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Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com FinQuiz.com CFA Level III Item-set - Solution Study Session 15 June 2018 Copyright © 2010-2018 FinQuiz.com All rights reserved Copying, reproduction or redistribution of this material is strictly prohibited info@finquiz.com FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com FinQuiz Level III 2018 – Item-sets Solution Reading 28: Risk Management Applications of Forward and Futures Strategies Question ID: 8813 Correct Answer: C The statement is incorrect with respect to the portfolio return If the foreign stock market risk is hedged, the portfolio’s return will be the foreign risk free, before converting to the domestic currency In other words, the portfolio will earn the foreign risk free rate in local currency terms Question ID: 8814 Correct Answer: B The statement is incorrect Although it is true that for the risk management of foreign currency, forwards are preferred over futures because of their greater liquidity and customization benefit, the risk of most bond portfolios is still managed using Treasury bond futures Question ID: 8815 Correct Answer: A A forward contract will be more appropriate in this case because the client would most likely prefer the precision provided by customized transactions The risk of inflows and outcomes of specific currency transactions, especially those associated with very specific dates, is better managed using forward contracts, because of their customization benefit Question ID: 8816 Correct Answer: C Clint is correct with respect to the first benefit Since forward contracts can be customized to meet the exact specific needs of an investor, they offer a better hedge than futures However, since they can provide a close to perfect hedge, they tend to be more costly Question ID: 8817 Correct Answer: C Forward contracts are essentially unregulated while futures are heavily regulated However, this difference is not usually a major consideration in deciding which type of contract to use for hedging The other two factors are important for deciding which contract to use Question ID: 8818 Correct Answer: A The statement is correct Futures or forwards can be used to change the risk of certain asset classes or alter the allocations between asset classes Instead of asking one manager to sell securities and another to buy securities, derivatives can be used to change the allocation (or risk) of a portfolio Thus, the asset class managers can concentrate on doing the best they can within their respective areas of responsibility and need not even know that the overall asset allocation (risk) has been changed FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com Question ID: 8806 Correct Answer: B To hedge the European market return, AMA would have to achieve a beta of zero on their €20 million portfolio To reduce the beta to zero, AMA will have to sell futures contracts The required number equals: – 1.10/0.95[20,000,000/155,000] = – 149.40 Therefore AMA will need to sell 149 futures contracts Question ID: 8807 Correct Answer: C After hedging the European market return, the portfolio will be perfectly hedged against all European stock market risk Hence, it should earn the foreign risk free rate The Euro interest rate is 5% and since the investment is made for six months, AMA should expect to earn 0.05 × (180/360) = 2.5% Question ID: 8808 Correct Answer: C If AMA hedges the European market return, the portfolio would grow to a value of €20,000,000[1+0.05(180/360)] = €20,500,000 Hence, AMA could hedge the currency risk of this portfolio with a forward contract with this much notional principal 10 Question ID: 8809 Correct Answer: A If the European market return is hedged, the portfolio will grow to a value of €20,500,000 If AMA then decides to hedge the currency risk as well, it will enter a forward contract with a notional principal equal to €20,500,000 Given the current spot exchange rate, and the risk free rates in the two regions, the six month forward exchange rate equals: 1.078(1.055/1.05)0.5 = $1.080/€ Hence, at contract expiration the notional principal will convert to a value of 20,500,000(1.080) = $22,151,554 11 Question ID: 8810 Correct Answer: B In dollar terms, the portfolio was originally worth 20,000,000(1.078) = $21,560,000 At the end of six months, the portfolio is worth $22,151,554 This translates to a return equal to: [22,151,554/21,560,000] – = 