Practice: Swaps, Forwards, and Futures Strategies
Q.
A European bond portfolio manager wants to increase the modified duration of his €30 million portfolio from 3 to 5. She would most likely enter a receive-fixed interest rate swap that has principal notional of €20 million and:
A.a modified duration of 2.
B.a modified duration of 3.
C.a modified duration of 4.
Solution
B is correct. The portfolio manager’s goal is to use the receive-fixed, pay-floating swap such that the €30 million of bonds, with modified duration of 3, and the €20 million swap will combine to make up a portfolio with a market value of €30 million and modified duration of 5. This relationship can be expressed as follows:€30,000,000(3) + (NS × MDURS) = €30,000,000(5).
Given the swap’s notional (NS) of €20,000,000, its required modified duration can be obtained as:MDURS = [(5 – 3)€30,000,000]/€20,000,000 = 3.
ModD portfolio * MV p + Ns * ModD swap = ModD target * MV p
Q.
A US bond portfolio manager wants to hedge a long position in a 10-year Treasury bond against a potential rise in domestic interest rates. He would most likely:
A.sell fixed-income (bond) futures.
B.enter a receive-fixed 10-year interest rate swap.
C.sell a strip of 90-day Eurodollar futures contracts.
long bond, meaning get interest rate; to hedge, meaning gives interest rate; so not B sell fixed futures, think futures price drop, interest rate rise, so good.
Sell Eurodollar futures doesn't matter here to interest rate
Solution
A is correct. The portfolio manager would most likely use a longer-dated fixed-income (bond) futures contract to hedge his interest rate risk exposure. The choice of the hedging instrument, in fact, will depend on the maturity of the bond being hedged. Interest rate futures, like 90-day Eurodollar futures, have a limited number of maturities and can be used to hedge short-term bonds. The mark-to-market value of a receive-fixed 10-year interest rate swap will become negative if interest rates rises, and thus the swap cannot be used as a hedge in this case.
Q.
The CIO of a Canadian private equity company wants to lock in the interest on a three-month “bridge” loan his firm will take out in six months to complete an LBO deal. He sells the relevant interest rate futures contracts at 98.05. In six-months’ time, he initiates the loan at 2.70% and unwinds the hedge at 97.30. The effective interest rate on the loan is:
A.0.75%.
B.1.95%.
C.2.70%.
Solution
B is correct. The CIO sells the relevant interest rate future contracts at 98.05. After six months, the CIO initiates the bridge loan at a rate of 2.70%, but he unwinds the hedge at the lower futures price of 97.30, thus gaining 75 bps (= 98.05 – 97.30). The effective interest rate on the loan is 1.95% (= 2.70% – 0.75%).
Q.
A US institutional investor in search of yield decides to buy Italian government bonds for her portfolio but wants to hedge against the risk of exchange rate fluctuations. She enters a cross-currency basis swap, with the same payment dates as the bonds, where at inception she delivers US dollars in exchange for euros for use in purchasing the Italian bonds. The notional principals on the swap are most likely exchanged:
A.at inception only.
B.at maturity only.
C.both at inception and at maturity.
Solution
C is correct. In a cross-currency basis swap, the goals of the transaction are to achieve favorable funding and exchange rates and to swap the foreign currency amounts back to the currency of choice—in this case, the US dollar—at maturity. There is one exchange rate specified in the swap that is used to determine the notional principals in the two currencies, exchanged at inception and at maturity.
Q.
Continuing from the previous question, assume demand for US dollars is strong relative to demand for euros, so there is a positive basis for “lending” US dollars. By hedging the position in Italian government bonds with the currency basis swap, the US investor will most likely increase the periodic net interest payments received from the swap counterparty in:
QuestionQ.
Continuing from the previous question, assume demand for US dollars is strong relative to demand for euros, so there is a positive basis for “lending” US dollars. By hedging the position in Italian government bonds with the currency basis swap, the US investor will most likely increase the periodic net interest payments received from the swap counterparty in:
A.euros only.
