kduffey, Author at Next Level Finance

November 26, 2018 by kduffey

Investable Assets: Why you should run hard to the key level of $500,000

Investable assets are a worthwhile consideration for calculating your level of wealth. Net worth is probably more common, but often, some individuals will include things such as their home or automobiles in a net worth calculation.

What are investable assets?

Investable assets are typically limited to things like cash, funds in bank or savings accounts, retirement accounts, stocks, bonds, CDs, insurance contracts with cash value, etc. Don’t include things like precious jewels or things not easily converted to cash. You might consider investable assets to be everything you can easily convert to cash without selling your residence or belongings.

Why is monitoring your amount of investable assets important?

Your investable assets are essentially the assets you own that are working for you, or generating a return. This is the key to generating significant levels of wealth.

If you’re early in your career or adulthood, your main financial goal needs to be to get as much money as possible working for you as quickly as possible.

For many young investors, the early years can be discouraging. Let’s face it, your income isn’t typically very high during these years, and socking away a couple hundred bucks every now and then can result in you feeling like the entire exercise is pointless. Young investors have to work hard to save small amounts of money, and the resulting balances don’t increase very quickly.

But over time, as incomes rise and as prudent investors sock more and more money away, the balances do, in fact, begin to grow quickly.

The key level of investable assets

To me, the key level is $500,000 of investable assets. For most, at this level, the annual returns on this sum of money should outpace the annual contributions.

In the beginning, nearly all the growth in your wealth is due to contributions. In other words, nothing more than saving money.

In the end, nearly all the growth is due to returns. At some point, you crossover into returns equaling and then outpacing contributions, and the $500,000 level is a conservative estimate for many investors.

Of course, wise investors don’t stop contributing to their investable assets once they hit this milestone. But, with contributions and increasing returns, the balance of your assets begins to grow quickly. Accumulating wealth starts to kick in to a higher gear.

Let’s look at some examples to illustrate the point.

Example 1: $18,500 annual contributions, 4% annual returns

It makes sense to test this with some pretty conservative figures. Let’s start with a 4% rate of return.

As shown in the below charts, returns begin to overtake contributions between year 18 and 19 based on the $18,500 annual contribution and 4% annual return levels.

The following chart shows the balance growth, and which component is contributing to the balance (contributions and returns). As you can see, again, in the 18-19 year mark, the $500,000 threshold is crossed and returns begin to increase much more rapidly.

Example 2: $18,500 annual contributions, 6% annual returns

By tinkering with the numbers, you can see how the results change. It can get pretty fun, especially as you plug in different levels of return. Let’s keep the contribution level the same while changing the annual returns to 6%. You can see that the numbers grow much more quickly.

Moreover, you can see the crossover point where annual returns eclipse annual contributions happens much earlier in the 12 to 13 year range.

By looking at the overall balance growth, you can see that the crossover point mentioned above occurs much earlier than the $500,000 balance level. This is due to the higher return level.

Example 3: $24,000 annual contributions, 8.8% annual returns

One more example just for kicks…

In this example, we’re going to use Vangaurd’s 60% stocks / 40% bonds allocation history. Here, this allocation has averaged 8.8% going back many decades. So, let’s plug in 8.8% for annual returns.

Let’s also tweak the contribution level. Let’s assume an individual is maxing out his or her 401(k) with the maximum contribution of $18,500 as well as plowing away $5,500 each year in an IRA. The total amount saved in a given year is $24,000.

Here you can see the crossover point between annual contributions and annual returns is around the 9 year mark.

In looking at this next chart, it’s immediately obvious how fast the assets grow toward the end of the curve with the higher rate of return compared to previous examples. With enough time and decent rate of return, money will start to grow very, very quickly as shown here.

Let’s get back to the $500,000 “key level”

As the above examples show, the $500,000 level becomes less relevant to the crossover point when the rate of return gets higher. Still, I think it makes sense to push hard for the $500,000 level with regards to investable assets, because we should plan for more conservative rates of return.

Another reason I like the $500,000 level has to do with the common debate over whether one should pay down his or her mortgage versus keep investing. The advice over this topic can vary. Dave Ramsey, for instance, will advocate paying down the mortgage with all extra money as long as you’re contributing 15% of your income towards retirement. Definitely a reasonable approach.

Others will advocate putting all money towards investing since the mortgage is cheap money. If your mortgage is 4.5% and you’re getting 8.8% on a conservative Vanguard fund, why pay off the mortgage? Also a reasonable argument.

