**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.

**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?