B.US dollars only.
C.both euros and US dollars.
Solution
B is correct. By hedging the position in Italian government bonds with the cross-currency basis swap, the US investor will most likely increase the periodic net interest she receives in US dollars. The reason is that the periodic net interest payments made by the swap counterparty to the investor will include the positive basis resulting from the relatively strong demand for US dollars versus euros.
Q.
An equity portfolio manager is invested 100% in US large-cap stocks, but he wants to reduce the current allocation by 20%, to 80%, and allocate 20% to US small caps. He decides not to sell the stocks because of the high transaction costs. Rather, he will use S&P 500 Index futures and Russell 2000 Index futures for achieving the desired exposure in, respectively, US large caps and small caps. To achieve the new allocation, he will for an equivalent of 20% of the portfolio value:
A.purchase Russell 2000 futures only.
B.purchase Russell 2000 futures and sell S&P 500 futures.
C.sell Russell 2000 futures and purchase S&P 500 futures.
Solution
B is correct. To reduce the current allocation by 20%, to 80%, in US large-cap stocks, the portfolio manager will sell S&P 500 futures. At the same time, to allocate this 20% to US small caps, he will purchase Russell 2000 futures for the same notional amount.
Q.
A volatility trader observes that the VIX term structure is upward sloping. In particular, the VIX is at 13.50, the front-month futures contract trades at 14.10, and the second-month futures contract trades at 15.40. Assuming the shape of the VIX term structure will remain constant over the next three-month period, the trader decides to implement a trade that would profit from the VIX carry roll down. She will most likely purchase the:
A.VIX and sell the VIX second-month futures.
B.VIX and sell the VIX front-month futures.
C.VIX front-month futures and sell the VIX second-month futures.
Solution
C is correct. VIX futures converge to the spot VIX as expiration approaches, and the two must be equal at expiration. When the VIX futures curve is in contango and assuming volatility remains stable, the VIX futures will get “pulled” closer to the spot VIX, and they will decrease in price as they approach expiration. Traders calculate the difference between the front-month VIX futures price and the VIX as 0.60, and the spread between the front-month and the second-month futures is 1.30. Assuming that the spread declines linearly until settlement, the trader would realize roll-down gains as the spread decreases from 1.30 to 0.60 as the front-month futures approaches its expiration. At expiration, VIX futures are equal to the VIX, and the spread with the old second-month (and now the front-month) futures contract will be 0.60. Finally, since one cannot directly invest in the VIX, trades focusing on the VIX term structure must be implemented using either VIX futures or VIX options, so Answers A and B are not feasible.
Q.
A volatility trader observes that the VIX term structure is upward sloping. In particular, the VIX is at 13.50, the front-month futures contract trades at 14.10, and the second-month futures contract trades at 15.40. Assuming the shape of the VIX term structure will remain constant over the next three-month period, the trader decides to implement a trade that would profit from the VIX carry roll down. She will most likely purchase the:
A.VIX and sell the VIX second-month futures.
B.VIX and sell the VIX front-month futures.
C.VIX front-month futures and sell the VIX second-month futures.
Solution
C is correct. VIX futures converge to the spot VIX as expiration approaches, and the two must be equal at expiration. When the VIX futures curve is in contango and assuming volatility remains stable, the VIX futures will get “pulled” closer to the spot VIX, and they will decrease in price as they approach expiration. Traders calculate the difference between the front-month VIX futures price and the VIX as 0.60, and the spread between the front-month and the second-month futures is 1.30. Assuming that the spread declines linearly until settlement, the trader would realize roll-down gains as the spread decreases from 1.30 to 0.60 as the front-month futures approaches its expiration. At expiration, VIX futures are equal to the VIX, and the spread with the old second-month (and now the front-month) futures contract will be 0.60. Finally, since one cannot directly invest in the VIX, trades focusing on the VIX term structure must be implemented using either VIX futures or VIX options, so Answers A and B are not feasible.
