Do The Following Problems: Assume The Hong Kong Dollar HK Va

Do The Following Problemsassume The Hong Kong Dollar Hk Value Is Ti

Do The Following Problemsassume The Hong Kong Dollar Hk Value Is Ti

Do the following problems Assume the Hong Kong dollar (HK$) value is tied to the U.S. dollar and will remain tied to the U.S. dollar. Assume that interest rate parity exists. Today, an Australian dollar (A$) is worth $.50 and HK$3.9. The one-year interest rate on the Australian dollar is 11%, while the one-year interest rate on the U.S. dollar is 7%. You believe in the international Fisher effect.

You will receive A$1 million in one year from selling products to Australia, and will convert these proceeds into Hong Kong dollars in the spot market at that time to purchase imports from Hong Kong. Forecast the amount of Hong Kong dollars that you will be able to purchase in the spot market one year from now with A$1 million. Show your work. You believe that the Singapore dollar’s exchange rate movements are mostly attributed to purchasing power parity. Today, the nominal annual interest rate in Singapore is 18%.

The nominal annual interest rate in the U.S. is 3%. You expect that annual inflation will be about 4% in Singapore and 1% in the U.S. Assume that interest rate parity holds. Today the spot rate of the Singapore dollar is $.63. Do you think the one-year forward rate would underestimate, overestimate, or be an unbiased estimate of the future spot rate in one year? Explain.

Given S = £0.6361 and the 180-day Forward rate is £0.6352/$, what is the dollar forward premium? Based on the unbiased forward expectations hypothesis, by how much is the dollar expected to appreciate or depreciate over the next 180 days? Provide a forecast of the spot rate of exchange in 180 days. Suppose $1.25/£ and the 1-year forward rate is $1.20/£.

The real interest rate on a risk-free government security is 2 percent in both the United Kingdom and the United States. The US inflation rate is 5 percent. What is the UK’s inflation rate if the equilibrium relationships hold? What is the UK’s nominal required return on risk-free government securities? Quotes for the US dollar and Thai Baht (Bt) are as follows: Spot contract midpoint = Bt 24.96/$ 1-year forward contract midpoint = Bt 25.64/$ 1-year Eurodollar interest rate = 6.125% annually Your newspaper does not quote 1-year Eurocurrency interest rates on Thai baht. Make your own estimate. Suppose that you can either borrow or lend at a Thai Eurocurrency interest rate of 10% per year. Based on a $1 million initial amount, how much profit can you generate through covered interest arbitrage?

Paper For Above instruction

This comprehensive analysis explores various aspects of international finance, including foreign exchange rate forecasting, interest rate parity, purchasing power parity, forward premiums, and arbitrage opportunities. The goal is to demonstrate an understanding of how interest rates, inflation, and currency expectations influence exchange rates and investment strategies across different countries and currencies.

Forecasting Hong Kong Dollar Purchases Based on Australian Dollar Proceeds

Given that the Australian dollar (A$) trades at $.50 USD and HK$3.9, the current exchange rates are established. The annual interest rates are 11% in Australia and 7% in the United States. Assuming interest rate parity (IRP) holds, the future expected spot rate can be forecasted using the IRP condition, which links interest differentials to expected currency movements. According to the interest rate parity formula:

E(S) = S × [(1 + i_domestic) / (1 + i_foreign)]

Where:

- S = current spot exchange rate (HK$ per A$, which depends on USD conversion)

- E(S) = expected future exchange rate

- i_domestic = interest rate in Hong Kong (tied to US dollar, 7%)

- i_foreign = interest rate in Australia (11%)

Alternatively, since HK$ is pegged to USD, the relevant calculations focus on the USD-A$ exchange rate for the initial conversion. The key is to determine the expected amount of HK$1 million A$ proceeds can buy in a year's time through this relationship, factoring in interest rates and exchange rate expectations.

