Question Paper Financial Risk Management - I (231) : April 2006 Section A : Basic Concepts (30 Marks)
1.
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This section consists of questions with serial number 1 - 30. Answer all questions.
• • • •
Each question carries one mark. Maximum time for answering Section A is 30 Minutes.
< Answer >
A reverse time spread option involves (a) Purchase and sell a call with the same time to maturity but different strike prices (b) Sell a long period of time call and write another call with shorter time period to maturity, both having same strike prices (c) Purchase a long period of time call and write another call with shorter time period maturity, both having same strike prices (d) Purchase a call expiring in a short period of time and write another call with longer time period to maturity, both having same strike prices (e) Sell a short period of time call and write another call with longer time period to maturity, both having same strike prices.
2.
An Indian exporter is exporting goods to his Japanese clients. The payment in Yen will be made on July 01, 2006. The current spot rate is Rs.38.39/100¥. The exporter hedges the receivables by selling July Yen futures. If Rupee appreciates in the spot market and basis remains unchanged till the payment is received, which of the following condition must be true? (a) (b) (c) (d) (e)
3.
Gain in the spot market is more than the gain in the futures market Gain in the futures market is more than the gain in the spot market Loss in the spot market is more than the gain in the futures market Loss in the futures market is equal to the gain in the spot market Loss in the spot market is equal to the gain in the futures market.
If speculators believe interest rates will _______, they would consider ______ a T-bill futures contract today. (a) Increase; selling (c) Decrease, selling (e) Increase; purchasing a call option on.
4.
6.
(b) 6.49%
(c) 7.89%
(d) 9.81%
< Answer >
(e) 10.58%.
Which of the following statements is not true regarding Swap markets? (a)
< Answer >
(b) Risk handling costs (d) Social costs
XYZ Corporation sells for Rs.35 per share; the SEP option series has exactly six months until expiration. At the moment, the SEP 35 call sells for Rs.3, and the SEP 35 put sells for Rs.1.40. What annual interest rate is implied in the option prices? (a) 5.62%
< Answer >
(b) Increase; buying (d) Decrease; selling a call option on
Costs involved in increased precautions and limits on the risky activities in order to reduce the chances of recurrence of risk is known as (a) Loss financing costs (c) Loss control costs (e) Residual uncertainty costs.
5.
< Answer >
The swap deal cannot be terminated without the agreement of parties involved in the transaction
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(b) (c) (d) (e) 7.
The swap market is an exchange controlled market Swaps are not easily tradable Comparative advantage theorem used in swap market is illusionary It is difficult to identify a Counterparty to take opposite side of the transaction once a party has approached the swap dealer with his requirements.
Which of the following kinds of swap is useful to those users of fund that need funds immediately but do not consider the current rates of interest very attractive and feel that the rates may fall in future? (a) Extendible Swap (c) Putable Swap (e) Deferred Rate Swap.
8.
< Answer >
The financial instrument is not pre-payable. The fair value of swap is positive at origin. The principal amount and the notional amount of the swap matches. All variable rates of interest payments or receipts on the instrument beyond the swap term are designated as hedged.
(a) Both (I) and (II) above (c) Both (III) and (IV) above (e) (II), (III) and (IV) above. 9.
(b) Roller-Coaster Swap (d) Forward Swap
The cash flow hedge between an interest-bearing financial instrument and an interest rate swap is said to be effective if, I. II. III. IV.
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(b) Both (I) and (III) above (d) (I), (II) and (III) above
Which of the following is not a derivative financial instrument according to FASB–133? (a) Interest only obligations (c) Note issuance facility (e) Interest rate indexes.
< Answer >
(b) Letters of credit (d) Forward rate agreements
10. Mr. Shyam has written APR 06 call option with strike price of Rs.45, priced at Rs.5 and purchased JUN 06 call option with strike price of Rs.45, priced at Rs.6. Under which of the following situation the investor will make profit on both the calls?
< Answer >
(a) Stock price remains below Rs.50 until April, 06 and then starts increasing (b) Stock price remains above Rs.45 until April, 06 and then starts decreasing (c) Stock price remains below Rs.45 until April, 06 and then starts increasing (d) Stock prices remains above Rs.44 until June, 06 and then starts decreasing (e) Stock prices remains below Rs.51 until June, 06 and then starts increasing. 11.
Which of the following statements is not true?
< Answer >
(a)
Delta of call will be most sensitive to change in the stock prices, when the underlying stock prices approaches the exercise price (b) For a put option that is near-the-money gamma decreases as expiration approaches (c) Rho will be lower for deep-out-of-the-money call option (d) Vega will be highest for a near-the-money put option (e) Normally, theta is always less then zero. 12. If a risk less portfolio can be constructed by combining 500 long call options on TTK Ltd. with a short position of 100 shares of TTK Ltd. Which of the following statements is true? (a) (b) (c) (d) (e)
< Answer >
The option’s hedge ratio is 0.20 The option’s lambda is 0.5213 The option’s delta is 5.00 The option’s theta is 5.00 The option’s gamma is 0.25.
