Currency Choice and FX Effects in Stock Correlation Matrices

Summary

The document asks whether correlations for a portfolio holding stocks quoted in Brazilian reais, euros, and US dollars should be calculated from each stock’s local-currency returns or from returns converted into the portfolio’s base currency. One response outlines the standard route from returns to a variance-covariance matrix and then to correlations by standardizing with asset volatilities. Another argues that percentage returns are unchanged by currency units, so converting prices by a fixed currency factor does not change returns or correlations.

That reasoning applies when the conversion factor is constant over the return interval. If exchange rates move, base-currency returns include FX changes, which can alter both correlations and portfolio risk; the two methods are then not generally equivalent. The discussion gives no numerical comparison or empirical evidence and leaves this important exchange-rate qualification unstated in its accepted answer. The practical choice depends on whether the analysis concerns local asset performance or the returns actually experienced by a base-currency investor.

Key ideas

• A correlation matrix is obtained by standardizing a variance-covariance matrix with asset volatilities.
• A fixed currency denomination factor cancels when computing percentage returns.
• Changing exchange rates affect converted returns and can change correlations for a base-currency investor.
• Choose return series that match the portfolio’s intended performance and risk perspective.

Tags

# Stock Correlation Matrix, Multiple Currencies


# Stock Correlation Matrix, Multiple Currencies












If i have a portfolio of stocks from different currencies and i want to generate a correlation matrix from the stocks, how is the correct procedure ?

Imagine a portfolio which the base currency is Brazilian Reais (BRL) and i have stocks quoted in BRL, EUR and USD. The correct way to generate a correlation matrix is :

a) Use the returns on the stocks in each currency and generate the matrix

b) Adjust all returns to the portfolio base currency and then generate the matrix

c) Other Solution

## Answer by I. Я. Newb (score 1)

https://quant.stackexchange.com/a/39237

What You can do is to just calculate the daily returns, Mean Returns and Excess Returns for each asset, Generate a Variance-Covariance Matrix and multiply it by the Standard Deviation Matrix to generate a Correlation Matrix.

## Answer by Shahar (score -1)

https://quant.stackexchange.com/a/14520

Both ways are equivalent (assuming we are talking about net returns, and not forgetting any kind of transaction cost).

Remember that returns are percentages: they are calculated as $$ \frac{P_1 - P_0}{P_0}\times 100$$ [where $P_0$ is the price at the beginning of the period and $P_1$ is the price at the end] so it does not matter what currency you quote the price in: the "units" [of currency] fall off.

So you can stick with your a) to save some time and don't worry about doing b).

Good luck!

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