I use the $500,000 level of investable assets as another factor to consider on the discussion of paying off your mortgage vs. investing additional funds. I prefer the idea of putting all money towards investable assets until the key level of $500,000 is reached. After the $500,000 level of investable assets is reached, then throwing some extra money at the mortgage to pay that down makes sense (as long as tax advantaged options such as 401(k) contributions and IRA contributions are still being maxed).

How long will it take to reach $500,000 in investable assets?

As we showed in our previous examples, the length of time will vary based on how much money you’re socking away and what returns you’re getting. The below table shows a number of scenarios to help you see how long it will take to reach this key level.

Note: The following table is calculated using annual contributions and annual compounding.

Annual Contribution	Annual Return	Years to $500,000+ Balance
$ 5,000	4%	41
$ 5,000	6%	33
$ 5,000	8%	28
$ 10,000	4%	28
$ 10,000	6%	24
$ 10,000	8%	21
$ 15,000	4%	22
$ 15,000	6%	19
$ 15,000	8%	17
$ 20,000	4%	18
$ 20,000	6%	16
$ 20,000	8%	14
$ 25,000	4%	15
$ 25,000	6%	13
$ 25,000	8%	12
$ 30,000	4%	13
$ 30,000	6%	12
$ 30,000	8%	11
$ 35,000	4%	12
$ 35,000	6%	11
$ 35,000	8%	10
$ 40,000	4%	11
$ 40,000	6%	10
$ 40,000	8%	9
$ 45,000	4%	10
$ 45,000	6%	9
$ 45,000	8%	8
$ 50,000	4%	9
$ 50,000	6%	8
$ 50,000	8%	8

A few notes above the table above:

Saving only $5,000 per year is a long slog toward any significant wealth accumulation. Even with higher levels of return, you’re looking at multiple decades to reach significant levels such as $500,000 and up.
With higher contribution levels, rate of return doesn’t move the needle as much on the march to the $500,000 level. However, rate of return moves the needle tremendously long-term (as shown in the previous examples and charts).

Investable Assets Key Takeaways

Going hard towards the $500,000 level in investable assets as early as possible in your life will dramatically alter your financial life

By getting to this key level early in your life, it will move your long-term financial trajectory in a very significant way. Obviously, saving money at an early age is difficult. Most people in their 20’s aren’t earning significant money, and socking away $5,000 can feel like an uphill battle. Watching the balances grow quite slowly year after year of $5,000 contributions doesn’t exactly help light the fire either.

Still, finding aggressive ways to sock away additional money, especially early on, can lead to tremendous benefits. Working an extra job, finding secondary income, finding ultra-low cost living situations while working as a young, single adult are ways young people can getting early contributions up.

According to the above table, going from the $5,000 annual contribution level to $15,000 can reduce the time to $500,000 by anywhere from 7 to 13 years (based on the range of returns shown).

If you can simply max out your 401(k) each year, the rest is pretty simple

While achieving the kind of financial security discussed here definitely takes work, it’s not rocket science. If you want the uber simple approach, just max out your 401(k) every year at a minimum and go with a conservative Vanguard fund that mixes stocks and bonds. Keep at it every year, and you’ll have millions in a few decades.

The growth towards the end of your working years will be quite dramatic based on simple compounding. The earlier you can start, the more high powered years you’ll have on your curve. The above charts show 35 years of investing. Change the time span to 40 years, and those extra 5 years generate incredible returns.

So, run hard after that $500,000 investable assets level. Then, just stay the course and keep it simple,

September 19, 2018 by kduffey

Pandas tutorial: A guide to mastering this key data science library in Python

This pandas tutorial will cover the basics and help Python programmers get up to speed quickly on this great data analysis library.

Pandas is a widely used Python library in the data science field. It comes with a number of excellent functions that make working with large data sets super convenient. It’s recommended to be familiar with the numpy library if you’re learning pandas. You can check out our numpy tutorial.

Pandas tutorial table of contents

For quick reference, here are the areas we will cover in this tutorial:

Understanding the pandas Series

The Series in the pandas library refers to a 1-dimensional labeled array which can hold any type of data. For 2-dimensional data, we’ll use the dataframe object which we’ll cover next.

You can create a Series a few different ways: from a list, from a numpy array or from a Python dict. Let’s look at how to do this.