Q.
The CEO of a corporation owns 100 million shares of his company’s stock, which is currently priced at €30 a share. Given the huge exposure of his personal wealth to this one company, he has decided to sell 10% of his position and invest the funds in a floating interest rate instrument. A derivatives dealer suggests that he do so using an equity swap.
Explain how to structure such a swap.
Your Answer:instead of selling, just give 10% of equity to swap to another counterparty and receive floating interest rate
Solution
The swap is structured such that the executive pays the return on 10 million shares of the company’s stock, which is 10% of his holdings, and he receives the return based on a floating interest rate, such as the market reference rate, on a notional principal of €300 million (= €30/share × 10 million shares).
Q.
A $30 million investment account of a bank trust fund is allocated one-third to stocks and two-thirds to bonds. The portfolio manager wants to change the overall allocation to 50% stock and 50% bonds and the allocation within the stock fund from 70% domestic stock and 30% foreign stock to 60% domestic and 40% foreign. The bond allocation will remain entirely invested in domestic corporate issues.
Explain how swaps can be used to implement this adjustment. The market reference rate is assumed to be flat for all swaps, and you do not need to refer to specific stock and bond indexes.
Your Answer:before1/3 stocks, 2/3 bonds stock domestic foreign ratio change to 50/50;stock 7:3 to 7:4 can open equity swap, take equity, give interests open bond swap open domestic equity swap & foreign equity swap
Current:
total 30m, equity 10m (foreign 3, domestic 7), bond 20m
Result equity 15 (local 9, foreign 6), bond 15
equity swap - 5
foreign swap - 3, domestic 2 (5-2)
Solution
Currently the allocation is $10 million in stocks and $20 million in bonds. Within the stock category, the current allocation is $7 million domestic and $3 million foreign. The desired allocation is $15 million in stocks and $15 million in bonds. Thus, the allocation must change by moving $5 million into stocks and out of bonds. The desired stock allocation is $9 million domestic and $6 million foreign. The desired bond allocation is $15 million, all domestic corporate.
To make the changes with swaps, the manager must enter into swaps against the market reference rate, which is assumed to be flat for all swaps in this example. Using the swaps, the bank trust fund portfolio manager needs to
(1) receive the returns on $2 million based on a domestic equity index and on $3 million based on a foreign equity index and
(2) pay the return on $5 million based on a domestic corporate bond index.
The market reference rate outflows from the swaps in (1) and the inflows from the swap in (2) will cancel out through summation.
Q.
Sarah Ko, a private wealth adviser in Singapore, is developing a short-term interest rate forecast for her private wealth clients who have holdings in the US fixed-income markets. Ko needs to understand current market expectations for possible upcoming central bank (i.e., US Federal Reserve Board) rate actions. The current price for the fed funds futures contract expiring after the next FOMC meeting is 97.175. The current federal funds rate target range is set between 2.50% and 2.75%.
Explain how Ko can use this information to understand potential movements in the current federal funds rate. Calculate the probabilty of an increase of 25 bps in the target range.
Your Answer:The current federal funds rate target range is 2.50% to 2.75%. The implied rate of 2.825% is above the current upper bound of the target range (2.75%), suggesting that the market expects an increase in the federal funds rate.
Solution
First, Ko knows that the FFE rate implied by the futures contract price of 97.175 is 2.825% (= 100 – 97.175). This is the rate that market participants expect to be the average federal funds rate for that month.
Second, Ko should determine the probability of a rate change. She knows the 2.825% FFE rate implied by the futures signals a fairly high chance that the FOMC will increase rates by 25 bps from its current target range of 2.50%–2.75% to the new target range of 2.75%–3.00%. She calculates the probability of a rate hike as follows- 2.825%−2.625% / 2.875%−2.625%=0.80, or 80%
Ko can now incorporate this probability of a Fed rate hike into her forecast of short-term US interest rates.
