# Futures and Forwards on Currencies

**Interest rate Parity**

**Formula to remember:**- If Spot rate is given in USD/INR terms then take American Risk-free rate as the first rate
- In other words, individual who is interested in USD/INR rates would be an American (Indian will always think in Rupees not dollars!!!!!), which implies foreign currency (r
_{f}) in his case would be r_{INR}

The forward rate of a 3-month EUR/USD foreign exchange contract is 1.1565 USD per EUR. USD LIBOR is 4% and EUR LIBOR is 2%. The spot USD per EUR exchange rate is?

F_{0} = S_{0} e^{(r-rf)t}

1.1565 e^{-(.04- .02).25 }= 1.1507

Assume that the current 1-year forward exchange rate is 1.200 USD per EUR. An American bank pays 2.4% annual interest rate on a 1-year deposit and a 4.0% annual interest rate on a 3-year USD deposit. A European bank pays a 1.5% annual interest rate for a 1-year deposit and a 2.0% annual interest rate for a 3-year EUR deposit. The forward exchange rate in USD per EUR for exchange three years from today is closest to:

The 2 year forward rate in US = [(1.04)^{3} / 1.024] â€“ 1 = 4.81%

The 2 year forward rate in Europe = [(1.02)^{3} / 1.015] â€“ 1 = 2.25%

The forward exchange rate in USD per EUR for exchange three years: 1.2 *(1.0481^{2}) / (1.0225^{2}) = 1.261

The two-year risk-free rate in the United Kingdom is 8% per annum, continuously compounded . The two-year risk-free rate in France is 5% per annum, continuously compounded. The current French Franc to the GBP currency exchange rate is 1GBP = 0.75 French Franc.

What is the two-year forward price of one unit of the GBP in terms of the French Franc so that no arbitrage opportunity exists?

- 0.578
- 0.706
- 0.796
- 0.973

Ans = 0.75*e^{(0.05-0.08)*2 }= 0.706

A bank has a USD50,000,000 portfolio available for investing. The cost of funds for the USD50,000,000 is 4.5%. The bank lends 50% of the assets to domestic customers at an average loan rate of 6.25%. The rest of the portfolio is lent to UK clients at 7%. The current exchange rate is USD1.642/GBP. At the same time, the bank sells a forward contract equal to the expected receipts one year from now. The forward rate is USD1.58/GBP. The weighted average return to the bank on its investments is closest to:

The return from UK customers, $25,000,000/1.642 = GBP 15,225,335* 1.07 = GBP 16,291,108

The bank sells a forward contract: GBP 16,291,108*1.58 = USD 25,739,951

Earnings (USD 25,739,951 â€“ 25,000,000) / 25,000,000 = 2.96%

Weighted average return = 6.25%*.5 + 2.96%*0.5 = 4.61%

Given the following:

Current spot CHF/USD rate: 1.3680 (CHF1.3680 = USD1)

3-month USD interest rates: 1.05% ; 3-month Swiss interest rates: 0.35%

A currency trader notices that the 3-month forward price is USD / CHF 0.7350. In order to arbitrage, the trader should

- The spot is quoted in terms of Swiss Francs per USD. To convert this into USD per Swiss Franc, we get: 1/1.3680 = 0.7310. The theoretical futures price = 0.7310 * exp((0.0105 â€“ 0.0035) * 0.25) = 0.7323. Therefore, the quoted futures price is too high. Thus, one should sell the overvalued CHF futures contract.
- In order to arbitrage, one would do the following:
- Borrow USD 0.7310 * exp((-0.0035)*0.25) = USD 0.7304 for 3 months
- Buy spot exp((-0.0035)*0.25) = CHF0.9991, invest at 0.35% for 3 months
- Short a futures contract on CHF1

- At maturity,
- Pay back 0.7304 * exp((0.0105) * 0.25) = USD 0.7323
- Receive 0.9991 * exp((0.0035) * 0.25) = CHF 1
- Delivers CHF 1 on the futures contract, receives USD 0.7350
- An arbitrage profit of USD0.7350 â€“ USD0.7323 = USD 0.0027 would be realized in 3 monthsâ€™ time