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日期:2020-07-16 11:31

BU MET CS-677: Data Science With Python, v.2.0 CS-677: Day Trading with Oracle

Assignment

In this assignment, you will use Python to analyze the distribution

of returns and a number of trading strategies. This

assignment has to be done in Python only (no NumPy or Pandas)

except for generating daily returns data and saving it to

a file.

As part of the preliminary assignment, you have generated a

daily stock file for your stock and a daily file ”spy.csv” for the

S&P-500 (using the symbol ”spy”). For both files, you have

data for 2015 - 2019 (5 years).

In this assignment, you will investigate 2 sets of questions concerning

daily returns

1. If you buy a stock for just one day, what is the best day of

the week to do so. Specifically you will analyze the daily

returns for each day of the week. A ”Monday” return is

the percent change in (adjusted) closing price from previous

Friday to Monday. A ”Tuesday” return is the percent

change in price from Monday to Tuesday and so on.

2. comparison of returns if you have an ”oracle” that can predict

the future behavior of your stock price

We start with introducing some notation. Let R = {r1, . . . , rn}

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BU MET CS-677: Data Science With Python, v.2.0 CS-677: Day Trading with Oracle

denote your daily returns for your stock for n days. The mean

of the daily returns

μ(R) = r1 + · · · + rnn

To compute the standard deviation σ(R) we can use

Let us split the daily returns R into two sets

1. R?: all negative returns

2. R+: all non-negative returns

Finally, let |R?| denote the number of days with negative returns,

and |R+| denote the number of days with non-negative

returns.

Question 1:

1. for each of the 5 years, compute the mean and standard

deviation for the sets R, R? and R+ of daily returns for

your stock for each day of the week

2. summarize your results in the table as shown below (5 tables

total).

3. are there more days with negative or non-negative returns?

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BU MET CS-677: Data Science With Python, v.2.0 CS-677: Day Trading with Oracle

Day μ(R) σ(R) |R?| μ(R?) σ(R?) |R+| μ(R+) σ(R+)

Monday

Tuesday

Wednesday

Thursday

Friday

4. does your stock lose more on a ”down” day than it gains

on an ”up” days.

5. are these results the same across days of the week?

Question 2: Examine your 5 tables.

1. are there any patterns across days of the week?

2. are there any patterns across different years for the same

day of the week?

3. what are the best and worst days of the week to be invested

for each year.

4. do these days change from year to year for your stock?

Question 3: Compute the aggregate table across all 5 years,

one table for both your stock and one table for S&P-500 (using

data for ”spy”).

1. what is the best and worst days of the week for each?

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BU MET CS-677: Data Science With Python, v.2.0 CS-677: Day Trading with Oracle

2. are these days the same for your stock as they are for S&P-

500?

For the next questions, suppose that you have an ”oracle”.

On any day, this oracle could tell you whether price of any

stock would increase or decrease the next day. Assume that

you have no transaction costs. You start with $100 on the first

trading day of 2015 to trade your stock and another $100 to

trade ”spy”.

Question 4: You listen to the oracle and follow its advice.

How much much money will you have on the last trading day

of 2019:

1. your stock?

2. S&P-500 stock?

Question 5: Consider ”buy-and-hold” strategy: you buy

on the first trading day and sell on the last day. So you do not

listen to your oracle at all. As before, assume that you start

with $100 for both your stock and ”spy”.

1. how much money will you have on the last trading day of

2019?

2. how do these results compare with results obtained in question

4?

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BU MET CS-677: Data Science With Python, v.2.0 CS-677: Day Trading with Oracle

Question 6: Your oracle got very upset that you did not

follow its advice. It decided to take revenge by giving you

wrong advice from time to time. Specifically, let us consider

the following three scenarios:

(a) Oracle gave you wrong results for the best 10 trading days.

In other words, you missed the best 10 days and your overall

profit will be lower.

(b) Oracle gave you wrong results for worst 10 trading days. In

other words, you missed the worst 10 days and your overall

profit will be higher.

(c) Oracle gave you wrong results for best 5 days and for the

worst 5 days.

Please answer the following:

1. for each of the scenarios above (a,b and c), compute the

final amount that you will have for both your stock and

”spy”

2. do you gain more by missing the worst days or by missing

the best days?

3. are the results in part (c) different from results that you

obtained in question 4.

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