汇率

问题如下：

Question

An investor reviews the rate quotes for the Brazilian real (BRL) and the Australian dollar (AUD) and decides to short BRL520,000.

Spot rate BRL/AUD: 2.1150

BRL 1-year interest rate: 4.3%

Forward rate BRL/AUD: 2.1410

AUD 1-year interest rate: 3.3%

What is the closest risk-free arbitrage profit available?

选项：

A.–BRL6,500.
B.BRL1,400. C.BRL6,580.

解释：

Solution

1. Correct. The equation below represents the "covered interest arbitrage relationship." If this relationship is not satisfied, a risk-free arbitrage opportunity exists.

   

   (1+id)=Sf/d(1+if)(1Ff/d)$\left(1+i_d\right)=S_{f/d}\left(1+i_f\right)\left(\frac{1}{F_{f/d}}\right)$

   
   

   Left Side of Equation: BRL520,000 × (1 + 0.043) = BRL542,360

   Right Side of Equation:

   Step Transaction Explanation

   1 BRL520,000 × (1/2.1150AUD/BRL) = AUD245,862.88 Convert domestic to foreign

   2 AUD245,862.88 × (1.033) = AUD253,976.36 Invest foreign at foreign rate

   3 AUD253,976.36 × 2.1410 = BRL543,763.39 Convert foreign to domestic

   Arbitrage profit = BRL543,763.39 – BRL542,360 ≈ BRL1,403

Exchange Rate Calculations

• explain the arbitrage relationship between spot and forward exchange rates and interest rates, calculate a forward rate using points or in percentage terms, and interpret a forward discount or premium

等式左侧:BRL520,000 × (1 + 0.043) = BRL542,360


等式左边:BRL520,000 × (1 + 0.043) = BRL542,360

等式右边：
步骤交易说明：

1 BRL520,000 × (1/2.1150 aud /BRL) = AUD245,862.88，即用本币兑换外币

2 AUD245,862.88 × (1.033) = AUD253,976.36，即按外国汇率进行海外投资

3 AUD253,976.36 × 2.1410 = BRL543,763.39，即外币兑换国内货币

套利利润= BRL543,763.39 - BRL542,360≈BRL1,403