Hafiz a cross-rate trader at Deutsche Bank, notices that Crédit Lyonnais is buying dollars at 0.8171, the same as the Deutsche Bank's bid price. Similarly, he observes that Barclays is buying the British pound at 1.4650, the same as Deutsche Bank. He next

To determine if Hafiz has an arbitrage opportunity, we need to analyze the exchange rates involved. The relevant rates provided are: - **Deutsche Bank's Bid Price for USD/EUR:** \(0.8171\) (which is the same as Crédit Lyonnais) - **Deutsche Bank's Bid Price for GBP/EUR:** \(1.4650\) (which is the same as Barclays) - **Credit Agricole's Ask Price for GBP/EUR:** \(1.1910\) Now, let's break down the potential arbitrage steps. 1. **Convert US Dollars to Euros:** Hafiz starts with \(1,500,000\) USD. Utilizing the Deutsche Bank's bid rate, he can convert to Euros: \[ \text{Euros} = 1,500,000 \times 0.8171 = 1,225,650 \text{ EUR} \] 2. **Convert Euros to British Pounds:** Next, Hafiz can use the Euro to Pound exchange rate provided by Credit Agricole. Since Credite Agricole's ask price is given, first, we need to find the equivalent bid price for GBP/EUR. The bid price can be derived from the ask price by taking the reciprocal of the ask price: \[ \text{Bid Price for GBP/EUR} = \frac{1}{1.1910} \approx 0.8397 \] However, since we are looking for the arbitrage sequence based on buying from Credit Agricole: To convert the Euros into British Pounds using the bid rate: \[ \text{British Pounds} = \frac{1,225,650}{1.1910} \approx 1,028,462.38 \text{ GBP} \] 3. **Convert British Pounds back to US Dollars:** Now Hafiz can convert the British Pounds back into US Dollars using the Deutsche Bank's bid price: \[ \text{US Dollars} = 1,028,462.38 \times 1.4650 \approx 1,505,309.84 \text{ USD} \] 4. **Calculate the profit:** Now we can calculate the profit: \[ \text{Profit} = \text{Final Amount in USD} - \text{Initial Amount in USD} = 1,505,309.84 - 1,500,000 \approx 5,309.84 \text{ USD} \] ### Conclusion Yes, Hafiz has an arbitrage opportunity. By converting $1,500,000 into Euros, then to British Pounds, and converting the British Pounds back into US Dollars, he can generate a profit of approximately **$5,309.84**. Update (2024-08-11): To assess whether Hafiz has an arbitrage opportunity, we need to analyze the exchange rates given and check for discrepancies that he can exploit. ### Given Information: 1. **USD/EUR**: Hafiz can sell dollars at the bid price of **0.8171** (implying he can buy euros for 1 / 0.8171 = **1.2250** euros per dollar). 2. **GBP/EUR**: Hafiz finds that the ask price for euros per pound at Crédit Agricole is **1.1910** (meaning he can sell pounds for euros at this rate). 3. **GBP/USD**: Barclays' rate is the same as Deutsche Bank's, which is **1.4650**. ### Conversion Rates: 1. **EUR per USD**: \( \text{EUR per USD} = \frac{1}{0.8171} \approx 1.2250 \) 2. **EUR per GBP (ask price)**: \( 1.1910 \) 3. **GBP per USD**: \( \text{GBP per USD} = \frac{1}{1.4650} \approx 0.6826 \) (implying it takes about 0.6826 pounds to buy a dollar) ### a. Arbitrage Opportunity? We need to find out if trading in dollars, GBP, and euros can yield a profit. If Hafiz converts USD to GBP and then to EUR and back to USD, he gets: 1. **Convert USD to GBP**: - \( 1,500,000 \text{ USD} \times 0.6826 \text{ GBP/USD} \approx 1,023,900 \text{ GBP} \) 2. **Convert GBP to EUR**: - At the ask price of **1.1910**: - \( 1,023,900 \text{ GBP} \times 1.1910 \text{ EUR/GBP} \approx 1,220,427 \text{ EUR} \) 3. **Convert EUR back to USD**: - At the rate of \( 0.8171 \text{ EUR/USD} \), he can convert euros back to USD: - \( 1,220,427 \text{ EUR} \times \frac{1}{0.8171} \approx 1,493,060 \text{ USD} \) ### Profit Calculation: Now we can calculate the total profit: - Starting with **$1,500,000 USD** and ending with approximately **$1,493,060 USD** results in a loss rather than a profit. Thus, calculating yields: \[ \text{Profit} = 1,493,060 \text{ USD} - 1,500,000 \text{ USD} \approx -6,940 \text{ USD} \] ### Conclusion: **a.** There is NO arbitrage opportunity; Hafiz would lose money if he attempted to engage in these trades instead of making a profit. **b.** Since there is no arbitrage opportunity, there are no steps to take, and he does not make any profit; instead, he incurs a potential loss.