8. Foreign exchange

8.x Interest rate parity INDIRECT vs DIRECT quote

INDIRECT QUOTE

• Viewed from an Australian perspective, the ISO pair AUD/USD is an indirect quote for the USD. 1 AUD is expressed in terms of USD
• Forward premium $ p_i $ for an indirect quote $ i $ is: $$p_i=\frac{ \left( 1 + r_f \right)}{\left( 1 + r_d \right)} - 1 $$

DIRECT QUOTE

• Viewed from an Australian perspective, the ISO pair USD/AUD is an direct quote for the USD. 1 USD is expressed in terms of AUD
• Forward premium $ p_d $ formula for a direct quote is: $$p_d=\frac{\left( 1 + r_d \right)} { \left( 1 + r_f \right)} - 1 $$
• where
  • $r_f$ is the foreign interest rate
  • $r_d$ is the domestic interest rate

Example 8.x

• Viewed from an Australian perspective using an INDIRECT quote for the USD
• Spot rate: $A1 = $US0.7577. (AUD/USD = 0.7577; using ISO currency codes)
• $A interest rate (90 days) $r_d$: 6.00% p.a.
• $US interest rate (90 days) $r_f$: 6.50% p.a.
• Assume
  • Zero spread
  • Zero transaction costs

Interest rate differentials

• HIGHER U.S. interest rates - as in example 8.x.1
• investors sell AUD for USD driving down the AUD spot price
• use USD to buy U.S. Treasury securities
• investors obtain forward contract allowing AUD to be bought back with USD driving up the AUD forward price
• result: AUD is at a premium in the forward market

• Stay at home (Australia): $\text{AUD} 5,000,000 \times (1+0.06 \times 90/365)=\text{AUD}5,073,972.60$ in 90 days
• Invest abroad (U.S.A)
  • $\text{AUD} 5,000,000 \times 0.7577 = \text{USD}3,788,500$
  • $\text{USD}3,788,500 \times (1+0.065 \times 90/360)=\text{USD}3,850,063.13$ in 90 days
  • $\text{USD}3,850,063.13 / 0.7588 = \text{AUD}5,073,883.93$ at forward rate

• LOWER U.S. interest rates
• investors buy AUD with USD driving up the AUD spot price
• use AUD to buy Australian Treasury securities
• investors obtain forward contract allowing USD to be bought back with AUD driving down the AUD forward price
• result: AUD is at a discount in the forward market

8.x.1 The numbers (INDIRECT quote)

• Forward premium for indirect quote $ p_i $:

Worksheet formula [=(1 + 6.5% * 90 / 360) / (1 + 6% *90 / 365) -1] returns 0.001434

• Forward premium for the AUD equals $0.001434260 = 0.1434\%$ against the USD
• Thus the AUD/USD forward rate is: $0.7577 * (1 + 0.001434) = 0.758787 = 0.7588 $

8.x.2 The numbers (DIRECT quote)

• Spot rate: $USD1 = $A1.3198 (USD/AUD = 1.3198; an ISO quote)
• Forward premium for direct quote $ p_d $:

Worksheet formula [=(1 + 6% * 90 / 365) / (1 + 6.5% *90 / 360) -1] returns -0.001432

• Forward premium for the USD equals $-0.00143221 = -0.1432\%$ against the AUD. In other words, a forward discount of $0.1432\%$
• Thus the USD/AUD forward rate is: $1.3198 * (1 - 0.001432) = 1.3179 $
• Reconciliation: $1 / 1.3179 = 0.7588$

• Revised: Saturday 25th of February 2023 - 10:12 AM, [Australian Eastern Time (AET)]