LOS h: Calculate and interpret the price of Treasury bond futures, stock index futures, and currency futures.

Q1. 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)   Champion is incorrect and Silvers is correct.

C)   they are both correct.

Q2. 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.

Q3. According to the no-arbitrage formula for futures contracts there should be a:

A)   negative correlation between the basis and interest rates and a positive correlation between the basis and the spot price.

B)   positive correlation between the basis and interest rates and a negative correlation between the basis and the spot price.

C)   positive correlation between the basis and both interest rates and the spot price.

Q4. Oil futures prices might be higher than the spot price because:

A)   there are more costs than benefits to holding the asset.

B)   there are more benefits than costs to holding the asset.

C)   of reverse contango.

Q5. 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)   not justified because the Eurodollar futures market is not very liquid, and LIBOR is more correlated with short-term loan rates that T-bills.

C)   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.

Q6. The forward rate associated with a forward rate agreement (FRA) is:

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

B)   less 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.

Q7. An index is currently 876, the risk-free rate (R_f) 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)   947.1.

C)   943.0.

LOS h: Calculate and interpret the price of Treasury bond futures, stock index futures, and currency futures. fficeffice" />

Q1. Craig Champion, CFA, manages portfolios of ffice:smarttags" />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)   Champion is incorrect and Silvers is correct.

C)   they are both correct.

Correct answer is C)

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.

Q2. 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.

Correct answer is B)

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.

Q3. According to the no-arbitrage formula for futures contracts there should be a:

A)   negative correlation between the basis and interest rates and a positive correlation between the basis and the spot price.

B)   positive correlation between the basis and interest rates and a negative correlation between the basis and the spot price.

C)   positive correlation between the basis and both interest rates and the spot price.

Correct answer is C)

The equation for the no-arbitrage price of a futures contract is FP = S₀ × (1 + R)_T, and the equation for the basis is: basis = futures price – spot price. Clearly an increase in R will increase the basis. The basis grows proportionally with the spot price. So the basis is positively correlated with both the interest rate and the spot price.

Q4. Oil futures prices might be higher than the spot price because:

A)   there are more costs than benefits to holding the asset.

B)   there are more benefits than costs to holding the asset.

C)   of reverse contango.

Correct answer is A)

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.

Q5. 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)   not justified because the Eurodollar futures market is not very liquid, and LIBOR is more correlated with short-term loan rates that T-bills.

C)   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.

Correct answer is C)

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.

Q6. The forward rate associated with a forward rate agreement (FRA) is:

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

B)   less 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.

Correct answer is B)

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.

Q7. An index is currently 876, the risk-free rate (R_f) 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)   947.1.

C)   943.0.

Correct answer is B)

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

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