Exam FM/2 Review Intro to derivatives & options

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## Exam FM/2 Review Intro to derivatives & options

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**Basic derivatives**• Derivatives are products with value derived from underlying assets • Ask price- Market maker asks for this price, so you can buy here • Bid price- Market maker bids this price, so you can sell here • Bid-ask spread is an inherent cost in transactions**Short versus long**• Short position- You profit from declines in underlying asset value • Long position- You profit from increases in underlying asset value • Short-selling • Basic short position • Borrow stock, sell it to someone else, then buy stock at end and return to lender • You must pay dividends to lender • Lender may demand that the proceeds and possibly more (haircut) be held by a third party to avoid credit risk • You may get interest on the proceeds and/or hair cut • Forward contract • Basic long position • Agreement to enter transaction in future for specified date and price**What is an option**• Gives you the option to enter a transaction • Buying one limits your losses • Often used in combinations to hedge risk • Call option • Option to buy asset at strike price • Think COB=Call-Option-Buy • Put option • Option to sell asset at strike price • Think POS= Put-Option-Sell**Features**• Style • European- can only exercise at expiration • American- can be exercised at any time • Bermudan- can exercise during specified times, but this style is rare • Position • In-the-money- Profit if exercised now • At-the-money- Neutral is exercised now • Out-of-the-money- Loss if exercised now • Covered call- writing a call when you own the asset • Covered put- writing a put when you are short in the asset**Put Call Parity**• Cost of buying asset with forward contract must equal the cost of buying it at a fixed rate with options, due to the concept of no arbitrage**Problem 1**• Samantha buys 100 shares of stock but changes her mind and immediately sells the stock. The broker’s commission is $20 on a purchase or sale. Samantha lost $70 on this transaction. What was the difference between the bid and ask price per share?ASM p.487 Answer: $.30**Problem 2**• John short sells a stock for $10,000. The proceeds of the sale are retained by the lender. (Ignose interest on the proceeds.) John must deposit $5,000 with the lender as collateral. He earns 6% effective on this haircut. At the end of one year, he closes his short position by buying the stock for $8,000 and returning it to the lender. A dividend of $500 was payable one day before he covered the short. What was John’s effective rate of interest on his investment?ASM p.488 Answer: 36%**Problem 3**• You initiate a 200-share short position on ABC Corp. common stock. At that time, the bid and ask prices are $27.50 and $28.00, respectively. At the time you close your position, the bid and ask prices are $23.75 and $24.25, respectively. The commission rate is 0.65%. Ignoring interest income, what was the total profit on your short position?ASM p.489 Answer: $583 profit**Problem 4**• Arnold buys a one-year 125-strike European call for a premium of $16.86. He also sells a 100-strike call on the same underlying asset for a premium of $31.93. The spot price at expiration is $110. The effective annual intrest rate is 3.5%. What is Arnold’s total profit at expiration for the two options? ASM p.512 Answer: $5.60**Problem 5**• Marge buys a 6-month 65-strike European put with a premium of $4.53. She also writes a 6-month 75-strike European put with a premium of $10.56 on the same underlying asset. The risk-free rate of interest is 6% effective per annnum. The spot price at expiration is $68. Marge’s total profit on the two options is X. Determine X. ASM p.524 Answer: -$.79**Problem 6**• The premium for a one-year off-market forward contract with a forward price of $200 is $18.18. The premium for a 200-strike one-year European call is $32.98 and for a 200-strike one-year European put is X. The risk-free rate of interest is 10% effective per annum. Determine X. ASM p.577 Answer: $14.80