2.744% which is approximately equal to the U.S risk free rate for six months (5.5/2 = 2.75%) FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 12 Question ID: 8811 Correct Answer: B The foreign market risk should be hedged if it is expected that the stock market will go down (weak market), so that the portfolio is hedged against such losses The currency risk should not be hedged if it is expected that the foreign currency would be strong over the holding period (stronger than implied by the interest rate differential), so that gains from appreciation of the foreign currency can be reaped 13 Question ID: 8799 Correct Answer: B Since Superior Goods Inc has to deliver the foreign currency for the planned purchase, it is short the pound, and therefore, to hedge the exchange rate risk, it should go long the forward contract 14 Question ID: 8800 Correct Answer: B Under the forward contract, Superior Goods will have to pay 1.355(50,000,000) = $67,750,000 to purchase ₤50 million If the spot exchange rate is $1.298/₤ in one month, Superior Goods will only have to pay (1.298)(50,000,000) = $64,900,000 to purchase the required ₤50 million This means it will be $2,850,000 better off in the spot market (that is, without the hedge in place) 15 Question ID: 8801 Correct Answer: C If Superior Goods hedges the purchase of the raw material, it will purchase ₤50 million from the dealer, and pay 50,000,000/0.756= $66,137,566 16 Question ID: 8802 Correct Answer: C If the spot rate after one month is ₤0.758/$, to purchase the ₤50 million, Superior Goods would need 50,000,000/0.758 = $65,963,061 only Hence, it would be $1,786,939 ($67,750,000 – $65,963,061) better off in the spot market (since to settle the forward contract it needs $67,750,000) 17 Question ID: 8803 Correct Answer: C Since Oil Explorers Limited has to make a payment of $4.5 million, therefore it is short dollars Hence to hedge the foreign currency risk, it should go long the forward contract The notional principal will equal $4,500,000 18 Question ID: 8804 Correct Answer: B Oil Explorers Ltd will close the contract by receiving $4.5 million and delivering 4,500,000(0.987) = CAD4,441,500 in return FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 19 Question ID: 8792 Correct Answer: B Since the company has to make payment in Japanese yen, it is short the foreign currency (yen) Therefore, to hedge the exchange rate risk, the company should go long a forward contract (that is, a contract that allows buying the foreign currency at a fixed exchange rate) A currency swap is usually used to hedge a series of foreign cash flows 20 Question ID: 8793 Correct Answer: A Since SSI will receive euros for the sale to Blue-Ray Technologies, it is effectively long the euro in its software sale, so a short position in the forward contract, denominated in dollars/euro, is appropriate 21 Question ID: 8794 Correct Answer: C Since SSI is long the euro, it should take a short position in the forward contract If the contract is cash settled, the company would sell the euros on the market for St and the forward contract would be cash settled for –(St –F) The net effect is that the company receives F, the forward rate for the euros 22 Question ID: 8795 Correct Answer: C The sale is worth €35 million, and the forward exchange rate is $0.997/€ Therefore, SSI will deliver €35 million and receive a rate of $0.997/€ The total amount it will receive equals: 35,000,000(0.997) = $34,895,000 23 Question ID: 8796 Correct Answer: A Under the forward contract, SSI would receive 35,000,000(0.997) = $34,895,000 If the realized spot exchange rate in three months is $0.967/€, SSI would receive 35,000,000(0.967) = $33,845,000, or $1,050,000 less than with the forward hedge in place 24 Question ID: 8797 Correct Answer: A If the realized spot exchange rate in three months is $1.253/€, SSI would receive 35,000,000(1.253) = $43,855,000 if it transacted in the spot market This is $8,960,000 more than what SSI would receive under the forward contract at a forward rate of $0.997/€ Therefore, SSI would be better off not hedging under this scenario 25 Question ID: 8774 Correct Answer: C To increase the portfolio’s duration, the number of futures contracts to buy equals: (7.7 – 5.55/6.27) ($187,500,000/375,000) (1.2) = 205.74 FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 26 Question ID: 8775 Correct Answer: C In this case, the number of futures contracts would equal: (7.7 – 