def _get_contents(self):
return lp.Frame([
lp.Block(self.block_contents, title=self.block_title),
pl.VFill(),
pl.UnorderedList([
lp.DimAndRevealListItems(
self.main_contents,
vertical_fill=True,
)
])
],
title=self.title,
**self.kwargs)
def get_content():
random.seed(1000)
next_until_end_ov = lp.Overlay([lp.UntilEnd(lp.NextWithIncrement())])
next_slide = lp.Overlay([lp.NextWithIncrement()])
numpy_mono = pl.Monospace('numpy')
lecture = get_dynamic_salary_python_lecture()
return [
pl.Section(
[
lp.DimRevealListFrame(
[
'We have seen how structure and organization can help the readability and maintainability of '
'an Excel model. The same concept exists for our Python models.',
['We already learned that we should use functions to organize logic and a',
pl.Monospace('dataclass'),
'for the model inputs'],
"Typically you'll have functions for each step, those may be wrapped up into other functions which "
"perform larger steps, and ultimately you'll have one function which does everything by calling the"
"other functions.",
"Those are good ideas with any Python model, but working in Jupyter allows us some additional "
"organization and presentation of the model"
],
title='How to Structure a Python Financial Model'
),
lp.DimRevealListFrame(
[
'In Jupyter, we can have code, nicely formatted text, equations, sections, hyperlinks, '
'and graphics, all in one document',
['For all you can do with these nicely formatted "Markdown" cells, see',
Hyperlink('https://www.markdownguide.org/basic-syntax/', 'here'), 'and',
Hyperlink('https://www.markdownguide.org/extended-syntax/', 'here.')],
'We can think of sections in Jupyter as analagous to Excel sheets/tabs. One section for each '
'logical part of your model. Then you can have smaller headings for subsections of the model.',
'Break your code up into small sections dealing with each step, with nicely formatted text '
'explaining it. Add comments where anything is unclear in the code.',
],
title='Using Jupyter for Structure of a Model'
),
lp.GraphicFrame(
[
get_model_structure_graphic()
],
title='Structuring a Python Model'
),
lp.DimRevealListFrame(
[
'When I develop in Jupyter, I have lots of cells going everywhere testing things out',
['When I finish a project in Jupyter, I remove these testing cells and make sure it runs and '
'logically flows from end to end', pl.Monospace('(restart kernel and run all cells)')],
"Run your model with different inputs, and make sure the outputs change in the expected fashion. This "
"is a good way to check your work.",
'There may be outputs in each section, but the final output should be at the end of the notebook',
],
title='Workflow and Final Output'
),
],
title='Structuring a Model in Python and Jupyter',
short_title='Model Structure'
),
pl.Section(
[
lp.DimRevealListFrame(
[
'The first project is aimed at approaching a new time value of money and cash flow model',
'It covers the same concepts as the retirement model, but in a capital budgeting setting',
'We need to introduce some economic equations to handle this model. You should have covered these in microeconomics.'
],
title='Introducing Project 1'
),
lp.GraphicFrame(
images_path('supply-demand-graph.png'),
title='A Quick Review of Supply and Demand'
),
lp.Frame(
[
lp.Block(
[
"There are a couple of basic economic equations we haven't talked about that "
"we'll need for this:",
pl.Equation(str_eq='R = PQ', inline=False),
pl.Equation(str_eq='Q = min(D, S)', inline=False),
pl.UnorderedList([
f'{pl.Equation(str_eq="R")}: Revenue',
f'{pl.Equation(str_eq="Q")}: Quantity Purchased',
f'{pl.Equation(str_eq="D")}: Quantity Demanded',
f'{pl.Equation(str_eq="S")}: Quantity Supplied',
])
],
title='New Required Equations'
)
],
title='Equations for Project 1'
),
lp.Frame(
[
pl.UnorderedList([
lp.DimAndRevealListItems([
'We need to cover one more Python concept and one gotcha before you can complete the first project.',
"On the next slide I'll introduce error handling, and show an example of how it's useful"
],
vertical_fill=True)
]),
lp.AlertBlock(
[
pl.UnorderedList([
f'The NPV function in {numpy_mono} works slightly differently than the NPV function in Excel.',
f'Excel treats the first cash flow as period 1, while {numpy_mono} treats the first cash flow as period 0.',
'If taking NPV where the first cash flow is period 1, pass directly to Excel, and for Python, pass 0 as the first cash flow, then the rest.',
'If taking NPV where the first cash flow is period 0, pass from period 1 to end to Excel and add period 0 separately, pass directly to Python.'
])
],
title='NPV Gotcha',
overlay=next_slide
)
],
title='A Couple More Things on the Python Side'
),
],
title='Project 1 Additional Material',
short_title='Project 1'
),
pl.Section(
[
get_retirement_model_overview_frame(),
lp.Frame(
[
lp.Block(
salary_block_content,
title='Salary with Promotions and Cost of Living Raises'
)
],
title='Revisiting the Model Salary Equation'
),
lp.Frame(
[
pl.UnorderedList([
'For wealths, we need to add the investment return and then the savings in each year',
], overlay=next_until_end_ov),
pl.VFill(),
lp.Block(
[
lp.adjust_to_full_size_and_center(
pl.Equation(str_eq=r'W_t = W_{t-1} (1 + r_i) + S_t v')),
pl.UnorderedList([
f'{pl.Equation(str_eq="S_t")}: Salary at year {pl.Equation(str_eq="t")}',
f'{pl.Equation(str_eq="W_t")}: Wealth at year {pl.Equation(str_eq="t")}',
f'{pl.Equation(str_eq="r_i")}: Investment return',
f'{pl.Equation(str_eq="t")}: Number of years',
f'{pl.Equation(str_eq="v")}: Savings rate',
])
],
title='Calculating Wealth',
overlay=next_until_end_ov,
)
],
title='Building the Wealth Model'
),
InClassExampleFrame(
[
'I will now show the process I use to create a full model.',
'I will be recreating the model "Dynamic Salary Retirement Model.ipynb"',
'Go ahead and download that to follow along as you will also extend it in a lab exercise',
],
title='Creating a Full Model in Python',
block_title='Dynamic Salary Retirement Model in Python',
),
get_extend_dynamic_retirement_python_lab_lecture().to_pyexlatex().presentation_frames(),
LabExercise(
[
[
"Usually I would try to have smaller labs but it didn't fit the format of this lecture. "
"Most will not be able to complete this during class.",
"For this lab, attempt the practice problem "
'"P1 Python Retirement Savings Rate Problem.pdf"',
'This is similar to how the projects will be assigned, so it is good preparation',
"I would encourage you to try it from scratch. If you are totally stuck, try working off "
"of the retirement model I completed today to have a lot of the structure already. If you "
"still are having trouble with that, check the solution and see me in office hours.",
'Note: this is not an official lab exercise you need to submit, it is practice only, but '
'I would highly encourage you to complete it.'
]
],
block_title='Practice Building A Model',
frame_title='Extending the Simple Retirement Model in a Different Way',
label='lab:retire-model'
),
],
title='Building the Dynamic Salary Retirement Model',
short_title='Build the Model'
),
pl.PresentationAppendix(
[
lecture.pyexlatex_resources_frame,
get_extend_dynamic_retirement_python_lab_lecture().to_pyexlatex().appendix_frames(),
]
)
]
def get_content():
lecture = get_python_basics_lecture()
conditionals_lab = get_python_basics_conditionals_lab_lecture().to_pyexlatex()
lists_lab = get_python_basics_lists_lab_lecture().to_pyexlatex()
functions_lab = get_python_basics_functions_lab_lecture().to_pyexlatex()
data_types_lab = get_python_basics_data_types_lab_lecture().to_pyexlatex()
classes_lab = get_python_basics_classes_lab_lecture().to_pyexlatex()
appendix_frames = [
*conditionals_lab.appendix_frames(),
*lists_lab.appendix_frames(),
*functions_lab.appendix_frames(),
*data_types_lab.appendix_frames(),
*classes_lab.appendix_frames()
]
next_slide = lp.Overlay([lp.NextWithIncrement()])
function_example = pl.Python(
"""
def my_func(a, b, c=10):
return a + b + c
>>> my_func(5, 6)
21
""")
use_class_example = pl.Python(
"""
from car_example import Car
>>> my_car = Car('Honda', 'Civic')
>>> print(my_car)
Car(make='Honda', model='Civic')
>>> type(my_car)
car_example.Car
>>> my_car.make
'Honda'
>>> my_car.drive()
'The Honda Civic is driving away!'