Note: We’ll often use the head() method on a pandas series to print the first five rows of the Series, rather than the entire Series.

import numpy as np
import pandas as pd

#create a pandas Series from a list
mylist = [‘a’, ‘b’, ‘c’, ‘d’, ‘e’, ‘f’, ‘g’]
s1 = pd.Series(mylist)

#print the Series
print(s1.head())
0 a
1 b
2 c
3 d
4 e
dtype: object

#create a pandas Series from a dict
mydict = {‘b’ : 1, ‘a’ : 0, ‘c’ : 2}
s2 = pd.Series(mydict)

#print the Series
print(s2.head())
a 0
b 1
c 2
dtype: int64

#create a pandas Series from a numpy array
myarr = np.arange(20)
s3 = pd.Series(myarr)

#print the Series
print(s3.head())
0 0
1 1
2 2
3 3
4 4
dtype: int64

Understanding the pandas DataFrame

A pandas Dataframe is a two dimensional (can be more than two dimensions) structure used in data analysis. The pandas library provides a number of native functions for the DataFrame data structure that makes a wide range of analysis very easy to do. Commonly, the pandas DataFrame is two-dimensional and resembles a table with rows and columns. The columns have names and the rows have indexes.

You can create a DataFrame in a number of different ways. Reading in a csv file directly into a newly created DataFrame is a very handy feature provided by pandas.

import pandas as pd

#read in the csv
df = pd.read_csv(‘https://nextlevel.finance/wp-content/uploads/2018/09/test.csv’, ‘,’)

#print the information about the DataFrame
print(type(df))
<class ‘pandas.core.frame.DataFrame’>class

#print the DataFrame
print(df)
2 1 3 0 0.1
0 7 1 3 5 9
1 2 5 3 3 4
2 2 1 3 9 8
3 8 1 3 0 7
4 2 3 2 3 3
5 1 1 3 4 4
6 8 1 3 3 4
7 3 1 1 5 9
8 2 1 6 6 4

If you notice when we print the above dataframe, it used our first row as a header row. Since this example csv file is just raw data, we don’t want the first row to be used as column names, we want it to be actual data. So, we’ll need to read in that csv file again with a few parameters set.

import pandas as pd

#read in the csv
df = pd.read_csv(‘https://nextlevel.finance/wp-content/uploads/2018/09/test.csv’, sep=’,’, header=None)

#print the DataFrame
print(df)
0 1 2 3 4
0 2 1 3 0 0
1 7 1 3 5 9
2 2 5 3 3 4
3 2 1 3 9 8
4 8 1 3 0 7
5 2 3 2 3 3
6 1 1 3 4 4
7 8 1 3 3 4
8 3 1 1 5 9
9 2 1 6 6 4

#we can also rename the columns
df.columns = [‘a’, ‘b’, ‘c’, ‘d’, ‘e’]
print(df)
a b c d e
0 2 1 3 0 0
1 7 1 3 5 9
2 2 5 3 3 4
3 2 1 3 9 8
4 8 1 3 0 7
5 2 3 2 3 3
6 1 1 3 4 4
7 8 1 3 3 4
8 3 1 1 5 9
9 2 1 6 6 4

You can also create a DataFrame using one or more pandas Series.

import pandas as pd

#create the dict of Series
d = {‘col1’ : pd.Series([1, 2, 3], index=[‘a’, ‘b’, ‘c’]), ‘col2’ : pd.Series([1, 2, 3, 4], index=[‘a’, ‘b’, ‘c’, ‘d’])}

#create the DataFrame
df = pd.DataFrame(d)

#print the DataFrame
print(df)
col1 col2
a 1.0 1
b 2.0 2
c 3.0 3
d NaN 4

Using DataFrames for time series data

Pandas has some great features for creating and analyzing time series data.

Often in time series data, you’ll want the row indexes to be dates. Let’s look at how to build this kind of DataFrame in pandas.

import pandas as pd

#create the range of dates
startdate = ‘2012-01-01’
enddate = ‘2012-12-31’
dates = pd.date_range(startdate, enddate)

#print the range of dates – note the DatetimeIndex object
print(dates)
DatetimeIndex([‘2012-01-01’, ‘2012-01-02’, ‘2012-01-03’, ‘2012-01-04’,
‘2012-01-05’, ‘2012-01-06’, ‘2012-01-07’, ‘2012-01-08’,
‘2012-01-09’, ‘2012-01-10’,
…
‘2012-12-22’, ‘2012-12-23’, ‘2012-12-24’, ‘2012-12-25’,
‘2012-12-26’, ‘2012-12-27’, ‘2012-12-28’, ‘2012-12-29’,
‘2012-12-30’, ‘2012-12-31′],
dtype=’datetime64[ns]’, length=366, freq=’D’)

#Let’s create an empty DataFrame where the row indexes are the dates created in the previous step
df = pd.DataFrame(index=dates)

#print the DataFrame
print(df)
Empty DataFrame
Columns: []
Index: [2012-01-01 00:00:00, 2012-01-02 00:00:00 … ]

In the above step, we still have an empty DataFrame which isn’t overly useful, but it’s now ready for joining other data to it. We’ll look at joining in the next section.