13. If a day’s temperature is 720 F, then Heating Degree Days (HDD) index is
< Answer >
(a) – 7
(b) –5
(c) 0
(d) 5
(e) 7. < Answer >
14. The contract size for futures contracts on weather derivatives in CME is (a) (b) (c) (d) (e)
$1 million $100 times the CME Degree Day Index $ 200 times the CME Degree Day Index 100 future contracts 20 future contracts.
15. In a single period binomial option-pricing model, the underlying stock is currently selling for Rs.80 and will rise or fall by 15% over the next period. A call option with an exercise price of Rs.95 would have a premium of (a) Zero
(b) Rs.3
(c) Rs.5
(d) Rs.8
< Answer >
(e) Rs.15. < Answer >
16. Which of the following statements is not true with respect to Value At Risk (VAR)? (a)
Prices may not respond in a linear fashion to change in the market variables, resulting in erroneous measurement by VAR (b) Intra-day positions are considered in VAR (c) It is based on the past data (d) It focuses on single arbitrary point (e) Firms with market risk measurement systems which apply portfolio diversification theory can lower their risk with the use of VAR. < Answer >
17. Which of the following is an implied warranty in Marine Insurance? (a) (b) (c) (d) (e)
The ship will sail on a particular day The ship is neutral and will remain so during the voyage The ship is seaworthy on a particular day The ship is not overloaded or badly loaded The ship will proceed to the destination without any deviation.
18. The road transit insurance policy ceases _____ days after arrival of lorry at the destination named in the policy. (a) 3
(b) 7
(c) 10
(d) 14
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(e) 30. < Answer >
19. Options in inter-bank market are quoted in terms of (a) Explicit volatility (b) Historical volatility (c) Future volatility (d) Implied volatility (e) Market volatility. 20. Which of the following statements does not explain the fact that mispricing or arbitrage opportunities in stock index persist for a short period of time? (a) (b) (c) (d) (e)
< Answer >
Large orders are not guaranteed and any price or prices can change quickly There can be a potential tracking error There is a dividend risk There is transaction costs involved in the trading It is easy to duplicate the underlying stocks comprising the index.
21. The discount yield on a 90-day T-bill futures of remaining maturity 60 days and size $1,000,000, traded on IMM at $992,417 is (a) 4.45%
(b) 4.50%
(c) 4.55%
(d) 4.60%
(e) 4.65%.
22. An investor has taken long position in Microsys stock for Rs.6,00,000. The beta of the stock is 1.5. To hedge its position against the market movement, what would be the appropriate action? (a) Short on index futures for Rs.4,00,000 (b) Short on index futures for Rs.6,00,000
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(c) Long on index futures for Rs.6,00,000 (d) Short on index futures for Rs.9,00,000 (e) Long on index futures for Rs.4,00,000. 23. If the previous fixed day payment date and forthcoming fixed day payment date are 01-08-2005 and 0103-2006, then fixed day count fraction as per 30/360 convention will be (a) 208/360
(b) 209/360
(c) 210/360
(d) 212/360
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(e) 214/360. < Answer >
24. Which of the following statements is/are not true regarding portfolio insurance? I. II.
It is a dynamic hedging strategy which uses stock index future. It implies buying and selling securities periodically in order to maintain limit of the portfolio value. III. The working of portfolio insurance is similar to buying an index call option. IV. Portfolio insurance can be done by using listed index options. (a) Only (II) above (c) Both (I) and (IV) above (e) (I), (II) and (IV) above.
(b) Only (III) above (d) Both (II) and (III) above
25. An order to execute a transaction at the best available price, when the market reaches a price specified by the customer is called (a) Market Order (c) Market on close Order
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(b) Market-if-touched Order (d) Stop-loss Order (e) Not held Order.
26. Which of the following is/are not true with respect to US T-bill futures and Eurodollar futures quoted in US exchanges?
< Answer >
I. II.
Unlike Eurodollar futures, T-bill futures are cash settled. Eurodollar future contract is a future contract on an interest rate whereas T-bill future contract is a future contract on price of a T-bill. III. Minimum tick size for both the contracts is 10 basis points each. (a) Only (I) above (c) Only (III) above (e) Both (I) and (III) above.
(b) Only (II) above (d) Both (II) and (III) above
27. An investor buys a strap using July call of 140 with a premium of Rs.5 and July put of 140 with a premium of Rs.6. What will be the break-even points for the strategy? (a) Rs.124 and Rs.148 (c) Rs.134 and Rs.150 (e) Rs.123 and Rs.147.5.
(b) Rs.136 and Rs.145 (d) Rs.131.5 and Rs.157
28. A US exporter is exporting goods to his Australian client. On September 14, 2005, the exporter got confirmation from the Australian importer that the payment of AUS$6,00,000 will be made on November 1, 2005. The exporter uses futures market to cover the exchange risk. On September 14, 2005, the spot exchange rate is 0.7462$/AUS$ and December futures contract rate is 0.7497$/AUS$. If, on November 1, 2005 the spot exchange rate is 0.7446$/AUS$ and December futures rate is 0.7481$/AUS$, what will be US$ cash flow to the exporter? (a) $4,45,800
(b) $4,46,760
(c) $4,47,720
(d) $4,47,960
< Answer >
(e) $4,48,860.
