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发表于 2011-3-25 11:48 | 只看该作者

Reading 61: Futures Markets and Contracts-LOS h 习题精选

2011, reputation, exchange, investor, example

Craig Champion, CFA, manages portfolios of U.S. securities for European investors. His clients have differing tastes with respect to hedging exchange rate risk and the types of securities they hold. Francois Levisque is a Belgian investor who holds a large diversified portfolio of U.S. equities. Levisque has a reputation for some success in timing the U.S. equity market. For example, he has often locked in gains on his portfolio with derivatives shortly before a market correction. Sometimes he also hedges his portfolio’s currency risk. Levisque has just instructed Champion to take a large short position in S& 500 index, either with futures or with a forward contract. Champion notices that the futures price is less than the current spot price and consults with his colleague Danielle Silvers, CFA. Champion says he thinks that the futures price is less than the spot price because the dividend yield of the S& 500 is greater than the Treasury Bill rate. Silvers says that it could just be backwardation. Silvers also notes that the use of a forward contract might be a good idea because the contract will not attract the attention of other market participants who might react to Levisque’s move. Champion tells Silvers that the reason Levisque wants to hedge his equity position is that he thinks all U.S. interest rates will increase soon. This, he believes, is bearish for equities, and he also thinks the negative relationship between equity prices and interest rates makes a short forward contract more attractive than a short futures contract.

Ragnar Hvammen is a Norwegian investor with a large investment in oil-related assets that he often hedges with futures contracts. Champion notices that the price of the oil futures contract is usually higher than the spot price. Hvammen uses short-term borrowings in dollars, from both European and U.S. banks, to meet the liquidity needs of his oil investments, and he has Champion hedge these short positions with Eurodollar futures. Silvers suggests that Champion should consider using T-bill futures to hedge the loans from U.S. banks, and use Eurodollar futures only for the Eurodollar loans. Champion says he will look into that, as well as forward rate agreements, as alternative hedging tools for Hvammen.

Champion and Silvers each gave a reason for why the futures price of the S& 500 index might be less than the spot price. With respect to their statements:

A)
 they are both incorrect.
B)
 they are both correct.
C)
 Champion is incorrect and Silvers is correct.

The equation for the price of a futures contract on an equity index is FP = S0 × e(R ? σ) × T, where σ is the dividend yield and R is the risk-free rate. If R < σ, then FP < S0 and Champion is correct. Silvers could be correct in that backwardation is defined as FP < S0, with the relationship being caused by the risk aversion of hedgers of long asset positions. Their risk aversion makes them willing to take short contracts at lower prices than otherwise might be the case.

If Champion thinks that the S& 500 index is negatively correlated with interest rates, then choosing the short forward contract over the short futures contract is:

A)
 counterproductive because a short futures contract would benefit more from a higher borrowing rate.
B)
 counterproductive because a short futures contract would benefit more from a higher reinvestment rate.
C)
 appropriate because the forward contract would benefit more from a higher reinvestment rate.

When hedging a position, futures contracts are better if the hedge produces a positive cash flow, via marking-to-market, when interest rates rise and is hurt when interest rates fall. In this case, when interest rates rise and cause equity values to fall, a short futures position will receive a positive cash flow that can be reinvested at the higher rate. If interest rates fall, and the short futures position must be marked to market with a negative cash flow, the opportunity cost of the negative cash flow is lower. Forward contracts that do not require marking-to-market do not “benefit” from changes in interest rates.

For a futures contract on an asset with no storage costs, convenience yield, or other expected cash flows over the term of the contract, there should be a:

A)
 positive correlation between the futures price and both interest rates and the spot price.
B)
 negative correlation between the futures price and interest rates and a positive correlation between the futures price and the spot price.
C)
 positive correlation between the futures price and interest rates and a negative correlation between the futures price and the spot price.

The equation for the no-arbitrage price of a futures contract with no storage costs, convenience yield, or other expected cash flows over the term of the contract is FP = S0 × (1 + R)T, so the futures price is positively correlated with both the interest rate and the spot price.