5.55/6.27) ($187,500,000/375,000) (1) = 171.45 27 Question ID: 8776 Correct Answer: A The return on the futures contract equals: 206(385,000 – 375,000) = $2,060,000 The overall gain with the futures contract = 5,013,750+$2,060,000 = $7,073,750 The return without the futures contract = 5,013,750/187,500,000 = 0.026740 = 2.674% The return with the futures contract = $7,073,750/187,500,000 = 0.0377 = 3.773% Difference = 2.674 – 3.773 = –1.099% 28 Question ID: 8777 Correct Answer: C The duration of the portfolio can be measured by dividing the percentage change in the portfolio value by the 48 bps change in the portfolio yield Without the futures contract: 0.02674/0.0048 = 5.57 With the futures contract: 0.03772/0.0048 = 7.86 29 Question ID: 8778 Correct Answer: B To eliminate all interest rate risk means decreasing the duration to zero For this, the number of contracts needed would equal: (0 – 5.55/6.27)($187,500,000/375,000)(1.2) = – 531.10 (so we need to sell this many contracts) 30 Question ID: 8779 Correct Answer: B Statement is incorrect Changing the duration, whether increasing it or reducing it, is an inexact process, because duration provides only an approximation of the change in bond prices Statement is correct FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 31 Question ID: 8764 Correct Answer: B By selling futures, one can indeed reduce the duration of a portfolio to replicate a short-term instrument However, if cash is needed, the fund would still have to sell the long-term bonds and buy back the futures Although the latter would not present a liquidity problem, the sale of the long term bonds would Therefore, this conversion does not handle the liquidity problem 32 Question ID: 8765 Correct Answer: C The amount invested in bonds equals (56%)($40 million) = $22.4 million Of this $22.4 million 37% or (0.37)(22.4) = $8.288 million needs to be converted to six month instruments with a duration of three months or 0.25 So the number of futures contracts needed equals: [0.25-5.7/6.12][8,288,000/37,500] = – 196.81 or – 197 contracts (the negative sign means we need to sell contracts) 33 Question ID: 8766 Correct Answer: B Out of the $22.4 million, $8.288 million has been converted to short-term instruments The duration of the remaining $14.1120 million needs to be increased from the current level of 5.7 to 6.5 For this we need to buy: [6.5-5.7/6.12][14,112,000/37,500] = 49.19 or 49 contracts 34 Question ID: 8767 Correct Answer: A After the adjustments the duration of $8.288 million will have been converted to 0.25, and the duration of $14.1120 million will have been raised to 6.5 The overall duration would be: (8.288/22.4)0.25 + (14.1120/22.4)6.5 = 4.1875 35 Question ID: 8768 Correct Answer: C The bond portfolio is worth $22.4 million 50% of this amount equals 0.50(22.4)= $11.2 million The objective is to increase the duration of $11.2 from its current level of 5.7 to 6.7, and decrease the duration of the other $11.2 million from 5.7 to 5.0 The number of futures contracts to increase the duration equals: [6.7-5.7/6.12][11,200,000/37,500] = 48.80, so we need to buy 49 contracts The number of futures contracts to decrease the duration equals: [5.0-5.7/6.12][11,200,000/37,500] = -34.15, so we need to sell 34 contracts Since these transactions involve the same futures contract, the net effect is that, to achieve the objective, we need to buy 49-34 = 15 contracts FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 36 Question ID: 8769 Correct Answer: B Option B is inaccurate Reducing the duration of a bond portfolio to replicate a short-term instrument does not remove the problem that long-term instruments (which will still be held) may have to be liquidated Hence, this conversion does not solve the illiquidity problem of the long-term instruments The other options are correct 37 Question ID: 8757 Correct Answer: B With the current allocation, Robust Chemicals has $345 million invested in stocks and $230 million invested in bonds To change the allocation to 50%-50%, $287.5 million needs to be invested in both bonds and stocks This means $57.5 million needs to be moved from stocks to bonds Thus, Claudius will need to sell $57.5 million of stock and buy $57.5 million of bonds The number of stock index futures to sell equals: (0 – 1.3/1.1)(57,500,000/266,500) = – 254.988 or – 255 contracts 38 Question ID: 8758 Correct Answer: C With the current allocation, Robust Chemicals has $345 million invested in stocks