Lecture 7 Flashcards
Currency future/forward valuation
Ft = S * ((1+Rdc)^t/(1+Rfc)^t)
The interest rates in the US and UK are 5% and 6.5% respectively. The current spot is $1.653/GBP. What is the price of a one-year future?
F1 = 1.653 * ((1.05)^1/(1.065)^1) = $1.612/GBP
A US investor makes a 90-day euro-denominated investment valued at €1million. The spot exchange rate is $1.2888/€. In 90 days, the spot rate is $1.2760/€, and the expected return on the investment is 5%. What is the unhedged dollar return on this investment?
Should the investor buy or sell euro futures in order to hedge the currency risk?
The futures exchange rate quoted today is $1.2891/€ and will be $1.2763/€ in 90 days. What is the dollar return to the above-mentioned investment if futures contract is used to hedge the principal?
Unhedged return:
Initial investment
$1.2888*1,000,000 = $1,288,800
After 90 days:
$1.2760*1,050,000 = $1,339,800
Return = (1,339,800-1,288,800)/1,288,800 = 3.957%
5-3.957% = 1.043% conversion loss
As the investor will need to sell Euros in the future, they should sell (short) the futures.
-(1.2763-1.2891) * 1,000,000 = $12,800
Sell Euros at the spot rate:
1,050,000 * 1.2760 = $1,339,800
Add Future gain/loss = $1,339,800 + $12,800 = $1,352,600 = 4.95% return
In the context of currency futues, what is the basis?
Basis: the difference between the spot and futures exchange rate at a point in time
Basis risk, what drives it and how it can be avoided
Basis risk: when the basis changes
The change in basis is driven by ratio in interest rates driven by covered IRP
To avoid basis risk we would have to match the maturity of the futures contract with the intended holding period
Minimum variance hedge
Please provide the formula and explain the parts that make up the formula
h = hT + hE
h is the combined hedge ratio.
hT relates to hedging on the transaction itself (principal)
hE is hedging of the economic gain or loss. The excess return made on the investment. (The 5% in the previous example)
Please outline trading costs and outline the benefits of short-term vs long-term contracts
There are trading costs incurred at inception and closing of contracts.
The more frequently the manager adjusts the hedge according to changes in the value of the currency position the greater the trading costs incurred.
Infrequent trading contracts reduces costs, but the value of the contract could deviate significantly from the value of the currency position.
Short term contracts may generate higher commission costs than long term contracts, but they may reduce the number of transactions necessary to adjust the hedge.
Currency option valuation:
Current exchange rate is 1.5USD/GBP, the continuously compounded interest rates in the US and the UK are 1% and 2%, the standard deviation of the underlying exchange rate is 0.3.
What is the value of a three-month currency call option with a strike exchange rate of 1.4USD/GBP?
Find answer handwritten in notes
What is the currency delta?
Delta shows how the value of the option changes in response to small changes in the underlying exchange rate and is calculated as the change in the option premium divided by the change in exchange rate.
- Long call options have positive delta ranging from 0 to 1; long put options have negative delta ranging -1 to 0.
- Delta indicates the number of options to purchase to hedge currency risk.
- For every unit of currency owned we should hold –(1/Δ) put options.
When should you purchase futures vs options?
If we expect exchange rates to be very volatile but have no strong feeling for which direction they will go we should pay the premium and buy options
If we are primarily concerned with unfavorable currency movements, we will use futures which are cheaper
Please outline key characteristics of currency swaps
- A currency swap exchanges both principal and interest rate payments with payments in different currencies.
- The exchange rate used in currency swaps is the spot exchange rate.
- The principals are exchanged at the inception and should have equal value using the spot exchange rate.
- The periodic cash flows are not netted as they are denominated in different currencies.
- Currency swap is not required by law to be shown on balance sheet of its user.
Explain a currency swap
STUDY THIS
Companies A and B enter into a fixed-for-fixed currency swap with periodic payments occurring annually. Company A pays a principal amount to B of USD 175 million, and B pays GBP 100 million to A at the inception of the swap.
Company A pays 6% in GBP to Company B and receives 5% in USD from Company B. Suppose the yield curves in the US and the UK are flat at 2% and 4% respectively, and the current spot exchange rate is 1.50USD/GBP.
Calculate the value of the currency swap if it will last for three more years.
For Company A:
Inflow of USD and outflow of GBP
Periodic payment = 100*6% = GBP 6 million
Periodic receipt = 175*5% = USD 8.75 million
At the end of the swap, the principal amounts are re-exchanged, so Company A will receive the principal of
USD 175 million and repay the principal of GBP 100 million.
Value of swap = PV(inflow) - PV(outflow)
PV(inflow) = 8.75/1.02 + 8.75/1.02^2 + (8.75+175)/1.02^3 = USD190.14m
PV(outflow) = 6/1.04 + 6/1.04^2 + (6+100)/1.04^3 = GBP105.55m
Value of swap company A = 190.14m - 105.55*1.5 = 31.82m USD
Company B = -31.82m USD