""")
dataclass_example = pl.Python(
"""
from dataclasses import dataclass
@dataclass
class ModelInputs:
interest_rates: tuple = (0.05, 0.06, 0.07)
pmt: float = 1000
>>> inputs = ModelInputs(pmt=2000)
>>> print(inputs)
ModelInputs(interest_rates=(0.05, 0.06, 0.07), pmt=2000)
>>> type(inputs)
__main__.ModelInputs
>>> inputs.interest_rates
(0.05, 0.06, 0.07)
>>> inputs.pmt
2000
""")
if_example = [pl.Python(
"""
>>> if 5 == 6:
>>> print('not true')
>>> else:
>>> print('else clause')
>>>
>>> this = 'woo'
>>> that = 'woo'
>>>
>>> if this == that:
>>> print('yes, print me')
>>> if this == 5:
>>> print('should not print')
"""
), pl.Monospace('else clause'), OutputLineBreak(), pl.Monospace('yes, print me')]
build_list_example = pl.Python(
"""
>>> inputs = [1, 2, 3]
>>> outputs = []
>>> for inp in inputs:
>>> outputs.append(
>>> inp + 10
>>> )
>>> outputs.insert(0, 'a')
>>> print(outputs)
['a', 11, 12, 13]
"""
)
enumerate_example = [pl.Python(
"""
>>> inputs = ['a', 'b', 'c']
>>> for i, inp in enumerate(inputs):
>>> print(f'input number {i}: {inp}')
"""
),
pl.Monospace('input number 0: a'),
OutputLineBreak(),
pl.Monospace('input number 1: b'),
OutputLineBreak(),
pl.Monospace('input number 2: c')
]
list_indexing_example = pl.Python(
"""
>>> my_list = ['a', 'b', 'c', 'd']
>>> my_list[0] # first item
'a'
>>> my_list[1] # second item
'b'
>>> my_list[-1] # last item
'd'
>>> my_list[:-1] # up until last item
['a', 'b', 'c']
>>> my_list[1:] # after the first item
['b', 'c', 'd']
>>> my_list[1:3] # from the second to the third item
['b', 'c']
"""
)
f_string_example = pl.Python(
"""
>>> my_num = 5 / 6
>>> print(my_num)
0.8333333333333334
>>> print(f'My number is {my_num:.2f}')
'My number is 0.83'
"""
)
f_string = pl.Monospace("f''")
f_mono = pl.Monospace('f')
try_except_example = pl.Python(
"""
>>> my_list = ['a', 'b']
>>> try:
>>> my_value = my_list[10]
>>> except IndexError:
>>> print('caught the error')
caught the error
"""
)
list_100_5 = pl.Monospace('[100] * 5')
next_slide = lp.Overlay([lp.NextWithIncrement()])
annuity_example = pl.Python(
"""
>>> annuity = [100] * 5
>>> annuities = [
>>> annuity,
>>> [0, 0, 0] + annuity
>>> ]
>>> n_years = 10
>>> output = [0] * n_years
>>> for i in range(n_years):
>>> for ann in annuities:
>>> try:
>>> output[i] += ann[i]
>>> except IndexError:
>>> pass
>>> print(output)
[100, 100, 100, 200, 200, 100, 100, 100, 0, 0]
"""
)
site_link = Hyperlink(SITE_URL, 'the course site')
return [
pl.Section(
[
lp.TwoColumnGraphicDimRevealFrame(
[
"Now we are going to build our first complex Python model",
"We will also learn a bit more Python before we can get there",
"Just as we did in Excel, we need to add structure to make the model navigatable",
"Logic should be organized in functions and be documented",
],
graphics=[
images_path('python-logo.png')
],
title='An Organized Structure of an Advanced Python Model'
),
lp.GraphicFrame(
[
get_model_structure_graphic()
],
title='The Structure of a Complex Model'
),
],
title='Introduction',
short_title='Intro'
),
pl.Section(
[
lp.Frame(
[
lp.Block(
[
pl.TextSize(-1),
if_example,
],
title='If Statements in Python'
),
],
title='Python Conditionals - If Statement'
),
lp.DimRevealListFrame(
[
'Use two equals signs to compare things (single to assign things)',
'Else is equivalent to value if false behavior in Excel',
'We can do a lot more than just set a single value, anything can be done in an if or else statement',
[pl.Monospace('elif'),
' is a shorthand for else if, e.g. not the last condition, but this condition']
],
title='Explaining the If-Else Statements'
),
InClassExampleFrame(
[
f"On {site_link}, there is a Jupyter notebook called Python Basics containing all "
f"of the examples for today's lecture",
'Now I will go through the example material under "Conditionals"'
],
title='Conditionals Example',
block_title='Trying out Conditionals'
),
conditionals_lab.presentation_frames(),
],
title='Conditionals'
),
pl.Section(
[
lp.Frame(
[
lp.Block(
build_list_example,
title='List Building'
),
pl.UnorderedList([
lp.DimAndRevealListItems([
['Use ', pl.Monospace('.append'), ' to add an item to the end of a list'],
['Use ', pl.Monospace('.insert'), ' to add an item at a certain position'],
])
])
],
title='Python Patterns - Building a List'
),
lp.Frame(
[
pl.UnorderedList([
'Index is base zero (0 means first item, 1 means second item)',
]),
pl.VFill(),
list_indexing_example,
],
title='List Indexing and Slicing'
),
InClassExampleFrame(
[
"We will keep working off of Python Basics.ipynb",
'Now I will go through the example material under "Working more with Lists"'
],
title='Lists Example',
block_title='Doing More with Lists'
),
lists_lab.presentation_frames(),
],
title='More with Lists',
short_title='Lists'
),
pl.Section(
[
lp.DimRevealListFrame(
[
"In Python, we can group logic into functions",
"Functions have a name, inputs, and outputs",
"Functions are objects like everything else in Python",
function_example,
],
title='Functions - Grouping Reusable Logic'
),
InClassExampleFrame(
[
"We will keep working off of Python Basics.ipynb",
'Now I will go through the example material under "Functions"'
],
title='Functions Example',
block_title='Structuring Code using Functions'
),
functions_lab.presentation_frames(),
],
title='Functions'
),
pl.Section(
[
lp.DimRevealListFrame(
[
'In Python, everything is an object except for variable names, which are references to objects',
'Every object has a type. We have learned about strings, numbers, lists, and booleans (True, False)',
'In the next section on classes, we will learn more about the relationship between the type '
'and the object'
],
title='What are Types?'
),
# TODO [#12]: add f-strings to Jupyter example
lp.Frame(
[
pl.UnorderedList([
lp.DimAndRevealListItems([
'You may have noticed that we can end up with a lot of decimals in Python output',
'Further, you may want to include your results as part of a larger output, such as a sentence.',
f'For these operations, we have {f_mono} strings: {f_string}'
],
vertical_fill=True)
]),
lp.Block(
f_string_example,
title='Example',
overlay=next_slide
)
],
title='Formatting Python Strings'
),
lp.DimRevealListFrame(
[
'So far I have just said that numbers are a type in Python, but this is a simplification',
['There are two main types of numbers in python:', pl.Monospace('float'), 'and',
pl.Monospace('int'), 'corresponding to a floating point number and an integer, respectively'],
['An', pl.Monospace('int'), 'is a number without decimals, while a', pl.Monospace('float'),
'has decimals, regardless of whether they are zero'],
['For example,', pl.Monospace('3.5'), 'and', pl.Monospace('3.0'), 'are floats, while',
pl.Monospace('3'), 'is an int, even though', pl.Monospace('3.0 == 3 is True')],
["Usually, this doesn't matter. But to loop a number of times, you must pass an",
pl.Monospace('int')]
],
title='Numeric Types'
),
lp.DimRevealListFrame(
[
['A', pl.Monospace('tuple'), 'is like a', pl.Monospace('list'), "but you can't change it after "
"it has been created (it is immutable)"],
['Tuples are in parentheses instead of brackets, e.g.', pl.Monospace('("a", "b")')],
['A', pl.Monospace('dict'), 'short for dictionary, stores a mapping. Use them if you want '
'to store values associated to other values'],
['We will come back to', pl.Monospace('dicts'), 'later in the course, but I wanted to',
'introduce them now as they are a very fundamental data type']
],
title='Additional Built-In Types'
),
InClassExampleFrame(
[
"We will keep working off of Python Basics.ipynb",
'Now I will go through the example material under "Exploring Data Types"'
],
title='Data Types Example',
block_title='Understanding the Different Data Types'
),
data_types_lab.presentation_frames(),
],
title='More about Data Types',
short_title='Data Types'
),
pl.Section(
[
lp.GraphicFrame(
images_path('class-object.pdf'),
title='Overview of Classes and Objects'
),
lp.DimRevealListFrame(
[
'In Python, everything is an object except for variable names, which are references to objects',
'Strings, floats, ints, lists, and tuples are types of objects. There are many more types of '
'objects and users can define their own types of objects',
'A class is a definition for a type of object. It defines how it is created, the data '
'stored in it, and the functions attached to it',
'We can write our own classes to create new types of objects to work with'
],
title='Everything is an Object. Every Object has a Class'
),
lp.DimRevealListFrame(
[
'From a single class definition, an unlimited number of objects can be created',
'Typically the class definition says it should accept some data to create the object',
'Then when you have multiple objects of the same type (created from the same class), '
'they will have the same functions (methods) attached to them, but different data stored within',
['For example, we can create two different lists. They will have different contents, but we can',
'do', pl.Monospace('.append'), 'on either of the lists']
],
title='Many Objects to One Class'
),
lp.MultiGraphicFrame(
[
images_path('class-object.pdf'),
images_path('list-object.pdf')
],
title='Lists are Objects',
vertical=False
),
lp.MultiGraphicFrame(
[
images_path('class-object.pdf'),
images_path('car-object.pdf')
],
title='We can Make Custom Objects Too',
vertical=False
),
lp.Frame(
[
pl.UnorderedList(['Constructing an object from a class looks like calling a function:']),
lp.Block(
[
pl.TextSize(-1),
use_class_example,
],
title='Using Custom Classes in Python'
),
],
title='Creating and Using Objects'
),
lp.DimRevealListFrame(
[
'I will not be teaching you about creating general classes in this course. It is very useful '
'but is generally more advanced. I encourage you to learn them outside the course.',
"We covered this material for two reasons:",
['To give a better understanding of how Python works in general, and why sometimes we '
'call functions as', pl.Monospace('something.my_func()'), 'rather than',
pl.Monospace('my_func()')],
['We are going to use', pl.Monospace('dataclasses'), 'to store our model data. They are',
'a simplified version of classes used mainly for storing data.']