and $230 million invested in bonds To change the allocation to 50%-50%, $287.5 million needs to be invested in both bonds and stocks This means $57.5 million needs to be moved from stocks to bonds Thus, Claudius will need to sell $57.5 million of stock and buy $57.5 million of bonds The number of bond futures to buy equals: (7.7-0/6.4) (57,500,000/175,000) (1.04) = 411.125 contracts or 411 contracts 39 Question ID: 8759 Correct Answer: B If the yield on the bond portfolio and the yield on the bond futures contract change one-for-one, the yield beta would equal The number of bond futures to buy equals: (7.7 – 0/6.4)(57,500,000/175,000)(1.0) = 395.31 contracts or 395 contracts 40 Question ID: 8760 Correct Answer: A With the current allocation, Robust Chemicals has $345 million invested in stocks and $230 million invested in bonds To change the allocation to 30%-70%, $172.5 million needs to be removed from stocks and invested in bonds Thus, Claudius will need to sell $172.5 million of stock and buy $172.5 million of bonds The number of stock index futures to sell equals: (0 – 1.3/1.1)(172,500,000/266,500) = – 764.966 or 765 contracts FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 41 Question ID: 8761 Correct Answer: A With the current allocation, Robust Chemicals has $345 million invested in stocks and $230 million invested in bonds To change the allocation to 30%-70%, $172.5 million needs to be removed from stocks and invested in bonds Thus, Claudius will need to sell $172.5 million of stock and buy $172.5 million of bonds The number of bond futures to buy equals: (7.7 – 0/6.4) (172,500,000/175,000) (1.04) = 1,233.375 contracts 42 Question ID: 8762 Correct Answer: C To convert a stock position to a bond position, or, in other words, reduce the allocation to stock and increase the allocation to bonds, we would need to sell stock index futures to reduce the beta to zero and effectively convert the stock to cash, and then buy bond futures to increase the duration on the cash to the desired level 43 Question ID: 8731 Correct Answer: C Economic exposure refers to the risk that the products or services of a domestic company will become less competitive with those of comparable foreign companies because of exchange rate movements The loss of sales of a domestic exporter due to an appreciation of the domestic currency relative to the foreign currency is an example of economic risk 44 Question ID: 8732 Correct Answer: A Transaction exposure is the risk that exchange rate fluctuations will cause foreign currency receipts to decrease in value in domestic terms, and cause foreign currency payments to increase in value in domestic terms For example, the sales of a company’s foreign subsidiary have to be converted back into the domestic currency, and thus the sales in domestic terms depend on the exchange rate movements 45 Question ID: 8733 Correct Answer: B Exchange rate volatility affects a company’s accounting statements When a consolidated balance sheet of a multinational company is composed, the numbers from the balance sheets of foreign subsidiaries need to be converted into the domestic currency at the appropriate exchange rate Changing exchange rates introduce variation in account values, and this risk is called translation exposure 46 Question ID: 8734 Correct Answer: B The statement is incorrect Economic exposure can affect any type of company, even if it does not sell its goods or services in foreign markets For example, a strong U.S dollar will make U.S products more expensive to non-U.S residents and will lead to a reduction in sales by a U.S company (whether it exports or not), because non-U.S residents would purchase fewer U.S products Option C refers to transaction exposure FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 47 Question ID: 8735 Correct Answer: B The management of a single cash flow is generally done using forward contracts, since futures tend to be too standardized to meet the needs of most companies A series of foreign cash flows is usually managed using currency swaps 48 Question ID: 8736 Correct Answer: A Futures are primarily used by dealers to manage their foreign exchange portfolios Currency options can be used to manage the currency risk of single cash flows (as are used by portfolio managers in some cases) Since movements in exchange rates are difficult to predict, even for experts in the foreign exchange business, most businesses manage transaction exposure by