Before we move on to the next section, let’s look at how we might read in time series data from a csv file as well.

Again, we’ll use the read_csv method, but we’ll add in the parameters parse_dates=True and tell the method to use the Date column as the index column.

import pandas as pd

#read in the csv file
df = pd.read_csv(‘https://nextlevel.finance/wp-content/uploads/2018/09/datestest.csv’, header=None, parse_dates=True, index_col=’Date’, names=[‘Date’,’A’,’B’,’C’,’D’,’E’])

#print the DataFrame
print(df)
A B C D E
Date
2013-01-01 2 1 3 0 0
2013-01-02 7 1 3 5 9
2013-01-03 2 5 3 3 4
2013-01-04 2 1 3 9 8
2013-01-05 8 1 3 0 7
2013-01-06 2 3 2 3 3
2013-01-07 1 1 3 4 4
2013-01-08 8 1 3 3 4
2013-01-09 3 1 1 5 9
2013-01-10 2 1 6 6 4

Joining multiple DataFrames

Slicing DataFrames

September 13, 2018 by kduffey

Numpy Tutorial: Quickly master this key Python library for data analysis

This numpy tutorial will cover all the basics of the numpy python library. Mastering this library is key if you wish to do meaningful data analysis in python. It’s heavily used for data analysis of all types including analyzing financial data.

The numpy library provides the ndarray object (an n-dimensional array) for holding data. A big reason why numpy is so popular is the advantages of the ndarray objects over typical lists in Python.

As you’ll see, key to the ndarray is that it allows vectorized operations. We’ll get into vectorized operations in this tutorial, but for now just know that it’s an important part of why we use numpy for data analysis.

Numpy tutorial table of contents

For quick reference, here are the areas we will cover in this tutorial:

Creating numpy arrays

There are a few different ways you can create a numpy array.

Perhaps one of the most common ways is to create a numpy array from a Python list. You can utilize the numpy.array function (or np.array function as it’s common to refer to numpy as np).

import numpy as np

#create the array
mylist = [0,1,2,3]
myarr = np.array(mylist)

#print the array
print(myarr)
[0 1 2 3]

#print the type
print(type(myarr))
<type ‘numpy.ndarray’>

It’s worth noting that even a 1-d array like above is still considered of type ndarray. The np.array function is just a function. There is not an array object in numpy.

You can also create a 2-d array from a Python list of lists.

import numpy as np

#create the array
mylist = [[0,1,2,3],[4,5,6,7]]
myarr = np.array(mylist)

#print the array
print(myarr)
[[0 1 2 3]
[4 5 6 7]]

Another consideration when creating numpy arrays is specifying the data type. Unlike lists in Python, all elements of a numpy array must be of the same data type.

You can specify the data type when creating the array as follows:

import numpy as np

#create the array
mylist = [[0,1,2,3],[4,5,6,7]]
myarr = np.array(mylist, dtype=’float’)

#print the array
print(myarr)
[[0. 1. 2. 3.]
[4. 5. 6. 7.]]

Note that the above decimal point indicates that the numbers are of float data type.

You can convert an existing array to a different data type by using the astype functon.

import numpy as np

#create the array
mylist = [[0,1,2,3],[4,5,6,7]]
myarr = np.array(mylist, dtype=’float’)
myarr2 = myarr.astype(‘int’)

#print the array
print(myarr)
[[0 1 2 3]
[4 5 6 7]]

Note that if you aren’t sure about data type or want to hold a variety of data types in the array, you can use dtype=’object’ as follows:

import numpy as np

#create the array
mylist = [0,1,’hello’]
myarr = np.array(mylist, dtype=’object’)

#print the array
print(myarr)
[0 1 ‘hello’]

Since we’ve talked about lists and the differences between them and numpy arrays, it’s also worth noting that you can convert a numpy array back to a list using the tolist() method.

import numpy as np

#create the array
mylist = [0,1,2]
myarr = np.array(mylist)
mylist2 = myarr.tolist()

#print the list
print(mylist2)
[0, 1, 2]

#print the type of the list
print(type(mylist2))
<type ‘list’>

You can also create numpy arrays of a specific size and a set of default values quite easily using some numpy methods.

import numpy as np

#create a 3×3 array with all zeroes
myarr = np.zeros([3,3])

#print the array
print(myarr)
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]

#create a 3×3 array with all ones
myarr = np.ones([3,3])

#print the array
print(myarr)
[[1. 1. 1.]
[1. 1. 1.]
[1. 1. 1.]]