],
title='Where we Will Focus in This Course'
),
lp.Frame(
[
pl.UnorderedList(['An organized way to store our model input data:']),
lp.Block(
[
pl.TextSize(-3),
dataclass_example,
],
title='Using Dataclasses in Python'
),
],
title='Dataclass Intro'
),
lp.DimRevealListFrame(
[
['A', pl.Monospace('dataclass'), 'is just a class which is more convenient to create, and',
'is typically used to group data together'],
['If you need to pass around multiple variables together, they make sense. For our models, we '
'will want to pass around all the inputs, so one', pl.Monospace('dataclass'), 'for all the',
'inputs to the model makes sense'],
'This way instead of having to pass around every input individually to every function, just '
'pass all the input data as one argument',
['Also enables easy tab-completion. What were the names of my inputs? Just hit tab after',
pl.Monospace('data.')]
],
title='What, When and Why Dataclasses?'
),
InClassExampleFrame(
[
"We will keep working off of Python Basics.ipynb",
'For this example, also go and download car_example.py and put it in the same folder',
'Now I will go through the example material under "Working with Classes"'
],
title='Classes Example',
block_title='Working with Classes and Creating Dataclasses'
),
classes_lab.presentation_frames(),
],
title='Classes and Dataclasses',
short_title='Classes'
),
pl.Section(
[
# TODO [#13]: add error handling to Jupyter example
lp.Frame(
[
pl.UnorderedList([
lp.DimAndRevealListItems([
"You have certainly already seen errors coming from your Python code. When they have come up, the code doesn't run.",
'Sometimes you actually expect to get an error, and want to handle it in some way, rather than having your program fail.'
],
vertical_fill=True)
]),
lp.Block(
try_except_example,
title='Example',
overlay=next_slide
)
],
title='Python Error Handling'
),
lp.DimRevealListFrame(
[
"Let's say you're receiving annuities. There is a single annuity which produces \$100 for 5 years. You receive this annuity in year 0 and in year 3.",
f"You might define the annuity cash flows as a list of 100, 5 times ({list_100_5})",
'Then you want to come up with your overall cash flows, going out to 15 years'
],
title='An Example where Error Handling is Useful'
),
lp.Frame(
[
lp.Block(
[
pl.TextSize(-1),
annuity_example,
],
title='Calculating the Sum of Unaligned Annuity Cash-Flows'
)
],
title='Applying Error Handling'
),
],
title='Error Handling',
short_title='Errors'
),
pl.PresentationAppendix(
[
lecture.pyexlatex_resources_frame,
*appendix_frames
]
)
]
def get_content():
random.seed(1000)
lecture = get_probability_lecture()
scenario_excel_lab = get_scenario_analysis_excel_lab_lecture().to_pyexlatex()
scenario_python_lab = get_scenario_analysis_python_lab_lecture().to_pyexlatex()
randomness_excel_lab = get_randomness_excel_lab_lecture().to_pyexlatex()
randomness_python_lab = get_randomness_python_lab_lecture().to_pyexlatex()
random_stock_lab = get_random_stock_model_lab_lecture().to_pyexlatex()
full_model_internal_randomness_lab = get_extend_model_internal_randomness_lab_lecture().to_pyexlatex()
appendix_frames = [
lecture.pyexlatex_resources_frame,
scenario_excel_lab.appendix_frames(),
scenario_python_lab.appendix_frames(),
randomness_excel_lab.appendix_frames(),
randomness_python_lab.appendix_frames(),
random_stock_lab.appendix_frames(),
full_model_internal_randomness_lab.appendix_frames(),
]
df_mono = pl.Monospace('DataFrame')
next_slide = lp.Overlay([lp.NextWithIncrement()])
with_previous = lp.Overlay([lp.NextWithoutIncrement()])
rand_mono = pl.Monospace('=RAND')
rand_between_mono = pl.Monospace('=RANDBETWEEN')
norm_inv_mono = pl.Monospace('=NORM.INV')
excel_random_normal_example = pl.Monospace('=NORM.INV(RAND(), 10, 1)')
random_module_mono = pl.Monospace('random')
py_rand_mono = pl.Monospace('random.random')
py_rand_uniform_mono = pl.Monospace('random.uniform')
py_rand_norm_mono = pl.Monospace('random.normalvariate')
py_random_link = Hyperlink('https://docs.python.org/3.7/library/random.html#real-valued-distributions',
'(and other distributions)')
py_random_normal_example = pl.Monospace('random.normalvariate(10, 1)')
random_seed_example = pl.Monospace('random.seed(0)')
next_slide = lp.Overlay([lp.NextWithIncrement()])
n_iter = pl.Equation(str_eq='n_{iter}')
df_mono = pl.Monospace('DataFrame')
df_std = pl.Monospace('df.std()')
df_mean = pl.Monospace('df.mean()')
random_choices_mono = pl.Monospace('random.choices')
random_choices_example = pl.Monospace("random.choices(['Recession', 'Normal', 'Expansion'], [0.3, 0.5, 0.2])")
return [
pl.Section(
[
lp.TwoColumnGraphicDimRevealFrame(
[
'So far everything in our models has been deterministic',
'Further, we have not explored any scenarios in our models, we have taken the base case as '
'the only case',
'Unfortunately, the real world is very random. Many possible scenarios could occur.'
],
[
images_path('dice.jpg'),
],
title='Why Model Probability'
),
lp.DimRevealListFrame(
[
'There are a few ways we can gain a richer understanding of the modeled situation by '
'incorporating probability',
f'The simplest is {pl.Bold("scenario modeling")}, in which different situations are defined with probabilities, '
'and the result of the model is the expected value across the cases.',
['Another is', pl.Bold('internal randomness'),
'where randomness is incorporated directly within '
'the model logic'],
['Finally,', pl.Bold("Monte Carlo simulation"),
'treats the model as deterministic but externally varies the '
'inputs to get a distribution of outputs.']
