Let's analyze the scenario step by step, addressing each part of the question with detailed calculations, explanations, and conclusions. --- ### **Part i) Checking whether the Interest Rate Parity (IRP) holds** **Given Data:** | Parameter | Value | |--------------|---------| | UK one-year interest rate, \( i_{UK} \) | 3% (per annum) | | Euro area one-year interest rate, \( i_{EU} \) | 2% (per annum) | | Current spot exchange rate, \( S_0 \) | €1.1500 /£ | | One-year forward exchange rate, \( F \) | €1.1400 /£ | --- ### **Step 1: Recall the IRP condition** The **Covered Interest Rate Parity** condition states: \[ F = S_0 \times \left( \frac{1 + i_{UK}}{1 + i_{EU}} \right) \] - \( F \): Forward rate (€/£) - \( S_0 \): Spot rate (€/£) - \( i_{UK} \): UK interest rate - \( i_{EU} \): Euro interest rate --- ### **Step 2: Convert interest rates into decimals** \[ i_{UK} = 3\% = 0.03 \] \[ i_{EU} = 2\% = 0.02 \] --- ### **Step 3: Calculate the theoretical forward rate per IRP** \[ F_{theoretical} = S_0 \times \frac{1 + i_{UK}}{1 + i_{EU}} = 1.1500 \times \frac{1 + 0.03}{1 + 0.02} = 1.1500 \times \frac{1.03}{1.02} \] \[ F_{theoretical} = 1.1500 \times 1.0098 \approx 1.1608 \] **Interpretation:** According to IRP, the forward rate should be approximately **€1.1608 /£**. --- ### **Step 4: Compare with observed forward rate** - Actual forward rate \( F = €1.1400 /£ \) - Theoretical forward rate \( \approx €1.1608 /£ \) **Conclusion:** Since the actual forward rate (€1.1400) is **lower** than the IRP predicted rate (€1.1608), **IRP does not hold perfectly** here. This suggests a potential arbitrage opportunity or market imperfections. --- ## **Part ii) Investment decision for a UK investor** ### **Given:** - Investment amount: **£200,000** - **Options:** 1. Invest in the UK at 3% interest. 2. Invest in the Euro area at 2%, with exchange rate hedging via the forward contract. --- ### **Step 1: Calculate UK investment return** \[ \text{UK investment after 1 year} = £200,000 \times (1 + 0.03) = £200,000 \times 1.03 = £206,000 \] --- ### **Step 2: Calculate Euro investment return with forward hedge** **Method:** - Convert initial pounds to euros at the current spot rate. - Invest in euros at 2%. - Convert back to pounds using the forward rate after one year. --- ### **Step 3: Convert initial amount to euros** \[ \text{Initial euros} = £200,000 \times 1.1500 = €230,000 \] ### **Step 4: Invest in euros at 2%** \[ €230,000 \times (1 + 0.02) = €230,000 \times 1.02 = €234,600 \] ### **Step 5: Convert euros back to pounds using the forward rate** The forward rate is **€1.1400 /£**, so: \[ \text{Pounds after 1 year} = \frac{€234,600}{1.1400} \approx £205,789.47 \] --- ### **Step 6: Compare returns** | Investment Option | Final amount in GBP | Return (%) | |---------------------|---------------------|------------| | UK investment | **£206,000** | \( \frac{206,000 - 200,000}{200,000} \times 100 = 3\% \) | | Euro investment (hedged) | **£205,789.47** | \( \frac{205,789.47 - 200,000}{200,000} \times 100 \approx 2.89\% \) | **Conclusion:** Investing in the UK yields a slightly higher return (3%) compared to the Euro area hedge (approximately 2.89%). Therefore, **the UK investment is marginally preferable**. --- ## **Part iii) Discussion on the support for Covered Interest Rate Parity (CIRP)** ### **Summary of findings:** - **Part i):** The observed forward rate (€1.1400) is **below** the IRP predicted rate (€1.1608), indicating that **IRP does not hold perfectly**. - **Part ii):** The difference in returns (UK vs. Euro investment with hedge) aligns with the forward rate deviation, suggesting **partial support** for CIRP, but not perfect. --- ### **Step-by-step analysis:** - **CIRP** posits that **no arbitrage** opportunities exist when considering interest rates and forward exchange rates. - If the actual forward rate deviates from the IRP-implied rate, arbitrageurs could profit, pushing the forward rate to restore parity. - In this scenario, the market forward rate (€1.1400) is **below** the IRP-implied rate (€1.1608), implying the euro is **undervalued** relative to IRP expectations. ### **Implications:** - The slight discrepancy suggests **market imperfections or transaction costs** prevent perfect CIRP enforcement. - The small difference in returns from the hedged Euro investment versus the UK investment reflects this deviation. - Overall, the evidence **partially supports** CIRP but indicates **market frictions** or **short-term anomalies**. --- ## **Final Conclusions** 1. **IRP does not hold exactly** in this scenario, as the actual forward rate (€1.1400) is below the rate predicted by IRP (€1.1608). 