29. A savings and loan association has long-term fixed-rate mortgages financed by short-term funds. It hedges by selling Treasury bond futures. If interest rates decline, and many mortgages are prepaid, (a) (b) (c) (d) (e)
< Answer >
The gain on the futures contracts offsets the loss on the mortgages The gain on the mortgages offsets the loss on the futures contracts The gain on the futures contracts more than offsets any unfavorable effects on mortgages A loss on the futures contracts more than offsets the favorable effect on the mortgage portfolio The loss on the mortgages offset by the gain on the futures contracts.
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30. Assume that a futures contract on Treasury bonds with a face value of $100,000 is purchased at 93-00. If the same contract is later sold at 94-18, what is the gain, ignoring transactions costs? (a) $1,180,000
(b) $118
(c) $11,800
END OF SECTION A
(d) $15,625
(e) $1,562.50.
< Answer >
Section B : Problems (50 Marks)
1.
• •
This section consists of questions with serial number 1 – 5.
• • • •
Answer all questions. Marks are indicated against each question.
• • • •
Detailed workings should form part of your answer. Do not spend more than 110 - 120 minutes on Section B.
On September 16, a London bank needs to issue $10 million for 180-day Eurodollar time deposits. The current rate on such deposits is 8.75%. The bank is considering the alternative of selling a Eurodollar futures contract and issuing a 90-day time deposit and rollover it. The following data is available for 90-day time deposit and Eurodollar future contract:
Date
Interest rate on Price of December 90-day time Eurodollar future deposit (%) contract on IMM ($)
September 16
8.25
91.37
December 16
7.96
92.04
Based on the above information you are
required to suggest the alternative that should be adopted by the bank. (10 marks) < Answer > 2.
Following information is available with respect to the share price and call options on the Call Option Strike Price
Variable
X = Rs.90
X = Rs.100
X = Rs.110
Price
Rs.16.33
Rs.10.30
Rs.6.06
Rs.100
Delta
0.5862
0.8025
0.4365
1
Gamma
0.0138
0.0181
0.0187
0
Vega
0.2046
0.2684
0.2766
0
shares of Anant Ltd.:
Stock
Mr. Manish, a trader, has sold 200 call options with the strike price of Rs.100 and each option is on 100 shares of stock. Using the above-mentioned information you are required to show what position Mr. Manish will take on calls with exercise prices Rs.90 and Rs.110 and on the stock to create a portfolio that is delta-gamma-vega neutral? (10 marks) < Answer >
3.
Ziemenns GmbH, a German firm, is in need of $200 million for its foreign investment requirements for 5 years. A US firm, Sandvik Inc., needs an amount of €160 million for its European operations for 5 years. Following information is available for borrowings in different markets for both the parties: Firm
US market ($)
Euro market (€)
Ziemenns GmbH
8%
6%
Sandvik Inc.
7%
8%
Both the firms swap their borrowings to meet their requirements. After a year interest rates have dropped uniformly by 75
bp in US market and by 50 bp in Euro market. At the end of the first year, you are required to find out i. Dollar value of the swap to Sandvik ii. Euro value of the swap to Ziemenns Spot rate at the time of entering in to swap was $ 1.25/€ and spot rate after a year is $ 1.22/€. (10 marks) < Answer >
4.
A European company has decided to take a 5-year floating rate loan of $250 million to finance its acquisition. The loan is indexed to 6 months LIBOR with a spread of 50 basis points. The company has identified the following caps and floors quoted by a European bank: Term
Cap Floor 5-years 5-years 5-years 5-years Underlying interest rate 6-m LIBOR 6-m LIBOR 6-m LIBOR 6-m LIBOR Strike rate 3.0% 3.5% 3.0% 3.5% Premium 2.0% 1.5% 1.2% 2.0% Face value $250million $250 million $250million $250 million You are required to state how the company can hedge its interest rate exposure by using an interest rate Collar strategy. Also calculate the effective cost of the loan showing all the relevant cash flows if the 6 months LIBOR at the 10 reset dates turn out to be: 3.60%, 4.00%, 3.55%, 3.40%, 2.90%, 2.80%, 2.65%, 2.75%, 3.00% and 3.25%. (Use a discount rate of 4% to amortize the premium) (10 marks) < Answer > 5.
Excel Export Inc. (EEI) of US has a one-month forward currency contract to sell AUS$ 310 million at the forward rate of AUS$1.58/US$. The spot rate is AUS$1.55/US$. The 1-month interest rate for US$ is 5% p.a. and the 1month interest rates in AUS$ is 7.30% p.a. The annual volatility of the AUS$/US $ exchange rate is 6.04%. The yield volatility of 1-month remaining maturity zero coupon AUS$ bond is 1.32% p.a. and the yield volatility of 1month remaining maturity zero coupon dollar bond is 1.88% p.a. The correlation of returns between two bonds is 0.55. You are required to compute 1-day VAR for the forward contract at 99% confidence level using variance/covariance approach. (Assume 250 days in a year). (10 marks) < Answer >
END OF SECTION B
Section C : Applied Theory (20 Marks)
6.