],
title='How to Bring Probability In'
),
],
title='Motivation for Probability Modeling',
short_title='Intro',
),
pl.Section(
[
lp.Frame(
[
pl.UnorderedList([
lp.DimAndRevealListItems([
['When something is measured numerically, it can be either a', pl.Bold('discrete'),
'variable, or a', pl.Bold('continuous'), 'variable.'],
])
]),
lp.Block(
[
pl.Equation(str_eq=r'x \in \{x_1, x_2, ... x_n\}', inline=False),
pl.VSpace(-0.4),
pl.UnorderedList([
[pl.Equation(str_eq=r'\{x_1, x_2, ... x_n\}:'), 'A specific set of values'],
])
],
title='Discrete Variables'
),
lp.Block(
[
pl.Equation(str_eq=r'x \in \mathbb{R} \text{ or } [a, b]', inline=False),
pl.VSpace(-0.4),
pl.UnorderedList([
[pl.Equation(str_eq='\mathbb{R}:'), 'All real numbers'],
[pl.Equation(str_eq='[a, b]:'), 'Some interval between two values or infinity'],
])
],
title='Continuous Variables'
),
],
title='Math Review: Discrete and Continuous Variables'
),
lp.Frame(
[
pl.TextSize(-3),
pl.UnorderedList([
lp.DimAndRevealListItems([
[pl.Bold('Expected value'), 'is the average outcome over repeated trials'],
"It is generally useful to get a single output from multiple possible cases",
], dim_earlier_items=False)
]),
lp.Block(
[
pl.Equation(str_eq=r'E[x] = \sum_{i=1}^{N} p_i x_i', inline=False),
pl.VSpace(-0.4),
pl.UnorderedList([
[pl.Equation(str_eq=r'E[x]:'), 'Expected value for', pl.Equation(str_eq='x')],
[pl.Equation(str_eq=r'x_i:'), 'A specific value for', pl.Equation(str_eq='x')],
[pl.Equation(str_eq=r'p_i:'), 'The probability associated with value',
pl.Equation(str_eq='x_i')],
[pl.Equation(str_eq=r'N:'), 'The total number of possible values of',
pl.Equation(str_eq='x')],
])
],
title='Discrete Variables'
),
lp.Block(
[
pl.Equation(str_eq=r'E[x] = \frac{1}{N} \sum_{i=1}^{N} x_i', inline=False),
pl.VSpace(-0.4),
pl.UnorderedList([
[pl.Equation(str_eq=r'N:'), 'The number of samples collected for',
pl.Equation(str_eq='x')],
])
],
title='Continuous Variables'
),
],
title='Math Review: Expected Value'
),
lp.GraphicFrame(
images_path('different-variance-plot.pdf'),
title='Math Review: Variance in One Picture'
),
lp.Frame(
[
pl.TextSize(-2),
pl.UnorderedList([
lp.DimAndRevealListItems([
[pl.Bold('Variance'), 'and', pl.Bold('standard deviation'),
'are measures of the dispersion '
'of values of a random variable.'],
'Variance is the real quantity of interest, but standard deviation is easier to understand '
'because it has the same units as the variable, while variance has units squared'
], dim_earlier_items=False),
]),
lp.Block(
[
EquationWithVariableDefinitions(
r'Var[x] = \sigma^2 = \frac{1}{N - 1} \sum_{i=1}^{N} (x_i - \mu)^2',
[
[pl.Equation(str_eq=r'N:'), 'Number of samples of', pl.Equation(str_eq=r'x')],
[pl.Equation(str_eq=r'\mu:'), 'Sample mean'],
]
),
],
title='Variance of a Continuous Variable'
),
lp.Block(
[
EquationWithVariableDefinitions(
r'\sigma = \sqrt{Var[x]}',
[
[pl.Equation(str_eq=r'\sigma:'), 'Standard deviation'],
],
space_adjustment=-0.5
),
],
title='Standard Deviation'
),
],
title='Math Review: Variance and Standard Deviation'
),
lp.TwoColumnGraphicDimRevealFrame(
[
['A', pl.Bold('probability distribution'),
'represents the probabilities of different values of '
'a variable'],
'For discrete variables, this is simply a mapping of possible values to probabilities, e.g. for a coin '
'toss, heads = 50% and tails = 50%',
'For continuous variables, a continuous distribution is needed, such as the normal distribution',
],
graphics=[
images_path('normal-distribution.png'),
],
title='Math Review: Probability Distributions'
),
lp.TwoColumnGraphicDimRevealFrame(
[
pl.TextSize(-2),
["You've probably heard of the", pl.Bold('normal distribution'),
'as it is very commonly used because it occurs a lot in nature'],
['It is so common because of the', pl.Bold('central limit theorem'), 'which says that '
'averages of variables will follow a normal distribution, regardless of the distribution of the '
'variable itself'],
'This has many applications. For example, we can view the investment rate as an average across '
'individual investment returns, and so it will be normally distributed.',
],
graphics=[
images_path('normal-distribution-percentages.png'),
],
title='Math Review: Normal Distribution'
),
lp.Frame(
[
pl.TextSize(-3),
pl.UnorderedList([
lp.DimAndRevealListItems([
'We want to extend our retirement model to say that the investment return is not constant.',
'We can treat the interest rate as either a discrete (specific values) or a continuous '
'(range of values, more realistic) variable'
], dim_earlier_items=False),
]),
lp.Block(
[
pl.Center(
[
lt.Tabular(
[
lt.ValuesTable.from_list_of_lists([
['Interest Rate', 'Probability']
]),
lt.MidRule(),
lt.ValuesTable.from_list_of_lists([
['2%', '30%'],
['5%', '50%'],
['7%', '20%'],
]),
],
align='cc'
)
]
)
],
title='As a Discrete Variable'
),
lp.Block(
[
pl.Equation(str_eq=r'r_i \sim N(\mu, \sigma^2)', inline=False),
pl.VSpace(-0.5),
pl.UnorderedList([
[pl.Equation(str_eq=r'N:'), 'Normal distribution'],
[pl.Equation(str_eq=r'\mu:'), 'Interest rate mean'],
[pl.Equation(str_eq=r'\sigma:'), 'Interest rate standard deviation'],
])
],
title='As a Continuous Variable'
),
],
title='A Non-Constant Interest Rate'
),
],
title='Mathematical Tools for Probability Modeling',
short_title='Math Review'
),
pl.Section(
[
lp.Frame(
[
pl.TextSize(-1),
lp.Block(
[
pl.Center(
[
lt.Tabular(
[
lt.ValuesTable.from_list_of_lists([
['State of Economy', 'Interest Rate', 'Savings Rate', 'Probability']
]),
lt.MidRule(),
lt.ValuesTable.from_list_of_lists([
['Recession', '2%', '35%', '30%'],
['Normal', '5%', '30%', '50%'],
['Expansion', '7%', '25%', '20%'],
]),
],
align='l|ccc'
)
]
)
],
title='Interest Rate Scenarios'
),
pl.UnorderedList([
lp.DimAndRevealListItems([
['In scenario modeling, different cases for model parameters are chosen. Several '
'parameters may be altered at once in a given case.'],
"Here we are making the different cases the state of the economy. When the economy is doing "
"poorly, the individual earns a lower return, but also saves more because they don't want to "
"overspend at a bad time",
"When the economy does well, the individual earns a higher return, but also spends more"
])
]),
],
title='Scenario Modeling'
),
lp.DimRevealListFrame(
[
['We can implement scenario modeling', pl.Bold('internal'), 'or', pl.Bold('external'),
'to our model'],
['With an internal implementation, the cases are built', pl.Underline('into the model logic'),
'itself, '
'and model logic also takes the expected value of the case outputs. The inputs of the model',
'are now the cases and probabilities.'],
['With an external implementation, the', pl.Underline('model logic is left unchanged,'),
'instead the '
'model is run separately with each case, then the expected value is calculated across the outputs '
'from the multiple model runs.'],
],
title='Implementing Scenario Modeling'
),
lp.Frame(
[
pl.Center(
[
lt.Tabular(
[
lt.ValuesTable.from_list_of_lists([
[pl.Bold('Internal'), pl.Bold('External')]
]),
lt.MidRule(),
lt.MidRule(),
lt.ValuesTable.from_list_of_lists([
['Original model is now an old version',
'Original model can still be used normally'],
]),
# TODO [#14]: each row should come one per slide, but need to allow overlays in lt items
lt.MidRule(),
lt.ValuesTable.from_list_of_lists([
['Model runs exactly as before',
'Getting full results of model requires running the model multiple times and '
'aggregating output']
]),
lt.MidRule(),
lt.ValuesTable.from_list_of_lists([
['Model complexity has increased', 'Model complexity unchanged']
]),
lt.MidRule(),
lt.ValuesTable.from_list_of_lists([
['Complexity to run model is unchanged',
'Complexity to run model has increased']
]),
],
align='L{5cm}|R{5cm}'
)
]
)
],
title='Internal or External Scenario Analysis?'
),
lp.DimRevealListFrame(
[
'For internal scenario analysis, set up a table of the cases and probabilities. Then calculate the '
'expected value of these cases for each model parameter. Then use the expected value as the new '
'model parameter.',
'For external scenario analysis, a data table is useful. Create the data table of outputs for each case '
'and another table of case probabilities, then combine them to produce the expected value of '
'the output.',
'If you are trying to change more than two inputs at once in external scenario '
'analysis, this becomes more '
'challenging but you can assign a number to each set of inputs and have the model look up the '
'inputs based on the case number, using the case number as the data table input.'
],
title='Scenario Analysis in Excel'
),
InClassExampleFrame(
[
'I will now go through adding external scenario analysis to the Dynamic Salary Retirement Model '
'in Excel',
'The completed exercise on the course site as "Dynamic Salary Retirement Model Sensitivity.xlsx"',
],
title='Scenario Analysis in Excel',
block_title='Adding Scenario Analysis to the Dynamic Retirement Excel Model'
),
scenario_excel_lab.presentation_frames(),
lp.DimRevealListFrame(
[
['For internal scenario analysis, set up a', df_mono,
'or dictionary of the cases and probabilities. Then calculate '
'the expected value of these cases for each model parameter. Then use the expected value as the new '
'model parameter.'],
'For external scenario analysis, just call your model function with each input case, collect the '
'results, and combine them to produce the expected value of the output.'
],
title='Scenario Analysis in Python'
),
InClassExampleFrame(
[
'I will now go through adding external scenario analysis to the Dynamic Salary Retirement Model '
'in Python',
'he completed exercise on the course site as "Dynamic Salary Retirement Model Scenario.ipynb"',
],
title='Scenario Analysis in Python',
block_title='Adding Scenario Analysis to the Dynamic Retirement Python Model'
),
scenario_python_lab.presentation_frames(),
],
title='Scenario Modeling'
),
pl.Section(
[
lp.DimRevealListFrame(
[
["Using the technique of", pl.Bold('internal randomness,'),
'something random is added internally to the model'],
'Instead of taking a fixed input, random values for that variable are drawn',
'This technique can be used with both discrete and continuous variables'
],
title='What is Internal Randomness?'
