✨ VIPSolutions

Let's answer step by step, clearly showing the calculations for **Aiden** and **Ellie**, and explain at each step. --- ### **Step 1: Calculate Aiden’s Return (U.S. investor in India, hedged with forward contract)** #### **Explanation:** Aiden invests in India but hedges his currency risk by selling Indian rupees forward for USD. According to **Interest Rate Parity (IRP)**, the return for a hedged US investor in India will be the same as the US interest rate. #### **Calculation:** - **US Interest Rate:** 5.80% - **India Interest Rate:** 8.25% - **Spot Rate (INR/USD):** $0.012 **Forward rate using IRP:** \[ \text{Forward Rate} = \text{Spot Rate} \times \left(\frac{1 + r_{India}}{1 + r_{US}}\right) \] \[ = 0.012 \times \left(\frac{1 + 0.0825}{1 + 0.058}\right) = 0.012 \times \frac{1.0825}{1.058} = 0.012 \times 1.02317 = 0.012278 \] - If Aiden invests $1 in India at 8.25%, he has $1 × 1.0825 = $1.0825 worth of INR at year-end. - He converts this back to USD at the forward rate. \[ \text{Final USD} = \frac{1.0825 \times 0.012278}{0.012} = 1.0825 \times 1.02317 = 1.1081 \] But since the forward rate locks in the parity, the USD return will always match the US rate. \[ \text{Aiden's hedged return in USD} = 5.80\% \] #### **Explanation:** The return matches the US interest rate, as required by covered interest rate parity. --- ### **Step 2: Calculate Ellie’s Return (Indian investor in Chile, unhedged)** #### **Explanation:** Ellie invests in Chilean CD at 10% without hedging. International Fisher Effect (IFE) applies, so the expected return for an Indian investor will be affected by both the Chilean interest rate and the expected change in exchange rates (INR/CLP). - **India Interest Rate:** 8.25% - **Chile Interest Rate:** 10% - **Spot Rate (CLP/USD):** $0.0011 **Expected depreciation of the Chilean peso vs. rupee:** \[ \text{IFE: } E\left(\frac{S_1}{S_0}\right) = \frac{1 + r_{India}}{1 + r_{Chile}} \] \[ = \frac{1.0825}{1.10} = 0.9841 \] So, the Chilean peso is expected to depreciate by: \[ \text{Depreciation} = 1 - 0.9841 = 0.0159 = 1.59\% \] **Unhedged return in INR:** \[ \text{Return} = (1 + r_{Chile}) \times \left(\frac{S_1}{S_0}\right) - 1 \] \[ = 1.10 \times 0.9841 - 1 = 1.0825 - 1 = 0.0825 = 8.25\% \] #### **Explanation:** Ellie’s expected return in rupees is 8.25%, same as the Indian rate, as explained by the international Fisher effect. --- ### **Step 3: Summarize and State Final Answers** #### **Aiden (US investor in India, hedged):** - **Return in USD:** **5.80%** - **Reason:** Covered IRP ensures Aiden gets the same return as US deposits when hedged. #### **Ellie (Indian investor in Chile, unhedged):** - **Return in INR:** **8.25%** - **Reason:** IFE predicts the expected INR return equals the Indian deposit rate due to anticipated currency depreciation offsetting the interest differential. --- ## **Final Answers** ### **Aiden’s Investment Return:** **5.80% (in USD)** ### **Ellie’s Investment Return:** **8.25% (in INR)** **Comment/Conclusion:** - Aiden’s hedged return matches the US interest rate due to IRP. - Ellie’s unhedged expected return matches the Indian interest rate due to the IFE. - Both theories predict no arbitrage profits in international investments when hedging (IRP) or on average (IFE).