Nisqually Uff is the portfolio manager for the Chehalis Fund (the Fund), which holds equities and bonds in its portfolio. Uff focuses on tactical portfolio strategies and uses derivatives to implement his strategies.
Uff has a positive short-term outlook for equities relative to bonds and decides to temporarily increase the beta of the portfolio’s equity allocation from 0.9 to 1.2. He will use three-month equity index futures contracts to adjust the beta. Exhibit 1 displays selected data for the Fund’s current equity allocation and the relevant futures contract.
Exhibit 1:
Selected Data for the Fund’s Current Equity Allocation and Futures Contract
Current portfolio beta
0.9
Target portfolio beta
1.2
Index futures contract value
€45,000
Beta of futures contract
1.0
QuestionQ.
Determine the appropriate number of equity index futures contracts that Uff should use to achieve the target portfolio beta. Identify whether the equity index futures contracts should be bought or sold.
Your Answer:(1.2 - 0.9) / 1.0 * 168300000 / 45000 = 0.3 * 3740 = 1122 buy 1122 futures contract
Solution
Because the number of futures contracts (Nf) is positive, Uff should buy 1,122 equity index futures contracts.
Q.
One month later, Uff expects interest rates to rise. He decides to reduce the modified duration of the bond allocation of the Fund’s portfolio without selling any of its existing bonds. To do so, Uff adds a negative-duration position by entering into an interest rate swap in which he pays the fixed rate and receives the floating rate. Exhibit 2 presents selected data for the Fund’s bond allocation and the relevant swap contract.
Exhibit 2:
Selected Data for the Fund’s Bond Allocation and Swap Contract
Current portfolio average modified duration
7.8000
Target portfolio modified duration
5.0000
Swap modified duration for fixed-rate payer
–2.4848
Determine the required notional principal for the interest rate swap in order to achieve the target modified duration for the portfolio.
Your Answer:(5 - 7.8) * 90100000 / -2,4848 101,529,298
Solution
Therefore, Uff should enter into the selected three-year par pay-fixed, receive-floating interest rate swap with a notional principal of approximately €101,529,298.
Q.
Six months later, Uff has since closed out both the equity index futures contract position and the interest rate swap position. In response to market movements, he now wants to implement a tactical rebalancing of the Fund’s portfolio. Exhibit 3 presents the current and target asset allocations for the Fund’s portfolio.
Exhibit 3:
Current and Target Asset Allocations for the Fund’s Portfolio
Equities
€201,384,000 (69.56%)
€188,181,500 (65.0%)
Bonds
€88,126,000 (30.44%)
€101,328,500 (35.0%)
Total
€289,510,000
€289,510,000
Uff decides to use equity index and bond futures contracts to rebalance the portfolio. Exhibit 4 shows selected data on the Fund’s portfolio and the relevant futures contracts.
Exhibit 4:
Selected Data on Fund’s Portfolio and Relevant Futures Contracts
Modified duration of the Fund’s bonds
4.59
Equity index futures contract value
€35,000
Beta of equity index futures contract
1.00
Basis point value of cheapest-to-deliver (CTD) bond
€91.26
Conversion factor (CF) for CTD bond
0.733194
Determine how many equity index and bond futures contracts Uff should use to rebalance the Fund’s portfolio to the target allocation. Identify whether the futures contracts should be bought or sold.
