Question Paper Financial Risk Management-I (231)–January 2006 Section A : Basic Concepts (30 Marks)
• 1.
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.
The changes are included in current income The changes are included in current net income The changes are included in other comprehensive income The changes are included in comprehensive net income The changes are included in earnings.
Zydus Ltd. stock is priced at Rs.30 with a standard deviation of 30%. The risk-free rate is 5%. There are put and call options available at exercise prices of Rs.30 and a time to expiration of six months. The call is priced at Rs.2.89 and the put costs Rs.2.15. There are no dividends on the stock and the options are European. An investor constructed a covered call. What is the breakeven stock price at expiration? (a) Rs.27.11
3.
(e) Rs.35.66. < Answer >
< Answer >
The profit is greater at all stock prices The profit is greater only at low stock prices The profit is greater only at high stock prices The range of possible profits is greater Profit is lower at all stock prices. < Answer >
Early exercise imposes a risk to all but one of the following transactions. (b) A short put (d) An uncovered call
Which of the following participant of derivative market perform a valuable economic function by feeding information and analysis into the derivative markets? (a) Arbitrageurs (c) Speculators
7.
(d) Rs.32.89
< Answer >
The lower breakeven and lower profit potential The lower breakeven and greater profit potential The higher breakeven and greater profit potential The higher breakeven and lower profit potential The greater premium and lower profit potential.
(a) A short call (c) A protective put (e) A covered call. 6.
(c) Rs.30.00
Which of the following statements is true about closing a long call position prior to expiration relative to holding it to expiration? (a) (b) (c) (d) (e)
5.
(b) Rs.29.89
Consider two put options differing only by exercise price. The one with the higher exercise price has (a) (b) (c) (d) (e)
4.
< Answer >
As per FASB 133, the accounting treatment accorded to a Foreign currency hedge is that (a) (b) (c) (d) (e)
2.
• •
(b) Financial institutions (d) Banks
< Answer >
(e) Hedgers.
Ignoring transactions costs, whether the futures price is at a discount or premium to the spot price, equilibrium non-arbitrage conditions imply that at the futures delivery date the futures price and the spot price will be equal. This result is referred to as the
< Answer >
(a) Convergence principle (c) Expected futures price (e) Arbitrage pricing. 8.
Which of the following statements is true about the purchase of a protective put at a higher exercise price relative to a lower exercise price? (a) (b) (c) (d) (e)
9.
(b) Delivery parity (d) Futures contract settlement < Answer >
The breakeven is lower The maximum loss is greater The insurance is less costly The insurance is more costly The put option with lower exercise price is more valuable.
Which of the following statements is/are true regarding Coffee Future Exchange India Limited (COFEI)?
< Answer >
I.
It aims at providing a hedging opportunity against price risk to all those within and outside coffee industry. II. COFEI permits trading in twelve contracts simultaneously covering 24 months forward. III. The clearing house is an entity separate from COFEI. (a) Only (I) above (c) Only (III) above (e) Both (II) and (III) above.
(b) Only (II) above (d) Both (I) and (III) above
10. What will be the optimal stock index futures hedge ratio if the portfolio is worth $2,400,000, the beta is 1.15 and the S&P 500 futures price is 450.70 with a multiplier of 500. (a) 10.65 11.
(b) 12.25
(c) 15.84
(d) 6123.80
(e) 5325.05.
Though a cross currency hedge has somewhat higher risk than an ordinary hedge, it will reduce risk if which of the following occurs? (a) (b) (c) (d) (e)
< Answer >
< Answer >
Futures prices are more volatile than spot prices The spot and futures contracts are correctly priced at the onset Spot and futures prices are positively correlated Futures prices are less volatile than spot prices Spot and future prices are negatively correlated.
12. If you buy 100 shares of TTK at Rs.79, and simultaneously write a MAR 80 straddle for Rs.6. The break-even point will be (a) Rs.76.5
(b) Rs.78
(c) Rs.79.5
(d) Rs.80.5
(e) Rs.85.