Lastly, you can create numpy arrays with random values quickly as well.

import numpy as np

# Create a 3×3 array with random numbers between [0,1)
print(np.random.rand(2,2))
[[0.5035 0.0745 0.3731]
[0.6996 0.1923 0.8273]
[0.3800 0.8746 0.7461]]

# Create a 3×3 array with random integers between [0, 10)
print(np.random.randint(0, 10, size=[3,3]))
[[5 3 9]
[7 7 8]
[3 6 3]]

Shape and size of numpy arrays

It can occasionally be important to know the shape and size of your numpy arrays. There are some built-in methods to help you do this.

How to determine the number of elements in a numpy array:

import numpy as np

#create the array
mylist = [[0,1,2],[3,4,5]]
myarr = np.array(mylist)

#print the number of elements
print(myarr.size)
6

How to determine the shape of a numpy array, and how to get the number of rows and columns of a 2d-array:

import numpy as np

#create the array
mylist = [[0,1,2],[3,4,5]]
myarr = np.array(mylist)

#print the shape
print(myarr.shape)
(2,3)

#print the number of dimensions
print(myarr.ndim)
2

#print the number of rows
print(myarr.shape[0])
2

#print the number of columns
print(myarr.shape[1])
3

Extracting items and slicing numpy arrays

Numpy arrays use zero-based indexing, so your indexing always begins at zero.

You can access a single element of an array using square brackets and indicating the index for each dimension:

import numpy as np

#create and print the array
mylist = [[0,1,2],[3,4,5]]
myarr = np.array(mylist)
print(myarr)
[[0 1 2]
[3 4 5]]

#print the element at 1,1
print(myarr[1,1])
4

You can also take subsets of numpy arrays, often called slices by providing a start and stop value for each dimension separated by a colon (:). Note that the start value of the slice is included in the subset, but the stop value is not.

import numpy as np

#create and print the array
mylist = [[0,1,2],[3,4,5],[6,7,8]]
myarr = np.array(mylist)
print(myarr)
[[0 1 2]
[3 4 5]
[6 7 8]]

#Take a 2×2 subset of the array starting with the 1,1 element
print(mylist2[1:3,1:3])
[[4 5]
[7 8]]

Similarly, you can leave off a starting value or stopping value to get the span of that dimension from either the zero-index on, or from a value to the end of the dimension:

import numpy as np

#create and print the array
mylist = [[0,1,2],[3,4,5],[6,7,8]]
myarr = np.array(mylist)
print(myarr)
[[0 1 2]
[3 4 5]
[6 7 8]]

#Take the same 2×2 as in the previous example
print(mylist2[1:,1:])
[[4 5]
[7 8]]

You can grab sets of rows or columns of a 2d-array very easily using this slicing convention. This lets you perform operations on rows and columns quite easily and will be something you do quite often in data analysis.

import numpy as np

#create and print the array
mylist = [[0,1,2],[3,4,5],[6,7,8]]
myarr = np.array(mylist)
print(myarr)
[[0 1 2]
[3 4 5]
[6 7 8]]

#Take 2nd row (index 1)
print(mylist2[1,:])
[3 4 5]

#Take the last two columns
print(mylist2[:,1:])
[[1 2]
[4 5]
[7 9]]

Vectorized operations on numpy arrays

Vectorized operations are a big reason why numpy arrays are so useful. The ability to use these operations is also a key difference between numpy arrays and Python lists. Vectorized operations let you apply a function on each element in a vector very quickly and with minimal lines of code. Whereas performing a calculation on each element in a list would typically require some sort of loop, the vectorized calculations push this looping mechanism into the compiled layer where it can execute much faster. As such, these operations are much less costly computationally.

In this simple example, we have a 2d-array and want to add 3 to each element.

import numpy as np

#create the array, and add 3 to each element
mylist = [[0,1,2],[3,4,5],[6,7,8]]
myarr = np.array(mylist)
myarr2 = myarr + 3

#print the array
print(myarr2)
[[3 4 5]
[6 7 8]
[9 10 11]]

Vector operations such as adding two arrays together is also easily possible.

import numpy as np

#create two arrays
myarr = np.array([[0,1],[2,3]])
myarr2 = np.array([[4,5],[6,7]])

#print the array
print(myarr + myarr2)
[[4,6]
[8 10]]

Statistical operations such as mean, min and max

Statistical analysis of numpy arrays is quite common and there are a number of functions built in to the numpy library.

mean(), max() and min() methods can be run on the numpy arrays directly to get the mean, max and min values of the entire array.

import numpy as np

#create an array
myarr = np.array([[0,1],[2,3]])

#print the mean, min, max of the array
print(myarr.mean())
1.5
print(myarr.min())
0
print(myarr.max())
3

Similarly, these functions can be run on slices of the array as well.

import numpy as np

#create an array
myarr = np.array([[0,1],[2,3]])

#print the mean, min, max of the first column of the array
print(myarr[:,0].mean())
1.0
print(myarr[:,0].min())
0
print(myarr[:,0].max())
2

Quite often you might want to calculate the mean of each column, or the max value of each row. Numpy also makes this very easy. The axis parameter is common in numpy. Remember that axis=0 refers to a column wise operation, and axis=1 refers to a row wise operation.