equity diff = 188181500 - 201384000 = 13202500
bond diff = 13202500
equity contracts = 13202500 / 35000 = 377.2 ~= 378 contract sell
bond contract = 377.2 / 0.733194 / 91.26 = 5.63 ~= 6 contract buy (wrong)
For bond,
MD futures = BPV (CTD) / (CF * 100) = 91.26 / 73.3194 = 1.2446910368
N = changes * MD (bonds) / (MD futures * Futures contract value)
= 13202500 * 4.59 / (1.244691 * 35000) = 1,391.03887746322 = 1392
Your Answer:equity diff = 188181500 - 201384000 = 13202500 bond diff = 13202500 equity contracts = 13202500 / 35000 = 377.2 ~= 378 contract sell bond contract = 377.2 / 0.733194 / 91.26 = 5.63 ~= 6 contract buy (wrong) For bond, MD futures = BPV (CTD) / (CF * 100) = 91.26 / 73.3194 = 1.2446910368 N = changes * MD (bonds) / (MD futures * Futures contract value) = 13202500 * 4.59 / (1.244691 * 35000) = 1,391.03887746322 = 1392
Solution
Uff needs to reduce the equity allocation by €13,202,500 (= €201,384,000 – €188,181,500).
... (Check later, got bug)
Canawacta Tioga is the CFO for Wyalusing Corporation, a multinational manufacturing company based in Canada. One year ago, Wyalusing issued fixed-rate coupon bonds in Canada. Tioga now expects Canadian interest rates to fall and remain low for three years. During this three-year period, Tioga wants to use a par interest rate swap to effectively convert the fixed-rate bond coupon payments into floating-rate payments.
QuestionQ.
Explain how to construct the swap that Tioga wants to use with regard to the swap:
i. tenor
ii. cash flows
iii. notional value
iv. settlement dates
Your Answer:
1) tenor - 3 yers 2) cash flow - receive fixed, pay float 3) notional value = the value of issued bonds 4) settlement dates = after 3 years (wrong? - semiannual seimilar with the bond coupon payment date)
Solution
Explain how to construct the swap that Tioga wants to use with regard to the swap:
The swap tenor will be three years, consistent with the length of time for which Tioga expects interest rates to remain low.
Tioga will establish an interest rate swap in which Wyalusing will make payments based on a floating reference rate and will receive payments based on a fixed rate.
The source of the reference rate and the value of the fixed rate will be set at the time of the swap’s inception.
The net effect for Wyalusing of the combination of making fixed payments on its coupon bond, receiving fixed payments on the swap, and making floating payments on the swap is to convert the fixed obligations of its bond coupon payments into floating-rate-based obligations.
This scenario will allow Wyalusing to benefit if Tioga’s expectation of low interest rates is realized.
The notional value of the swap should be set such that the fixed payments that Wyalusing receives will equal the fixed coupon payments that Wyalusing must make on its fixed-rate bond obligations.
Swap settlement dates should be set on the same days as the fixed-rate bond’s coupon payment dates.
Q.
Wyalusing will soon be building a new manufacturing plant in the United States. To fund construction of the plant, the company will borrow in its home currency of CAD because of favorable interest rates. Tioga plans to use a cross-currency basis swap so that Wyalusing will borrow in CAD but make interest payments in USD.
Describe how the swap will function, from the perspective of Wyalusing, in terms of the:
cash flows at inception.
periodic cash flows.
cash flows at maturity.
cash flow exchange at inception
periodic cash flows is the interest rates differential
cash flow exchange agn at maturity
Solution
Describe how the swap will function, from the perspective of Wyalusing, in terms of the:
At inception, Wyalusing will pay the notional principal of CAD and will receive an amount of USD according to the USD/CAD exchange rate, agreed to at inception.
At each swap payment date, Wyalusing will receive interest in CAD and will pay interest in USD.
Both payments are based on floating reference rates for their respective currencies.
The CAD rate will also include a basis rate that is quoted separately.
On each settlement date,
Wyalusing will receive an amount of CAD based on the CAD floating rate minus the basis rate applied to the swap notional value,
and it will pay an amount of USD based on the USD floating rate and the USD/CAD exchange rate that was set at inception.
At maturity, Wyalusing will receive the notional principal of CAD and will pay an amount of USD according to the USD/CAD exchange rate that was set at inception, applied to the CAD notional principal. The cash flows at maturity are the inverses of the cash flows at inception.
