Derivatives【 Reading 35】习题精选 investment, management, one, 2012, currently

mouse123

Jack Tarkenton and Gene Bowman are analysts for the firm Salisbury Consultants. Salisbury provides investment and risk management advice to portfolio managers.
One of Salisbury’s largest U.S. clients has taken a position in a German stock portfolio. The value of the position is currently EUR400,000. The client has a one month time horizon and will hedge translation currency risk with a futures contract that has a maturity of three months. The current and projected portfolio values, spot exchange rates, and futures prices are shown in the table below. To illustrate the effect of currency risk on foreign portfolio values, Tarkenton will calculate the hedged and unhedged return in dollars and Euros.

Original portfolio value in EUR	400,000
Original spot exchange rate	$1.02
Original futures price	$0.98
Portfolio value in 1 month in EUR	420,000
Spot exchange rate in 1 month	$1.07
Futures price in 1 month	$1.03

In his presentation to the client, Tarkenton discusses in more detail the hedging of currency risk for foreign investments using foreign currency futures contracts. Describing the basis for foreign currency futures contracts, he states that it is dependent on the covered interest rate parity relationship. Furthermore, Tarkenton states that basis risk is negligible because, unlike commodities such as corn and silver, foreign currency has no storage costs.
Bowman adds that according to his study of equity and currency markets, hedging foreign equity risk is not a simple task because there is a relationship between foreign stock returns and the changes in foreign currencies. For example, Bowman states that if the Swiss franc declines by 10%, then on average Swiss stocks increase by 4%. Bowman states that this relationship is due to the fact that a weaker Swiss franc makes Swiss exports more competitive in world markets.
Tarkenton states that if an investor had a portfolio of equities from several countries, he or she would run the regression below to hedge currency risk. As a result, the h terms in the regression would provide the optimal hedge ratios for hedging currency risk.
R = α + h1F1 + h2F2 + h3F3 + e.Turning their attention to lesser developed countries, Bowman states that investors should pay particular attention to countries with newly liberalized financial markets because there are significant financial changes post liberalization as reflected in the country’s stock market performance and diversification benefits. In particular, he makes the following comments:

Statement #1: After a country is liberalized, stock returns in the country decrease, perhaps due to the previously high returns associated with the announcement of the liberalization.
Statement #2: From a diversification standpoint, the research shows that stock return volatility declines post liberalization in the short run. Unfortunately though, liberalization leads to higher correlations and betas between the liberalized country and world markets.

In Tarkenton’s German stock portfolio example, what is the unhedged return in dollar terms?

A) 5.00%.

B) 5.25%.

C) 10.15%.

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The return on the unhedged portfolio in dollars factors in the beginning and ending spot rates:
The portfolio return in dollars = (€420,000 × $1.07/€) – (€400,000 × $1.02/€) / (€400,000 × $1.02/€) = ($449,400 − $408,000) / $408,000 = 10.15%.
Both the investment in Euro terms and the Euro itself increased in value. The investor benefited from both. (Study Session 14, LOS 35.a)

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In Tarkenton’s German stock portfolio example, what is the hedged return in dollar terms?

A) 15.05%.

B) 5.25%.

C) 5.00%.

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In a hedge of translation currency risk (i.e. a simple hedge of the principal), the manager would hedge the €400,000 principal. The manager shorts the Euro to hedge their long Euro position in the European stock. The loss on the futures contracts in dollars = €400,000 × ($0.98/€ –$1.03/€) = −$20,000.
The profit on the unhedged portfolio in dollars = (€420,000 × $1.07/€) – (€400,000 × $1.02/€) = $449,400-$408,000 = $41,400.
In net, the investor has made a dollar return of (−$20,000 + $41,400) / $408,000 = 5.25%. (Study Session 14, LOS 35.a)

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Regarding Tarkenton’s statement concerning basis risk, Tarkenton is:

A) incorrect because basis is dependent on the purchasing parity relationship.