),
lp.GraphicFrame(
internal_randomness_graphic(),
title='Internal Randomness in One Picture'
),
lp.DimRevealListFrame(
[
'Internal randomness makes sense when the random behavior is integral to your model',
'If you are just trying to see how changing inputs affects outputs, or trying to get confidence intervals for outputs, '
'an external method such as sensitivity analysis or Monte Carlo simulation would make more sense.',
'For example, if we want to allow investment returns to vary in our retirement model, an external method fits well because '
'the core model itself is deterministic',
'If instead we were modeling a portfolio, we might use internal randomness to get the returns for each asset.'
],
title='Should I Use Internal Randomness?'
),
lp.DimRevealListFrame(
[
'Similarly to our discussion of internal vs. external sensitivity analysis, internal randomness keeps '
'operational complexity (how to run the model) low, but increases model complexity.',
'The main drawback of internal randomness is that the same set of inputs will give different outputs each time the model is run',
'While this is the desired behavior, it can make it difficult to determine whether everything is working.'
],
title='Internal Randomness Advantages and Pitfalls'
),
lp.TwoColumnGraphicDimRevealFrame(
[
'Instead of taking the input as fixed, draw it from a distribution',
'We need to define a distribution for each input we want to randomize. This will typically be a normal distribution, and then '
'we just need to give it a reasonable mean and standard deviation',
'Put the most reasonable or usual value as the mean. Then think about the probabilities of the normal distribution relative '
'to standard deviation to set it'
],
graphics=[
images_path('normal-distribution-percentages.png'),
],
title='Internal Randomness with Continuous Variables'
),
lp.DimRevealListFrame(
[
['The main functions for randomness in Excel are', rand_mono, 'and', rand_between_mono],
'The latter gives a random number between two numbers, while the former gives a random number '
'between 0 and 1. Both of these draw from a uniform distribution (every number equally likely)',
['Meanwhile, the', norm_inv_mono,
'function gives the value for a certain normal distribution at a certain probability (it is not random)'],
'We can combine these two functions to draw random numbers from a normal distribution',
[excel_random_normal_example,
'would draw a number from a normal distribution with mean 10 and standard deviation 1'],
],
title='Internal Randomness with Continuous Variables in Excel'
),
InClassExampleFrame(
[
'I will now go through generating random continuous variables '
'in Excel',
'The completed exercise on the course site is called "Generating Random Numbers.xlsx"',
'We will focus only on the "Continuous" sheet for now',
],
title='Example for Continuous Random Variables in Excel',
block_title='Generating Random Numbers from Normal Distributions in Excel'
),
randomness_excel_lab.presentation_frames(),
lp.DimRevealListFrame(
[
['In Python, we have the built-in', random_module_mono, 'module'],
['It has functions analagous to those in Excel:', py_rand_mono, 'works like', rand_mono,
'and', py_rand_uniform_mono, 'works like', rand_between_mono],
['Drawing numbers from a normal distribution', py_random_link, 'is easier: just one function',
py_rand_norm_mono],
[py_random_normal_example,
'would draw a number from a normal distribution with mean 10 and standard deviation 1']
],
title='Internal Randomness with Continuous Variables in Python'
),
InClassExampleFrame(
[
'I will now go through generating random continuous variables '
'in Python',
'The completed exercise on the course site is called "Generating Random Numbers.ipynb"',
'We will focus only on the "Continuous" section for now',
],
title='Example for Continuous Random Variables in Python',
block_title='Generating Random Numbers from Normal Distributions in Python'
),
randomness_python_lab.presentation_frames(),
lp.DimRevealListFrame(
[
'We can also build randomness into the model for discrete variables',
"With discrete variables, our distribution is just a table of probabilities for the different values",
'To pick a random value for a discrete variable, first add another column to your table which has the '
'cumulative sum of the prior probabilties, and then another column which is that column plus the '
'current probability',
'Then generate a random number between 0 and 1 from a uniform distribution',
'If the generated number is between the probability and the cumulative sum of prior probabilities, choose that case'
],
title='Internal Randomness with Discrete Variables'
),
lp.Frame(
[
pl.TextSize(-1),
lp.Block(
[
pl.Center(
[
lt.Tabular(
[
lt.ValuesTable.from_list_of_lists([
['State of Economy', 'Interest Rate', 'Probability', 'Begin Range',
'End Range']
]),
lt.MidRule(),
lt.ValuesTable.from_list_of_lists([
['Recession', '2%', '30%', '0%', '30%'],
['Normal', '5%', '50%', '30%', '80%'],
['Expansion', '7%', '20%', '80%', '100%'],
]),
],
align='L{2cm}|cccc'
)
]
)
],
title='Interest Rate Scenarios'
),
pl.UnorderedList([
pl.TextSize(-2),
lp.DimAndRevealListItems([
'The Begin Range column is calculated as the cumulative sum of prior probabilities',
'The End Range column is calculated as Begin Range + Probability',
"Generate a random number between 0 and 1. If it is between the begin and end range, "
"that is the selected value",
"If it's 0.15, it's a recession. If it's 0.45, it's a normal period. If it's 0.94, it's "
"an expansion period."
], vertical_fill=True)
]),
],
title='An Example of Internal Randomness with Discrete Variables'
),
lp.DimRevealListFrame(
[
'The steps in the preceeding slides need to be carried out manually in Excel',
['In Python, there is a built-in function which is doing all of this in the background,',
random_choices_mono],
['Simply do', random_choices_example, 'to yield the exact same result for the prior example']
],
title='Random Discrete Variables in Python'
),
InClassExampleFrame(
[
'I will now go through generating random discrete variables '
'in both Excel and Python',
'We will be continuing with the same Excel workbook and Jupyter notebook from before, '
'"Generating Random Numbers.xlsx" and "Generating Random Numbers.ipynb"',
'We will focus only on the "Discrete" sheet/section now',
],
title='Example for Discrete Random Variables in Excel and Python',
block_title='Generating Random Numbers from Discrete Distributions in Excel and Python'
),
random_stock_lab.presentation_frames(),
InClassExampleFrame(
[
'I will now add internal randomness with discrete variables to '
'both the Excel and Python Dynamic Salary Retirement models to simulate economic conditions '
'changing year by year',
'The completed models on the course site are called '
'"Dynamic Salary Retirement Model Internal Randomness.xlsx" and '
'"Dynamic Salary Retirement Model Internal Randomness.ipynb"',
],
title='Adding Internal Randomness to Excel and Python Models',
block_title='Extending the Dynamic Salary Retirement Model with Internal Randomness'
),
full_model_internal_randomness_lab.presentation_frames(),
],
title='Internal Randomness'
),
pl.PresentationAppendix(appendix_frames),
]
def get_content():
random.seed(1000)
ev_bet = (999999 / 1000000) * 1 + (1 / 1000000) * (-750001)
xlwings_mono = pl.Monospace('xlwings')
pd_mono = pl.Monospace('pandas')
quickstart_mono = pl.Monospace('quickstart')
read_from_excel_example = pl.Python("""
my_value = xw.Range("G11").value # single value
# all values in cell range
my_value = xw.Range("G11:F13").value
# expands cell range down and left getting all values
my_values = xw.Range("G11").expand().value
""")
write_to_excel_example = pl.Python("""
xw.Range("G11").value = 10
xw.Range("G11").value = [10, 11] # horizontal
xw.Range("G11").value = [[10], [11]] # vertical
xw.Range("G11").value = [[10, 11], [12, 13]] # table
""")
ball_options = ['fill', 'circle', 'inner sep=8pt']
blue_ball_options = ball_options + ['blue']
red_ball_options = ball_options + ['red']
def rand_pos():
return random.randrange(-150, 150) / 100
blue_nodes = [
lg.Node(None, (rand_pos(), rand_pos()), options=blue_ball_options)
for _ in range(10)
]
red_nodes = [
lg.Node(None, (rand_pos(), rand_pos()), options=red_ball_options)
for _ in range(10)
]
red_blue_ball_graphic = lg.TikZPicture([
lg.Rectangle(5, 5, shape_options=['blue', 'thick']), *blue_nodes,
*red_nodes
])
lecture = get_monte_carlo_lecture()
intro_mc_python_lab = get_intro_monte_carlo_lab_lecture().to_pyexlatex()
mc_python_lab = get_python_retirement_monte_carlo_lab_lecture(
).to_pyexlatex()
mc_excel_lab = get_excel_retirement_monte_carlo_lab_lecture().to_pyexlatex(
)
return [
pl.Section([
lp.
TwoColumnGraphicDimRevealFrame([
[
pl.Bold('Monte Carlo Simulation'),
'is a technique which allows understanding the probability '
'of acheiving certain outputs from a model.'
