经济学

问题如下：

An investor examines the following rate quotes for the Brazilian real (BRL) and the Australian dollar (AUD) and shorts BRL500,000.

• Spot rate BRL/AUD: 2.1128

• BRL 1-year interest rate: 4.1%

• Forward rate BRL/AUD: 2.1388

• AUD 1-year interest rate: 3.1%

The risk-free arbitrage profit that is available is closest to:

选项：

A.–BRL6,327.

B.BRL1,344.

C.BRL6,405.

解释：

B is correct. The equation below is often called the “covered interest arbitrage relationship” because if it is not satisfied, a risk-free arbitrage opportunity exists. It is based on the required equivalence of the two possible investment paths: if the two paths do not produce the same terminal result, an arbitrage profit exists.

$\left(1+i_d\right)=S_{f/d}\left(1+i_f\right)\left(\frac{1}{F_{f/d}}\right)$ where

S_f/d = Spot rate: number of units of foreign currency (price currency) per one unit of domestic currency

F_f/d = Forward rate: number of units of foreign currency (price currency) per one unit of domestic currency

i_d = Domestic interest rate

i_f = Foreign interest rate

The left-hand side is 1 plus the return that is earned domestically. The right-hand side represents 1 plus the return from converting to foreign currency at the spot rate, investing at the foreign rate, and converting back to domestic currency using the forward rate.

The arbitrage profit is the right side of the equation minus the left side.

Left Side of Equation: BRL500,000 × (1 + 0.041) = BRL520,500

Arbitrage profit = BRL521,844 – BRL520,500= BRL1,344

A is incorrect. The right side of the equation uses inverted exchange rates in Steps One and Three and 4.1% in Step Two.

• Step One: BRL500,000 × (2.1128AUD/BRL) = AUD1,056,400

• Step Two: AUD1,056,400 × (1.041) = AUD1,099,712

• Step Three: AUD1,099,712 × (1/2.1388) = BRL514,173Arbitrage profit = BRL514,173 (right side above) – BRL520,500 (left side above) = –6,327

C is incorrect. The right side of the equation uses 4.1% and thus 1.041 incorrectly in Step Two.

• Step One: BRL500,000 × (1/2.1128AUD/BRL) = AUD236,653

• Step Two: AUD236,653 × (1.041) = AUD246,355

• Step Three: AUD246,355 × 2.1388 = BRL526,905Arbitrage profit = BRL526,905 (right side above) – BRL520,500 (left side above) = 6,405

中文解析

B正确。下面的等式通常被称为“利差套利关系”，因为如果不满足，则存在无风险套利机会。它基于两条可能的投资路径的必要等价性:如果两条路径不产生相同的最终结果，则存在套利利润。（流程如英文解析所示）
$1+i_d=S_{f/d}1+i_f\frac{1}{F_{f/d}}$ where


Sf/d =即期汇率:每单位本币兑换多少外币(价格货币)

Ff/d =远期汇率:每单位本币兑换外币(价格货币)的数量

id =国内利率

if =外国利率

左边是1加上国内收益。右边代表1加上以即期汇率兑换成外币，以外币汇率投资，并以远期汇率兑换回本国货币的收益。

套利利润是等式的右边减去左边。

等式左侧:BRL500,000 × (1 + 0.041) = BRL520,500


套利利润= BRL521,844 - BRL520,500= BRL1,344

A不正确。等式的右侧在步骤1和步骤3中使用反向汇率，在步骤2中使用4.1%。

第一步:50万澳币×(2.1128澳元/巴西雷亚尔)= 1,056,400澳币

第二步:1,056,400澳元×(1.041) = 1,099,712澳元

第三步:AUD1,099,712 × (1/2.1388) = BRL514,173套利利润= BRL514,173(上图右侧)- BRL520,500(上图左侧)= - 6,327

C选项不正确。等式的右边使用了4.1%，因此在第二步中错误地使用了1.041。

第一步:BRL500,000 × (1/2.1128AUD/BRL) = AUD236,653

第二步:AUD236,653 × (1.041) = AUD246,355

第三步:AUD246,355 × 2.1388 = BRL526,905套利利润= BRL526,905(右上)- BRL520,500(左上)= 6,405