13. If an investor buys a bullish vertical spread consisting of one July call of 270 with a premium of Rs.62 and a July call of 350 with a premium of Rs.12, what will be his profit or loss if spot price at expiration is Rs.325? (a) Rs. 5
(b) – Rs. 5
(c) – Rs. 20
(d) Rs. 20
< Answer >
< Answer >
(e) Rs.25.
14. Which of the following statements is false?
< Answer >
(a) Minimum value of an American call option is either zero or, S0 – X (b) Maximum value of an American call option can be the value of underlying asset (S0) (c) If two American call options have same exercise price, the option with longer maturity date will be worth less than the other option with shorter maturity. (d) An American call option can never be worth less than a European call option (e) The price difference between two American puts cannot exceed the difference in exercise prices. 15. According to put-call parity, writing a put is similar to (a) Buying a call, buying stock and lending (b) Writing a call, buying stock and borrowing (c) Writing a call, buying stock and lending
< Answer >
(d) Writing a call, selling stock and borrowing (e) Buying a call, selling stock and lending. < Answer >
16. Which of the following statements is/are true? I.
Black – Scholes model of option – pricing assumes that volatility of the underlying instrument is constant over the entire life of the option but is continuously compounded. II. The price prediction under Black – Scholes model focuses both the magnitude and direction of changes. III. According to the smile effect volatility of options deeply in the money is less than for those at the money. (a) Only (I) above (c) Both (I) and (III) above (e) Both (I) and (II) above.
(b) Only (II) above (d) Both (II) and (III) above < Answer >
17. Which of the following is true about a callable swap? (a) (b) (c) (d) (e)
The fixed rate receiver has the right to terminate the swap at any time before its maturity The fixed rate payer has the right to extend the swap beyond maturity The fixed rate payer has the right to terminate the swap at any time before its maturity Both fixed rate payer and receiver have right to terminate the swap at any time before its maturity Both fixed rate payer and receiver have right to extend the swap beyond maturity.
18. A swap quote for US dollar interest rate swap fixed vs. LIBOR is 10 – 30 basis points over 3-year US T-bills. This quote can be interpreted as (a) (b) (c) (d) (e)
< Answer >
The bid rate is 30 basis points over yields on the US Treasury Bills versus LIBOR The bid rate is 20 basis points over yields on the US Treasury Bills versus LIBOR The bid rate is 10 basis points over yields on the US Treasury Bills versus LIBOR The ask rate is 10 basis points over yields on the US Treasury Bills versus LIBOR The ask rate is 20 basis points over yields on the US Treasury Bills versus LIBOR. < Answer >
19. Which of the following statements is/are not true? I. Collectively, swap facilitators are known as ‘Swap Banks’. II. Swap brokers share the gain from a swap arrangement. III. Swap dealers bear the financial risk associated with a swap deal. (a) Only (I) above (b) Only (II) above (c) Only (III) above
(d) Both (I) and (II) above (e) Both (II) and (III) above.
20. Assume that there are two firms X and Y in need of $100 million and £50 million respectively. They can borrow these currencies at the following interest rates: Firms Firm X Firm Y (a) 0.7
Dollars 10.5% 8.5% (b) 1.3
Sterling 11.8% 12.5% (c) 2.0
The quality spread differential is (d) 2.7
(e) 3.8.
21. Which of the following is not true? (a) (b) (c) (d) (e)
< Answer >
< Answer >
Delta of a call option is always positive or zero Delta of a put option is always negative or zero Rho is a measure of the sensitivity of option value to changes in spot prices Gamma is the rate of change of the delta to the price of the underlying stock Vega of all options declines as the expiration date approaches.