locking in the exchange rate on future cash flows with the use of derivatives (instead of speculating future movements) 49 Question ID: 8724 Correct Answer: A Statement is correct In pre-investing, an investor effectively borrows against the cash he will receive in the future (he invests the cash before he actually receives it) Statement is incorrect An outright long position in futures is a fully leveraged position in the underlying as described by the following equation for pre-investing: Long underlying + Loan = Long futures 50 Question ID: 8725 Correct Answer: B To pre-invest $7 million in stocks, the approximate number of stock index futures is: 1.45-0/1.21[7,000,000/188,000] = 44.61 or 45 Therefore, Roberts should go long 45 stock index futures contracts 51 Question ID: 8726 Correct Answer: A To pre-invest $3 million in bonds, the approximate number of bond futures is: 5.5 – 0/5.7[3,000,000/139,000] = 20.825 or 21 contracts Therefore, Roberts should go long 21 bond futures contracts 52 Question ID: 8727 Correct Answer: A The difference in portfolio values when actually investing versus synthetically investing is due to the fact that stocks and bonds not always respond in the manner predicted by their betas and durations, and also, that the number of futures contracts is rounded off Option A is not a reason FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 53 Question ID: 8728 Correct Answer: B Pre-investing can result in significant losses This is because such a position is certainly a speculative one It involves taking a leveraged long position in the market The investor is speculating that the market will perform well enough to cover the cost of borrowing If this does not happen, losses can be significant due to leverage Also, the strategy has a specific horizon within which it has to earn profit (so Option B is incorrect), which increases its risk 54 Question ID: 8729 Correct Answer: A Option A is incorrect Pre-investing involves going long the underlying by borrowing against the cash to be received in the future The other two options are correct At the expiration of the futures contract, the investor closes the futures position and then invests the cash This transaction is equivalent to paying off this implicit loan 55 Question ID: 8699 Correct Answer: C To increase the beta of the portfolio, we have to buy futures The number of contracts to buy equals: [(1.5 – 0.7)/0.85][50,000,000/(1400×250)] = 134.4537 56 Question ID: 8700 Correct Answer: A To decrease the beta we need to sell futures The number of contracts to sell equals: [(0 – 0.7)/0.85] [50,000,000/(1400×250)] = – 117.647 57 Question ID: 8701 Correct Answer: C To achieve a beta of 1, we have to leverage the portfolio, which means buying futures contracts The number of contracts to buy equals: [(1 – 0.7)/0.85][50,000,000/(1400×250)] = 50.420 58 Question ID: 8702 Correct Answer: B The index increased by 2.5%, so the value of the equity position will increase by 1.75% and the value of the futures price will increase by 2.125% Profit from the equity position: 50,000,000 (1.0175) – 50,000,000 = $875,000 Profit from the futures contract: 50 ($350,000) (1.02125) – 50 ($350,000) = $371,875 FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 59 Question ID: 8703 Correct Answer: A The overall value of the portfolio equals the final value of the equity portfolio plus the futures position: 875,000 + 371,875 + 50,000,000 = $51,246,875 60 Question ID: 8704 Correct Answer: B The return on the portfolio equals: (875,000 + 371,875) / 50,000,000 = 2.4937% The effective beta on the portfolio equals: 0.024937/0.025 = 0.9975 61 Question ID: 8692 Correct Answer: A The statement is correct Stock market volatility is greater than bond market volatility; fortunately the stock market is more liquid than the bond market, especially when compared with long-term and corporate and municipal bonds 62 Question ID: 8693 Correct Answer: B Beta is a measure of systematic, nondiversifiable, or market risk When we measure the risk of a portfolio using beta, we assume that the portfolio contains no non-systematic or idiosyncratic risk 63 Question ID: 8694 Correct Answer: C Managing the risk of a small cap portfolio with futures on a large cap index will only manage the risk that large-cap stocks move with small-cap stocks If any divergence occurs, such as large cap stocks going up and small cap stocks going down (negative correlation), a transaction designed to