A client has asked you to create a decision tree/model for two stocks (Stock 1 and

Stock 2) using Silver Decisions and Excel. Your client has $100,000 to enter into option

positions and owns 100,000 shares of Stock 2 that were acquired on day 1 (see

spreadsheet) at that day’s closing price. You will be given the stock data for both stocks

for 100 days but will not make any trades until day 50. That data is attached. Your job is

to first analyze the stock price movements, and the volatility (standard deviation of a

sample) over a period of 50 days (no other time periods). Next, you will determine the

expected future price in 10 days (P(T+10)), using the standard future price formula

below:

            Future Price at time T = Current Price x (1 + r)T Assume 3% risk free rate per

annum

                So, the price 10 days in the future = P(T+10) = PT (1 + r)(10/365) where r is

the risk-free rate or P60 = P50 (1+r)(10/365)

Once P(T+10) is calculated, your decision tree will choose an option strategy from the

eight below based on the historical prices and volatility (i.e., what you believe is going to

happen based on the numbers) to determine which would be the most appropriate:

Bullish Neutral  Bearish

Covered Call (expect limited

growth and own stock)

Butterfly Spread (expect

stock to stay in a fairly

narrow range)

Protective Put (expect limited

downward movement and

own stock)

Call (expect significant

growth regardless of

ownership)

Straddle (expect stock to

be volatile)

Put (expect significant

downward movement of

ownership)

Bull Spread (expect limited

growth and do not own stock)  

Bear Spread (expect limited

downward movement and do

not own stock)

The best way to think about that as a decision tree would be to first determine if you are

bullish, bearish, or neutral, then another decision based on the best of the alternatives.

There is no "(W)Right" way to do this. Each of you have to come with your own method for

determining what you would do based solely on the past data, then how you execute a

strategy based thereon. If you could create a perfect system, you would not be in Law

School. But you MUST explain what data you are using to make your decision. 

After you have made your decision above, use the Black-Scholes model (“B-S”) (it's in the

attached spreadsheet) to price the option/option stock strategy for either a one-month or

two-month term (no other terms), and determine how you would deploy that strategy. It is

up to you to determine the strike prices for the options and use the 50-day volatility of the

stock and the risk-free rate. Assume the risk-free rate will remain constant. 

Then you will determine the size of the position of any strategy and employ the strategy

on that date. There will be a total of 10 positions and no one day’s positions can cost more

than 10% or less than 5% of the client’s cash, nor can any position involve the potential

sale of more than 20% of the client’s stock position. Remember, each option price

represents 100 shares. That means you will have to determine how many options to

purchase or sell. To be clear, you will put positions on in both Stock 1 and Stock 2 five

times each, at days 50, 60, 70, 80, and 90.

NOTE: EVEN THOUGH YOU KNOW THE FUTURE PRICES (P (T+10) ) BECAUSE YOU HAVE

ALL 100 DAYS OF PRICE DATA, YOUR DETERMINATION OF STRATEGY IN YOUR

DECISION TREE MUST BE BASED ONLY ON PAST DATA. THERE IS NO PERFECT WAY

OF DOING THAT. 

At the end of each 10 days, based on the then-current price of the stock, the option

strategy will either be unwound, meaning the options (i) will be exercised (and the

portfolio will be adjusted), or (ii) sold at the current market price. To determine that

market price, re-price the options at the then-current price and volatility using the B-S

(but with a duration 10 days shorter). Then calculate your gain or loss. You must have a

method for determining whether (i) or (ii) is more profitable (or generates the smallest

losses).

You are to then repeat the process until day 100 (i.e. 5 times). In other words,

 on day 50, it will determine an expected price on day 60, then figure out which option

strategy should be employed (Strategy 1-Stock1 and Strategy 1-Stock2), then on day

60, will determine the payoffs of Strategy 1-S1 and -S2;

 then on day 60, it will determine an expected price on day 70, then figure out which

option strategy should be employed (Strategy 2-S1 and -S2), then on day 60, will

determine the payoff of Strategy 2-S1 and -S2;

 …

 on day 90, it will determine an expected price on day 100, then figure out which option

strategy should be employed (Strategy 5-S1 and -S2), then on day 100, will determine

the payoff of Strategy 5-S1 and -S2.

You have all 100-days of prices, however as noted above, your model CANNOT look

forward at prices to determine what would actually work best (that is called backdating

options and is VERY illegal). At the end of each Strategy (i.e., days 60, 70, 80, 90 and 100),

after any payouts/purchases/sales for earlier Strategies have been determined/executed,

the client’s position must be rebalanced.

Your final product will include:

1. An easily followed model that does the calculations necessary.

2. The decision tree (Silver Decisions), laying out verbally what information/decision will

be used for each node, including a written explanation of the strategy you use [yes, this

is step 1 to creating a trading bot, but we are not programmers. Just explain your

analysis of how your strategy will use the data to make a decision].

3. For each iteration of strategy, as well as the overall result:

1. the profit table when the strategy is executed, and

2. the payout after 10 days, either through exercising the options or unwinding the

position.

What you will turn in is:

1. A pdf of your decision tree with explanations for any non-obvious decisions (can be a

separate word doc).

2. An explanation of how your Strategy makes its decisions about positions and sizes (can

be combined with 1 above).

3. A spreadsheet that shows your calculations and the results of the 10 trades.