What is the formula for calculating the variance of domestic-currency returns?

The formula for calculating the variance of domestic-currency returns involves understanding how the returns in domestic and foreign currencies interact. The correct formula incorporates the variances of both the domestic currency returns (RDC) and foreign currency returns (RFC and RFX), as well as the correlation between these two return types.

The variance of domestic-currency returns (σ²(RDC)) is expressed as:

σ²(RDC) ≈ σ²(RFC) + σ²(RFX) + 2σ(RFC)σ(RFX)ρ(RFC, RFX)

This equation accounts for the individual variances of the returns in both currencies and includes the correlation coefficient (ρ) between the two. The term 2σ(RFC)σ(RFX)ρ(RFC, RFX) reflects how the two return series move together; when there is a positive correlation, the combined variance will be higher than simply summing the variances of each return.

In various investment contexts, especially in portfolio management and international finance, recognizing how different components of returns interact is essential. This formula helps in quantifying the risk associated with exchange rate fluctuations alongside domestic market returns, which is vital for accurate risk assessment and financial decision-making.

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