],
'This gives the modeler a greater understanding of the likelihood of different outputs, rather '
'than relying on a single number',
],
graphics=[
images_path(
'random-numbers.jpg')
],
title=
'What is Monte Carlo Simulation?'),
lp.DimRevealListFrame([
r'Imagine you have a one-time opportunity to place a bet for \$1. ',
r'If you win the bet, you will receive \$2. If you lose the bet, you will lose \$750,000. '
r'You cannot avoid the payment by declaring bankruptcy.',
r'The odds of winning the bet are 999,999/1,000,000. In 1/1,000,000 you lose the \$750,000.',
fr'The expected profit from the bet is \${ev_bet:.2f}. Should you take it? Depends on your '
fr'risk tolerance.',
'Therefore not only the expected outcome matters, but also what other outcomes may occur and '
'their probabilities.'
],
title='Why Use Monte Carlo Simulation?'),
lp.GraphicFrame(explore_parameters_graphic(),
title='Monte Carlo Simulation in One Picture'),
lp.DimRevealListFrame([
'Monte Carlo simulation is carried out similarly to external scenario analysis.',
'The main difference is that we manually picked specific cases for the inputs with scenario '
'analysis.',
'In Monte Carlo simulation, we assign distributions to the inputs, and input values are drawn '
'from the distributions for each run of the model',
'Finally, we can fit a probability distribution to the outputs to be able to talk about the '
'chance of a certain outcome occurring'
],
title=
'Basic Process for Monte Carlo Simulation')
],
title='Introduction'),
pl.Section(
[
lp.DimRevealListFrame([
'Monte Carlo simulation can be applied to any model',
'It is generally easier to run them in Python than in Excel.',
"With pure Excel, you're either going to VBA or hacking something with data tables",
'In Python, just loop for N iterations, each time drawing inputs, running the model, and collecting '
'outputs.',
[
'We will start with a pure Python model, then move to using',
xlwings_mono, 'to add Monte Carlo '
'simulations to our Excel models.'
],
],
title=
'Running Monte Carlo Simulations - Python or Excel?'
),
lp.Frame([
lp.Block([
r'You have \$1,000 now and need to pay \$1,050 in one year. You have available to you '
r'two assets: a risk free asset that returns 3%, and a stock that returns 10% with a '
r'20% standard deviation. How much should you invest in the two assets to maximize '
r'your probability of having at least \$1,050 in one year?'
],
title='An Investment Problem'),
pl.VFill(),
pl.UnorderedList([
lp.DimAndRevealListItems([
'We must first construct the basic model which gets the portfolio value for given '
'returns',
'Then draw values of the stock return from a normal distribution, and run the model '
'many times and visualize the outputs. ',
'Then repeat this process with each weight to determine the best weight.'
])
])
],
title='An Example Application'),
InClassExampleFrame([
'Go to the course site and download the Jupyter notebook "MC Investment Returns.ipynb" from '
'Monte Carlo Examples',
'I will go through this example notebook to solve the problem from the prior slide.'
],
title='Simluating Portfolio Values',
block_title=
'Example for Simulating Portfolio Values'),
pl.TextSize(-2),
intro_mc_python_lab.presentation_frames(),
pl.TextSize(0),
],
title='Running a First Monte Carlo Simulation',
short_title='Run MC',
),
pl.Section(
[
lp.Frame([
pl.TextSize(-2), 'For the model given by:',
pl.Equation(str_eq='y = f(X)', inline=False),
pl.Equation(str_eq='X = [x_1, x_2, ..., x_n]',
inline=False),
pl.UnorderedList([[
pl.Equation(str_eq='y:'), 'Model output'
], [pl.Equation(str_eq='X:'), 'Model input matrix'],
[
pl.Equation(str_eq='x_i:'),
'Value of $i$th $x$ variable'
]]),
'To run $N$ Monte Carlo simulations, follow the following steps:',
pl.OrderedList(
[[
'Assign a probability distribution for each',
pl.Equation(str_eq='x_i')
],
[
'For each',
pl.Equation(str_eq='x_i'),
'randomly pick a value from its probability distribution. Store them as',
pl.Equation(str_eq='X_j')
],
[
'Repeat the previous step $N$ times, yielding',
pl.Equation(str_eq='[X_1, X_2, ..., X_N]')
],
[
'For each',
pl.Equation(str_eq='X_j'), 'calculate',
pl.Equation(str_eq='y_j = f(X_j)')
],
[
'Store the values of',
pl.Equation(str_eq='X_j'), 'mapped to',
pl.Equation(str_eq='y_j')
],
[
'Visualize and analyze',
pl.Equation(str_eq='y_j'), 'versus',
pl.Equation(str_eq='X_j')
]])
],
title='Monte Carlo Simulation Process'),
lp.DimRevealListFrame([
'There are a multitude of outputs we can get from a Monte Carlo simulation. We saw a few '
'already in the example.',
[
pl.Bold('Outcome probability distributions'),
'are the main output. We saw this with two '
'approaches in the example, a',
pl.Underline('histogram'), 'and a',
pl.Underline('probability table.')
],
[
'We also examined the',
pl.Bold('probability of a certain outcome'),
'in whether we reached '
'the desired cash.'
],
[
'The last main output is examining the',
pl.Bold('relationship between inputs and outputs.'),
'for which common approaches include',
pl.Underline('scatter plots'), 'and',
pl.Underline('regressions.')
]
],
title=
'Outputs from Monte Carlo Simulation'),
lp.TwoColumnGraphicDimRevealFrame(
[
pl.TextSize(-3),
'The outcome probability distribution represents the chance of receiving different '
'outcomes from your model.',
'There are two main ways to visualize a probability distribution: a plot and a table.',
[
'The plot, usually a',
pl.Underline('histogram'), 'or',
pl.Underline('KDE'),
'gives a high-level overview of the probabilities and can uncover any non-normal '
'features of the distribution.'
],
[
'The probability table represents the chance of receiving the given value or '
'lower.'
],
'The Value at Risk (VaR) is a common measure calculated in the industry, and it represents '
'the probability of losing at least a certain amount. This would be a subset of this analysis '
'and so this analysis can be used to calculate VaR',
],
graphics=[
images_path('outcome-probability-distribution.png'),
lt.Tabular([
pl.MultiColumnLabel('Probability Table', span=2),
lt.TopRule(),
lt.ValuesTable.from_list_of_lists(
[['Probability', 'Value']]),
lt.TableLineSegment(0, 1),
lt.ValuesTable.from_list_of_lists(
[['25%', '1020'], ['50%', '1039'],
['75%', '1053']]),
lt.BottomRule()
],
align='c|c')
],
title='Outcome Probability Distributions',
graphics_on_right=False,
),
lp.TwoColumnGraphicDimRevealFrame(
[
'Imagine a box which contains red and blue balls. You do not know in advance how many there '
'are of each color.',
'You want to estimate the probability of getting a blue ball when pulling a ball from the box.',
'To evaluate this, you grab a ball, write down its color, and put it back, 1,000 times.',
'You pull a blue ball in 350 out of the 1,000 trials. What is the probability of getting blue?'
],
graphics=[red_blue_ball_graphic
],
title='Probability of a Certain Outcome - A Simple Example'
),
lp.DimRevealListFrame([
'We followed the same logic when estimating the probability of receiving our desired cash '
'in the investment example.',
pl.Equation(
str_eq=
fr'p = \frac{{{pl.Text("Count of positive outcomes")}}}{{{pl.Text("Count of trials")}}}'
),
[
'For the balls example, this is simply',
pl.Equation(str_eq=r'p = \frac{350}{1000} = 0.35'),
],
[
'In the investment example, we used', pd_mono,
'to check for each trial, whether it was a '
'positive outcome (made it a 1) or not (made it a 0). Then the sum is the count of '
'positive outcomes and so the mean is the probability.'
],
],
title=
'Probability of a Certain Outcome, Formally'
),
lp.DimRevealListFrame([
'Monte Carlo simulation can also provide a more comprehensive look at the relationship between '
'inputs and outputs.',
'While sensitivity analysis can be used to estimate the relationship between an input and '
'output, it is usually done with other inputs at their base case',
'The values of inputs may affect how other inputs affect the output. E.g. for the retirement '
'model, an increase in interest rate increases wealth more if the initial salary was higher.',
'As all the inputs change each time, you can get a more realistic view of the relationship, e.g. '
'some trials with a higher interest rate will have high salary and some will have low salary.'
],
title=
'Why Monte Carlo Simulations Help Understand Inputs vs. Outputs'
),
lp.TwoColumnGraphicDimRevealFrame(
[
pl.TextSize(-1),
'A scatter plot is a simple way to visualize the relationship between two variables',
'If there is a relationship, you will see some defined pattern in the points. This may be '
'somewhat of an upward or downward line (linear relationship) or some other shape such '
'as a U (non-linear relationship).',
'If there is no relationship, then there will just be a random cloud of points (lower '
'plot) or a horizontal line.'
