Let's answer each part step by step: --- ### **a) If the spot exchange rate is ₹66.845/$, interest in the USA is i\_US = 4%, interest in India is i\_IN = 6%, then would you expect the forward rate one year from now to be more or fewer rupees per dollar? Why?** #### **Explanation:** This is a question about **Covered Interest Rate Parity (CIRP)**, which says: \[ F = S \times \frac{1 + i_\text{foreign}}{1 + i_\text{domestic}} \] Here, - \( S = \) Spot rate = ₹66.845/$ - \( i_\text{foreign} = i_\text{US} = 4\% = 0.04 \) - \( i_\text{domestic} = i_\text{IN} = 6\% = 0.06 \) Since the Indian interest rate is **higher** than the US interest rate, the **rupee is expected to depreciate** against the dollar (because investors need to be compensated for holding a currency with a higher interest rate). So, **the forward rate (₹/$) will be higher than the spot rate**—i.e., more rupees per dollar. **Final answer (a):** > The forward rate should be **more rupees per dollar** than the spot rate, because the Indian interest rate is higher than the US interest rate, so the rupee is expected to depreciate against the dollar. --- ### **b) How many rupees would you expect a dollar to be worth on the spot market in one year from now?** #### **Explanation:** According to **Interest Rate Parity**: \[ F = S \times \frac{1 + i_{IN}}{1 + i_{US}} \] Plug in the values: - \( S = 66.845 \) - \( i_{IN} = 0.06 \) - \( i_{US} = 0.04 \) So, \[ F = 66.845 \times \frac{1.06}{1.04} \] Calculate: \[ \frac{1.06}{1.04} = 1.019230769 \] \[ F = 66.845 \times 1.019230769 \approx 68.139 \] **Final answer (b):** > You would expect a dollar to be worth **₹68.14** (rounded to two decimals) on the spot market in one year from now. --- ### **c) What would a profit seeking arbitrager do if the actual 12-month forward rate was $0.016/₹?** #### **Explanation:** First, let's convert $0.016/₹ to ₹/$: \[ \text{If } \$0.016/\text{₹}, \text{then } 1\$ = \frac{1}{0.016} = 62.5\,\text{₹} \] So, the 12-month forward rate is **₹62.5/$**. Compare this with the rate from part (b): **₹68.14/$** - **Forward rate is below the expected rate.** - The dollar is *cheaper* in the forward market (you get fewer rupees per dollar). - The rupee is *stronger* in the forward market than interest rate parity suggests. **Arbitrage Strategy:** 1. **Borrow in Rupees:** At 6% interest rate. 2. **Convert to Dollars at Spot Rate:** At ₹66.845/$. 3. **Invest in Dollars:** At 4% interest rate. 4. **Sell Dollars Forward:** Enter into a forward contract to convert dollars back to rupees in one year at ₹62.5/$. **Numerical Example (optional):** Suppose you start with ₹6,684,500 (so calculations are easy). 1. **Borrow ₹6,684,500** for 1 year at 6%. You owe: \( 6,684,500 \times 1.06 = 7,085,570 \) rupees in one year. 2. **Convert to Dollars at Spot:** \( 6,684,500 / 66.845 = \$100,000 \) 3. **Invest in US at 4%:** \( \$100,000 \times 1.04 = \$104,000 \) 4. **Sell $104,000 Forward at ₹62.5/$:** \( 104,000 \times 62.5 = ₹6,500,000 \) 5. **Compare end values:** - Owe: ₹7,085,570 - Have: ₹6,500,000 *Loss*, so actually, this arbitrage loses money. **Alternate Strategy:** Reverse the process: 1. Borrow dollars at 4%, convert to rupees, invest in rupees at 6%, buy dollars forward at ₹62.5/$. - Borrow \$100,000 at 4% → owe \$104,000 in one year. - Convert \$100,000 to rupees: \( \$100,000 \times 66.845 = ₹6,684,500 \) - Invest ₹6,684,500 at 6%: \( ₹6,684,500 \times 1.06 = ₹7,085,570 \) - Buy dollars forward: \( ₹7,085,570 / 62.5 = \$113,369.12 \) - Repay \$104,000, keep the rest: \( \$113,369.12 - \$104,000 = \$9,369.12 \) **profit** So, **the arbitrager would:** - **Borrow dollars at 4%** - **Convert to rupees at the spot rate** - **Invest in rupees at 6%** - **Buy dollars forward at ₹62.5/$** **Final Answer (c):** > A profit-seeking arbitrager would borrow dollars at 4%, convert them to rupees at the spot rate, invest in India at 6%, and enter a forward contract to buy dollars at ₹62.5 per dollar in one year. This way, he would profit from the difference between the actual forward rate and the rate predicted by interest rate parity. --- ## **Summary Table** | Part | Final Answer | |------|--------------| | (a) | The forward rate should be **more rupees per dollar** than the spot rate, because the rupee is expected to depreciate (due to higher Indian interest rates). | | (b) | The expected spot rate in one year is **₹68.14/$**. | | (c) | Arbitrager would **borrow dollars, convert to rupees, invest in rupees, and buy dollars forward at ₹62.5/$**—profiting from the mispricing in the forward market. |