B) incorrect because basis is dependent on the purchasing parity relationship and because basis risk is not negligible for foreign currency futures contracts.

C) incorrect because basis risk is not negligible for foreign currency futures contracts.

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Tarkenton is incorrect because basis risk is not negligible for foreign currency futures contracts. If interest rate differentials in the home and foreign country change, the difference between the spot rate and futures rate (i.e. the basis) will change. The only way for basis risk to be eliminated is if the interest rate differential is constant or if the investor matches the maturity of the investment horizon with the maturity of the futures contract. In the latter case, the futures price will converge to the spot price at maturity.
Covered interest rate parity states that the difference between the spot rate and the forward or futures price is due to the interest rate differential between the two countries. (Study Session 14, LOS 35.c)

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Given Bowman’s study of the relationship between Swiss stock returns and changes in the Swiss franc, what would be the optimal amount of SF to hedge for an equity portfolio worth SF 500,000 if the investor wished to hedge both translation and economic risk?

A) SF 125,000.

B) SF 500,000.

C) SF 300,000.

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If the investor was only hedging translation risk, the hedged amount would simply be the principal of SF 500,000 (i.e. a hedge ratio of 1.0). However, in Bowman’s calculation, the relationship between Swiss stock returns and the changes in the Swiss franc is -0.40 (4% / −10%). This ratio would hedge economic risk. To hedge both translation risk and economic risk, the hedge ratio is 0.60 (1 − 0.40). Thus 60% of the principal would be hedged, i.e. SF 300,000. (Study Session 14, LOS 35.b)

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Regarding Tarkenton’s regression to provide the optimal hedge ratios, what do the R and F terms represent?

R term

F terms

A) Foreign asset return in local currency terms Changes in foreign currencies

B) Foreign asset return in domestic currency terms Changes in foreign asset factors

C) Foreign asset return in domestic currency terms Changes in foreign currencies

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The R term represents the return on the foreign asset in domestic currency terms (e.g. dollar terms for a U.S. investor) while the F terms represent changes in foreign currency values. The F terms may be the change in foreign currency futures prices or the change in foreign currency spot prices. The h terms in the regression will provide the optimal hedge ratios for determining the amount of currency exposure to hedge. (Study Session 14, LOS 35.e)

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Regarding Bowman’s comments on the financial changes post liberalization, are the comments correct?

Statement 1

Statement 2

A) Yes No

B) No No

C) No Yes

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Statement #1 is correct. When a country’s financial markets are liberalized, stock returns generally increase as investors bid up the prices of equities previously unavailable to them. After liberalization, stock returns subsequently decline, perhaps due to the previously high liberalization returns.
Statement #2 is incorrect. It is true that liberalization leads to higher correlations and betas with world markets. However, the empirical evidence demonstrates that liberalization does not affect the volatility of returns in the short run. (Study Session 12, LOS 30.c)

mouse123

The manager of a large, multi-currency portfolio is investigating methods to hedge the portfolio. If she regresses the return of the portfolio on several major currencies, she is most likely trying to solve the problem of:

A) illiquid forward and futures markets for some currencies.

B) the symmetry of the payoff of forward and futures contracts.

C) the asymmetry of the payoff of forward and futures contracts.

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The manager’s regression would most likely be part of setting up a cross-hedge, which is to remedy the problem that some of the currencies represented in the portfolio will probably have illiquid forward and futures markets.

mouse123

Which of the following equations represents the net profit/loss on a hedged position, in domestic currency terms?

A) V0 (-Ft + F0).

B) (Vt* - V0*) / V0*.

C) ( Vt St - V0 S0) – V0 (Ft - F0).

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Recall the following variables used in hedge analysis:

V0 – The value of the portfolio of foreign assets at time 0, stated in the foreign currency.

Vt – The value of the portfolio of foreign assets at time t, stated in the foreign currency.

