence in the document. Portfolio return calculations depend on the return convention and rebalancing assumptions, so the question remains unresolved here.

Key ideas

• The question concerns combining GARCH volatility forecasts with mean-variance portfolio weights.
• It asks whether weighted asset log returns represent the realized portfolio return.
• The document distinguishes modeling in log-return space from converting returns to simple-return terms.
• It offers no derivation or conclusion about the appropriate calculation for weekly data.
• The expectation that weekly log and simple returns differ little is presented as a question, not a demonstrated result.

Tags

# Modelling log-returns and calculating the portfolio return


# Modelling log-returns and calculating the portfolio return












I know this might be a trivial question, however, I would be grateful for some clarification. I am working on weekly log-return data, doing volatility-foracasting using GARCH models and then using these forecasts I solve a mean-variance asset allocation problem and obtain weights for each of the considered assets.

Having done so, I want to obtain realized portfolio returns. And here is my question: can I simply multiply the weights by the corresponding log-return series? Thus I would obtain a series of realized portfolio log-return which I can later easily transform into simple returns. I was reading this paper and in formula $1.21$ the author compares the results of portfolio returns obtained from simple and log returns and in this comparison he multiplies the weights by corresponding log-returns. In this paper the author works on the log-returns and than in formula $6$ uses the exponential transformation for obtaining simple returns in the asset allocation problem.

So my question in general is: when modelling the volatility on log-returns using GARCH models and obtaining weights in the log-return framework can I use the log-returns of assets to obtain the realized portfolio return? Or should I solve the asset allocation problem on simple returns, as in the second reference I mentioned.

I know that for daily data the difference is negligible, so for weekly data it might be the same.

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