2. **For the UK investor:** - Investing domestically yields a 3% return. - Investing in euros and hedging via the forward rate yields approximately 2.89%. - Therefore, **investing domestically in the UK offers a marginally higher return**. 3. **Support for CIRP:** - The deviation indicates **possible arbitrage opportunities** and **market imperfections**. - The results **partially support** the CIRP condition but highlight that **perfect parity does not always hold** in real markets. --- **Overall, this analysis underscores the importance of market frictions, transaction costs, and deviations that can cause real-world exchange rates and interest rates to diverge from theoretical parity conditions.**

Certainly! Let’s answer each part step by step, with clear explanations, calculations, and a structured conclusion. --- ## **i) Does Interest Rate Parity (IRP) hold?** ### **Given:** - **UK one-year interest rate:** 3% per annum (\(i_{UK} = 0.03\)) - **Euro area one-year interest rate:** 2% per annum (\(i_{EU} = 0.02\)) - **Spot exchange rate:** €1.1500/£ (\(S_0\)) - **One-year forward rate:** €1.1400/£ (\(F\)) ### **Step 1: IRP Formula** Covered Interest Rate Parity (CIRP) implies: \[ F = S_0 \times \left(\frac{1 + i_{UK}}{1 + i_{EU}}\right) \] ### **Step 2: Plug in the Numbers** \[ F_{IRP} = 1.1500 \times \left(\frac{1 + 0.03}{1 + 0.02}\right) = 1.1500 \times \left(\frac{1.03}{1.02}\right) = 1.1500 \times 1.0098 \approx 1.1608 \] ### **Step 3: Compare Actual Forward Rate** - **Calculated IRP forward rate:** €1.1608/£ - **Actual market forward rate:** €1.1400/£ ### **Step 4: Conclusion** **IRP does not hold** exactly, because the actual forward rate is less than the IRP-implied rate. - **Deviation:** €1.1608 − €1.1400 = €0.0208/£ --- ## **ii) Where should the UK investor put their money?** ### **Assume: £200,000 to invest for 1 year** #### **Option A: Invest in the UK at 3%** \[ £200,000 \times 1.03 = £206,000 \] #### **Option B: Invest in Euro area at 2%, hedge with forward** 1. **Convert £200,000 to euros at spot:** \[ £200,000 \times 1.1500 = €230,000 \] 2. **Invest at 2% for 1 year:** \[ €230,000 \times 1.02 = €234,600 \] 3. **Convert back to GBP at forward rate (€1.1400/£):** \[ £ = \frac{€234,600}{1.1400} \approx £205,789.47 \] ### **Summary Table** | Option | Final GBP amount | Return (%) | |----------------|-----------------|------------| | UK investment | £206,000 | 3.00% | | Euro (hedged) | £205,789.47 | 2.89% | ### **Conclusion** **Investing in the UK yields a higher return** (3% vs. 2.89%). The UK investment is preferable. --- ## **iii) Do the results support Covered Interest Rate Parity (CIRP)?** ### **Analysis** - **CIRP predicts:** Hedged returns from both countries (in the same base currency) should be equal if there are no arbitrage opportunities. - **In this scenario:** - The hedged euro investment yields **slightly less** than the UK investment. - This difference reflects the deviation of the actual forward rate from the IRP-implied rate. ### **Implications** - **Perfect CIRP does not hold** here, possibly due to market frictions, transaction costs, or other real-world factors. - The small difference in returns is evidence of a **minor arbitrage opportunity** (although in practice, such opportunities may be eliminated by costs and barriers). - **Partial support:** The results are close, indicating that CIRP largely holds, but is not exact in this case. --- ## **Overall Conclusion** 1. **IRP does not hold exactly**: The actual forward rate is lower than the theoretical parity rate. 2. **Investor should invest in the UK** for the highest hedged return. 3. **CIRP is only partially supported**: The real-world forward rate does not perfectly offset interest rate differentials, so covered arbitrage would slightly favor UK investments in this scenario. **In sum**: The results show that interest rate parity is a strong guiding principle, but in practice, small deviations exist, and investors should calculate actual returns before deciding where to invest.