22. A portfolio has a gamma of –2700. The delta and gamma of a call option are 0.65 and 0.90 respectively. The position in call option that could lead to gamma neutral portfolio is
< Answer >
(a) Short 3000
(b) Long 3000
(c) Long 5000
(d) Short 5000
(e) Short 1250. < Answer >
23. Which of the following correctly expresses the profit on a hedge? (a) (b) (c) (d) (e)
The basis when the hedge is closed The change in the basis The spot profit minus the futures profit The futures profit minus the spot profit Change in the price on the last day. < Answer >
24. Which of the following statements regarding cash flow hedges is/are true? I. II.
A non – derivative instrument can be designated as a hedging instrument for a cash flow hedge. The effective portion of gain or loss on the derivative instrument is reported in other comprehensive income for a cash flow hedge. III. The portion of gain or loss on the derivative instrument is reported in earning for a cash flow hedge. (a) Only (I) above (c) Both (II) and (III) above (e) All (I), (II) and (III) above.
(b) Only (II) above (d) Both (I) and (II) above < Answer >
25. Minimum tick size for a weather derivative in CME is (a) (b) (c) (d) (e)
1.00 degree day index point 1.25 degree day index point 2.00 degree day index point 3.00 degree day index point 5.00 degree day index point. < Answer >
26. Cooling degree days (CDD) index is used in (a) Winter months (c) Summer months (e) Throughout the year.
(b) Spring months (d) Autumn months < Answer >
27. Which of the following statements regarding methods of calculating VAR is/are true? I.
Under Monte Carlo Simulation method returns are expressed as a histogram of hypothetical values. II. The results obtained by Hybrid method are less precise as compared to the other methods of calculating VAR. III. Variance/Covariance Models are less flexible compared to other models. (a) Only (I) above (c) Both (I) and (II) above (e) All (I), (II) and (III) above.
(b) Only (III) above (d) Both (I) and (III) above
28. Bajaj share prices have exhibited an annual standard deviation of 28%. Assuming 30 days in a month, what would be the equivalent monthly standard deviation that may be used in the Black-Scholes model? (a) 6.80%
(b) 8.08%
(c) 10.89%
(d) 15.71%
(e) 20.28%.
29. Which of the following elements of an insurance contract gives a right to the insurer to stand in place of the insured, after settlement of a claim, so far as insured’s part of recovery from an alternative source is involved? (a) Utmost Good Faith (d) Assignment
(b) Indemnity (e) Subrogation.
< Answer >
(c) Warranties
30. Which of the following statements are true regarding different kinds of Fire Insurance Policies? I.
< Answer >
Under Declaration policy, adjustments are sought to be made by periodical declarations by the insured on the changing value of the goods.
< Answer >
II. III. IV. (a) (c) (e)
Under Floating policy value of the policy would be lowest of the rates taken for each of the locations calculated as if the policy is taken separately. The reinstatement policy is not useful when the property to be insured is stock, merchandise or materials. Declaration policy covers loss only over and above other policies whether affected by the insured or any other person covering the stocks hereby insured. Both (I) and (II) above (b) Both (III) and (IV) above (I), (II) and (III) above (d) (I), (III) and (IV) above (II), (III) and (IV) above.
END OF SECTION A
Section B : Problems (50 Marks) This section consists of questions with serial number 1 – 6. 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.
1.
A bank in US owns a portfolio of options on the dollar-euro exchange rate. The delta of the portfolio is 8604. The current exchange rate is $1.21/ €. The annual volatility of dollar-euro exchange rate is 8%. You are required to calculate the 10-day value at risk at 95% confidence level for the portfolio. (Assume 250 trading days in a year) (7 marks) < Answer >
2.
Current dollar-Can$ spot rate is $0.8265/Can$. A speculator is expecting that in the next two-three months dollar will not fluctuate much from the current spot rate against Can$. The following call options are available in the market: Strike price Premium Maturity ($/Can$) ($) Call 0.77 0.035 3 months Call 0.80 0.022 3 months Call 0.83 0.012 3 months Call 0.86 0.005 3 months The speculator wants to make a profit from his view by adopting an option strategy using all the four call options given above, and would like to limit his maximum potential loss.