Note that these functions return a ndarray object.

import numpy as np

#create an array
myarr = np.array([[0,1,2],[3,4,5]])

#print the mean, min, max of the each column
print(np.mean(myarr, axis=0))
[1.5 2.5 3.5]
print(np.amin(myarr, axis=0))
[0 1 2]
print(np.amax(myarr, axis=0))
[3 4 5]

#print the mean, min, max of the each row
print(np.mean(myarr, axis=1))
[1. 4.]
print(np.amin(myarr, axis=0))
[0 3]
print(np.amax(myarr, axis=0))
[2 5]

When you need the index of a minimum or a maximum value, rather than the value itself, the argmin() and argmax() functions can be used.

These functions can be used with or without an axis parameter. If no axis is used, then the array is flattened into a 1-dimensional array, and the index of the flattened array is returned.

import numpy as np

#create an array
myarr = np.array([[0,1,2],[3,4,5]])

#print the index of the max value in the array
print(np.argmax(myarr))
5

#print the index of the min value in each row
print(np.argmin(myarr, axis=1))
[2 2]

Conditional operations using where and take

On occasion, you may want to grab the elements of a numpy array that satisfy a particular condition. The where method from the numpy library is very useful for this.

Similarly, you can use the take method to grab the values of the array at a provided set of index values.

import numpy as np

#create an array
myarr = np.array([0,1,5,2,3,4,5,1])

#get the index of the elements that satisfy the condition of the element being larger than 2
i = np.where(myarr > 2)
print(i)
(array([2,4,5,6]),)

#take the values of the array based on the given index values
v = myarr.take(i)
print(v)
[[5 3 4 5]]

Loading data from a file into a numpy array

The np.genfromtxt function is quite useful in loading in a csv file or other data files. For this example, we’ll load in the data from this csv file. The np.genfromtxt function lets you specify a file address, web address and more.

import numpy as np

#load the data from web URL
url = ‘https://nextlevel.finance/wp-content/uploads/2018/09/test.csv’
data = np.genfromtxt(url, delimiter=’,’, skip_header=0, filling_values=-1, dtype=’int’)

#Let’s look at the resulting array
print(data)
[[2 1 3 0 0]
[7 1 3 5 9]
[2 5 3 3 4]
[2 1 3 9 8]
[8 1 3 0 7]
[2 3 2 3 3]
[1 1 3 4 4]
[8 1 3 3 4]
[3 1 1 5 9]
[2 1 6 6 4]]

print(data.shape)
(10,5)

Joining multiple numpy arrays

There are a few different ways you can concatenate numpy arrays. The numpy methods mostly used are np.concatenate, np.vstack and np.hstack.

import numpy as np

#create two arrays
myarr1 = np.zeros([2,2])
myarr2 = np.ones([2,2])
print(myarr1)
[[0. 0.]
[0. 0.]]

print(myarr2)
[[1. 1.]
[1. 1.]]

#Concat vertically using concatenate
myarr3 = np.concatenate([myarr1, myarr2], axis=0)
print(myarr3)
[[0. 0.]
[0. 0.]
[1. 1.]
[1. 1.]]

#Concat vertically using vstack
myarr4 = np.vstack([myarr1,myarr2])
print(myarr4)
[[0. 0.]
[0. 0.]
[1. 1.]
[1. 1.]]

#Concat horizontally using concatenate
myarr5 = np.concatenate([myarr1, myarr2], axis=1)
print(myarr5)
[[0. 0. 1. 1.]
[0. 0. 1. 1.]]

#Concat horizontally using vstack
myarr6 = np.hstack([myarr1,myarr2])
print(myarr6)
[[0. 0. 1. 1.]
[0. 0. 1. 1.]]