Certainly! Let me clarify the steps for checking whether **Interest Rate Parity (IRP)** holds, and explain **each component and step**: --- ### **Step 1: The CIRP (Covered Interest Rate Parity) Formula** **Covered Interest Rate Parity** (CIRP) tells us how the forward exchange rate should be set so investors earn the same return whether they invest at home or abroad (with currency risk hedged using a forward contract). The formula is: \[ F = S_0 \times \left( \frac{1 + i_{UK}}{1 + i_{EU}} \right) \] **Where:** - \( F \) = **Forward exchange rate** (here, € per £ to be received in the future) - \( S_0 \) = **Spot exchange rate** (here, € per £ today) - \( i_{UK} \) = **Interest rate in the UK** (expressed as a decimal, so 3% = 0.03) - \( i_{EU} \) = **Interest rate in Euro area** (as a decimal, so 2% = 0.02) --- #### **Explanation of Each Part** - **Spot Rate (\(S_0\))**: The number of euros you get for one pound today (€1.1500/£). - **Interest Rate in UK (\(i_{UK}\))**: The annual return you would get from investing in the UK (3%). - **Interest Rate in EU (\(i_{EU}\))**: The annual return from investing in the Euro area (2%). - **Forward Rate (\(F\))**: How many euros you will get for one pound in one year, according to the forward contract (€1.1400/£). --- #### **What Does the Formula Mean?** - The formula says that the **forward rate** should reflect both: - The current exchange rate, and - The difference in interest rates between the two countries. - If UK interest rates are higher than Euro rates, the pound should **depreciate in the forward market** (i.e., one pound will buy fewer euros in the future), so investors can’t make a risk-free profit by borrowing in euros, converting to pounds, and investing in the UK. --- #### **How to Use the Formula** To see if IRP holds: 1. Plug the given interest rates and spot rate into the formula. 2. Calculate the forward rate predicted by IRP. 3. Compare it to the actual market forward rate. If the two match, IRP holds. If not, there is a deviation. --- ### **In summary:** - **The formula** sets a “fair value” for the forward exchange rate, based on spot rate and interest rate differences. - **Why?** This prevents arbitrage (risk-free profit) by equalizing returns in both currencies when exchange rate risk is hedged. - **What to check?** Plug in the numbers, and compare the IRP-implied forward rate to the actual forward rate. --- **(You can now proceed to plug in the numbers as shown in the main calculations above!)**

Certainly! Here are detailed explanations of the two summary lines: --- **1. "Investing in the UK yields a higher return (3% vs. 2.89%)."** **Explanation:** When the UK investor chooses to invest their £200,000 in the UK at a 3% interest rate for one year, they end up with £206,000. If they instead convert the £200,000 to euros, invest at 2% in the Euro area, and then hedge the exchange rate by locking in the forward rate to convert back to pounds after one year, they would receive only about £205,789.47. This means the effective return on the euro investment (when hedged back to pounds) is approximately 2.89%, which is **lower** than the 3% return from the UK investment. --- **2. "The UK investment is preferable."** **Explanation:** Since the UK investment provides a higher final amount and a higher percentage return compared to the euro investment (after accounting for exchange rates and hedging), it is the better choice for the investor. **In other words, the investor should keep their money in the UK to maximize their return.**