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1、Which of the following is a definition of basis risk? Basis risk is the uncertainty about the difference between the:

A) spot price and the futures price at the time the hedge is removed.

B) current spot price and the current futures price.

C) current spot price and the spot price over the hedging horizon.

D) current spot price and the spot price at the time the hedge is removed

A) spot price increasing faster than the futures price over time.

B) spot price moving according to hyper-arithmetic Brownian motion.

C) futures price increasing faster than the spot price over time.

D) futures price moving according to hyper-arithmetic Brownian motion.

Basis is defined as the difference between the spot price and the futures price. Weakening of the basis occurs when the futures price increases relatively faster than the spot price

3、Which of the following is closest to the correct value for the basis associated with a spot position valued at $15 per unit and a futures contract with a value of $18 per unit?

4、Which of the following is TRUE concerning basis risk? In a hedge using futures contracts:

A) basis risk of the hedged security is replaced with price risk.

B) basis risk is eliminated but price risk still exists.

C) both basis risk and price risk are eliminated.

D) price risk of the hedged security is replaced with basis risk.

5、A corn grower is concerned that the price he can get from the field in mid-September will be less than he has forecasted. To protect himself from price declines, the farmer has decided to hedge. The best available futures contract he can find is for August delivery. Which of the following is the appropriate direction of his position and the source of basis risk that may impact the farmer?

A) Short futures; correlation.

B) Short futures; rollover.

C) Long futures; correlation.

D) Long futures; rollover.

The farmer needs to be short the futures contracts. The source of basis risk for this farmer arises from the fact that his contract and harvest dates do not perfectly match. As a result, he will be exposed to basis risk due to a necessary rollover in his position.

6、A portfolio manager has a $15 million mid-cap portfolio that has a beta of 1.3 relative to the S&

400. S&

500 futures are trading at 1,150 and have a multiplier of 250. The most significant risk this manager faces in attempting to hedge his position is:

A) correlation risk resulting from a rollover of positions between the S&

400 and S&

500.

B) volatility risk arising from unstable correlation predictions.

C) basis risk resulting from a cross-hedge.

D) improper profit forecasts of the underlying position.

Because the manager is considering hedging his S&

400 exposure with S&

500 contracts, his primary concern should be basis risk between the two.

7、A portfolio manager is constructing a portfolio of stocks and corporate bonds. The portfolio manager has estimated that stocks and corporate bond returns have daily standard deviations of 1.8 percent and 1.1 percent, respectively, and estimates a correlation coefficient of returns of 0.43. If the portfolio manager plans to allocate 35 percent of the portfolio to corporate bonds and the rest to stocks, what is the daily portfolio VAR (2.5 percent) on a percentage basis?

The correct answer is A

First, calculate the daily percentage VAR for stocks and corporate bonds:

Stocks: VAR(2.5%)_{Percentage Basis} = z_2.5% ′ σ = 1.96(0.018) = 0.0353 = 3.53%

Bonds: VAR(2.5%)_{Percentage Basis} = z_2.5% ′ σ = 1.96(0.011) = 0.0216 = 2.16%

Next calculate the portfolio VAR using weights of 35% for bonds and 65% for stocks:

[0.65²(0.0353²) + 0.35²(0.0216²) + 2(0.35)(0.65)(0.0353)(0.0216)(0.43)]^0.5 = 0.0271 = 2.71%

8、How will the value of a portfolio of non-callable corporate bonds hedged with Treasury futures change if the yield curve shifts up in a parallel manner by an anticipated amount? The value of the newly hedged portfolio:

The portfolio is hedged against parallel movements in the yield curve so its value will not change.

9、The purpose of computing a minimum variance hedge ratio is to minimize the variance of the:

A) hedging instrument.

B) combined hedged and hedging instrument portfolio.

C) instrument to be hedged.

D) correlation estimator.

The purpose of computing a minimum variance hedge ratio is to minimize the variance of the combined portfolio.

10、The minimum variance hedge ratio is equal to the product of the correlation coefficient between the spot and futures price changes and the ratio of the:

A) standard deviation of the futures to the standard deviation of the spot.

B) standard deviation of the spot to the standard deviation of the futures.

C) variance of the spot to the variance of the futures.

D) variance of the futures to the variance of the spot.

The minimum variance hedge ratio is defined as the product of the correlation coefficient times the ratio of the standard deviation of the spot price change and the standard deviation of the future price change.

11、A portfolio manager would like to use S&

500 stock index futures to help increase his exposure to movements in the stock market over the next three months. The current S&

500 futures contracts are trading at 1,205 with a multiplier of $250, and the portfolio manager would like to increase the portfolio beta from 0.92 to 1.05. If the value of the asset portfolio is $15 million, the position taken for stock index futures would be closest to which of the following?

A) Sell 6 contracts.

B) Sell 50 contracts.

C) Purchase 50 contracts.

D) Purchase 6 contracts.

The portfolio manager’s target equity exposure sensitivity measure is 1.05, while its current measure is 0.92. The number of futures contracts can be determined as [(1.05-0.92) $15 million] / ($250 x 1205)] ≈ 6 contracts. The portfolio manager wants to buy six S&

500 contracts to increase his exposure.

12、Craig Fullen is a portfolio manager with a $25,000,000 value portfolio with a beta of 0.75 relative to the S&

500. Fullen is concerned the market will fall, and wants to hedge the risk to his portfolio using S&

500 futures contracts. If the current value of the S&

500 is 1,050, what action should Fullen take to hedge his portfolio?

A) Sell 71 futures contracts.

B) Sell 95 futures contracts.

C) Buy 95 futures contracts.

D) Sell 119 futures contracts.

Because Fullen is long the portfolio, he will want to short futures contracts. number of contracts = β_portfolio × (portfolio value/value of futures contract). The value of the futures contract = 1,050 × 250 = $262,500. number of contracts = 0.75 × ($25,000,000 / $262,500) = 71 contracts.

13、Which of the following factors is/are often considered to be a problem with hedged positions?

I. Uncertainty with roll-over of the hedging instrument.
II. Perfect correlation between the asset and the hedging instrument.
III. Certainty with the date of the underlying asset’s purchase or sale.
IV. Imperfect correlation between the hedged asset and the hedging instrument.
A) I only.

B) I and II only.

C) I and IV only.

D) II and III only.

Imperfect correlations between the futures price and the underlying spot price decrease the effectiveness of a hedged position. When the hedging horizon is long relative to the maturity of the futures used in the hedging strategy, the hedge has to be rolled prior to expiration. As maturity of the hedging instrument approaches, the hedger must close out the existing position and replace it with another contract with a later maturity. Rolling the hedge forward exposes the hedger to the basis risk of the new position each time the hedge is rolled.