Six months US T bills has nominal rate of 4 percent, while default free Japanese bonds that mature in 6 months have a nominal rate of 2.5 percent. In the spot exchange market, JPY 1 equals to USD…

Solution to the Forward Exchange Rate Problem

Given:

• US T-bills (6 months, nominal rate): 4% = 0.04
• Japanese bonds (6 months, nominal rate): 2.5% = 0.025
• Spot exchange rate (JPY/USD): 1 JPY = USD 0.013 (or USD/JPY = 1/0.013 ≈ 76.9216)
• Interest Rate Parity (IRP) holds.

Objective:

Find the 6-month forward exchange rate (F) under IRP and interpret the result.

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Step 1: Understanding Interest Rate Parity (IRP)

IRP states that the forward exchange rate (F) should eliminate arbitrage opportunities between two currencies by accounting for interest rate differentials. The formula is:

$$F=S\times \frac{(1+r_{domestic})}{(1+r_{foreign})}$$

Where:

• $S$ = Spot exchange rate (USD/JPY)
• $r_{domestic}$ = US interest rate (4%)
• $r_{foreign}$ = Japanese interest rate (2.5%)

Since the US is the domestic currency (USD) and Japan is the foreign currency (JPY), we use the above formula.

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Step 2: Convert Spot Rate to USD/JPY

Given: $$1\text{ JPY}=0.013\text{ USD}⟹1\text{ USD}=\frac{1}{0.013}\text{ JPY}\approx 76.9216\text{ JPY}$$

So, Spot (S) = 76.9216 JPY/USD.

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Step 3: Apply IRP Formula

$$F=76.9216\times \frac{(1+0.04)}{(1+0.025)}$$

$$F=76.9216\times \frac{1.04}{1.025}$$

$$F=76.9216\times 1.014545\approx 78.02\text{ JPY/USD}$$

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Step 4: Interpretation of the Result

• The forward exchange rate (78.02 JPY/USD) is higher than the spot rate (76.92 JPY/USD).
• This means the USD is expected to depreciate against the JPY in 6 months (or JPY is expected to appreciate).
• Why?
  • The US has a higher interest rate (4%) than Japan (2.5%).
  • Under IRP, higher domestic interest rates lead to currency depreciation in the forward market (since investors demand higher returns, reducing demand for USD in the future).
  • Alternatively, investors prefer JPY-denominated assets (lower risk, higher safety), increasing demand for JPY and pushing its value up.

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Final Answer:

The 6-month forward exchange rate (F) under Interest Rate Parity is 78.02 JPY/USD. This indicates that the USD is expected to weaken against the JPY in the next 6 months due to the higher US interest rate.