],
graphics=[
images_path('scatter-plot-line.png'),
images_path('scatter-plot-no-relationship.png')
],
graphics_on_right=False,
title=
'Visualizing the Relationship between Inputs and Outputs'),
lp.TwoColumnGraphicDimRevealFrame([
pl.TextSize(-2),
'The scatter plots help give a broad understanding of the relationship but do not answer the '
'question, how much will my output change if my input changes? E.g. if I earn 10,000 more '
'for a starting salary, how much sooner can I retire?',
'Simply increasing the input in your model and checking the output is not enough, because it '
'does not take into account how all the other variables may be changing.',
'Multivariate regression is a general tool which is good at answering these kinds of questions, '
'while taking into account all the changing inputs.'
],
graphics=[
images_path(
'excel-multivariate-reg.png'
)
],
title=
'Numerically Analyzing the Relationships'
),
lp.DimRevealListFrame([
pl.TextSize(-1),
'The coefficient in a multivariate regression represents how much the outcome variable '
'changes with a one unit change in the input variable.',
'E.g. a coefficient of -.0002 on starting salary in explaining years to retirement would mean '
r'that a \$1 increase in starting salary is associated with a decrease in years to retirement by .0002 years, or '
r'a \$10,000 increase in starting salary is associated with a decrease in years to retirement by 2 years.',
'All interpretations are "all else constant", meaning that it does not consider relationships '
'between the inputs. E.g. if starting salary is higher because of a good economy, and interest '
'rates are also higher due to the good economy, the starting salary coefficient is not taking '
'into account the increase in interest rates.',
'Be careful about units. If you use decimals for percentages, you will need to multiply or '
'divide by 100 to get the effect in percentages.'
],
title='How to use Multivariate Regression'
),
InClassExampleFrame(
[
'I will now go through adding a Monte Carlo simulation to the Dynamic Salary Retirement '
'Model in Python',
'The completed example is on the course site in '
'Monte Carlo Examples',
],
title='Adding Monte Carlo Simulation to a Formal Model',
block_title='Dynamic Salary Retirement with Monte Carlo'),
mc_python_lab.presentation_frames(),
],
title='A More Formal Treatment of Monte Carlo Simulation',
short_title='Formal MC',
),
pl.Section([
lp.DimRevealListFrame([
'In pure Excel, it is much more difficult to run a Monte Carlo Simulation',
'Without going to VBA, typically the only way is to use a data table',
'A data table can be used in situations where you only want to have one or two inputs '
'varying at once. Just generate the random inputs and use them as the axes of the data table',
'If you want to vary more than two inputs, VBA or Python would be required',
'There are also add-ons that accomplish this but they are usually not free'
],
title=
"How is it Different Running MC in Excel?"),
lp.DimRevealListFrame([
'The process for Monte Carlo Simulation which works for any number of variables is '
'very similar to what we were doing in Python.',
'We are still just changing the inputs, running the model, and storing the outputs from each run',
[
'Using', xlwings_mono,
'from Python code we can change and retrieve the values of cells'
],
'This allows us to change inputs, run the model, and store outputs, just as in Python, but running our Excel model.',
'We can either analyze the outputs in Python or output them back to Excel for analysis'
],
title=
'Monte Carlo in Excel with More than Two Variables'
),
InClassExampleFrame([
'Go to the course site and download the "Dynamic Salary Retirement Model.xlsx" and '
'"Excel Monte Carlo.ipynb" from the Monte Carlo Examples',
'Open up the Jupyter notebook and follow along with me',
'The completed Excel model is also there in case you lose track. Visualizations '
'were added after running the Jupyter notebook on the original Excel model.',
],
title='Monte Carlo Excel Retirement Model',
block_title=
f'Using {xlwings_mono} to Run Monte Carlo Simulations'
),
mc_excel_lab.presentation_frames(),
],
title='Monte Carlo Simulation in Excel',
short_title='Excel MC'),
pl.PresentationAppendix([
lecture.pyexlatex_resources_frame,
intro_mc_python_lab.appendix_frames(),
mc_python_lab.appendix_frames(),
mc_excel_lab.appendix_frames(),
])
]
def get_content():
random.seed(1000)
dcf_overview_graphic = get_dcf_graphic()
cc_graphic = get_dcf_graphic(include_output=False, include_fcf=False)
fcf_graphic = get_dcf_graphic(include_output=False, include_coc=False)
lecture = get_dcf_cost_capital_lecture()
enterprise_equity_value_excercise = get_enterprise_value_lab_lecture().to_pyexlatex()
cost_equity_exercise = get_dcf_cost_equity_lab_lecture().to_pyexlatex()
cost_debt_exercise = get_dcf_cost_debt_lab_lecture().to_pyexlatex()
wacc_graphics = get_wacc_graphics()
return [
pl.Section(
[
lp.DimRevealListFrame(
[
pl.JinjaTemplate('A {{ "discounted cash flow valuation (DCF)" | Bold }} is a method of '
'determining the value of a stock.').render(),
'Other ways include the dividend discount model and approaches based on comparables',
'The dividend discount model only works well for stable companies that pay dividends with '
'constant growth.',
'Comparable approaches can give a rough idea of a valuation but never take into account the '
'specifics of the company',
'DCF valuation can be applied to any company and is based on the particulars of the company'
],
title='What is a DCF?'
),
lp.GraphicFrame(
dcf_overview_graphic,
title='The DCF in One Picture'
),
lp.Frame(
[
lp.Block(
[
pl.Equation(str_eq=r'V = \sum_{t=0}^T \frac{CF^t}{(1 + r)^t}', inline=False)
],
title='Financial Asset Value'
),
pl.UnorderedList([lp.DimAndRevealListItems([
'The value of any financial asset is the present value of its future cash flows',
'The cash flows for a stock are dividends. The dividend discount model takes the present '
'value of future dividends.',
'To find the value of a business, find the present value of its future free cash flows'
], vertical_fill=True)]),
],
title='Motivating the DCF'
),
lp.TwoColumnGraphicDimRevealFrame(
[
pl.TextSize(-1),
['The goal of cost of capital estimation is to determine the',
pl.Bold('weighted average cost of capital (WACC)')],
['This can broadly be broken down into two components: estimating the',
pl.Underline('cost of equity'), 'and estimating the', pl.Underline('cost of debt')],
'Cost of equity is typically estimated using the Capital Asset Pricing Model (CAPM)',
'Cost of debt is usually estimated from the interest payments and book value of debt'
],
graphics=[lp.adjust_to_full_size_and_center(cc_graphic)],
title='Overview of Cost of Capital Estimation'
),
lp.TwoColumnGraphicDimRevealFrame(
[
pl.TextSize(-1),
'The goal of free cash flow estimation is to determine the historical and future '
'free cash flows (FCF) for the company.',
'Historical financial statements, including the income statement, balance sheet, and '
'statement of cash flows are used to determine historical FCF',
'It is the job of the analyst building the model to project those FCF into the future',
'This is usually done by projecting the financial statements into the future'
],
graphics=[lp.adjust_to_full_size_and_center(fcf_graphic)],
title='Overview of Free Cash Flow Estimation'
)
],
title='Introduction to Discounted Cash Flow (DCF) Valuation',
short_title='DCF Intro'
),
pl.Section(
[
lp.DimRevealListFrame(
[
'The enterprise value of the business is the asset value or the cost to purchase the '
'entire company',
pl.Equation(
str_eq=f'{pl.Text("Enterprise Value")} = {pl.Text("Equity Value")} + '
f'{pl.Text("Debt Value")} - {pl.Text("Cash")}'
),
'A stock represents only the equity value or market capitalization of a business',
'By determining the enterprise value, we can back into the equity value to get the stock price'
],
title='Enterprise Value vs. Equity Value'
),
pl.TextSize(-1),
enterprise_equity_value_excercise.presentation_frames(),
pl.TextSize(0),
],
title='Enterprise and Equity Value',
short_title='EV'
),
pl.Section(
[
lp.Frame(
[
pl.TextSize(-1),
lp.Block(
[
EquationWithVariableDefinitions(
r'r_i = r_f + \beta (r_m - r_f) + \epsilon',
[
'$r_i$: Return on stock $i$',
'$r_f$: Return on risk free asset',
'$r_m$: Return on market portfolio',
r'$\beta$: Covariance of stock returns with market risk premium',
r'$\epsilon$: Idiosyncratic return, mean 0',
]
)
],
title='Capital Asset Pricing Model (CAPM)'
),
pl.UnorderedList([lp.DimAndRevealListItems([
'We will use historical stock price data along with CAPM to produce an estimate of the '
'cost of equity.',
'Ultimately, $r_i$ is the estimate of the cost of equity',
], vertical_fill=True)])
],
title='How Can CAPM be used for Estimating the Cost of Equity?'
),
lp.Frame(
[
lp.Block(
[
pl.Equation(str_eq=r'r_i = r_f + \beta (r_m - r_f) + \epsilon')
],
title='Capital Asset Pricing Model (CAPM)'
),
pl.UnorderedList([lp.DimAndRevealListItems([
r'The three returns can all be estimated from historical data. Therefore $\beta$ and '
r'$\epsilon$ are the unknowns. But $\epsilon$ has mean zero so we can ignore it '
r'for estimation.',
'We will estimate the historical beta, then assume that the beta is still valid today to '
'come up with the current $r_i$ as the cost of equity.',
r'$\beta$ can be estimated by regressing the historical stock returns of the company on '
r'the historical market risk premiums. The $\beta$ is then the coefficient of the market '
r'risk premium in the regression.'
