来源：财萃网 | 更新：2016-05-13 16:41:08 | 关键词：CFA三级考试
1.A German portfolio manager entered a 3-month forward contract with a U.S. bank to deliver $10,000,000 for euros at a forward rate of €0.8135/$. One month into the contract, the spot rate is €0.8170/$, the euro rate is 3.5%, and the U.S. rate is 4.0%. Determine the value and direction of any credit risk.
“The German manager (short position) has contracted with a U.S. bank to sell dollars at €0.8135, and the dollar has strengthened to €0.8170. The manager would be better off in the spot market than under the contract, so the bank faces the credit risk (the manager could default). From the perspective of the U.S. bank (the long position), the amount of the credit risk is:
Vbank (long) = €8,170,000 / (1.04)2/12 ? €8,135,000 / (1.035)2/12 = €28,278
(The positive sign indicates the bank faces the credit risk that the German manager might default.)”
2. Within the ‘Option Strategies’ section
Option Strike Premium
Call 1X1 = 20 c1 = 6
Call 2X2 = 30 c2 = 4
Put 1X1 = 20 p1 = 0.604
Put 2X2 = 30 p2 = 8.001
Risk-free rate continuously compounded: 4% annual
Option expiry: 6 months
Using the above data for a box spread, calculate what arbitrage profit can be achieved at the end of 6 months.
“First, work out the cost of the box spread. Combine the two call options into a bull spread (buy the low strike call and sell the high strike call), and the two put options into a bear spread (buy the high strike put and sell the low strike put). Combining those two gives a box spread. To calculate the initial cost, work out the net premia:
Cost = c1 – c2 + p2 – p1 = 6 – 4 + 8.001 – 0.604 = $9.397
The payoff from the box spread will be the difference between the strike levels, ie 30 – 20 = $10.
If you borrowed $9.397 at the beginning in order to enter the box spread, how much would you have to pay back after 6 months? You need to compound the cost at the risk-free rate:
$9.397 x e0.04 x 0.5 = $9.58683
So the arbitrage profit would be the difference between the payoff and what you have to pay back on the loan, ie $10 – $9.58683 = $0.41317”
3. Assume Felix Burrow is a US investor, holding some euro-denominated assets. Given the information below, calculate the domestic return for Burrow over the year.
“The domestic return (return in USD terms) depends on the EUR-return of the asset,as well as on the change in exchange rates:
RDC = (1+RFC) (1+RFX) -1
where RFX is the change in spot rates, using the domestic currency as the price currency (ie we require a USD/EUR quote). In this example, the exchange rate is quoted as such, so we can use the quote provided (otherwise, if the domestic currency was the base currency, we would need to invert the quote first).
RFC = -1 = 0.0078 = 0.78%
RFX = -1 = 0.0261 = 2.61%
RDC = (1 + 0.78%)(1 + 2.61%) – 1 = 3.41%
Burrow’s domestic currency return was higher than the underlying asset return, because he further benefits from the appreciation of the Euro (depreciation of the USD).”
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