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 Strike PriceCallPut $80$28.34$2.07 9021.464.41 10015.797.96 11011.3312.71 1207.9518.55

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