increase risk could end up decreasing risk 64 Question ID: 8695 Correct Answer: A The statement is correct Since the value of the futures is zero at the start of each day (the contract is marked to market at the end of each day) the target beta when applied to the value of the futures will equal zero (because the value of the futures is zero) Therefore the market value of the portfolio will be the same as the market value of the stock, and the dollar beta of the combination of stock and futures will be the product of the target beta and the market value of the stock position FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 65 Question ID: 8696 Correct Answer: B Statement is incorrect To increase the beta of a portfolio, the target beta will exceed the portfolio beta, which means that we must buy futures Buying futures will add risk Statement is correct Dividends can interfere with how the transaction (carried out to manage risk) performs This is because index futures typically are based only on price indices; they not reflect the payment and reinvestment of dividends 66 Question ID: 8697 Correct Answer: A The statement is correct A portfolio manager may want to adjust the beta upward (downward) if he expects the market to move up (down) Also, the betas of equity portfolios change constantly by virtue of the market value of the portfolio changing Therefore, futures can be used to adjust the beta to its desired level 67 Question ID: 8676 Correct Answer: C Statement is incorrect Using futures contracts to increase and decrease the beta of a portfolio, would consequently increase and decrease the portfolio’s systematic risk, not total risk Statement is incorrect Even if there is no mispricing in the market (the futures prices move to a new level based on the cost-of-carry model), the effective beta might still not equal the target beta, because the number of futures bought or sold have to be rounded up to a whole number 68 Question ID: 8677 Correct Answer: B Since the dollar beta of the portfolio equals $25.125 million, the current beta equals: 25.125/37.5 = 0.67 Increasing it to $45 means a target beta of: 45/37.5= 1.2 Now that we have all the data necessary, the number of futures contracts needed equals: [(1.2-0.67/1.35)][37,500,000/300,000] = 49.074 (the positive sign means we buy contracts) 69 Question ID: 8678 Correct Answer: C If the market increases by 3.5%, the stock portfolio will increase by 2.345% and the futures contract will increase by 4.725% The rate of return on the stock portfolio is 2.345% The rate of return on the futures position is: 49(300,000) (1.04725) – 49 (300,000) = $694,575; return = 694,575/37,500,000 = 0.018522= 1.8522% Total return = 1.8522+2.345= 4.1972% FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 70 Question ID: 8679 Correct Answer: A We have to solve for x in the following equation: [(x – 0.67/1.35)][37,500,000/300,000] = – 60 X = 0.022 71 Question ID: 8680 Correct Answer: A Since the dollar beta is greater, and everything else remains the same, the current beta of the portfolio is greater Increasing beta with a higher value, than one with a lower value will require lesser number of contracts (higher current beta, lower numerator) holding everything else constant 72 Question ID: 8681 Correct Answer: A The statement is correct The futures contract will hedge only the risk associated with the relationship between the portfolio and the index on which the futures contract is based Therefore, it will manage only the risk that the portfolio moves with the index Any divergence in the relationship can make a transaction used to adjust risk, inappropriate 73 Question ID: 8660 Correct Answer: B We have to find x in the following equation to determine the amount originally invested: X(1.04)0.25/50(1890) = 1602.94 X = €149,999,821 74 Question ID: 8661 Correct Answer: C To round up, Forman would buy 1603 contracts This would translate into an amount equal to: 1603(50)(1890)/(1.04)0.25= € 150,005,435.5 75 Question ID: 8662 Correct Answer: A The number of units of stock effectively purchased is: 1603(50)/(1.0275)0.25= 79,608.25 76 Question ID: 8663 Correct Answer: B The number of units of stock received will equal: 79,608.25 (1.0275)0.25 = 80,150 or 1603 (50) = 80,150 The amount paid will equal: 1603 (50) (1890) = €151,483,500 Or €150,005,435 (1.04)0.25 = €151,483,499.5 (the slight difference is due to rounding) FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 77 