Vt* - The value of the portfolio of foreign assets at time t, stated in the domestic currency.

St – The spot rate, quoted at time t.

Ft – The futures exchange rate, quoted at time t.

(Vt* - V0*) / V0* is the portfolio rate of return, stated in domestic currency terms. Vt St - V0 S0 is the gain or loss on a portfolio, stated in domestic currency terms. V0 (-Ft + F0) is the gain or loss on a futures position, stated in domestic currency terms. Therefore, the net profit/loss, in domestic currency, is equal to (Vt St - V0 S0) – V0 (Ft - F0).

mouse123

A U.S.-based investor has purchased a 15,000,000 peso office building in Mexico. He has hedged his investment by selling forward futures at $0.1098/peso. Two months later, the futures exchange rate has fallen to $0.0921/peso. The investor’s net change in the futures position is:

A) $1,647,000.

B) -$265,500.

C) $265,500.

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The realized gain on the futures position is:
V0 (-Ft + F0) = 15,000,000 pesos × (-$0.0921/peso + $0.1098/peso) = $265,500.

andytrader

A U.S. investor who holds a £2,000,000 investment wishes to hedge the portfolio against currency risk. The investor should:

A) sell £2,000,000 worth of futures for U.S. dollars.

B) buy £2,000,000 worth of futures for U.S. dollars.

C) sell $2,000,000 worth of futures for British pounds.

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The investor should sell £2,000,000 worth of futures contracts for U.S. dollars. This will offset the existing long position in pound-denominated assets. In so doing, the investor has effectively fixed the exchange rate for pounds into dollars for the duration of the futures contract.

andytrader

A basic strategy for hedging a portfolio against currency risk, where the investor hedges the foreign currency value of the foreign asset, is called:

A) cross-hedging.

B) hedging the basis.

C) hedging the principal.

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Cross-hedging is a strategy whereby a third currency is used to hedge a foreign currency exposure in a currency for which standard hedging vehicles are unavailable. Basis risk is the exposure to changes in the relationship between the forward price of an asset and its spot price. Hedging the principal is the basic strategy used by managers of foreign portfolios to minimize exposure to currency risk.

andytrader

The basic underlying goal of a currency hedge is to minimize a portfolio’s exposure to changes in:

A) exchange rates.

B) interest rates.

C) the basis.

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The management of currency risk is relevant for a portfolio with foreign investments. A currency hedge is utilized to minimize the negative effects caused by a change in the exchange rate between the domestic currency and the foreign currency.

andytrader

The manager of a single-currency portfolio is investigating methods to hedge the portfolio. If he regresses the return of the portfolio on the return of the currency, the:

A) slope coefficient of the regression represents the delta risk.

B) slope coefficient of the regression represents the economic risk.

C) intercept coefficient of the regression represents the economic risk.

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This is the measure of economic risk; it is the covariance of the portfolio return with the currency return over the variance of the currency return. Estimating this measure is part of composing a minimum-variance hedge.

andytrader

One issue addressed in a minimum-variance hedge over a hedge of the principal strategy is:

A) estimation risk.

B) the covariance of the local return (in the foreign market) and the exchange rate.

C) exchange rate risk.

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Both hedges address translation and exchange rate risk. Both hedges are subject to estimation risk. The minimum-variance hedge addresses the fact that the changes in the exchange rate can be correlated with the return in the foreign market.

andytrader

An analyst is exploring methods to hedge the return of a foreign asset in a foreign country as well as hedge the foreign exchange risk of the hedged amount. To implement a minimum-variance hedge over a hedge of the principal strategy a portfolio manager needs to set the hedge ratio for:

A) translation risk equal to one.

B) economic risk equal to one.

C) translation risk equal to zero.

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To implement a minimum-variance spread, the analyst should set the hedge ratio for translation risk equal to one and the hedge ratio for economic risk equal to the covariance of the local currency return with the currency return divided by the variance of the foreign currency.