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1.

(1) NTD to GBP:

  • We will buy GBP with NTD at the ask price of 50.66 NTD/GBP.
  • The maximum amount of GBP we can buy is 10,000 / 50.66 = 197.19 GBP.

(2)GBP to CNY:

  • We will sell the GBP we just bought for CNY at the bid price of 9.7195 CNY/GBP.
  • The total amount of CNY we will receive is 197.19 * 9.7195 = 1,915.28 CNY.

(3)CNY to NTD:

  • We will sell the CNY we just bought for NTD at the bid price of 5.125 NTD/CNY.
  • The total amount of NTD we will receive is 1,915.28 * 5.125 = 9,812.79 NTD.

The starting NTD amount was 10,000 NTD, and the final NTD amount is 9,812.79 NTD, so we made a profit of 187.21 NTD.

Therefore, by implementing the triangular arbitrage strategy, the profit made would be 187.21 NTD.

 

2.

To determine if there is an arbitrage opportunity, we can use the cross exchange rate between EUR/GBP to check if it matches the direct exchange rate. The cross exchange rate should be the exchange rate obtained from the direct exchange rates of the two currencies.

In this case, the cross exchange rate can be calculated as follows:

EUR/GBP = EUR/USD ÷ GBP/USD = 1.2 ÷ 1.4 = 0.8571

However, the direct exchange rate for EUR/GBP is 0.8, which is lower than the calculated cross exchange rate of 0.8571. This indicates that there is an arbitrage opportunity.

Here’s how we can perform triangular arbitrage:

  1. Buy euros with dollars: We can buy euros with USD at the exchange rate of EUR/USD = 1.2. If we invest $1,000, we will get 1,000/1.2 = 833.33 euros.
  2. Buy pounds with euros: We can buy pounds with euros at the exchange rate of EUR/GBP = 0.8. We can get 833.33 x 0.8 = 666.67 pounds.
  3. Buy dollars with pounds: We can buy dollars with pounds at the exchange rate of GBP/USD = 1.4. We can get 666.67 x 1.4 = 933.33 dollars.

At the end of this triangular arbitrage, we started with $1,000 and ended up with $933.33. This means that we made a profit of $933.33 – $1,000 = -$66.67.

Therefore, there is no arbitrage opportunity in this case, and trying to execute the arbitrage will result in a loss of $66.67.

 

3.

(1)利率平價條件成立與否的判斷需要比較未來利率的期望值,而不是當前的利率水平。根據利率平價理論,若兩國貨幣的利率平價條件不成立,則可以通過外匯市場進行套利操作。利率平價條件是指兩個國家貨幣的利率之間的差異應該等於這兩個國家貨幣之間的遠期匯率與即期匯率之間的差異。
在這個例子中,未來利率期望的計算如下:

• 台灣的未來利率:5%
• 美國的未來利率:3%
• 台幣的期望遠期匯率:30.3 NT/US
• 即期匯率:30.0 NT/US

根據利率平價條件,預期未來的遠期匯率應該等於即期匯率乘以(1+台灣利率)除以(1+美國利率)的比率,即:
30.5 NT/US = 30.0 NT/US x (1+5%)/(1+3%)
然而,預期未來的遠期匯率是30.3 NT/US,而不是30.5 NT/US。因此,利率平價條件不成立。

(2) 未拋補的利率平價理論是指,貨幣的利率水平應該反映出該貨幣的預期升值或貶值趨勢。在這種情況下,由於美國的利率低於台灣的利率,因此未拋補的利率平價理論表明,美元的預期貶值速度將高於新台幣的預期貶值速度,因此選用新台幣存款更有利。
因此,依據未拋補的利率平價理論,應該要選擇新台幣存款。

周子琪國際財管第五次作業
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