Southern Sloth Sanctuary (Sanctuary) is a charitable organization that cares for orphaned and injured sloths from the rain forest in the country of Lushland. The organization is supported by both domestic and international contributions. The Sanctuary’s CFO typically invests any funds that are not immediately needed for short-term operational expenses into a domestic index fund that tracks the Lushland 100 stock index, which is denominated in Lushland dollars (LLD).
The Sanctuary just received a large contribution from a local benefactor in the amount of LLD1,000,000. These funds are not needed for short-term operational expenses. The CFO intends to equitize this excess cash position using futures contracts to replicate the return on the Lushland 100 stock index. Exhibit 1 shows selected data for the Lushland 100 Index futures contract.
Exhibit 1:
Selected Data for Lushland 100 Index Futures Contract
Contract multiplier
LLD 200
Contract beta
1.00
QuestionQ.
Determine the appropriate number of futures contracts that the CFO should buy to equitize the excess cash position.
1m / 200 = 500 contracts
Your Answer:1m / 200 = 5000 (wrong, need divide 1247 further)
Solution
Therefore, the CFO should buy four Lushland 100 Index futures contracts to equitize the excess cash position.
Q.
A Japanese benefactor recently donated a plot of land in Japan to the Sanctuary. Ownership of the land has been transferred to the Sanctuary, which has a binding contract to sell the property for JPY500,000,000. The property sale will be completed in 30 days. The Sanctuary’s CFO wants to hedge the risk of JPY depreciation using futures contracts. The CFO assumes a hedge ratio of 1.
Describe a strategy to implement the CFO’s desired hedge.
Your Answer:500m. 30 days JPY buy cross currency swap LLD/JPY for 30 days
Solution
The Sanctuary’s CFO can use currency futures contracts to lock in the current LLD/JPY exchange rate. The CFO can hedge the Sanctuary’s exchange rate risk by selling JPY futures contracts with the closest expiry to the expected future JPY inflow.
When the futures contracts expire, the Sanctuary will receive (pay) any depreciation (appreciation) in JPY relative to LLD (when compared with the original LLD/JPY futures contract price).
The CFO can determine the number of contracts needed by dividing the property’s sale price of JPY500,000,000 by the JPY futures contract value. Because the hedge ratio is assumed to equal 1, the changes in futures and spot prices will be equal during the life of the futures contract, and so the hedge will be fully effective.
Global Mega (Global) is a diversified financial services firm. Yasuko Regan, senior trader, and Marcus Whitacre, junior trader, both work on the firm’s derivatives desk. Regan and Whitacre assist in structuring and implementing trades for clients in the financial services industry that have limited derivatives expertise. Regan and Whitacre are currently assisting one of Global’s clients—Monatize, an asset management firm—with two of its portfolios: Portfolio A and Portfolio B.
Portfolio A is a bond portfolio composed solely of US Treasury bonds. Monatize has asked Global to quote the number of Treasury futures contracts necessary to fully hedge this bond portfolio against a rise in interest rates. Exhibit 1 presents selected data on Portfolio A, the relevant Treasury futures contract, and the cheapest-to-deliver (CTD) bond.
Exhibit 1:
Selected Data on Portfolio A, the Treasury Futures Contract, and the CTD Bond
Portfolio A
Futures Contract and CTD Bond
Market value
$143,234,000
Price
145.20
Modified duration
9.10
Modified duration
8.75
Basis point value
$130,342.94
Basis point value
$127.05
Conversion factor
0.72382
Contract size
$100,000
Q.
