1. **Problem Statement:**
We have four parts: (a) compare triangular arbitrage and covered interest arbitrage, (b) find the TZS/KES spot exchange rate using the law of one price, (c) find the one-year TZS/KES exchange rate given expected prices, and (d) find the equivalent annual return in Kenya's money market given US returns and forward exchange rates.
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2. **Part (a): Compare Triangular Arbitrage and Covered Interest Arbitrage**
- **Triangular Arbitrage:** Exploits discrepancies between three different currency exchange rates to make a riskless profit by converting one currency to another through a third currency and back.
- **Covered Interest Arbitrage:** Involves capitalizing on interest rate differentials between two countries while using forward contracts to hedge exchange rate risk.
Both seek riskless profits but triangular arbitrage exploits spot exchange rate inconsistencies, while covered interest arbitrage exploits interest rate differentials with forward contracts.
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3. **Part (b): Law of One Price for Spot Exchange Rate**
Formula: $$\text{Spot rate } (\frac{TZS}{KES}) = \frac{\text{Price in Tanzania}}{\text{Price in Kenya}}$$
Given:
Price in Tanzania = 325 TZS
Price in Kenya = 135 KES
Calculate:
$$\frac{325}{135} = 2.4074$$
So, the spot exchange rate should be approximately $2.41$ TZS per KES.
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4. **Part (c): One Year Forward Exchange Rate Using Expected Prices**
Formula:
$$\text{Forward rate } (\frac{TZS}{KES}) = \frac{\text{Expected price in Tanzania}}{\text{Expected price in Kenya}}$$
Given:
Expected price Tanzania = 350 TZS
Expected price Kenya = 160 KES
Calculate:
$$\frac{350}{160} = 2.1875$$
So, the one-year forward exchange rate should be approximately $2.19$ TZS per KES.
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5. **Part (d): Equivalent Annual Return in Kenya's Money Market**
Given:
Spot rate: 1 US$ = 129 Ksh
9 months forward rate: 1 US$ = 132 Ksh
US annual return: 14% or 0.14
Step 1: Calculate the forward premium/discount:
$$\text{Forward premium} = \frac{132 - 129}{129} = \frac{3}{129} = 0.02326$$
Step 2: Convert 9 months to years:
$$\frac{9}{12} = 0.75 \text{ years}$$
Step 3: Calculate the implied Kenyan interest rate using covered interest parity formula:
$$1 + i_{Kenya} = (1 + i_{US}) \times \frac{\text{Forward rate}}{\text{Spot rate}}$$
Calculate:
$$1 + i_{Kenya} = (1 + 0.14) \times \frac{132}{129} = 1.14 \times 1.02326 = 1.1674$$
Step 4: Since this is for 9 months, convert to annual rate:
$$i_{Kenya} = (1.1674)^{\frac{12}{9}} - 1 = (1.1674)^{1.3333} - 1$$
Calculate exponent:
$$1.1674^{1.3333} \approx 1.2305$$
So,
$$i_{Kenya} = 1.2305 - 1 = 0.2305 = 23.05\%$$
**Final answer:** The equivalent annual return in Kenya's money market is approximately 23.05%.
Exchange Arbitrage 3D947A
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