Calculating Real Domestic Returns on Foreign Assets

Summary

The document asks how to calculate the real return, in domestic terms, of an asset priced in a foreign currency. It establishes two ingredients: convert the foreign asset’s nominal price into domestic currency using the exchange rate, and adjust for inflation using the consumer price index. It then proposes taking the ratio of those inflation-adjusted domestic values across two periods as the return calculation.

The text is a question rather than a worked answer. It does not specify the exchange-rate quotation convention, so the conversion formula depends on whether the rate is expressed as domestic currency per unit of foreign currency or the reverse. It also does not discuss whether to report a simple return or a log return, how to handle distributions, or which CPI series should represent domestic purchasing power. These choices should be made consistently when applying the proposed calculation.

Key ideas

• A foreign asset’s nominal price must be converted into domestic currency before measuring domestic returns.
• Deflating domestic values by the CPI expresses them in real purchasing-power terms.
• The ratio of real values across periods provides the basis for a real return calculation.
• The exchange-rate quotation convention determines whether the rate is multiplied or divided.
• The document poses the method but does not resolve treatment of distributions or return conventions.

Tags

# Real domestic return


# Real domestic return












I would like to calculate the real domestic return of a foreign asset

What I know

Real price is $$P_{Real, t} = \frac{P_{Nominal, t}}{CPI_t}$$

where CPI is consumer price index.

And I know that the nominal domestic return of a foreign asset is calculated as follows:

$$R_{Nominal, Domestic, t} = \frac{(P_{Nominal, Domestic, t}) \times E_t}{(P_{Nominal, Domestic, t-1}) \times E_{t-1}}$$

Then, when I want to calculate the real domestic return of a foreign asset, would I do as follows?

$$R_{Nominal, Domestic, t} = \frac{((P_{Nominal, Domestic, t}) \times E_t )/ CPI_t}{((P_{Nominal, Domestic, t-1}) \times E_{t-1}) /CPI_{t-1}}$$

where E shows the exchange rate.

Is this way true? How can I calculate?

Please share your ideas with me. Thank you in advance.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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