Interest Rate and Purchasing Power Parity in Singapore and US

Given the current spot rate of $.63 per Singapore dollar, the interest rates in Singapore (18%) and the US (3%) and expected inflation rates (4% in Singapore and 1% in the US), we analyze the forward rate's relation to future spot rates. Based on the uncovered interest parity (UIP) and purchasing power parity (PPP), the forward rate should reflect relative inflation differences and interest rates, adjusted by the Fisher effect:

(1 + i_Singapore) = (1 + i_US) × (Expected future spot / Current spot rate)

Since PPP suggests that inflation differentials should match exchange rate movements, if the forward rate deviates significantly from the expected future spot rate, it would either underestimate or overestimate the future rate. Typically, forward rates are unbiased estimates under the efficient market hypothesis.

Forward Premium and Exchange Rate Forecast

Using the provided spot rate (S = £0.6361) and the 180-day forward rate (£0.6352/$), the forward premium can be calculated:

Forward premium = [(Forward rate - Spot rate) / Spot rate] × (360 / days to maturity)

Substituting values:

= [(£0.6352 - £0.6361) / £0.6361] × 2 ≈ -0.00137 or -0.137%

This indicates a slight forward discount. According to the unbiased forward hypothesis, the dollar is expected to appreciate by approximately the same proportion over 180 days, forecasting a future spot rate by adjusting current rate expectations.

Exchange Rate and Forward Rate in the GBP/USD Market

Given the current spot rate of $1.25/£ and a 1-year forward rate of $1.20/£, the forward premium can be computed:

Forward premium = [(F - S) / S] × 100%

= [($1.20 - $1.25) / $1.25] × 100% = -4%

The negative premium indicates the dollar is expected to appreciate relative to the pound over the next year, consistent with differential inflation or interest rate expectations between the UK and the US.

Estimating UK Inflation Rate and Nominal Return

Applying the Fisher effect:

(1 + real interest rate) = (1 + nominal interest rate) / (1 + inflation rate)

For the US:

0.02 = (1 + 0.05) / (1 + Inflation_US)

=> Inflation_US = (1 + 0.05) / (1 + 0.02) - 1 ≈ 0.0294 or 2.94%

For the UK:

0.02 = (1 + nominal return) / (1 + Inflation_UK)

Given the equilibrium conditions, and assuming the nominal risk-free rate in the UK equals the US (but UK inflation is unknown), solving for Inflation_UK involves using the formula:

Inflation_UK = (1 + Nominal UK rate) / (1 + Real rate) - 1

If the nominal UK rate is not provided, and assuming the real rate is 2%, the nominal UK rate would be roughly corresponding to the risk-free rate adjusted for inflation differences.

Covered Interest Arbitrage with Thai Baht and Eurocurrency Rates

Given the spot and forward quotes (Bt 24.96/$ and Bt 25.64/$) and the Eurodollar interest rate (6.125%), alongside the Thai Eurocurrency rate (estimated at 10%), arbitrage opportunities depend on comparing the theoretical forward rate derived from interest arbitrage and the actual forward rate.

The forward rate should satisfy:

F = S × [(1 + i_domestic) / (1 + i_foreign)]

Where, for arbitrage:

Profit per dollar = (F - actual forward quote)

Calculating potential profit on $1 million involves evaluating the discrepancy between the implied forward rate and the actual quoted rate, factoring in borrowing costs and interest differentials.

If the actual forward rate is higher than the arbitrage implied rate, investing in the lower-interest currency and covering the position via forward contracts can generate a profit, net of transaction costs, demonstrating the profitability of covered interest arbitrage.

Conclusion

This analysis underscores the interconnected forces of interest rates, inflation, and exchange rate expectations in international finance. Exchange rate forecasts rely on uncovered or covered interest parity, with deviations revealing potential arbitrage opportunities. Recognizing the impact of inflation differentials and interest rate differentials is essential for effective currency and investment strategies in global markets.

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