Question ID: 8664 Correct Answer: C Not all synthetic replication strategies fail to capture the effect of dividends Those based on price indices fail to so because such indices capture only the index performance without dividends The values of some stock indices, however, called total return indices, include reinvested dividends If a futures contract on a total return index is used, then the strategy would capture the dividends 78 Question ID: 8665 Correct Answer: C Even if the futures contract expires later than the desired date, the strategy can still be successful if the futures contract is correctly priced when the strategy is completed This emphasizes the importance of understanding the pricing of futures contracts 79 Question ID: 8650 Correct Answer: C The current beta of the portfolio equals the covariance between the market and the portfolio, divided by the variance of the market: 0.04235/0.0484 = 0.875 The beta of the futures contract equals: 505,375/388750 = 1.3 The target beta is 1.4 Using this information, we can solve for the number of contracts: [(1.4 – 0.875)/1.3][20,000,000/388,750] = 20.7766 contracts 80 Question ID: 8651 Correct Answer: A The higher the covariance between the portfolio and the index, holding everything else constant, the greater will be the current beta of the portfolio Increasing a beta that is high, compared to one that is low, would require lesser number of contracts 81 Question ID: 8652 Correct Answer: A The dollar beta of the combined portfolio will equal the target beta multiplied by the value of the stock position (since the value of the futures at the start of each day is zero due to being marked to market): 1.4×20,000,000 = $28 million 82 Question ID: 8653 Correct Answer: B If the market increases by 2.5%, the futures position would increase by 3.25% The gain on the stock portfolio would equal: 20,460,000 – 20,000,000 = $460,000 Since we are long futures, the gain on the futures contract would equal: 21(388,750)(1.0325) – 21(388,750) = $265,321.875 FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com The overall return of the position equals: 265,321.875+460,000/20,000,000 = 0.036266 83 Question ID: 8654 Correct Answer: C The overall return of the position equals: 265,321.875+460,000/20,000,000 = 0.036266 The effective beta equals: 0.036266/0.025 = 1.4506 The difference: 1.4506 – 1.4 = 0.05064 84 Question ID: 8655 Correct Answer: B If the effective beta is 1.78, then the return on the overall portfolio will be: x/0.025 = 1.78 x= 0445 85 Question ID: 8643 Correct Answer: A The equity allocation is worth 0.4675(200) = $93.5 million Since the dollar beta of the portfolio equals $112.2, the portfolio’s beta equals 112.2/93.5 = 1.2 The dollar beta of the futures contract equals $170,625; the beta will equal $170,625/$131,250* =1.3 *1750 x 75 = 131,250 Using these values, the number of contracts needed equals: [(0.8 – 1.2)/1.3][93,500,000/131,250] = – 219.194 contracts 86 Question ID: 8644 Correct Answer: C If the market decreases by 6.75%, the stock portfolio would decrease by 8.1% and the futures position would decrease by 8.775% The loss on the stock portfolio would equal: 93,500,000(0.919) – 93,500,000 = – $7,573,500 Since we are short futures, the gain on the futures contract would equal: 219(131,250) – 219(131,250)(0.91225) = $2,522,264 The overall value of the position equals: 93,500,000 + (–7,573,500) + 2,522,264 = $88,448,764 FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 87 Question ID: 8645 Correct Answer: B The return on the portfolio will equal: – $7,573,500+ $2,522,264/$93,500,000 = – 0.054024 The effective beta will equal: – 0.054024/– 0.0675 = 0.800354 88 Question ID: 8646 Correct Answer: B If the market increases by 4.35%, the stock portfolio would increase by 5.22% and the futures position would increase by 5.655% The gain on the stock portfolio would equal: 93,500,000(1.0522) – 93,500,000 = $4,880,700 Since we are short futures, the loss on the futures contract would equal: 235(131,250) – 235(131,250)(1.05655) = – $1,744,214.06 The overall value of the position equals: 93,500,000 + (–1, 744,214.06) + 4,880,700 = $96,636,485.94 89 Question ID: 8647 Correct Answer: A With 235 contracts sold, the target beta would equal: [(x – 1.2)/1.3][93,500,000/131,250]= – 235 x= 0.771156 Since 235 contracts exactly meet the objective, the target beta is 0.771156, and the effective beta would be the same The rate of return on the portfolio will