Option
You are required to suggest a strategy to the speculator and prepare pay-off profile indicating maximum profit, maximum loss, and break-even points. Also draw the pay-off diagram for the strategy. (8 marks) < Answer >
3.
Cavin Cally Ltd., a large export house from India entered into a five-year interest rate swap with the ICICI Bank, under which it has contracted to pay 8% and receive six-month LIBOR semi-annually, on a notional principal amount of US $ 25 million. This deal was set-up on April 01, 2003. On April 01, 2005, after the swap payments were settled, the Treasurer of Cavin Cally suggested that the swap be cancelled as the rates in the market have dropped considerably. He approached the bank, which agreed to cancel the deal at 6%, which is also the current rate for the 3 years swap deal for fixed vs LIBOR. You are required to find out the following: a. If the deal was to be cancelled on April 1, 2005, what amount of money would be required to be paid? By whom? b. Instead of canceling the existing deal, if a new deal was made and allowed to run for 3 years (till the maturity of the original deal), what would be the cash flow on the fixed leg of the new deal? (Assume that each period is exactly 6 months). (6 + 1 = 7 marks) < Answer >
4.
A fund manager has a well-diversified portfolio that mirrors the performance of the S&P 500 and is worth $360 million. The value of the S&P 500 is 1,200 and the portfolio manager would
like to buy insurance against a reduction of more than 5% in the value of the portfolio over the next six months. The risk-free interest rate is 6% per annum. The dividend yield on both the portfolio and the S&P 500 is 3% and the volatility of the index is 30% per annum. a. If the fund manager buys traded European put options for the insurance, how much would the insurance cost? b.
Explain carefully alternative strategies open to the fund manager involving traded European call options such that they lead to the same result. (8 + 4 = 12 marks) < Answer >
5.
On January 10, 2006, Black Berry Inc. (BBI), a US based firm is expecting $20 million from a foreign subsidiary in the month of March. BBI intends to invest the funds in three month US Tbills. Looking at the present economic scenario BBI expects the interest rates to decline further in the near future. Therefore it decides to hedge through 3-month T-bill futures contracts. The March T-bill futures are quoting at 96.24 at the time of entering into the hedge. You are required to a. Explain how BBI can hedge using T-bill futures. b. Calculate the annualized yield, if in March T-bills futures are quoted at (i) 95.65 and (ii) 96.74. (3 + 5 = 8 marks) < Answer >
6.
Mr. Rajat, a trader in T-bill market, wants to invest in a 90-day T-bill which is trading at 8.25%. In order to finance his purchase of the T-bill he will use 30-day money market interest rate of 8%. You are required to calculate break-even discount rate on the 90-day T-bill after 30 days. (8 marks) < Answer >
END OF SECTION B
Section C : Applied Theory (20 Marks) This section consists of questions with serial number 7 - 8. Answer all questions. Marks are indicated against each question. Do not spend more than 25 -30 minutes on section C.
7.
a. Explain how the option on the futures become the same as an option on the asset. b. How are spread and arbitrage strategies forms of speculation? How can they be interpreted as hedges? (4 + 6 = 12 marks) < Answer > 8.
FASB - 133 specifies recognition of all derivatives instruments in the balance sheet as assets or liabilities measured at fair value. However there are certain contracts that are not subject to the requirements of FASB – 133. Explain these contracts. (10 marks) < Answer >
END OF SECTION C END OF QUESTION PAPER
Suggested Answers Financial Risk Management - I (231) : January 2006 Section A : Basic Concepts 1.
Answer : (d) Reason: For a fair value hedge, changes are included in current net income. For a cash flow hedge, changes are included in other comprehensive income. For a foreign currency hedge, changes are included in comprehensive net income as part of cumulative transaction adjustment. Hence, option (d) is the correct answer.
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2.
Answer : (a) Reason: Break even price for the investor = So – P Rs.30 – Rs.2.89 Rs.27.11 Hence, option (a) is the correct answer.
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3.
Answer : (c) Reason: Suppose there are two put options.