], vertical_fill=True)])
],
title='Overview of Cost of Equity Estimation'
),
InClassExampleFrame(
[
'Go to the course site and download "Determining the Cost of Equity.ipynb" '
'and "price data.xlsx" from '
'Cost of Equity Python Examples',
'Make sure that you place these two in the same folder',
'We are using historical prices to calculate the cost of equity using CAPM',
'We will use a risk free rate of 3% for the exercise',
],
title='Using Price Data to Estimate Cost of Equity in Python',
block_title='Python CAPM Estimation'
),
InClassExampleFrame(
[
'Go to the course site and download "DCF Cost of Equity.xlsx" from '
'Cost of Equity Excel Examples',
'We are using historical prices to calculate the cost of equity using CAPM',
'We will use a risk free rate of 3% for the exercise',
],
title='Using Price Data to Estimate Cost of Equity in Excel',
block_title='Excel CAPM Estimation'
),
cost_equity_exercise.presentation_frames(),
lp.DimRevealListFrame(
[
'As we will cover in more detail when we get to WACC, we need to have the market values of '
'both equity and debt along with the costs to be able to caluclate the WACC.',
'The market value of equity for a publicly traded company is straightforward. Just calculate '
f'the {pl.Bold("market capitalization")} as the number of shares outstanding multiplied by the current '
'share price.',
'The market capitalization can be used directly as the market value of equity.'
],
title='Market Value of Equity'
)
],
title='Cost of Equity Estimation',
short_title='Equity'
),
pl.Section(
[
lp.DimRevealListFrame(
[
'We want to estimate the cost of debt for the company, which more specifically should be '
'the marginal interest cost of raising one additional dollar via debt.',
['There are two general approaches to estimating this: the',
pl.Underline('financial statements approach'), 'and the',
pl.Underline('market rate of bonds approach')],
'The market rate of bonds approach is better able to capture the current rate when it has '
'changed substantially over time, but it requires price, coupon, and maturity information on '
'a bond.',
'The financial statements approach uses only the income statement and balance sheet, and '
'represents a weighted average historical cost of debt.'
],
title='Overview of Estimating the Cost of Debt'
),
lp.DimRevealListFrame(
[
'The financial statements approach uses interest expense from the income statement and '
'total debt from the balance sheet to estimate the cost of debt',
'With this approach, we can estimate the cost of debt by a very simple formula',
pl.Equation(
str_eq=rf'r_d = \frac{{{pl.Text("Interest Expense")}}}{{{pl.Text("Total Debt")}}}'
),
'Calculate this for the most recent data available and use this as the cost of debt'
],
title='The Financial Statements Approach to Cost of Debt'
),
lp.DimRevealListFrame(
[
'The cost of debt is about raising new debt, so it is more accurate to look at the market to '
'determine how much the company would have to pay for new debt.',
"The yield to maturity (YTM) of the company's bonds can be calculated. A weighted average of "
"the YTMs can be used as an estimate of the cost of debt.",
'The YTM is representing the required rate of return on the bond for the investor, which is '
'equivalent to the cost of the bond for the company',
'The YTM is simply the IRR of the bond, considering the current market price of the bond'
],
title='The Market Rate of Bonds Approach to Cost of Debt'
),
lp.DimRevealListFrame(
[
pl.TextSize(-1),
['Debt has an interesting feature in our tax system: debt is', pl.Underline('tax deductible.')],
'The amount a company has to pay in income tax is taken as a percentage of earnings before tax (EBT).',
'As interest is taken out while calculating EBT, it lowers the tax payment.',
'Think about two hypothetical companies with the exact same operations, revenues, costs, etc. '
'One is financed completely with equity and the other with 50% debt. They will both have the '
'same EBIT but the EBT will be lower for the debt firm and so the taxes will be lower for the '
'debt firm, likely giving the debt firm a higher value than the equity firm.',
'What this means for cost of capital estimation is that all our calculations will be based on '
f'pre-tax numbers, then we multiply by $(1 - {pl.Text("tax rate")})$ to get the after-tax cost '
f'of debt to use in the WACC.'
],
title='After-Tax Cost of Debt'
),
cost_debt_exercise.presentation_frames(),
lp.DimRevealListFrame(
[
"If you have taken a debt course, you should be familiar with the fact that bonds' values "
"change over time.",
'The value of a bond can be determined (just like any financial asset) by taking the present value of '
'future cash flows (here, interest and principal payments). ',
"If the discount rate for the company changes, the value of the bonds change, as the interest "
"payments are contracted and will remain the same",
"The discount rate will change when the riskiness of the firm's debt changes, e.g. taking on "
"additional debt, starting a new project, having a bad operating year, etc."
],
title='What is the Market Value of Debt?'
),
lp.DimRevealListFrame(
[
'Say a company issues a 3-year bond with a 10% coupon. When issued, the riskiness of the firm implies '
'it should have a 10% discount rate. In other words, the true cost of debt is 10%. '
'The bond is at par (value 1,000).',
'One year later, the firm has a bad year, and now lenders are requiring a 15% rate to lend to the company',
r'Due to this, the price of the existing bond has dropped to \$918.71.',
r'If we calculate the IRR on this \$918.71 bond, it comes to 15%, which is the true YTM or cost of debt',
'The coupon rate on the bond is still 10%, and the book value of debt on the balance sheet is '
'still 1,000 so based on the financial statements approach the cost of debt would still be 10%.'
],
title='Why Should we Care about the Market Value of Debt?'
),
lp.DimRevealListFrame(
[
'There are three main approaches to calculating the market value of debt for use in the '
'WACC calculation, depending on what data you have available',
['If all you have is financial statements, you must just',
pl.Underline('assume the book value of debt equals the market value of debt.')],
['If you also have an estimate of the current cost of debt obtained from the market as well '
'as an average maturity of debt, you can use the', pl.Underline('hypothetical bond approach.')],
['Finally, if you have all the individual debt instruments, you can',
pl.Underline('calculate the market value of individual instruments.')]
],
title='Approaches to Calculating the Market Value of Debt'
),
lp.DimRevealListFrame(
[
"For the purposes of this class, we won't deal with seniority. But you should keep it in mind "
"in the future when estimating the market value and cost of debt.",
'Seniority represents the payoff order during bankruptcy. The most senior loans will be paid '
'first, and if there is still money left over, then the more junior loans will be paid.',
'As there is a higher expected value in recovery, senior loans are less risky and so should '
'have a lower rate associated with them.',
'In the prior exercise, when valuing individual debt instruments, we assumed a single cost of '
'debt, when in reality, it should be adjusted for the seniority.',
],
title='Dealing with Seniority of Debt'
),
InClassExampleFrame(
[
'Go to the course site and download "Market Value of Debt.ipynb" and "debt data.xlsx" from '
'Cost of Debt Examples',
'Ensure you have the Jupyter notebook and the Excel spreadsheet in the same folder.',
'We will go through the Jupyter notebook to show the three approaches to estimating '
'the market value of debt.'
],
title='Calculating the Market Value of Debt',
block_title='MV Debt Example'
),
],
title='Cost of Debt Estimation',
short_title='Debt'
),
pl.Section(
[
lp.Frame(
[
lp.Block(
[
EquationWithVariableDefinitions(
f'{pl.Text("WACC")} = r_e w_e + r_d (1 - t) w_d',
[
'$r_e$: Cost of equity',
'$w_e$: Weight of equity',
'$r_d$: Pre-tax cost of debt',
'$t$: Tax rate',
'$w_d$: Weight of debt'
],
space_adjustment=-0.4
)
],
title='Weighted Average Cost of Capital (WACC)'
),
pl.UnorderedList([lp.DimAndRevealListItems([
'So now from the prior sections we have the cost of equity, market value of equity, '
'cost of debt, and market value of debt.',
'The weights of debt and equity are found by dividing that market value by the sum of '
'both market values.'
], vertical_fill=True)])
],
title='Calculating WACC'
),
lp.Frame(
[
pl.Center(adjust_to_size(wacc_graphics[0], 0.9, 0.35, keep_aspect_ratio=True)),
pl.Center(adjust_to_size(wacc_graphics[1], 0.9, 0.35, keep_aspect_ratio=True)),
],
title='What the Weighted Part of WACC Means'
)
],
title='Putting it All Together: Calculating the WACC',
short_title='WACC'
),
pl.PresentationAppendix(
[
pl.TextSize(-2),
lecture.pyexlatex_resources_frame,
pl.TextSize(-1),
enterprise_equity_value_excercise.appendix_frames(),
cost_equity_exercise.appendix_frames(),
cost_debt_exercise.appendix_frames(),
pl.TextSize(0),
]
)
]