Sorting numpy arrays

When sorting numpy arrays, typically you want to maintain the integrity of the rows while sorting on a specific column. To do so, you want to use a two-step process using the argsort method rather than the sort method. The sort method will sort every column (or row) and thus corrupt the row (or column) integrity. We’ll look at the more complex case using argsort first since it’s the more common use case.

import numpy as np

#create the array
myarr = np.array([[9,5,4],[2,1,6],[4,8,2]])
print(myarr)
[[9 5 4]
[2 1 6]
[4 8 2]]

#Let’s argsort the first column, and see what happens
sorted_index_col1 = myarr[:, 0].argsort()

#The output is the index numbers of the sorted values, So the 1st item is smallest, then the 2nd item, then the 0th item.
print(sorted_index_col1)
[1 2 0]

#Now we can use the index information to sort the array
sorted_arr = myarr[sorted_index_col1]
print(sorted_arr)
[[2 1 6]
[4 8 2]
[9 5 4]]

#We can also sort using the index information in a reversed or descending order
sorted_arr = myarr[sorted_index_col1[::-1]]
print(sorted_arr)
[[9 5 4]
[4 8 2]
[2 1 6]]

Lastly, let’s quickly look at using the numpy sort() method which does not maintain row/record integrity.

import numpy as np

#create the array
myarr = np.array([[9,5,4],[2,1,6],[4,8,2]])
print(myarr)
[[9 5 4]
[2 1 6]
[4 8 2]]

#Let’s sort the columns of the numpy array
sorted_arr = np.sort(myarr, axis=0)
print(sorted_arr)
[[1 2 6]
[2 4 8]
[4 5 9]]

#Let’s sort the rows of the numpy array
sorted_arr = np.sort(myarr, axis=1)
print(sorted_arr)
[[4 5 9]
[1 2 6]
[2 4 8]]

Working with dates in numpy arrays

Numpy uses the datetime64 object to implement dates. The object comes with a number of functions for manipulating dates.

import numpy as np

#create a date
mydate = np.datetime64(‘2018-08-25 15:30:30’)
print(mydate)
2018-08-25T15:30:30

#create a range of dates
mydaterange = np.arange(np.datetime64(‘2018-08-01’), np.datetime64(‘2018-08-10’))
print(mydaterange)
[‘2018-08-01’ ‘2018-08-02’ ‘2018-08-03’ ‘2018-08-04’ ‘2018-08-05’ ‘2018-08-06’ ‘2018-08-07’ ‘2018-08-08’ ‘2018-08-09’]

September 10, 2018 by kduffey

Saving money and why you should view it like an economist

If you’ve read any basic personal finance information, have a good amount of common sense or ever listen to Dave Ramsey, you know the basics about saving money and the reasons for it. Our focus here is to move beyond the basics, so when it comes to saving money, let’s quickly get the basics out of the way.

If it’s not obvious, saving money is the result of spending less money than you make. The reasons why saving money is a good thing are plenty: having a emergency fund is useful for unanticipated events and expenses, having financial margin in your life will reduce stress as you go about your life, and of course, saving money leads to things like saving for college, investing and having the ability to retire later in life with some money.

Before we get into why you should view saving money as an economist, no discussion on saving money is complete without some tips on how to save money, right? Fine. let’s throw out a few for your consideration.

Tips for saving money

It’s not hard to find tips for saving money out there, so we won’t spend too much time on the topic. Here are a few bigger picture things to think about as you make your plan to find more money to save.

Focus on the big things.
Yes, managing your spend at Starbucks can be useful, but it’s hard to make headways on latte savings when you’re paying $500 per month on a car that you can’t afford. Start with your major expenses such as housing, auto, health care, etc. Knocking out several hundred bucks a month (or more) right away will create some momentum for you in the area of budgeting. Then, start fine-tuning things like how much you spend eating out, or how often you go to the movies.

Track your expenses like a business would.
If you’re not a detailed numbers type, then you’re not going to love this, but there’s no better way to get a hold of your budget than to track it to extreme detail. Create a spreadsheet with a written budget (one row per category). Then track how much you spend in that category for each month. Each subsequent column should be a month. Adjust your target amounts in your budget based on reality after a few months. Once you know where you’re money is going to a very detailed level, finding more money to save gets much easier.

Work out your differences with your spouse now. Not later.
Fewer things will be more impactful to your financial health than finally getting on the same page with your spouse about your money. Have honest conversations about expectations for current lifestyle, savings goals, travel, retirement expectations and more. Often times, relationships are harder to manage than executing a budget. Some couple wait years or decades before they actually get on the same page. Doing so will make your finances suffer. Do everything you can to work it out now. Get a third-party counselor to assist even if it costs you money. The future ROI on this investment will be huge.

How economists view saving money

Economists view savings typically different than individuals do. Individuals view it as a personal finance action as a result of spending less than you make. Economists view saving as consuming less in the present in order to consume more in the future.