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Put option A
Put option B
Strike price
Rs.100
Rs.120
Premium
Rs.10
Rs.12
Break even prices will Rs.90 Rs.108 be For put option the profit is maximum when the stock price is zero at the expiration. So the maximum profit will be Rs.90 and Rs.108 respectively for both the options. Thus, it can be concluded that the put option with the higher exercise price has the higher breakeven price and greater profit potential. Hence, option (c) is the correct answer.
4.
Answer : (a) Reason: Closing a long call position prior to expiration relative to holding it to expiration will give greater profit at all stock prices, since for a given stock price, the longer a call is held, the more time value it loses and lower the profit. Hence, option (a) is the correct answer.
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5.
Answer : (c) Reason: A protective put strategy involves buying a stock and buying a put option on the same stock. Early exercise imposes a risk for option writer and not option buyer. All other strategies except protective put involve writing call or put options and hence involves risk of early exercise. Hence, option (c) is the correct answer.
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6.
Answer : (c) Reason: Speculators has a view in the market and based on the forecast the speculator would like to make gains by taking long and short positions on the derivatives. They perform a valuable economic function by feeding information and analysis into the derivative markets. Hencew, option (c) is the correct answer.
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7.
Answer : (a) Reason: As future contract approaches maturity, the cash and future prices come closer and ultimately, on maturity, both coincide to a particular price. This process is called as convergence. Hence, option (a) is the correct answer.
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8.
Answer : (d) Reason: Purchase of a protective put at a higher exercise price relative to a lower exercise price will involve more outlay of funds as option premium. The breakeven price for higher exercise price option will be higher and maximum loss will be lower than option with lower exercise price. Hence, option (d) is the correct answer.
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9.
Answer : (a) Reason: COFEI aims at porviding hedging opportunity against price risk to all those within and outside coffee industry. Hence, statement (I) is true. COFEI permits trading in nine contracts simultaneously covering 18 months forward. Hence,statement (II) is false. The clearing house is a part of COFEI itself and not a separate entity. Hence, statement (III) is false. Hence, option (a) is the correct answer.
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10.
Answer :
(b)
$24, 00, 000 × 1.15 450.70 × 500 Reason: Optimal stock index future hedge ratio = 12.25
< TOP >
Hence, option (b) is the correct answer. 11.
< TOP Answer : (c) > Reason: A cross hedge will reduce risk if spot prices and future prices are positively correlated. Hence, option (c) is the correct answer.
12.
Answer : (a) Reason: The strategy will give profit if the prices are goes up. The break-even point will be Rs.76.5 since, Initial inflow + gain from stock +Gain from put +Gain from call = 6 + (-2.5) + (-3.5) + 0 = 0 Hence, option (a) is the correct answer.
13.
< TOP Answer : (a) > Reason: If spot price at expiration is Rs.325, then call with strike price 270 will be exercised and call with strike price 350 will not be exercised. Initial investment = 62 – 12 = Rs.50 Profit or loss = (325 – 270) + 0 – 50 = Rs.5.
14.
< TOP Answer : (c) > Reason: If two American call options have the same exercise price, the option with longer maturity date will be more than the other option with shorter maturity, so alternative (c) is false. All other alternatives are correct.
15.
< TOP Answer : (b) > Reason: A short put position is equivalent to a long asset position plus shorting a call. To fund the purchase of the asset, we need to borrow. This is because the value of call or put is small relative to the value of the asset.
16.
Answer : (a) Reason: Black – Scholes model of option – pricing assumes that volatility of the underlying instrument is constant over the entire life of the option but is continuously compounded. Hence, statement (I) is true. The price prediction under Black – Scholes model focuses on the magnitude of changes and not on the direction of changes. Hence, statement (II) is false. According to the smile effect volatility of options deeply in the money is greater than for those at the money. Hence, statement (III) is false. Hence, option (a) is the correct answer.
17.
Answer : (c) Reason: A callable swap gives the holder, i.e. the fixed rate payer, the right to terminate the swap at any time before its maturity. Should the interest rates fall, the fixed rate payer exercises his right and terminates the swap since the funds will be available at a lower rate. Hence (c) is the answer.
