Certainly! Let’s walk through the detailed steps for engaging in covered interest rate arbitrage with the given data:
### Step 1: Calculate the Proceeds from Investing in the US
First, let's determine the amount we would have after 90 days if we invest the [tex]$800,000 in the US.
- Initial Investment: $[/tex]800,000
- Interest Rate: 2% annualized for 90 days
- Interest for 90 days: [tex]\( \frac{90}{360} \times 2\% = 0.5\% \)[/tex]
So, the proceeds after 90 days in the US:
[tex]\[ \text{US Proceeds} = 800,000 \times (1 + 0.005) = 803,999.9999999999 \][/tex]
Thus, the proceeds would be approximately [tex]$804,000.
### Step 2: Convert USD to GBP at the Current Spot Rate
Next, convert the initial $[/tex]800,000 to GBP at the current spot rate.
- Spot Rate: 1.60 USD/GBP
[tex]\[ \text{Investment in GBP} = \frac{800,000}{1.60} = 500,000 \text{ GBP} \][/tex]
### Step 3: Invest in the UK and Calculate the Proceeds in GBP
Now, invest the converted amount in the UK at the 4% annual interest rate for 90 days.
- Interest Rate: 4% annualized for 90 days
- Interest for 90 days: [tex]\( \frac{90}{360} \times 4\% = 1\% \)[/tex]
So, the proceeds after 90 days in the UK:
[tex]\[ \text{UK Proceeds in GBP} = 500,000 \times (1 + 0.01) = 505,000 \text{ GBP} \][/tex]
### Step 4: Convert GBP Proceeds Back to USD at the Forward Rate
Finally, convert the proceeds from GBP back to USD at the 90-day forward rate.
- Forward Rate: 1.60 USD/GBP
[tex]\[ \text{UK Proceeds in USD} = 505,000 \times 1.60 = 808,000 \text{ USD} \][/tex]
### Step 5: Calculate the Arbitrage Profit
Now, let's determine the gain from engaging in covered interest rate arbitrage by comparing the proceeds from both investments.
- US Proceeds after 90 days: [tex]$803,999.9999999999 (approximately $[/tex]804,000)
- UK Proceeds after converting back to USD: [tex]$808,000
\[ \text{Arbitrage Profit} = \text{UK Proceeds in USD} - \text{US Proceeds} \]
\[ \text{Arbitrage Profit} = 808,000 - 803,999.9999999999 = 4000.0000000001164 \]
So, by engaging in covered interest rate arbitrage, your proceeds would be $[/tex]808,000 and the arbitrage profit would be approximately $4,000.