Based on Exhibit 1, the number of Treasury futures contracts Whitacre should sell to fully hedge Portfolio A is closest to:
9.1/9.75 * 143234000 / 145.20
Solution
B is correct. The basis point value of Portfolio A (BPVP) is $130,342.94, and the basis point value of the cheapest-to-deliver bond (BPVCTD) is $127.05 with a conversion factor of 0.72382. The basis point value hedge ratio (BPVHR), in the special case of complete hedging, provides the number of futures contracts needed, calculated as follows:BPVHR=−BPVPBPVCTD×CF=−$130,342.94$127.05×0.72382=−742.58𝐵𝑃𝑉𝐻𝑅=−𝐵𝑃𝑉𝑃𝐵𝑃𝑉𝐶𝑇𝐷×𝐶𝐹=−$130,342.94$127.05×0.72382=−742.58
Therefore, Whitacre should sell 743 Treasury bond futures to fully hedge Portfolio A.
A is incorrect because it incorrectly uses the price of the cheapest-to-deliver bond (rather than its basis point value, BPVCTD) in the denominator of the BPVHR calculation:BPVHR=−BPVPCTDBondPrice×CF=−$130,342.94$145.20×0.72382=−649.76𝐵𝑃𝑉𝐻𝑅=−𝐵𝑃𝑉𝑃𝐶𝑇𝐷 𝐵𝑜𝑛𝑑 𝑃𝑟𝑖𝑐𝑒×𝐶𝐹=−$130,342.94$145.20×0.72382=−649.76
C is incorrect because it does not include the conversion factor for the cheapest-to-deliver bond when calculating BPVHR:BPVHR=−BPVPBPVCTD=−$130,342.94$127.05=−1,025.92
Q.
Based on Exhibit 1, the number of Treasury futures contracts Whitacre should sell to achieve Monetize’s objective with respect to Portfolio A is closest to:
After an internal discussion, Monatize elects to not hedge Portfolio A but rather decrease the portfolio’s modified duration to 3.10. Regan asks Whitacre to compute the number of Treasury futures contracts to sell in order to achieve this objective. Regan tells Whitacre to assume the yield curve is flat.
Portfolio B is a $100,000,000 equity portfolio indexed to the S&P 500 Index, with excess cash of $4,800,000. Monatize is required to equitize its excess cash to be fully invested, and the firm directs Global to purchase futures contracts to do so. To replicate the return of Portfolio B’s target index, Whitacre purchases S&P 500 futures contracts, at a price of 3,300 per contract, that have a multiplier of $250 per index point and a beta of 1.00.
Monatize’s CFO and Regan discuss two potential hedging strategies for Portfolio B to protect against a hypothetical extreme sell-off in equities. Regan first suggests that Monatize could enter into a total return equity swap, whereby Monatize agrees to pay the return on the S&P 500 and receive a fixed interest rate at pre-specified dates in exchange for a fee.
The number of S&P 500 futures contracts that Whitacre should buy to equitize Portfolio B’s excess cash position is closest to:
4.8m / (3300 * 250) = 5.8 ~= 6
Monatize’s CFO and Regan discuss two potential hedging strategies for Portfolio B to protect against a hypothetical extreme sell-off in equities. Regan first suggests that Monatize could enter into a total return equity swap, whereby Monatize agrees to pay the return on the S&P 500 and receive a fixed interest rate at pre-specified dates in exchange for a fee.
Q.
The derivative product first suggested by Regan as a potential hedge strategy for Portfolio B:
Solution
C is correct. The first hedging strategy suggested by Regan is entering into a total return equity swap in exchange for a fee.
Equity swaps, which are relatively illiquid contracts and are OTC derivative instruments in which each party bears counterparty risk, do not confer voting rights to the counterparty receiving the performance of the underlying.
Under the terms of the total return equity swap, at pre-specified dates, the counterparties will net the index total return (increase/decrease plus dividends) against the fixed interest payment.
If the index total return exceeds the fixed interest payment, Monatize will pay the counterparty the net payment. If the index total return is less than the fixed interest payment, then Monatize will receive the net payment from the counterparty.
A is incorrect because equity swaps are relatively illiquid contracts.
B is incorrect because equity swaps are OTC derivative instruments, and each counterparty in the equity swap bears the risk exposure to the other counterparty. For this reason, equity swaps are usually collateralized in order to reduce credit risk exposure.