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18.
Answer :
< TOP >
(c)
< TOP >
Reason: The given quote can be interpreted as bid rate is 10 basis points over yields on the US Treasury Bills versus LIBOR and ask rate is 30 basis points over yields on US Treasury Bills versus LIBOR. 19.
Answer : (b) Reason: Both the counterparties and not the swap brokers share the net gain from the swap. Hence, statement (II) is false. All other statements are correct. Hence, option (b) is the correct answer.
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20.
Answer : (d) Reason: Here, firm X has comparative advantage in Sterling market while firm Y has comaparative advantage in Dollar market. Therefore, quality spread differtial will be [(10.5 – 8.5) + (12.5 – 11.8)] = 2.7%. Hence, option (d) is the correct answer.
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21.
Answer : (c) Reason: Rho is a measure of the sensitivity of option value to change in the interest rates. All other statements are correct. Hence, option (c) is the correct answer.
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22.
Answer : (b) Reason: For making gamma nentral portfolio a long position in traded option is
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2, 700 = 3, 000. 0.90
needed to the extent of Hence, option (b) is the correct answer. 23.
Answer : (b) Reason: Profit on a hedge is expressed as change in the basis points over the hedge period. Hence, option (b) is the correct answer.
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24.
Answer : (c) Reason: A non - derivative instrument can not be designated as a hedging instrumnet for a cash flow hedge. Hence, statement (I) is not true. All other statemnts are true regarding cash flow hedges. Hence, option (c) is the correct answer.
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25.
Answer : (a) Reason: Minimum tick size for a weather derivative in CME is 1.00 degree day index point. Hence, option (a) is the correct answer.
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26.
Answer : (c) Reason: Cooling degree days (CDD) index is used to measure warmth in summer months. Hence, option (c) is the correct answer.
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27.
Answer :
< TOP >
(d)
Reason: The results obtained by Hybrid method are more precise as compared to the other methods of calculating VAR. Hence, statement (II) is false. All other statements are corrrect. Hence, option (d) is the correct answer. 28.
Answer :
(b)
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Reason: Equivalent monthly σ = (σ yearl) / Number of months = 0.28/ 12 = 8.08% 29.
Answer : (e) Reason: Doctraine of Subrogation refers to “the right of the insurer to stand in place of the insured, after settlement of a claim, so far as the insured’s right of recovery from an alternative source is involved”. Hence, option (e) is the correct answer.
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30.
Answer : (d) Reason: Under Floating policy value of the policy would be highest of the rates taken for each of the locations calculated as if the policy is taken separately. Hence, statement (II) is false. All other statements are correct. Hence, option (d) is the correct answer.
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Section B : Problems 1.
Current Euro – Dollar Exchange rate = 1.21 Delta of the portfolio = 8604 Volatility = 0.08 The approximate relationship between daily change in the portfolio value ∆P , and the daily change in the exchange rate ∆S , ∆P = 8604 ∆S Proportionate change in the exchange rate in one day ∆X =
S 1.21
P 8604 X 1.21 P 10410.84 X
8%
Daily volatility in the exchange rate ( ∆X )= 250 = 0.51% ∆P = 10410.84 0.0051 = 53.10 10 days VAR at 95% confidence level = 53.10 1.645 10 = $276.22 So 10 days VAR is $276.22. < TOP >
2. The condor spread strategy is a suitable strategy for the speculator. Condor spread can be created by buying two options at 0.77 and 0.86, and selling two options at 0.80 and 0.83. Initial outflow = 0.035 + 0.005 - (0.022 + 0.012) = 0.006 Pay-off Profile
Spot price 0.75 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88
(+) C = 0.77 0 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11
Gain/loss (–) C = (–) C = 0.80 0.83 0 0 0 0 0 0 0 0 0 0 0 0 -0.01 0 -0.02 0 -0.03 0 -0.04 -0.01 -0.05 -0.02 -0.06 -0.03 -0.07 -0.04 -0.08 -0.05
(+) C = 0.86 0 0 0 0 0 0 0 0 0 0 0 0 0.01 0.02
Maximum profit Maximum loss Break-even points
$ 0.024 $ 0.006 $ 0.776 & $0.854
Initial outflow -0.006 -0.006 -0.006 -0.006 -0.006 -0.006 -0.006 -0.006 -0.006 -0.006 -0.006 -0.006 -0.006 -0.006
Net gain/loss -0.006 -0.006 -0.006 0.004 0.014 0.024 0.024 0.024 0.024 0.014 0.004 -0.006 -0.006 -0.006
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3.
