Assignment 2 - Options Markets

This problem set is to be completed separately by each student. You can discuss the portfolios and the methodology with other students.

Part A. Due date: November 6, 1995 at beginning of class.

1(a). You have been given $1,000,000 to invest in a portfolio of stocks and options. You enter the market using closing prices for November 6 (which will not be available until the next day). Hence, your positions are proposed trades (i.e. you don't know precisely the prices you will get.) If you go slightly over the $1,000,000 then you can borrow at 2% (annualized) over the 30-day Treasury rate. If you are under, then invest at the bill rate. If there are big differences, you will have to downsize/upsize your trades. You must close your portfolio no later than the trading day before November 27.

You are not limited to the contracts quoted in the WSJ (although most active contracts are reported in the WSJ). Nevertheless, there are some international quotations available through DATASTREAM (in library) which are not reported in the WSJ.

Your $1,000,000 should be used either to purchase call or put options or to purchase stocks. All stocks and options purchased must have prices that are quoted in the WSJ. In purchasing these stocks and options, no buying on margin may be done in this exercise. You may write covered calls up to a $100,000 premium received and placed in escrow for you (money market account earning the yield of a one month Treasury bill). You may not write naked puts or write naked calls. If you short stocks, 50% of the value of the stock must be placed in a money market account. Furthermore, you do not receive the procedes from the short when it is executed. For example, if you short 100 shares of IBM at $100 per share, then this is a cash out transaction of $5000. If the price of IBM drops to $90, then your profit at close out is $1000. You may spread options. This involves buying and selling options on the same stock.

To keep the problem somewhat realistic, to make sure that all people play both markets and to make sure no one goes broke, you are limited in your option purchases to a minimum expenditure of $100,000 on options and a maximum expenditure of $500,000 on options. (The values of the underlying assets will be much larger than these prices paid for the options.) Obviously, this means that you must spend between $500,000 and $900,000 on stocks.

It is best not to invest in options that expire during the trading period. I recommend that you build a spread sheet to keep track of your portfolio. I also recommend that you keep your portfolio relatively simple -- if you buy 25 different options the accounting will quite difficult.

If it turns out that your options do not trade on the liquidation date, you can get out at the Black-Scholes price using the estimate of implied volatility from the last day the option traded. You are not allowed to take an unreasonable position -- e.g. spreading more options than underlying stock available. If you want to make a big trade, then you must check in the library how much stock is outstanding and you are restricted to no more than 10% of that for your options position. I also reserve the right to revise unreasonably large trades downwards.

1(b). You are responsible for having an Excel spreadsheet which can produce the Black-Scholes formula. Within Excel, there is a built-in function which calculates the cumulative normal distribution. Along with your position, for each option you must submit computations of (1) the dollar move in the value of the option for a $1 move in the underlying asset's price (the option's delta), (2) the percentage move in the value of the option for a 1% move in the value of the underlying asset (option's omega), and (3) the implied volatility of the underlying asset's annual rate of return. Comment on these computations. Is the underlying asset of higher or lower risk than a typical stock like IBM? Are these options very risky in dollar terms? In percentage terms?

1(c). If you have a combined position i.e. you are in the stock and an option on the stock), graph the payoffs for your combined stocks-options portfolio at expiration with value at expiration on the y-axis and S^* on the x-axis. [If you have more than one combined position, pick one.] Is your combined position bullish or bearish on the movement of the stock? If you are spreading options, are you betting on increased or decreased volatility?

1(d). Not required -- but encouraged! To make the options and futures assignments more interesting, clip five dollars to your handin. If everyone participates, we should have approximately $600 that will be awarded to the people that make the most combined money in assignment 2 (options) and 3 (futures). Of course, if you choose not to attach the $5, then you are not eligible for the prize. Note: your grade is not determined by the amount you make.


Part B. Due date: November 27, 1995 at the beginning of class.

2(a). You must hand in a day-by-day table of your gains and losses for each different option and stock position. You should assume that you liquidated all positions on the last trading day at the closing prices for that day. On the cover page write the "bottom line" total gains or losses on your portfolio.

2(b). For each option in your portfolio, graph the day-by-day prices of the options versus the prices of the underlying assets (use two scales -- one for the option and one for the stock). Also, plot the daily option price changes (y-axis) versus the changes in the underlying asset's price (x-axis). Comment on whether these plots look as expected.

2(c). With this day-by-day worksheet on your positions, you should supply a paragraph of comments on whether or not you took too much or too little risk relative to your own comfort level (or "risk tolerance"). Did the volatility of the positions correspond with your prior beliefs? What, if anything, would you do differently the next time?


Trading is allowed. Trades are entered between 8:30 am -- 4:15 pm by e-mail ceb4@mail.duke.edu. There are no telephone trades. The trade takes effect at the close of trading on the day the trade is initiated.