Portfolio B is a $100,000,000 equity portfolio indexed to the S&P 500 Index, with excess cash of $4,800,000. Monatize is required to equitize its excess cash to be fully invested, and the firm directs Global to purchase futures contracts to do so.
Regan next suggests that Monatize could alternatively hedge Portfolio B using variance swaps. Monatize’s CFO asks Regan to calculate what the gain would be in five months on a purchase of $1,000,000 vega notional of a one-year variance swap on the S&P 500 at a strike of 15% (quoted as annual volatility), assuming the following:
Over the next five months, the S&P 500 experiences a realized volatility of 20%;
At the end of the five-month period, the fair strike of a new seven-month variance swap on the S&P 500 will be 18%; and
The annual interest rate is 1.50%.
Q.
Based on the CFO’s set of assumptions, the gain on the purchase of the variance swap on the S&P 500 in five months would be closest to:
Regan and Whitacre discuss the use of federal funds futures contracts to infer probabilities of future monetary policy changes. Whitacre makes the following three statements about fed funds futures contracts:
Statement 1
Typical end-of-month activity by large financial and banking institutions often induces “dips” in the effective fed funds rate.
Statement 2
Especially for the longer-term horizon, the probabilities inferred from the pricing of fed funds futures usually have strong predictive power.
Statement 3
To derive probabilities of Federal Reserve interest rate actions, market participants look at the pricing of fed funds futures, which are tied to the Federal Reserve’s target fed funds rate.
Q.
Which of Whitacre’s three statements about fed funds futures is correct?
Solution
A is correct. Typical end-of-month (EOM) activity by large financial and banking institutions often induces “dips” in the effective federal funds (FFE) rate that create bias issues when using the rate as the basis for probability calculations of potential Federal Open Market Committee rate moves. If EOM activity increases the price for the relevant fed funds contract, the FFE rate would decline. A decline in the FFE rate would decrease the probability of a change in the fed funds rate. To overcome this EOM bias, data providers have implemented various methods of “smoothing” EOM dips.
Statement 2 is incorrect because the probabilities inferred from the pricing of fed funds futures usually do not have strong predictive power, especially for the longer-term horizon.
Statement 3 is incorrect because, to derive probabilities of Fed interest rate actions, market participants look at the pricing of fed funds futures, which are tied to the FFE rate—that is, the rate used in actual transactions between depository institutions, not the Fed’s target fed funds rate.
B is incorrect because the probabilities inferred from the pricing of fed funds futures usually do not have strong predictive power, especially for the longer-term horizon.
C is incorrect because, to derive probabilities of Fed interest rate actions, market participants look at the pricing of fed funds futures, which are tied to the FFE rate—that is, the rate that depository institutions actually use for lending to each other, not the Fed’s target federal funds rate. The underlying assumption is that the implied futures market rates are predicting the value of the monthly average FFE rate.
Whitacre then proposes to Regan that Global explore opportunities in bond futures arbitrage. Whitacre makes the following two statements:
Statement 1
If the basis is positive, a trader would make a profit by “selling the basis.”
Statement 2
If the basis is negative, a trader would make a profit by selling the bond and buying the futures.
QuestionQ.
Which of Whitacre’s two statements regarding bond futures arbitrage is correct?
Solution
A is correct. If the basis is positive, a trader would make a profit by “selling the basis”—that is, selling the bond and buying the futures. In contrast, when the basis is negative, the trader would make a profit by “buying the basis,” in which the trader would purchase the bond and short the futures.
B is incorrect because Statement 5 is incorrect. If the basis is negative, a trader would make a profit by “buying the basis”—that is, purchasing (not selling) the bond and shorting (not buying) the futures.
C is incorrect because Statement 5 is incorrect. If the basis is negative, a trader would make a profit by “buying the basis”—that is, purchasing (not selling) the bond and shorting (not buying) the futures.
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