3.Wanda Brock works as an investment strategist for Globos, an international investment bank. Brock has been tasked with designing a strategy for investing in derivatives in Mazakhastan, an Eastern European country with impressive economic growth. One of the first tasks Brock tackles involves hedging. Globos wants to hedge some of its investments in Mazakhastan against interest-rate and currency volatility. After a bit of research, Brock has gathered the following data: §
The U.S. risk-free rate is 5.5 percent, and most investors can borrow at 2 percent above that rate. §
The Federal Reserve Board is expected to raise the fed funds rate by 0.25 percent in one week. §
The current spot rate for the Mazakhastanian currency, the gluck, is 9.4073G/$. §
Annualized 90-day LIBOR is 7.6 percent. §
Globos’ economists expect annualized 90-day LIBOR to rise to 7.9% over the next 60 days. §
In Mazakhastan, commodities can be bartered at no charge through an ancient and informal trading system, but futures trades cost 3 percent of the contract value. §
The Mazakhastan risk-free rate is 3.75 percent, and most investors can borrow at 1.5 percent above that rate. Using the above data, Brock develops some hedging strategies, and then delivers them to Globos’ futures desk. Brock then turns her attention to Mazakhastanian commodities. Globos has acquired the rights to large deposits of copper, silver, and molybdenum in Mazakhastan and suspects the futures markets may be mispriced. Brock has assembled the following data to aid her in making recommendations to Globos’ futures desk: Copper
Spot price: $3.15/pound.
1-year futures price: $3.54/pound. Silver
Spot price: $12.75/pound.
1-year futures price: $12.82/pound. Molybdenum
Spot price: $34.45/pound.
1-year futures price: $35.23/pound. After making some calculations, Brock assesses the arbitrage opportunities in Mazakhastan and passes the information on to the futures desk. Shortly afterward, she is informed that Globos’ Mazakhastan subsidiary uses its silver holdings as collateral for business loans, which allows the unit to obtain a favorable interest rate. Jonah Mason, one of Globos’ traders, asks Brock for a few details about the Mazakhastan financial markets. Brock sends Mason a short e-mail containing the following observations: §
Mazakhastan’s investors don’t like relying on old valuation data because asset values have changed rapidly in the past, so they generally use a mark-to-market valuation system. §
Standard & Poor’s just raised Mazakhastan’s sovereign debt to investment grade. §
Interest rates tend to move in the same direction as asset values. §
New technological innovations and commercial expansion has substantially boosted the income of the average Mazakhastanian. Before Mason receives the e-mail, he turns his attention to a memo about a futures contract a subordinate is considering. Unfortunately, the memo arrives without the summary page to the notes. Mason must deduce the nature of the hedge based on its characteristics: The risk-free rate used in calculating the futures price, and that price adjusted to account for individual future dividends. The value of a 75-day gluck future is closest to: A) 9.3750G/$. B) 0.1081$/G. C) 0.1045$/G. D) 9.4429G/$. The correct answer was A) To calculate the value of a currency future, use the following equation:
Spot exchange rate × (1 + domestic risk-free rate)t / (1 + foreign risk-free rate)t.
In this case, since the exchange rate is expressed in glucks per dollar, the Mazakhastan interest rate is considered domestic. Since we are pricing a 75-day future, the time variable “t” is 75/365.
9.4073G/$ x (1.0375)(75/365) / (1.055)(75/365) = 9.3750G/$. 4.Based on the information he received from Brock, Mason can best conclude that: A) prices of corporate bonds in Mazakhastan are likely to rise. B) futures prices are higher than forward prices in Mazakhastan. C) the Mazakhastanian market is in a state of normal backwardation. D) inflation in Mazakhastan is likely to rise. The correct answer was B) Since Mazakhastanian investors prefer mark-to-market accounting and interest rates are positively correlated to asset values, Mason can conclude that futures prices are higher than forward prices. The upgrade of sovereign debt could spill over into the private sector, driving up bond prices. And an increase in consumer income could spark spending that drives up inflation. But neither the debt information nor the income information is sufficient to draw conclusions. Normal backwardation reflects the relationship between futures prices and spot prices, and we cannot draw a conclusion regarding backwardation based on the information presented here. 5.Based on the two characteristics of the futures contract in Mason’s memo, which of the following does the contract refer to?
| Treasury bond futures?
| Stock index futures?