(a)
• • • •
This section consists of questions with serial number 6 - 7. Answer all questions.
• • • •
Marks are indicated against each question. Do not spend more than 25 -30 minutes on section C.
How interest rate swaps can be terminated? Explain.
(b) Are swaps similar to forward contracts? Discuss. (5 + 5 = 10 marks) < Answer > 7.
The liquidity of stock index futures has made them the market of choice especially for institutional investors. Explain various features of index futures contracts and mechanism of pricing of index futures contracts. (10 marks) < Answer > END OF SECTION C END OF QUESTION PAPER
Suggested Answers Financial Risk Management - I (231) : April 2006 Section A : Basic Concepts 1.
Answer : (d) Reason: The reverse time spread options involves the purchase of a call expiring in a short period of time and writing another call with longer expiry period until maturity both having same strike prices, as the investor believes that the price of the underlying stock will decline before expiration of the written call. The purchase of the short-term call is to protect the investor in case the stock moves in the opposite direction in the short-term.
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2.
Answer : (e) Reason: As Rupee is appreciating there will be a loss in the spot market. But given the basis is unchanged the loss in the spot market arising from the appreciation of dollar, is offset by the profit in the futures market. Hence (e) is the answer.
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3.
Answer : (a) Reason: If the speculators believe the interest rates will increase, they should sell a Tbill futures contract today. This is because rise in interest rates will reduce the prices of T-bills futures which enables the speculators to make profit by selling T-bill futures today at higher
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price and buying it back in future when prices decrease because of rise in interest rates. Hence, option (a) is the correct answer. 4.
Answer : (c) Reason: Loss control costs are the increased precautions and limits on the risky activities in order to reduce the chances of recurrence of risks. Hence, option (c) is the correct answer.
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5.
Answer : (d) Reason: C – P = S – K/(1+R)T 3 – 1.40 = 35 – 35/(1 + R)0.5 1.60 – 35 = -35/(1 + R)0.5 33.40 = 35/(1 + R)0.5 1.0479 = (1 + R)0.5 R = 9.81%
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6.
Answer : (b) Reason: Swap market is not exchange controlled and it is an over-the –counter market. Hence, statement (b) is false. All other statements are correct. Hence, option (b) is the correct answer.
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7.
Answer : (e) Reason: A deferred rate swap allows the fixed rate payer to enter in to the swap at any time up to a specified future date. It is particulary attractive to those users of funds that needs funds immediately but do not consider the current rates of interest very attractive and feel that the rates may fall in future.
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8.
Answer : (b) Reason: The assumption of no inefectiveness in a cash flow hedge between an interest bearing financial instruments and an interst rate swap canbe assumed if the fair value of swap is zero at origin and all variable rate of interst payments or receipts on the instrument during the swap term are designated as hedged and
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none beyond that term. Hence, statement (II) and (IV) are false. Hence, option (b) is the correct answer. Answer : (a) Reason: According to FASB-133, DFI exclude mortgage-backed securities, interest only obligations, principal only obligations, indexed debt and contracts that require exchange for a nonfinancial commodity.
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10 Answer : (c) . Reason: A long time spread using calls will allow investor to purchase a call with several months until expiration and write a call only several weeks until expiration. Both the calls having same exercise price. Investors using this strategy will make profits on both the calls if the stock remains below the exercise price until the written call expires, allowing investor to capture 100% of the premium written. After the expiration of of the written call, investor would hope for the underlying stock to make a bullish move making the purchased call even more valuable. Hence, option (c) is the correct answer.
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11. Answer : (b) Reason: Delta of call will be most sensitive to change in the stock prices, when the underlying stock prices approaches the exercise price. Hence, statement (a) is true. For a put option that is near-themoney gamma increases as expiration approaches. Hence, statement (b) is false. Rho will be lower for deep-out-ofthe-money call option. Hence, statement (c) is true. Vega will be highest for a near-the-money put option. For deep-inthe-money and deep-out-of-the-money, the Vega will always be low and tends to be zero. Hence, statement (d) is true. Theta of a call and a put can be greater or less than zero but in normal
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9.
circumstances, it is always less than zero. Hence, statement (e) is true. Hence, option (b) is the correct answer. 12 Answer : (a) . Reason: The given portfolio is a riskless portfolio. The value of the long calls = Value of the underlying assets. No. of long calls x Unit pirce = No. of underlying assets x Unit price. 500 x Unit price = 100 x Unit price Unit price of long call Unitprice of undelying
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100 500
= Hedge ratio or Delta = 0.20. 13 Answer : (c) . Reason: HDD = ( 0 or 65 – Actual temperature) HDD cannot be negative. Here, actual temperature is more than 65. Hence, HDD will be zero.
