Question 11: The Bid-Ask Quote At Bank X For The New Zealand

Question 11the Bid Ask Quote At Bank X For The New Zealand Dollar Is

Given the bid-ask quotes at Bank X and Bank Y for the New Zealand dollar (NZD) in USD/NZD and the details provided, the task is to calculate the potential gain from executing a cycle of locational arbitrage with $1,000,000 USD. The bid-ask spreads are as follows: Bank X: 0.33 - 0.335 USD/NZD; Bank Y: 0.32 - 0.325 USD/NZD.

Locational arbitrage involves exploiting discrepancies in exchange rates across different markets or banks to profit without net currency exposure. The trader would start with USD, convert to NZD at one bank, then convert back to USD at another, aiming to end up with more USD than initially invested.

Paper For Above instruction

In the foreign exchange market, arbitrage opportunities often arise when there are inconsistencies in currency quotes across different financial institutions. These discrepancies can be temporary, providing traders with possibilities to earn riskless profits through arbitrage. This paper examines the process of locational arbitrage using bid-ask quotes from two banks, with a focus on the New Zealand dollar (NZD) quoted against the US dollar (USD), to determine the potential profit achievable with an initial capital of $1,000,000 USD.

Given the bid-ask quotes: at Bank X, the bid price for USD/NZD is 0.33 USD/NZD, and the ask price is 0.335 USD/NZD; at Bank Y, the bid price is 0.32 USD/NZD, with an ask of 0.325 USD/NZD. The arbitrage process entails executing three steps:

  1. Convert USD to NZD at Bank Y's bid price (since the goal is to buy NZD at the lowest possible price). Because when converting USD to NZD, the effective rate is the ask price. We will buy NZD at the lower ask rate from Bank Y.
  2. Convert NZD back to USD at Bank X's bid price (since selling NZD to get USD at the higher bid price minimizes loss).

However, since the initial conversion involves buying NZD, the trader will buy at the lower ask rate at Bank Y, which is 0.325 USD/NZD. After acquiring NZD, the trader will then sell NZD to Bank X at the bid rate of 0.33 USD/NZD. If the product of these two transactions exceeds the initial USD investment, arbitrage profit exists.

First, determine how many NZD can be bought with $1,000,000 at Bank Y's ask price:

NZD purchased at Bank Y:

\[ \text{NZD} = \frac{\$1,000,000}{0.325\, \text{USD/NZD}} ≈ 3,076,923.08\, \text{NZD} \]

Next, convert these NZD to USD at Bank X's bid price:

USD received at Bank X's bid:

\[ \text{USD} = 3,076,923.08\, \text{NZD} \times 0.33\, \text{USD/NZD} ≈ \$1,016,153.85 \]

Compare this to the initial capital of \$1,000,000:

Profit:

\[ \$1,016,153.85 - \$1,000,000 = \$16,153.85 \]

Thus, executing one cycle of locational arbitrage results in a profit of approximately \$16,153.85. This represents a gain of about 1.615% over the original capital, purely risk-free due to disparities in bid-ask quotes between the two banks. Such arbitrage profits typically diminish as market participants exploit these differences, driving the quotes toward equilibrium.

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