Exam FM/2 Review Intro to derivatives & options

1. Exam FM/2 ReviewIntro to derivatives& options

2. 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

3. 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

4. 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 • Put option • Option to sell asset at strike price

5. 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

6. 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

7. 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

8. 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%

9. 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

10. 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

11. 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

12. 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

13. What is risk management? • Different ways of reducing your potential losses, or securing your gains • Diversifiable risk can be hedged, while nondiversifiable or systematic risk cannot • There will likely be simple word problems involving the concept of hedging

14. Financial instruments • Options can be combined in infinite ways to pursue many different strategies • Synthetic forward • Obtain stock in future at price fixed today • Buy call, sell put at same strike price • Spread • Bear • Buy call and sell higher call or buy put and sell higher put • Profit with increase, up to a limit • Bull (opposite of bear) • Sell a call and buy a higher call or sell a put and buy a higher put • Profit with decline in price, to a limit

15. Financial instruments cont. • More spreads • Box • Combination of long and short synthetic forwards or bull and bear spreads • No market risk, so only useful for borrowing or lending money • Ratio • Buying and selling unequal numbers of options • Can be used for more complicated hedging strategies • Collars • Buy a put and sell a higher call, basically a short forward with a flat range in the middle • Commonly used when owning the stock, then it’s a collared stock • If premiums are equal, it’s a zero cost collar

16. Financial instruments cont. • Straddles • Purchase call and put with same strike price • Profit with volatility in either direction • Write a straddle to bet on stability • Strangles • Straddle with out-of-the-money options to reduce costs • Reduced profit with volatility, but lose less in the middle • Butterfly spread • Write a straddle, then buy put and call on far sides for protection • Bets on stability while protecting against losses in either direction • Can be asymmetric to shift location of peak • Paylater • Sell a put and buy two lower puts, so that the premiums cancel out • This “insurance” costs less if not needed, but more if it is needed

17. Take the following premiums for one-year European options for an underlying asset with a current spot price of $100. The risk-free annual effective rate of interest is 8.5%. Determine the net financing cost (net premiums) of: 1. A 100-110 bull spread using call options 2. A 100-120 box spread 3. A ratio spread using 90 and 110-strike options, with a payoff of 20 at expiration price 110 and payoff of 0 at expiration price 120 4. A collar with a width of $10 using 90 and 100-strike options 5. A straddle using at-the-money options 6. An 80-120 strangle 7. A butterfly spread with a at-the-money straddle and insurance options out $10

18. Answers 1. $4.46 2. $18.43 3. -$12.53 4. -$11.38 5. $23.75 6. $10.02 7. -$8.01