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14 Answer : (b) . Reason: The contract size for future contracton weather derivatives in CME is $100 times the CME Degree Day Index. Hence, option (b) is the correct answer.
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15 Answer : (a) . Reason: The price after one year can be either Rs. 92 or Rs. 68. The call option with exercise price of Rs. 95 will be out-ofthe money, so the value of call will be zero according to binomial option pricing model.
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16 Answer : (b) . Reason: Intra-day positions are not considered in VAR, which usualy takes only the closing position into consideration. Hence, statement (b) is false. Prices may not respond in a linear fashion to changes in the market variables, resulting in erroneous measurement by VAR. Hence, statement (a) is true. Calculationof VAR is based on past
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data. Hence, statement (c) is true. It focuses on single arbitrary point. Hence, statement (d) is true. Firms with market risk measurement systems which apply portfolio diversification theory can lower their risk with the use of VAR. Hence, statement (e) is true. Hence, option (b) is correct answer. 17 Answer : (d) . Reason: In marine insurance, an express warranty might be generally included as: • • that the ship is seaworthy on a paricular day; • • the ship will sail on a particular day; • • the ship will proceed to the destination without any deviations; • • the ship isneutral and will remain so during the voyage.
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Hence, option (d) is the correct answer.
18 Answer : (b) . Reason: The road transit insurance policy commences with the loading of each package into the vehicle and ceases 7 days after arrival of the lorry at the destination named in the policy. Hence, option (b) is the correct answer.
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19 Answer : (d) . Reason: Options in inter-bank market is quoted in terms of implied volatiliy. Hence, option (d) is the correct answer.
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20 Answer : (e) . Reason: The stock index arbitrage or program trading is not simple, since mispricing does not persist for a long period of time, the arbitrageur who wants to be ahead of the pack in exploiting the opportunity must have extensive resources including elaborate telecommunications networks to quickly spot and act upon such opportunities.
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Moreover it may not be easy to duplicate the underlying stocks comprising the index, which is being imitated. This happens mainly because the said stocks may not be easily available or may not have takers while selling the same. Hence (e) is the answer. 21 Answer : .
(c)
r 60 × 1 − Reason: 992,417 = 1,000,000 100 360
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Or, r = 4.55%. 22 Answer : (d) . Reason: In order to hedge his position, the investor simply sells the index futures contract. By doing so, he is said to have hedged away his index exposure. In order to determine the number of futures he has to sell, the beta of the stock should be known. Here beta =1.5 the size of the position that the investor needs to hedge his index exposure is 1.5 x 6,00,000 = Rs 9,00,000. Once he does this his position will be as follows: Long stock : 6,00,000 Short index futures : 9,00,000
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23 Answer : (a) . Reason: In 30/360 convention each month will be taken as 30days, including previous fixed date and excluding forthcoming fixed date. However, there are certain exception to this rule. If the forthcoming fixed date is 1st of any month and the previous month does not have 30 days then actual days in that month will be taken for calculating fixed day count fraction. Therefore, in this case, the fixed day count fraction will be (30 x 6 + 28) i.e. 208/360.
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24 Answer : (b) . Reason: Portfolio insurance is an investment
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strategy where various financial instrumnets like equities and debts and derivatives are combined in such a way that degradation of portfolio value is protected. The working of portfolio insurance is akin to buying an index put option. Hence, statement (III) is false. Hence, option (b) is the correct answer. 25 Answer : (b) . Reason: A Market Order is the one which has to be executed immediately at the best possible rate after order reaches the trading floor. A Market–If–Touched order is an order to execute a transaction at the best available price when the market reaches a price specified by the customer. Market On Close is the one, under which an instruction is given to the broker to execute the order during the official period for the contract. A Stop-Loss-Order is an order to buy or sell when the price reaches a specified level. A Not Held Order is a type of discretionary order, where the broker is given a discretion to wait to buy if he feels that the prices will go further down or wait to sell if he feels that the prices may go further up.
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26 Answer : (e) . Reason: Unlike T-bill futures, Eurodollar futures are cash settled. Hence, statement (I) is false. Eurodollar future contract is a future contract on an interest rate whereas T-bill future contract is a future contract on price of a T-bill or a discount rate. Hence, statement (II) is true. Minimum tick size for both the contracts is 1 basis points each. Hence, statement (III) is false. Hence, option (e) is the correct answer.
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27 Answer :
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(a)
Reason: A long strap involves buying two call options and one put option with the same exercise price and expiration date. Therefore, initial outflow = (10 + 6) = Rs.16. The break-even point will be Rs.124 and Rs.148. When the stock price is Rs.124, net cash flow will be Initial inflow + Gain from put + Gain from calls = (-16) + 16 + 0 = 0 When stock price is Rs.148, net cash flow wil be, Initial inflow +Gain from put +Gain from calls = (-16) + 0+ 2(8) = (-16) + 0 + 16 = 0. Hence, option (a) is the correct answer.