Oil futures prices might be higher than the spot price because:

A)
 there are more benefits than costs to holding the asset.
B)
 of reverse contango.
C)
 there are more costs than benefits to holding the asset.

In calculating the futures price, we would subtract the benefits of holding the asset, e.g., the present value of dividends and coupons, and add the costs of holding the asset. Oil does not pay a dividend, and there would be costs for holding oil. Contango describes the situation where the futures price exceeds the spot price, and there is not such thing as reverse contango.

With respect to using Eurodollar futures, instead of T-bill futures, to hedge short-term loans from U.S. banks, Champion is:

A)
 justified because the Eurodollar futures market is very liquid, and LIBOR is less correlated with short-term loan rates than is the T-bill rate.
B)
 justified because the Eurodollar futures market is very liquid, and LIBOR is more correlated with short-term loan rates than is the T-bill rate.
C)
 not justified because the Eurodollar futures market is not very liquid, and LIBOR is more correlated with short-term loan rates that T-bills.

Eurodollar futures are futures on dollar LIBOR, and LIBOR is the prevailing rate on very large bank loans called Eurocurrency loans. The rates on T-bills can be driven by influences (e.g., a flight to quality) that are different than those that drive dollar LIBOR rates. As a result, Eurodollar futures are more highly correlated with (dollar) bank loan rates should provide a better hedge for the client’s bank loan exposure. Moreover, the Eurodollar futures market is large and very liquid.

The forward rate associated with a forward rate agreement (FRA) is:

A)
 less than that implied by the Eurodollar futures rate especially when the maturity of the contracts is longer.
B)
 greater than that implied by the Eurodollar futures rate especially when the maturity of the contracts is longer.
C)
 greater than that implied by the Eurodollar futures rate especially when the maturity of the contracts is shorter.

The forward (FRA) rate = implied futures rate – convexity bias. The convexity bias is considered negligible for contracts of less than one or two years. It is generally viewed as a consideration for contracts with a maturity of longer than two years.

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2#
发表于 2011-3-25 11:48 | 只看该作者

An index is currently 876, the risk-free rate (Rf) is 7%, and the dividend yield on the index portfolio is 1.8%. Assuming that these are continuously compounded yields, the price of an 18-month index future is closest to:

A)
 945.2.
B)
 943.0.
C)
 947.1.

FP = 876 e(0.07-0.018)1.5 = 947.1.

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3#
发表于 2011-3-25 11:49 | 只看该作者

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 price of a 75-day gluck future should be closest to:

A)
 0.1081$/G.
B)
 9.4429G/$.
C)
 9.3750G/$.

To calculate the price 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 59.h)

Based on the information he received from Brock, Mason can best conclude that:

A)
 futures prices are higher than forward prices in Mazakhastan.
B)
 inflation in Mazakhastan is likely to rise.
C)
 prices of corporate bonds in Mazakhastan are likely to rise.

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 59.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)
Yes No
C)
No Yes

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 59.f)

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4#
发表于 2011-3-25 11:49 | 只看该作者
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 do not trade molybdenum.
C)
 Buy copper, sell silver, and sell 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 59.h)

Assume that Globos has taken a position in the Eurodollar futures contract, it is now 60 days later and the contract is expiring. Globos interest rate forecast for 90-day LIBOR was correct. The value of the futures contract at expiration is closest to:

A)
 $980,250.
B)
 $921,000.
C)
 $981,000.

The Eurodollar futures contract is based on 90-day LIBOR.
The forecast for 90-day LIBOR was 7.9%. Thus, the contract price at expiration is:

$1,000,000 × (1 ? (0.079 × 90/360)) = $980,250. (Study Session 16, LOS 59.g)

Which of the following would be most likely to cause a contango situation with silver futures in Mazakhastan?

A)
 A shortage of warehouse space that drives up rental rates.
B)
 An increase in the availability of asset-backed loans.
C)
 A huge silver discovery.

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 59.e)

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