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A) No Yes B) Yes Yes C) Yes No D) No No The correct answer was C) Both Treasury bond futures and stock index futures require the use of the risk-free rate to determine price. But while the pricing of bond futures requires the discounting of individual dividends, the pricing of stock-index futures does not, instead using a continuously compounded dividend yield. 6.Based on Brock’s information, how should traders best take advantage of arbitrage opportunities in Mazakhastan? A) Buy copper, sell silver, and sell molybdenum. B) Buy copper, sell silver, and do not trade molybdenum. C) Buy copper, do not trade silver, and sell molybdenum. D) Do not trade copper, do not trade silver, and do not trade molybdenum. The correct answer was B) First we must determine whether the futures contracts are mispriced, by multiplying the commodity price by (1 + the risk-free rate), or 1.0375. The basic equation uses the risk-free rate, but we have the actual borrowing rate, and for real-world purposes the actual borrowing rate provides a more accurate price estimate. For practical purposes, we should probably use the borrowing rate, but both rates provide the same answer to the question above. For illustration purposes, we use the risk-free rate in the discussion below. It turns out that all three contracts are mispriced. Copper futures are overpriced, and silver and molybdenum futures are underpriced. However, transaction costs muddy the water. Assuming a 3% commission on futures trades, the price differential on molybdenum is not sufficient to justify an arbitrage trade. Thus, the traders should buy copper, for which the futures contract is overpriced, and sell silver, for which the futures contract is underpriced, and make no trades in molybdenum despite the fact that the futures contract is underpriced.
| Copper (per pound) | Silver (per ounce) | Molybdenum (per pound) | Spot price | $3.15 | $12.75 | $34.45 | Futures price | $3.54 | $12.82 | $35.23 | No-arbitrage futures price | $3.27 | $13.23 | $35.74 | Potential arbitrage profits | $0.27 | $0.41 | $0.51 | Transaction costs | $0.11 | $0.38 | $1.06 | Arbitrage opportunity | Yes | Yes | No |
7.The value of a 150-day, $1,000,000 eurodollar add-on yield futures contract at expiration is closest to: A) $929,368. B) $981,171. C) $981,854. D) $926,784. The correct answer was B) To calculate the expiration value of a 150-day eurodollar futures contract using 90-day LIBOR, the only interest rate provided that works for the contract, we do the following: Divide $1,000,000 by (1 + expected 90-day LIBOR, 60 days from now).
If expected annualized LIBOR is 7.9%, the actual interest rate expected for the 90-day period is 1.92%, or (1 + 7.9%).25–1. Thus, the expiration value is closest to $981,171. 8.Which of the following would be most likely to cause a contango situation with silver futures in Mazakhastan? A) A huge silver discovery. B) A shortage of warehouse space that drives up rental rates. C) An increase in the availability of asset-backed loans. D) The entry of 10 large foreign insurance companies into the Mazakhastan market. The correct answer was B) In a contango situation, futures prices are higher than the spot price. This normally occurs when there are no benefits to holding an asset, or when the costs of storing an asset are high enough to offset the benefits of holding the asset. An increase in the availability of asset-backed loans would increase the convenience yield of silver, which would not cause a contango situation. The entry of many new insurers is likely to increase competition and drive down insurance prices, thus lowering the cost of holding assets such as silver, which would not cause a contango situation. A silver discovery could have some effect on the price of silver, but should not affect a contango situation one way or another. On the other hand, an increase in storage costs would offset some of the convenience yield. We don’t know whether such an increase in costs would be enough to make the net cost of holding silver positive, but any increase in costs could contribute to a contango situation.
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发表于 2008-4-18 14:40
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