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28 Answer : (c) . Reason: If AUS$ depreciates there will be a loss to the exporter. To cover this risk the exporter can sell six AUS$ future contract, as the size of each contract is AUS$ 1,00,000, at the prevailing rate in the market. He will make profit on future market = (0.7497 – 0.7481) x 6 x 1,00,000 = $960. He will sell AUS$ 6,00,000 in spot market at the exchange rate of AUS$0.7466/$. Therefore on November 1, 2005 the exporter will have cash flow of (6,00,000 x 0.7446) = $4,46,760+ $960 = $4,47,720.
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29 Answer : (d) . Reason: Due to decline in the interest rates prices of T-bond futures will increase. As the association is short on T-bond futures contracts, it will make losses in futures market due to decline in interest rates. Benefit of decline in interest rates on mortgages will be less than loss in Tbond futures market as many mortgages will be pre-paid.
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.
Hence, option (d) is the correct answer. 30 Answer : (e) . Reason: The T-bond futures contract is purchased at 93-00 and sold at 94-18. In US T-bond futures contract 1% change is equal to 32 bp. Therefore total change is (32 + 18) = 50 b.p. For US T-bond future contract tick size is $31.25. Hence, gain on the futures contract = (50 x 31.25) = $1562.50 Hence, option (e) is the correct answer.
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Section B : Problems 1.
Alternative-I: Issue of 180-day time deposit: If the bank issues 180-day time deposit it will have to pay back 180 10, 000, 000 1 0.0875 360
= $10,437,500 on maturity i.e. on March 16. Thus, the effective annual borrowing rate for the company will be
365 10437500 180 1 100 10000000
= 9.07% p.a. Alternative-II: Issue of 90-day time deposit & rollover it and selling Eurodollar future contract. On September 16: - The bank will issue 90-day time deposits of $10,000,000 at the rate of 8.25% p.a. and sell Eurodollar futures contract. On Sep. 16 December Eurodollar futures contract is selling at 91.37. As the standard size of Eurodollar futures contract is $1,000,000, the bank needs to sell 10 futures contracts. On December 16: - The 90-day time deposit issued on Sep. 16 will mature and thus, bank will have to pay 90 10, 000, 000 1 0.0825 360 = $10,206,250
Eurodollar futures contract is quoting at 92.04. Loss on futures market = (92.04 – 91.37) x 100 x $25 x 10 = $16,750 Therefore, total funds required on December 16 = $10,206,250 + $16,750 = $10,223,000 In order to raise these funds bank will issue new 90-day time deposit for $10,223,000 at the interest rate of 7.96%. Therefore, on March 16, bank will pay off the new time deposit owning 90 10, 223, 000 1 0.0796 360 = $10426437.7 ≈ $10,426,438.
Thus, the effective annual borrowing rate for the company will be
365 10426438 180 1 100 10000000
= 8.84% p.a. Thus, bank should raise the funds by selling Eurodollar future contract and issuing 90-day time deposit and rollover it as the effective cost of fund for this alternative less by 23 basis point than alternative-I.
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2.
As the trader wants to create a portfolio that is delta-gamma-vega neutral, he must simultaneously solve the number of shares to purchase, the position in the Rs.110 calls and the position in the Rs.90 calls. Suppose the number of shares required to be purchased to create delta-gamma-vega neutral portfolio is S, the position required in Rs.110 calls is K110, and position required in Rs.90 calls is K90. That is, he must choose the position in these securities so that the portfolio’s delta, gamma and vega all equal to zero. To solve this problem we begin by noting that the gamma and the vega of the stock are zero and that the position in the option with the strike price of Rs.100 is given i.e. K100 = -200. Thus, to be gamma neutral implies (-200 x 100 x 0.0181) + (S x 0) + (K110 x 100 x 0.0187) + (K90 x 100 x 0.0138) = 0 -362 + 0 + 1.87K110 + 1.38K90 = 0 -362 + 1.87K110 + 1.38K90 = 0 ----------------------------(I) And, to be vega neutral implies (-200 x 100 x 0.2684) + (S x 0) + (K110 x 100 x 0.2766) + (K90 x 100 x 0.2046) = 0 -5368 + 0 + 27.66K110 + 20.46K90 = 0 -5368 + 27.66K110 + 20.46K90 = 0 ----------------------(II) Solving these two equations simultaneously, we get K110 = -13.37 ≈ -13 and K90 = 280.44 ≈ 280 for any values of S. Then, solving for the number of shares is accomplished by noting that the delta of share is 1 and that the trader also wants to hold a delta-neutral portfolio. Accordingly, (-200 x 100 x 0.8025) + (S x 1) + (-13 x 100 x 0.4365) + (280 x 100 x 0.5862) = 0 -16050 + S – 567.45 + 16413.6 = 0 -203.85 + S = 0 S = 203.85 ≈ 204 Therefore, in order to make the portfolio delta-gamma-vega neutral the trader should buy 204 shares of Anant Ltd. and simultaneously sell 13 call options with strike price of Rs.110 and buy 280 call option with strike price of Rs.90. < TOP >
3. Firm Ziemenns Sandvik
US market ($) Euro market (€) 8% 6% 7% 8%
Requirement:
Euro 160 million US$ 200 million The German firm Ziemenns can borrow in € at 6% and the US firm Sandvik Inc. borrow in $ at 7%. Then they swap their borrowings to meet their requirements. Euro borrowings was worth € 160 million when the swap was contracted, with a Euro interest rate of 6%. The value of the borrowings after a year when the interest rate falls to 5.5%.
