A client has asked you to create a decision tree/model for two stoc
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.
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.
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