Why do foreign investors care about real interest rates if exchange rates can change independently of inflation?

External question — Economics Stack Exchange Author: Parth Agarwal Original post: https://economics.stackexchange.com/questions/61172 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I am trying to understand why the real interest rate is considered important for a foreign investor when deciding whether to invest in another country. I recently watched a video discussing the depreciation of the Indian rupee. The video gives this example: India: nominal interest rate = 6.5% India: inflation = 6% Real interest rate ≈ 0.5% It then compares this with the US: US nominal interest rate = 4.5% US inflation = 2% Real interest rate ≈ 2.5% The video argues that investors may prefer the US because its real interest rate is higher. I understand why the real interest rate matters to a domestic investor . However, I am confused about why it should be the relevant measure for a foreign investor . Suppose an American investor invests in India. He converts dollars into rupees, earns interest in India, and eventually converts his money back into dollars. Therefore, shouldn't his relevant return depend on: Indian nominal interest rate − rupee depreciation against the dollar rather than simply: Indian nominal interest rate − Indian inflation? For example, suppose: Indian nominal interest rate = 10% Indian inflation = 8% Rupee depreciation = 3% Wouldn't the foreign investor's approximate return in dollars be 10% − 3% = 7% , rather than the Indian real interest rate of 10% − 8% = 2% ? My main difficulty I understand that inflation and exchange rates are related through ideas such as purchasing power parity. However, a country's currency does not necessarily depreciate by exactly the same percentage as its inflation rate over a particular period. For example, if inflation is 8%, the currency might depreciate by 3%, 8%, 12%, or potentially even appreciate, depending on other factors affecting the exchange rate. Therefore, if I already know or estimate the expected exchange-rate change, why do I need to subtract inflation separately when calculating the foreign investor's return? Would doing both potentially double-count the effect of inflation ? My current understanding is: Real interest rate measures the change in purchasing power after accounting for inflation. Exchange-rate changes determine how the investment's return translates into the foreign investor's home currency. Therefore, for a foreign investor, shouldn't the expected exchange-rate change be considered separately from the real interest rate? Am I misunderstanding the role of the real interest rate here? Why would a foreign investor use the real interest rate rather than directly considering the nominal interest rate and expected currency depreciation? I would appreciate a simple numerical example showing how these two concepts should be combined.

External answer — Economics Stack Exchange Author: 1muflon1 Original post: https://economics.stackexchange.com/a/61173 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Therefore, shouldn't his relevant return depend on: Indian nominal interest rate − rupee depreciation against the dollar No, depreciation does matter, and you might want to adjust for that, but in the ended investors care about real returns not nominal returns. This is the formula for real return on foreign investment; $$r_t^{D} = \frac{(1+R_t^{F})\left(\frac{S_{t+1}}{S_t}\right)} {1+\pi_t^{D}} -1$$ $$\begin{aligned} r_t^{D} &= \text{real return in domestic currency},\\ R_t^{F} &= \text{nominal return on the foreign investment in foreign currency},\\ S_t &= \text{exchange rate at time } t \text{ (domestic currency per unit of foreign currency)},\\ S_{t+1} &= \text{exchange rate at time } t+1,\\ \pi_t^{D} &= \text{domestic inflation rate}. \end{aligned}$$ For small levels of inflation, returns etc this can be approximated as; $$r^D \approx R^f + \Delta S- \pi^D$$ This is the return that matters for investment decisions, as this represents the actual “real” financial gain/loss from the investment. Would doing both potentially double-count the effect of inflation? There is no double counting as long as we distinguish what each adjustment does. For a foreign investor, $1+r^H = \frac{(1+i^F)\left(\frac{S_{t+1}}{S_t}\right)} {1+\pi^H}$ where $i^F$ is the nominal return on the foreign investment, $S_{t+1}/S_t$ captures the exchange-rate change, and $\pi^H$ is inflation in the investor’s home country. The exchange rate converts the foreign investment return into the investor’s home currency. Inflation then tells us how much the purchasing power of that home-currency return has changed. These are different adjustments. For example, suppose a European investor earns 10% on a US investment, but the dollar depreciates 5%: $1+R^{EU}=1.10(0.95)=1.045$ The investor therefore earns a 4.5% nominal return in euros. If European inflation is 3%, the real return is $r^{EU} = \frac{1.045}{1.03}-1 \approx 1.46\%$ So the sequence is simply foreign nominal return -> exchange-rate adjustment -> home inflation adjustment PPP is a theory about how inflation differences may affect exchange rates. It does not imply that observed exchange rate depreciation already constitutes an adjustment for the investor’s loss of purchasing power.