V€ = (160 x 0.06) x PVIFA (5.5%,4) + 160 x PVIF (5.5%, 4) = €162.804 Similarly the dollar borrowings was worth $ 200 million when swap was contracted, with a dollar interest rate of 7%. The value of the borrowings after a year when interest rate falls to 6.25%. V$ = (200 x 0.07) x PVIFA (6.25%,4) + 200 x PVIF (6.25%, 4) = $205.168 Dollar value of the swap to Sandvick = $ 205.168 - [€ 162.804 x $1.22 /€] = $6.547 1 Euro value of swap to Ziemenns = €162.804 - $205.168 x 1.22 = - €5.366 < TOP >
4.
The company should go for interest rate collar i.e. it should buy the cap at a higher strike rate and sell the floor at the lower strike rate. Therefore, the company should buy cap at the strike rate of 3.5% and sell floor at the strike rate of 3.0%. Net premium outflow = (1.5% – 1.2%) of $ 250 million = $ 750,000 $750, 000 750, 000 = PVIFA(2.00%,10) 8.9826
Amortization of premium = = $ 83,495 Time LIBOR semester (%) 0 1
Cash flow on loan
Amortization Cash flow of premium from Cap
250,000,000 – – 83,495 +125,000 5,125,000 2 4.00 – 5,625,000 – 83,495 +625,000 3 3.55 – 5,062,500 –83,495 +62,500 4 3.40 – 4,875,000 –83,495 – 5 2.90 – 4,250,000 –83,495 – 6 2.80 – 4,125,000 –83,495 _ 7 2.65 – 3,937,500 –83,495 _ 8 2.75 – 4,062,500 –83,495 _ 9 3.00 – 4,375,000 –83,495 _ 10 3.25 – 4,687,500 –83,495 _ – 250,000,000 Effective cost ‘r’ is given by the following equation: 250,000,000 = 5,083,495 PVIF (r, 1) + 5,083,495 PVIF (r, 2) + 5,083,495 PVIF (r, 3) + 4,958,495 PVIF (r, 4) + 4,458,495 PVIF (r, 5) + 4,458,495 PVIF (r, 6) + 4,458,495 PVIF (r, 7) + 4,458,495 PVIF (r, 8) 3.60
Cash flow from floor
Net cash flow
–
250,000,000 5,083,495
_ _ _ -125,000 –250,000 –437,500 –312,500 – –
5,083,495 5,083,495 4,958,495 4,458,495 4,458,495 4,458,495 4,458,495 4,458,495 254,770,995
+ 4,458,495 PVIF (r, 9) + 254,770,995 PVIF (r, 10) Therefore, r = 1.90% ∴ Annualized rate = 3.80% < TOP >
5.
EFI will sell AUS$310 million at a 1-month forward rate of AUS$1.58/$ to buy US$. At forward rate, AUS$310 million = $310/1.58 million = $196.20 million The forward position can be broken down into the following two positions:
i.
ii.
Going short on 1-month zero-coupon AUS$ bond at AUS$308.13 where maturity value is AUS$310 million.
310 = 1 + 0.073 12 , million
196.20 = 1 + 0.05 12 , where Going long on 1-month zero-coupon US$ bond at $ 195.39 million
maturity value is US$ 196.20 million. The value of this bond in AUS$ is AUS$302.85 million at spot market. For AUS$, yield volatility = 1.32% Duration = 0.083 year Yield = 7.30% 0.083 1.073 =
Modified duration = 0.0774 Delta yield = Yield × Yield volatility = 7.30 × 1.32 = 9.636% Price volatility
= Modified duration × Delta yield
= 0.0774 × 9.636 = 0.7458% 0.7458
Price volatility for 1-day = 250 = 0.0472% 1-day volatility of AUS$ bond = 308.13 × 0.000472 = AUS$0.1453 million For $, yield volatility = 1.88% Duration = 0.0833 year Yield = 5.0% Modified duration Delta yield =
0.0833 1.05 =
= 5.0 × 1.88
0.0794
= Price volatility
9.40% = 0.0794 × 9.40 = 0.7464% 0.7464
Price volatility for 1-day = 250 = 0.0472% 1-day volatility of $ bond = 195.39 × 0.000472 = $ 0.0922 million 1-day volatility of AUS$ bond in dollar term 1 0.0604 1 + 250 = AUS$0.1453 × 1.55 × = $0.0941 The standard deviation of portfolio value for 1-day
0.09412 + 0.09222 − 2 × 0.55 × 0.0941× 0.0922 =
1
2
= $0.0884 million 1-day VAR at 99% confidence level = 0.0884 × 2.33 = $ 0.2060 million. < TOP
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Section C: Applied Theory 6.
a.
b.