a.
Principal amount = $25 million Interest rate on fixed leg = 8% Interest rate on floating leg = LIBOR Present market quote for three year swap = 6% v/s LIBOR In order to cancel the deal on April 01,2005 (after settling payments), the present value of future cash flows would have to be paid. The discount rate applicable should be the current
rate of interest in the market i.e. 6% p.a. or 3% for six months. Present value of amount to be paid as per the original contract = 1
b.
Value of Fixed leg of interest = 1 PVIFA3%.6 25 PVIF3%,6 = $26.3543 million Value of Floating leg of interest = $25 million (as the interest is just paid) Value of swap to Cavin Cally = 25 – 26.3543 = -$1.3543million This amount is to be paid by the company to the bank. The company should pay to the bank every six month = 25x0.06/2 = $0.75 million < TOP >
4.
The fund is worth $300,000 times the value of the index. When the value of the portfolio falls by 5% (to $342 million), the value of the S&P 500 also falls by 5% to 1140. The fund manager therefore requires European put options on the 300,000 times the S&P 500 with exercise price 1140. a.
S0 = 1200, X = 1140, r = 0.06, σ = 0.30, T = 0.50 and q = 0.03. Hence: 0.09 1200 0.06 0.03 0.5 1140 2 0.4186 0.3 0.5
ln
d1 =
b.
d2 = d1 – 0.3 0.5 = 0.2064 N(d1) = 0.6622; N(d2) = 0.5818 N(-d1) = 0.3378; N( -d2) = 0.4182 The value of one put option is 1140e-r (T-t) N(-d2) - 1200e-q(T-t) N(-d1) = 1140e-0.06 x 0.5 0.4182 - 1200e-0.03 x 0.5 0.3378 = 63.34 The total cost of the insurance is therefore 300,000 63.34 = $19,002,000 From put-call parity. S0e-qT + p = c + Xe-rT or: p = c - Soe-qT + Xe-rT This shows that a put option can be created by selling (or shorting) e-qT of the index, buying a call option and investing the remainder at the risk-free rate of interest. Applying this to the situation under consideration, the fund manager should: (i) Sell 360e-0.03 x 0.5 = $354.64 million of stock (ii) Buy 300,000 call options on the S&P 500 with exercise price 1140 and maturity in six months. (iii) Invest the remaining cash at the risk-free interest rate of 5% per annum. This strategy
gives the same result as buying put options directly. < TOP >
5.
Investment = $20,000,000.00 Months = 3 March T- Bill future contract = 96.24 Number of contracts required = 20 a. As the company will invest funds for a period of 3 – months, so it will buy T-bill future contract to lock – up a yield of (100 – 96.24) = 3.76%. If the yield on date of investment i.e. in March declines, the loss in the spot market will be offset by gain in the future market. In case the interest rate rises, profit on spot market will be offset in the loss in the future market. Thus, by buying T-bill future contract BBI will be able to lock up yield of 3.76%. b. If March future is at 95.65 Price of cash T – bill =
$20, 000, 000 × 1 − 0.0435 ×
3 12 = $19,782,500
Loss in future = (96.24 – 95.65) ×20 × 25 × 100 = $29,500. Effective purchase price = $19,782,500 + $29,500 = $19,812,000 20, 000, 000 − 19, 812, 000 12 19, 812, 000 Annualized yield = If March future is at 96.74
Price of cash T-bill =
×
3
× 100
= 3.80%
$20, 000, 000 × 1 − 0.0326 ×
3 12 = $19,837,000
Gain in future = (96.74 – 96.24) ×20 × 25 × 100 = $25,000 Effective purchase price = $19,837,000 – $25,000 = $19,812,000 20, 000, 000 − 19, 812, 000 12
Annualized yield =
19, 812, 000
×
3
× 100
=3.80% < TOP >
6.
