汇率表达式

问题如下：

Question

The following information is available:

• New Zealand dollar (NZD) to British pound (GBP) spot exchange rate: 2.0979

• Libor interest rates for the British pound: 1.6025%

• Libor interest rates for the New Zealand dollar: 3.2875%

• All Libor interest rates are quoted on a 360-day year basis

The 180-day forward points (scaled up by four decimal places) in NZD/GBP is closest to:

选项：

A.39 B.348 C.176

解释：

Solution

C is correct. Covered interest arbitrage will ensure identical terminal values by investing the same initial amounts at the respective country’s domestic interest rates:

GBP investment: ₤1 × (1 + 0.016025 × 180/360) = ₤1.008013

NZD investment: NZ$2.0979 × (1 + 0.032875 × 180/360) = NZ$2.13238

The forward rate is determined by equating these two terminal amounts:

NZD/GBP forward rate = NZ$2.13238/₤1.008013 = 2.115429

Forward points = (Forward – Spot) × 10,000

= (2.1155– 2.0979) × 10,000

= 175.3 =176 (rounded)

A is incorrect. It inverts the currencies.

GBP investment: ₤2.0979 × (1 + 0.016025 × 180/360) = ₤2.1147

NZD investment: NZ$1 × (1 + 0.032875 × 180/360) = NZ$1.0164

The forward rate is determined by equating these two terminal amounts:

NZD/GBP forward rate = NZ$1.0164/₤2.1147 = 0.4806

Inverted Spot: 1/2.0979 = 0.47667

Forward points = (Forward – Spot) × 10,000

= (0.4806– 0.4767) × 10,000

= 39

B is incorrect. It ignores the half-year time frame of the contract:

GBP investment: ₤1 × (1 + 0.016025) = ₤1.016025

NZD investment: NZ$2.0979 × (1 + 0.032875) = NZ$2.16687

NZD/GBP forward rate = NZ$2.16687/₤1.016025 = 2.1327

Forward points = (Forward – Spot) × 10,000

= (2.1327 – 2.0979) × 10,000

= 347.9

中文解析：

C正确。备兑利息套利将通过按各自国家的国内利率投资相同的初始金额来确保相同的终端价值:

英镑投资:1英镑× (1 + 0.016025 × 180/360) = 1.008013英镑

纽元投资:NZ$2.0979 × (1 + 0.032875 × 180/360) = NZ$2.13238

远期汇率是通过将这两个终端金额相等来确定的:

纽元兑英镑远期汇率= 2.13238纽元兑1.008013英镑= 2.115429

远期点=(远期点)× 10000

= (2.1155 - 2.0979) × 10000

= 175.3 =176(四舍五入)

A不正确。它颠倒了货币。

英镑投资:£2.0979 × (1 + 0.016025 × 180/360) =£2.1147

新西兰元投资:新西兰元1 × (1 + 0.032875 × 180/360) =新西兰元1.0164

远期汇率是通过将这两个终端金额相等来确定的:

纽元兑英镑远期汇率=纽元兑1.0164英镑兑2.1147英镑= 0.4806

倒挂即期汇率:1/2.0979 = 0.47667

远期点=(远期点)× 10000

= (0.4806 - 0.4767) × 10000

= 39

B不正确。它忽略了合同的半年时间框架:

英镑投资:1英镑×(1 + 0.016025) = 1.016025英镑

纽元投资:NZ$2.0979 × (1 + 0.032875) = NZ$2.16687

纽元兑英镑远期汇率= 2.16687纽元兑1.016025英镑= 2.1327

远期点=(远期点)× 10000

= (2.1327 - 2.0979) × 10,000

= 347.9