Here’s a simple example from the Library of Economics and Liberty: “to economists, saving means only one thing—consuming less in the present in order to consume more in the future.
An easy way to understand the economist’s view of saving—and its importance for economic growth—is to consider an economy in which there is a single commodity, say, corn. The amount of corn on hand at any point in time can either be consumed (literally gobbled up) or saved. Any corn that is saved is immediately planted (invested), yielding more corn in the future. Hence, saving adds to the stock of corn in the ground, or in economic jargon, the stock of capital. The greater the stock of capital, the greater the amount of future corn, which can, in turn, either be consumed or saved.”

This example illuminates a view of savings with an emphasis toward not just future consumption, but future production.

Too often in personal finance circles, the idea of saving money is limited to saving up for a purchase in the future, or saving up for a retirement where you can spend that money on a retired lifestyle. Future consumption is emphasized.

Instead, I suggest a focus on future production is key to changing the game when it comes to your finances, life and success.

Every dollar you save is a dollar that can work for you. Spending your dollars means literally removing dollars that are working for you. Get enough dollars working for you, and you might not have to worry about money ever again.

I find the endowment approach also an interesting example. When a major University wants to fund a new program that costs $50 million per year, they don’t try to raise that $50 million. Instead, they try to raise a sum of money that funds an endowment that then funds this program in perpetuity. They seek to put enough dollars to work that will produce enough money every year to cover all the expenses of this program. Again, it’s a focus on what your savings will produce for you.

In economics, capital formation refers to the addition of capital stock to the economy. Capital formation is crucial for economic growth. It leads to increased productivity, increase production and the ability to innovate.

Similarly, your savings and investing in productivity is crucial for your financial growth. It leads to increased gain, increased production and the ability to invest in yourself and your family.

A real world example

Let’s make this a bit more concrete.

John Doe makes $115,000 per year. After taxes and life expenses, he’s putting away $1,000 each month toward savings. He also has a 401(k) with his company in which he’s putting away another $800 per month, plus $400 per month in company matching for a total of $1,200 per month. Add it up, and John is saving $26,400 per year (this includes the company match).

John’s 401(k) money is automatically going into long-term investments because that’s how his company’s 401(k) is structured. So, of the $26,400 that he’s saving each year, $14,400 is going into retirement savings and $12,000 is going into a general savings account.

This is a pretty typical situation for a worker making a nice salary, albeit an example that is rather atypical compared to the average person (most people aren’t saving this much). But let’s continue the example to bring home some of the concepts discussed in this article.

Since the 401(k) contributions are spoken for, let’s focus on the $12,000 in general savings each year. As most personal finance pros will tell you, you should have an emergency fund of somewhere in the range of 3-6 months of your regular expenses. This is fine.

What about when you’ve got that covered, and you’re still contributing cash into the savings? This excess savings can be distributed in a mix of the following ways: college savings (if you have kids), more investment accounts, saving for a house/paying down your mortgage or piling up dry powder in anticipation of an investment opportunity.

In an ideal world, you’ve already knocked out college savings and your mortgage, and your focus is just on additional investment opportunities. For most of you, this is probably not the case. As such, finding a good mix on a monthly basis probably makes sense. Maybe its a third toward your mortgage, a third toward your kid’s college fund and a third toward an investment account or a cash pile that’ll eventually get invested.

Let’s now assume that mortgage is paid off and kid’s college is funded. What do we do with excess savings? This is where the production mindset can really kick in…

I like to pile up cash as much as possible (in a high yield savings account) while I wait patiently for high quality investment opportunities. These dollars are working for me, by earning interest. The cash pile is growing in two ways: by my continuous contributions of more cash and by the interest it’s earning.

Meanwhile, I’m on the lookout for better ways to allocate these dollars so they can work even harder for me.

It’s at this point where many of you will likely ask: Why not just put these excess dollars into the stock market via a diversified portfolio like most people? That’s, after all, what investing is, right?

The answer to this question is: sure. That’s not an unreasonable approach. For me, since I’m already put the bulk of my savings into the stock market in long-term focused retirement accounts, I’m interested in being a bit more tactile with this growing pile of cash.

Now, this doesn’t mean that this cash doesn’t end up in the stock market. It very well could. For instance, if the stock market tanks 50%, I’m going to put a large chunk of my excess capital into the stock market. At that point in time, it would be a very nice buying opportunity of the stock market – or, exactly the kind of opportunity I’m patiently waiting for.

Or, I might find an extremely attractive real estate investment. An investment that most people won’t be able to jump on quickly because they don’t have the capital available. I will have the capital available. I’ll be able to move quickly to deploy my capital into areas that will produce for me. This in turn will generate more excess savings and excess capital to invest.

For much of the remaining chapters of this course, we’ll be looking at how to get better at investing and how to find these excellent opportunities to deploy capital. But, we had to start with saving money, because saving money leads to capital, which leads to financial growth for you.