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%, and most investors can borrow at 2% above that rate. * The Federal Reserve Board is expected to raise the fed funds rate by 0.25% in one week. * The current spot rate for the Mazakhastanian currency, the gluck, is 9.4073G/$. * Annualized 90-day LIBOR is 7.6%. * 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% of the contract value. * The Mazakhastan risk-free rate is 3.75%, and most investors can borrow at 1.5% 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) 0.1081/G. B) 9.3750G/. C) 9.4429G/. Based on the information he received from Brock, Mason can best conclude that: A) inflation in Mazakhastan is likely to rise. B) futures prices are higher than forward prices in Mazakhastan. C) prices of corporate bonds in Mazakhastan are likely to rise. 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? A) Yes Yes B) No Yes C) YesNo Based on Brock’s information, how should traders best take advantage of arbitrage opportunities in Mazakhastan? A) Buy copper, do not trade silver, and sell molybdenum. B) Buy copper, sell silver, and sell molybdenum. C) Buy copper, sell silver, and do not trade molybdenum. The value of a 150-day, $1,000,000 eurodollar add-on yield futures contract at expiration is closest to: A) $981,854. B) $981,171. C) $929,368. Which of the following would be most likely to cause a contango situation with silver futures in Mazakhastan? A) An increase in the availability of asset-backed loans. B) A shortage of warehouse space that drives up rental rates. C) A huge silver discovery.
- Gluck future: 9.4073 * (1.0375/1.055)^(75/365) = 9.3750 B 2. B) futures prices are higher than forward prices in Mazakhastan. because they prefer the mark-to-market feature. 3. C) Yes No Both the treasury bond future and the stock index future require the risk free rate. But the stock index future would not require the dividend yield measure. (Continuous dividend yield is what it would require). 4. Copper Spot price: $3.15/pound. 1-year futures price: $3.54/pound. Calculated forward: 3.15 * 1.0375 = 3.27 Commission: 3% - 3.37 Future is still overpriced. So if you buy the Copper future a quick buck thro’ arbitrage could be made. Silver Spot price: $12.75/pound. 1-year futures price: $12.82/pound. 12.75 * 1.0375 * 1.03 = 13.62 -> Sell the future so you can make the money thro’ arbitrage. Molybdenum Spot price: $34.45/pound. 1-year futures price: $35.23/pound. Moly: 34.45 * 1.0375 * 1.03 > 35.23 – you would sell it - Given the choices B) Buy copper, sell silver, and sell molybdenum. C) Buy copper, sell silver, and do not trade molybdenum. I am inclined to go B… but I know the answer that Schweser gives is C. (Do not understand why). 5. Eurodollar future: (1+0.079*90/360) -1 = Add on yield = 0.01975 So future price = (1-0.01975) * 1 Mill = 980250 --> closest answer is 981171. B. Brent Lekvin Manager from Schweser has written this to me in an email regarding this question: “Yes, I see your point on this. The problem assumes that the rate given is an effective yield, which differs from market convention. Fortunately, the answer given is “closest” to the value that would also be derived using LIBOR convention ($1m x (1 - 0.079/4) = $980,250 according to my calculations). We’ll mark this item for review in the “off season” which comes after June 6.”. 6. Contango situation would be caused if Shortage of warehouse space drives up rental rates.
Q1. B [9.37502245 G/$] Q2. B [Fut>fwd] Q3. C [RFR for both and ‘individual’ dividend rate for none] Q4. B [buy gold, sell gold future][sell silver, buy silver future][sell moly, buy moly future] Q5. B [980250] Q6. B [shortage raises cost of storage and hence future cost > spot = contango]
Q5 answer is counterintuitive… ‘’ 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. ‘’ If Libor 90 is annualized, then we should divide it by 4… Not raise it to power 0.25 to get rates for 90 days… What’s do you think?
ans to VinceMTLs question above: I had written to Brent Lekvin, Schweser’s Level II Manager about this as follows: "Why is the ^0.25 convention being used for a EuroDollar future based on the LIBOR? Shouldn’t the (1+0.079/4) convention have been used instead? There is no details provided in the book about calculating this amount —> but the question shows up in Qbank. Thanks for your clarification. " And here’s his response: “Yes, I see your point on this. The problem assumes that the rate given is an effective yield, which differs from market convention. Fortunately, the answer given is “closest” to the value that would also be derived using LIBOR convention ($1m x (1 - 0.079/4) = $980,250 according to my calculations). We’ll mark this item for review in the “off season” which comes after June 6.”.
The value of a 75-day gluck future is closest to: A) 0.1081$/G. B) 9.3750G/. C) 9.4429G/. Your answer: B was correct! 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/ × (1.0375)(75/365) / (1.055)(75/365) = 9.3750G/. (Study Session 16, LOS 61.h) -------------------------------------------------------------------------------- Based on the information he received from Brock, Mason can best conclude that: A) inflation in Mazakhastan is likely to rise. B) futures prices are higher than forward prices in Mazakhastan. C) prices of corporate bonds in Mazakhastan are likely to rise. Your answer: B was correct! 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. (Study Session 16, LOS 61.c) -------------------------------------------------------------------------------- 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? A) Yes Yes B) No Yes C) Yes No Your answer: B was incorrect. The correct answer was C) Yes No 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. (Study Session 16, LOS 61.f) -------------------------------------------------------------------------------- Based on Brock’s information, how should traders best take advantage of arbitrage opportunities in Mazakhastan? A) Buy copper, do not trade silver, and sell molybdenum. B) Buy copper, sell silver, and sell molybdenum. C) Buy copper, sell silver, and do not trade molybdenum. Your answer: A was incorrect. The correct answer was C) Buy copper, sell silver, and do not trade molybdenum. 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 (Study Session 16, LOS 61.h) -------------------------------------------------------------------------------- The value of a 150-day, $1,000,000 eurodollar add-on yield futures contract at expiration is closest to: A) $981,854. B) $981,171. C) $929,368. Your answer: A was incorrect. The correct answer was B) $981,171. 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. (Study Session 16, LOS 61.g) -------------------------------------------------------------------------------- Which of the following would be most likely to cause a contango situation with silver futures in Mazakhastan? A) An increase in the availability of asset-backed loans. B) A shortage of warehouse space that drives up rental rates. C) A huge silver discovery. Your answer: B was correct! 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. 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. (Study Session 16, LOS 61.e)
please help me understand the trading decision reasong in the problem with buying / selling copper, silver etc. if the arbitrage free price is greater than the current futures price, then isnt this underpriced? the silver option for e.g. wouldn’t we buy the spot / future because its really worth the higher arbitrage-free price? what am i missing? may my thought process only works for put/call parity or equity valuation. EDIT - nvm. i was thinking in the right direction but forgetting that the opp effect has to be spot price and that’s what the question was asking.
same here. Also how dividend came in the picture for treasury bond.
dividend is not required for the treasury bond. This statement drives the answer: Quote: The risk-free rate used in calculating the futures price, and that price adjusted to account for individual future dividends. End Quote. both treasury bond and the stock index require the risk free rate. so the hedge instrument a could be either. hedge instrument b - price is adjusted for future dividends. Stock index future requires a continuous dividend yield - so it cannot be a stock index future. does that make sense?
but the explaination they gave us is confusing especially “pricing of bond futures requires discounting the dividends”: Your answer: B was incorrect. The correct answer was C) Yes No 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. (Study Session 16, LOS 61.f)
they asked you to identify the hedge instruments (in crappy language)
I have same question as cfaboston28. Why would pricing a bond future require discounting for dividends when a bond doesn’t even have dividends.