Hi,

I have a second question on a homework problem I'm doing for Finance. It's number 2 and here is the excel file.

Thanks.

Problem 2 The main concept to remember from this question is that an exchange will alter the terms of options contracts if a company decides to significantly change the number of shares it has outstanding. Assuming the market capitalization of the company remains constant, an increase in the number of shares outstanding will automatically result in a decrease in the price per share. The terms of an options contract usually do not change when a cash dividend is paid by the company (although a large special dividend would be an exception to this). Consider a call option to buy 100 shares of a company for $60 per share. How do the terms of the option contract change in each of the following cases? (If there is no change in the terms, write in the original terms of the contract.) No. of shares to buy Strike price Original terms of the option contract: 100 $60.00 A cash dividend: Dividend amount $5.00 A stock split: Split ratio 4/1 A stock dividend: Dividend percentage 10% (Please see the excel file which is attached)

Walidah

BASICS OF OPTIONS Textbook Reference: Points Section 1.8, pp. 14-16; Section 10.4, pp. 215-219 Problem 1 The key principle to take away from this problem is that leverage can have significant effects when it comes to investing. Leverage allows relatively small amounts of capital to generate large profits - a magnification effect. The danger of leverage is that losses are also magnified. Options contracts are a leverage tool as they allow investors to multiply the power of their starting capital. The current price of DISH Network stock is $31.50 per share, and six-month European call options on the stock with a strike price of $32.50 are currently trading at $3.60. An investor, who has $10,000 of capital to invest, believes that the price of the stock will increase by 20% over the next six months. The investor is trying to decide between two strategies - (A) buying shares or (B) buying call options. What return will each strategy produce after six months, if the investor is correct in their assessment of the stock? Assume that either a whole number of shares can be bought OR a whole number of option contracts cane be bought (representing the right to buy 100 shares per option contract). This information is summarized in the tables below. Price of security Strike price of the call options Amount available for investment Anticipated change in stock price Strategy A: Strategy B: Buy shares Buy call options $31.50 $3.60 $32.50 $10,000 20% How many shares can be purchased under Strategy A? How many option contracts can be purchased under Strategy B? (Round your answers to the nearest whole number.) Strategy A Strategy B 3, 3 How much uninvested cash does the investor still have? (Assume that this cash remains in a noninterest-bearing account.) Strategy A Strategy B 3, 3 Assume that the anticipated change in stock price is realized over the next six months. What is the price of a share of the stock? 2 What is the value of all of the shares purchased if the anticipated change in stock price is realized? What is the intrinsic value of the options purchased, assuming they are all exercised at maturity if the anticipated change in stock price is realized? Strategy A Strategy B Strategy A Strategy B 2, 2 What is the total profit made in dollar terms? 2, 2 What is the total profit made (in percentage terms)? In other words, express the answers above as a percentage of the initial capital available for investment. Strategy A Strategy B 1, 1 Now consider the outcome to the two strategies if the stock price were to decrease by 20%. Anticipated change in stock price -20% What is the price of a share of the stock in this second scenario? 2 What is the value of all of the shares purchased if the anticipated change in stock price is realized? What is the intrinsic value of the options purchased, assuming they are all exercised at maturity if the anticipated change in stock price is realized? Strategy A Strategy B Strategy A Strategy B 2, 2 What is the total loss made in dollar terms? 2, 2 What is the total profit made (in percentage terms)? In other words, express the answers above as a percentage of the initial capital available for investment. Strategy A Strategy B 1, 1 Which strategy has a higher standard deviation of returns? In other words, which investment strategy is riskier? 4 Problem 2 The main concept to remember from this question is that an exchange will alter the terms of options contracts if a company decides to significantly change the number of shares it has outstanding. Assuming the market capitalization of the company remains constant, an increase in the number of shares outstanding will automatically result in a decrease in the price per share. The terms of an options contract usually do not change when a cash dividend is paid by the company (although a large special dividend would be an exception to this). Consider a call option to buy 100 shares of a company for $60 per share. How do the terms of the option contract change in each of the following cases? (If there is no change in the terms, write in the original terms of the contract.) No. of shares Strike price to buy 1, 1 2, 2 2, 2 Original terms of the option contract: A cash dividend: Dividend amount A stock split: Split ratio A stock dividend: Dividend percentage 100 $60.00 $5.00 4/1 10% Problem 3 The central idea to recognize in this example is that writing options (that is, selling them) involves risk for the party that is doing the selling. An exchange will require that margin be put up by the option writer to mitigate the possibility that they will default on a loss-making position. An investor buying an option does not have a margin requirement, as the maximum loss is the cost of the option and this is paid up front. A United States investor writes eight naked call option contracts and eleven naked put option contracts (each contract is for options on 100 shares). The call option price is $5.00, the put option price is $10.55, the strike price for both calls and puts is $90.00, and the stock price is $84.00. What is the initial margin requirement for the investor? This information is summarized in the table below. No. of call option contracts sold Call option price No. of put option contracts sold Put option price Strike price Stock price 8 $5.00 11 $10.55 $90.00 $84.00 The initial and maintenance margin for a written naked call option is the greater of the following two calculations: Calculation 1: A total of 100% of the proceeds of the sale plus 20% of the underlying share price less the amount if any by which the option is out of the money 4 4 Margin requirement for all written call option contracts Calculation 2: A total of 100% of the option proceeds plus 10% of the underlying share price Margin requirement for all written call option contracts Therefore, the initial and maintenance margin for all written naked call options is: 1 The initial and maintenance margin for a written naked put option is the greater of: Calculation 1: A total of 100% of the proceeds of the sale plus 20% of the underlying share price less the amount if any by which the option is out of the money 4 4 Margin requirement for all written put option contracts Calculation 2: A total of 100% of the option proceeds plus 10% of the exercise price Margin requirement for all written put option contracts Therefore, the initial and maintenance margin for all written naked put options is: 1 Hence, the total initial margin requirement for the investor is: 2 Problem 4 The key principle to take away from this problem is that arbitrage opportunities arise when securities are not trading at their theoretical prices. If security A is overvalued relative to security B, then security A should be sold and security B should be bought ("buy low, sell high"). As more and more market participants observe the arbitrage opportunity, selling pressure will cause the price of security A to decrease and buying pressure will cause the price of security B to increase until an equilibrium is reached where the arbitrage opportunity no longer exists. (Note that selling a zerocoupon bond is equivalent to borrowing money, and buying a zero-coupon bond is equivalent to investing.) A European call option and put option on a stock both have a strike price of $20 and an expiration date in three months. Both sell for $3. The risk-free interest rate is 10% per annum, the current stock price is $19, and a $1 dividend is expected in one month. What is the arbitrage opportunity open to a trader? This information is summarized in the table below. Price of European call option Price of European put option Strike price of both options Time to expiration (months) Risk-free interest rate Current stock price Expected dividend Time until dividend received (months) $3.00 $3.00 $20.00 3 10% $19.00 $1.00 1 Put-call parity with dividends: ++^()=+_0 What is the present value of the expected dividend? 2 What is the value of the Left-Hand Side (LHS) of the put-call parity equation above? 4 What is the value of the Right-Hand Side (RHS) of the put-call parity equation above? 3 Which side of the put-call parity equation is overvalued (and should therefore be "sold")? 1 Payoff Table for the Arbitrage Opportunity Action 2, 1 2, 1, 1 2, 1 2, 1 2, 1 2, 1 1 T=0 T = 1/12 T = 3/12 ST K ST