equal: –1, 744,214.06 + 4,880,700/93,500,000 = 0.033545 The effective beta equals: 0.033545/0.0435 = 0.771156 90 Question ID: 8648 Correct Answer: B If the market increases by 3.33%, the stock portfolio would increase by 3.996% and the futures position would increase by 4.329% The gain on the stock portfolio would equal: 93,500,000(1.03996) – 93,500,000 = $3,736,260 Return = 0.03996 The return on the futures position is – 0.0167 The overall return of the position equals: – 0.0167+0.03996 = 0.02326 FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com The effective beta equals= 0.02326/0.0333 = 0.69849 91 Question ID: 8633 Correct Answer: A Since the portfolio is as risky as the average stock in the market, its beta is To double the portfolio’s risk, its beta must be increased to The number of contracts needed to this will equal: [(2-1)/1.5][35,000,000/87,500] = 266.6667 92 Question ID: 8634 Correct Answer: A To completely hedge the portfolio against market risk, its beta should equal To decrease the portfolio’s beta to equal 0, the number of contracts to sell will equal: [(0-1)/1.5][35,000,000/87,500] = -266.6667 This number equals the number necessary to decrease the portfolio beta to 93 Question ID: 8635 Correct Answer: A We have to find ‘x’ in the following equation: [(x–1)/1.5][35,000,000/87,500] = 100 [(x–1)/1.5] = 0.25 x= 1.375 94 Question ID: 8636 Correct Answer: B The stock portfolio’s beta is and the futures contract has a beta of 1.5 If the market decreases by 4.3% then the stock portfolio would decrease by 4.3% and the futures contract would decrease by 6.45% The loss on the stock portfolio would be: 35,000,000 (0.957) – 35,000,000 = – $1,505,000 The loss on the futures contract would equal: 267(87,500)(0.9355) – 267(87,500) = – $1,506,881.25 Rate of return on stock portfolio: – 1505000/35,000,000 = – 0.043 Rate of return on futures position: – 1,506,881.25/35,000,000 = – 0.043054 95 Question ID: 8637 Correct Answer: A The rate of return on the overall portfolio equals: [–1,505,000+ (–1,506,881.25)]/35,000,000 = –0.086054 The effective beta equals: –0.086054/–0.043 = 2.00125 FinQuiz.com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz.com 96 Question ID: 8638 Correct Answer: C Since the beta of the portfolio has been decreased, it will be less reactive to changes in the market returns An increase in the market as a whole will decrease the combined portfolio’s return (stock + futures) compared to the previous high beta portfolio 97 Question ID: 8626 Correct Answer: C [(1.7–1.1)/1.3][(40,000,000/(2000×50)] = 184.615 98 Question ID: 8627 Correct Answer: A [(0 –1.1)/1.3][(40,000,000/(2000×50)] = –338.461 99 Question ID: 8628 Correct Answer: B If the market increases by 5%, the portfolio would increase by 5.5% and the futures position would increase by 6.5% The profit on the stock portfolio and futures position would equal: Stock portfolio: 40,000,000(1.055) – 40,000,000= $2,200,000 Futures position: 185(100,000)(1.065) – 185(100,000) = $1,202,500 The combined portfolio’s return would equal: 2,200,000+1,202,500/40,000,000 = 0.085063 The effective beta equals: 0.085063/0.05 = 1.70125 100 Question ID: 8629 Correct Answer: A Due to the rounding up of futures contracts, the effective beta might not equal the target beta, because the number of contracts bought or sold may not equal the actual number needed to adjust the beta However, this discrepancy is usually small 101 Question ID: 8630 Correct Answer: C To reduce exposure by 50% we need to decrease the beta to half of its current value The number of contracts to sell would equal: [(0.325 – 0.65)/0.82][55,000,000/355,000] = –61.405 102 Question ID: 8631 Correct Answer: C The greater the beta of the futures contract, the lesser the number of contracts needed, all else constant FinQuiz.com © 2018- All rights reserved ... 4,880,700/ 93, 500,000 = 0. 033 545 The effective beta equals: 0. 033 545/0.0 435 = 0.771156 90 Question ID: 8648 Correct Answer: B If the market increases by 3. 33% , the stock portfolio would increase by 3. 996%... 0.0167+0. 039 96 = 0.0 232 6 FinQuiz. com © 2018- All rights reserved Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz. com The effective beta equals= 0.0 232 6/0. 033 3 = 0.69849.. .Reading 28 Risk Management Applications of Forward and Futures Strategies FinQuiz. com FinQuiz Level III 2018 – Item- sets Solution Reading 28: Risk Management Applications
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