There are several ways to terminate a swap. A party can go back to the counterparty and ask for an offsetting swap. The parties effectively create the opposite swap. They then hold opposite positions to each other. They can keep the two swaps in place with each making their series of payments, but there will be credit risk. Alternatively, the parties can cancel the two swaps, with the party owing the greater amount making a cash payment of the net amount owed on the two swaps to the other party. If this method is used, the parties simply agree to accept whatever terms exist in the market at the time the opposite swap is put in place. Another means of canceling the swap is for one party to have already entered into either a forward contract or an option on a swap of the opposite position. This arrangement permits establishment of the terms of the offsetting swap before that swap is needed. Swaps are similar to forward contracts in that they involve the commitment to make a fixed payment and receive a floating payment at a future date. While a forward contract is a single payment, a swap is a series of payments. Thus, a swap is like a series of forward contracts. Both swaps and forward contracts require no up front payments, and both are subject to default risk. There are some differences, however, in that in a swap both sides of the first payment are known. Also, for a swap, all of the fixed payments are the same, whereas in a series of forward contracts, each contract would be priced separately and would have different fixed rates. < TOP >
7.
The first index futures contract was introduced in 1982 at the Kansas City Board of Trade and today, index futures are one of the most popular types of futures as far as trading is concerned. An index futures contract is basically an obligation to deliver at settlement, an amount equal to 'x' times the difference between the stock index value on the expiration date of the contract and the price at whi9h the contract was originally struck. The value of 'x', which is referred to 'as the multiple, is predetermined for each stock market index. For example, futures contracts on S&P 500 Stock Index use a multiple of 250 while the futures contracts on BSE Sensex use a multiple of 50. Stock index futures are based on complex cash instruments. The multiple enables us to calculate the monetary value of an index futures contract. Forz example, if the settlement price of the S&P 500 futures contract is 350, the value of the contract in monetary terms is 350 x 25 = $87,500. The salient features of the index futures contracts are as follows:
1.
The index futures contracts are cash settled; there is usually no d,elivery of the underlying stocks or stock certificates, as matching the physical stocks as per the index may be quite difficult and costlier than settling the contract by cash. 2. An investor can either buy or sell an index futures contract. When an investor goes long in the index futures contract, he will receive a cash settlement on the expiration date, if the closing price exceeds the contract price. On the other hand, if the closing price is less than the contract price, the investor will be required to pay the difference. 3. Since index futures contracts are listed and traded on futures exchanges, the investor can offset his position on any day prior to the expiration day. 4. The performance of all index futures contracts are guaranteed by the exchange clearing house. As in case of options exchanges, the clearing house becomes the counterparty to both the buyer and the seller. 5. The index future carries the margin requirements that are applicable to both the buyer and the seller. The purpose of maintaining margin money is to minimize the risk of default by either party. The payment of margin ensures that the risk is limited to the previous day's price movement on each outstanding position. Margin money is a kind of security deposit or insurance against a possible future loss of value. The margin can be maintained either in the form of risk-free short dated government securities or in the form of cash. Additional margin is imposed only when the exchange fears that the market has become too volatile and may result in some critical situation, like payment crisis. This is a protective measure available to the exchange to prevent any breakdown. Pricing-of Index Futures Contracts Unlike options, the valuation of index futures is easy to understand. To start with, let us consider an investor who wants to hold a portfolio, which is identical to the composition of a stock market index for a period of one year. During the course of the year, he will receive dividends and at the end of the year, the principal value would have changed in line with the change in the index. If we denote the current index value as, Io the expiration day index value as It and the dividends received as Dt the rupee return earned by the investor is given by the equation (It - Io) + Dt If the investor contemplated investment in an index futures contract as an alternative to
investing in the underlying portfolio, he will buy the index futures contract and invest all his money in risk-free treasury bills or short-dated government securities. If we denote the current price of the index futures contract as Fo, the expiration day price as Ft and the interest earned as Rf, the rupee return, earned by the investor is given by the equation (Ft - Fo) + Rf If the investor has to be indifferent between the two alternatives then the above equation will be (It - Io) + Dt = (Ft - Fo) + Rf Since Ft = It, i.e. the final settlement price of the index futures contract is set equal to the spot index value, the above equation can be simplified as Fo = 10 + (Rf - Dt) The above equation states that the current index futures price must be equal to the index value plus the difference between the risk-free interest" and dividends obtainable over the life of the contract. The difference between Rf and Dt is referred to as the 'cost-of-carry' and we can say that the futures contract must be priced to reflect the 'cost-of-carry'. The 'cost-of-carry' or the 'basis' is typically positive because the annualized risk-free rate of interest (about 10% in the Indian context) exceeds the annualized dividend yield (which is around 1% for the BSE National Index). But then this need not always be true. Depending upon the timing of the settlement date and the initiation of the position, the impact of cost-of-carry, i.e. difference between Rf and Dt can vary substantially. We can have a situation where the dividend yield exceeds the risk-free return and in that case, the theoretical price of the index futures can be below that of the index.
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