The break-even price is computed as follows. Let P be the price at which the trader has to sell the T-bill after 30 days so that he breaks even. Let B be the current price of the bill. Then, 30 ö æ B ´ ç1 +0.08 ´ ÷=P. è 360 ø
30 ö æ If P >B ´ ç 1 +0.08 ´ ÷, the trader will have money left over. è 360 ø 30 ö æ If P
Given the discount yield of d = 8.25%, B = 97.9375. 30 ö æ P =97.9375 ´ ç1 +0.08 ´ ÷=98.59042. è 360 ø
The break-even price is The discount yield of the 90-day T-bill after 30 days, which sells at a price of 98.59042 can be computed as d = [(100 – 98.59042)/100] × [360/60] 8.4575% < TOP >
7.
a.
b.
Section C: Applied Theory In an option on a futures contract, the underlying is a futures contract. Thus, if the holder exercises a call option on futures it creates a long position in a futures contract, and if the holder exercises a put option on a futures it creates a short position in a futures contract. As in options on assets, an option on a future requires that the buyer pay the premium up front. There are two expirations, the expiration of the option and the expiration of the underlying futures, though for some contracts, these expirations are the same. In that case, exercise of the option on the futures creates a futures contract that immediately expires, thereby turning into the spot asset and making the option on the futures the same as an option on the asset. A spread strategy is a long position in one futures contract and a short position in another futures contract. The prices of the two contracts are normally highly correlated so that the gains on one contract are at least partially offset by the losses on the other. The objective is to take a small amount of risk in the hope of a small profit. An arbitrage strategy involves a near risk less transaction in one or more futures contracts and possibly a spot transaction. Arbitrage trading is usually triggered by a deviation from the theoretical relationship between the prices of two instruments. Both transactions can be viewed as hedges. A hedge is a position in the spot market and an opposite position in the futures market. Thus, it is similar to a spread in that the gain on one position is at least partially offset by the loss on the other. Arbitrage is like hedging in that it is designed to have low risk and it often involves a position in the spot market and an opposite position in the futures market. < TOP >
8.
The contracts that are not subject to the requirements of FASB-133 are: 1. Regular way security trades Delivery of a security readily convertible into cash within the specific time period established by marketplace regulations or conventions where the trade takes place rather than by the usual procedure of an individual enterprise. For instance the trades that are excluded are forward purchases or sales of to-be- announced securities and when issued, as-issued or if-issued securities. 2. Normal purchases and normal sales Contracts for future delivery of assets convertible into cash and for that there is no net settlement provision and no market mechanism to ease the net settlement. Terms must be consistent with normal transactions and quantities must be reasonable in relation to needs. 3. Certain insurance contracts
4.
5.
Contracts where the holder is only compensated when an insurable event takes place and the value of the holder’s asset or liability is adversely affected or the holder incurs a liability. The contracts that are not considered to be derivative instruments are traditional life insurance and traditional property and casualty insurance policies. Certain financial guarantee contracts Contracts that call for payments only to reimburse for a loss from debtor failure to pay when due. But a credit-indexed contract requiring payment for changes in credit ratings would not be an exception. Certain contracts that are not exchange traded a. Climatic or geologically other physical variable b. Value or price involving a non-financial asset not readily converted into cash or a nonfinancial liability that does not require delivery of an asset that is readily converted into cash. c. Specified volumes of revenue of one of the parties: examples are royalty agreements or contingent rentals based on related sales. < TOP >
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