Jekyll2020-09-04T17:36:49+00:00/feed.xmlVizlitData driven articlesAmortization Visualized2020-08-25T00:00:00+00:002020-08-25T00:00:00+00:00/finance/2020/08/25/amortization<p>The majority of consumer debt in America is <a href="https://www.newyorkfed.org/microeconomics/hhdc.html">housing related</a>. You will likely find yourself saddled with a mortgage at some point. In this article we will visualize the concept at the heart of paying off a mortgage: amortization.</p>
<h2 id="amortization">Amortization</h2>
<p>Most home buyers do not have enough money to buy a home outright. Instead, they pay a small fraction of the home price and take out a loan to cover the rest. They then slowly pay off the loan over some period of time (usually 15 or 30 years) by making monthly payments.</p>
<p>This process of paying a loan off over time through regular payments is called amortization. Some portion of every mortgage payment goes towards paying interest: the monthly cost of borrowing the money. Another portion of the payment goes towards principal: the remaining balance due. Other portions of the monthly payment may go towards things like property taxes, private mortgage insurance, and homeowners insurance. These other categories will not be addressed in this article.</p>
<p>What’s interesting about the interest and principal payments is that their amounts change over the life of the loan. As time progresses, the portion of each monthly payment that goes towards interest shrinks while the amount going towards principal increases.</p>
<p>This happens because the amount of interest owed in a given month depends on the remaining balance of the loan at that time. Take a yearly interest rate of 3% and a remaining balance of $100,000 for example. The interest owed on the next mortgage payment is equal to the <em>monthly</em> interest rate times the remaining loan balance: (0.03/12) * $100,000 = $250. If the interest and principal portion of the mortgage payment was $1,000 in this case, $250 would go to interest and $750 would go to the remaining balance. Now the remaining balance is $99,828.4 which means the interest on next month’s payment will be $249.57 meaining more of that payment will go towards decreasing the loan balance. The visualization below illustrates this phenomenon.</p>
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<p>Try changing the interest rate and mortgage amount. If the interest rate is high enough, a borrower will end up paying more interest than principal over the life of a loan!</p>
<p>If borrowers have the means, they can choose to make extra principal payments towards their loan balance. Doing so will result in them paying <em>less</em> total interest than if they only made regular payments. I will visualize this concept in another post coming soon!</p>
<script src="/assets/js/custom/amortization.js"></script>Sam CallisterThe majority of consumer debt in America is housing related. You will likely find yourself saddled with a mortgage at some point. In this article we will visualize the concept at the heart of paying off a mortgage: amortization.The Cheapest State2020-07-15T00:00:00+00:002020-07-15T00:00:00+00:00/finance/2020/07/15/cost-of-living<p>There have been a lot of attempts to rank the 50 states by affordability, and different methodologies have come up with different answers for which state is the cheapest (<a href="https://financer.com/us/cheapest-states-to-live/">Mississippi</a>, <a href="https://www.usnews.com/news/best-states/slideshows/10-most-affordable-states">Iowa</a>, <a href="https://www.bhg.com/home-improvement/moving/cheapest-states-to-buy-home/">West Virginia</a>). As enticing as it may be to come up with one definitive answer for the cheapest state to live in, the usefulness of these rankings is a bit dubious. Moving to <a href="https://worldpopulationreview.com/state-rankings/cheapest-states-to-live-in">Mississippi</a> will not necessarily improve your financial situation.</p>
<p>In reality, the “cheapest” state for a person to live in depends on their family size, their occupation, and their financial goals. To illustrate this point, let’s consider a few examples.</p>
<p>Tom is a single middle school teacher without any kids. Rather than save up his leftover income after paying for his living expenses, he wants to put his money toward living in a nicer house. The “cheapest” state for Tom is going to be the one where his basic living expenses make up the lowest percentage of his overall salary. To estimate the percent of Tom’s annual income that would go toward living expenses in a given state, we take the typical annual living expenses for a single adult in that state, divide it by the average annual salary for middle school teachers in that state, and multiply the result by 100 to get a percent (percent of income used on living expenses = (living expenses/income)*100). For example, in Idaho, the typical annual living expenses for a single adult are $34,348, and the average annual salary for middle school teachers is $53,060. So, the percent of a middle school teacher’s income that would go toward living expenses is ($34,348/$53,060)*100 = 64.7%. When we do this calculation for all 50 states, we find that the “cheapest” state for single middle school teachers who want to use their leftover income on better living conditions is Michigan (where only 50.9% of their income would go toward living expenses), and the most “expensive” state is Arizona (where 85% of their income would go toward living expenses).</p>
<p>Next let’s consider Maria, a married mechanical engineer with 3 kids. Maria’s husband does not work, and her goal is to maximize retirement savings after paying her family’s living expenses. The “cheapest” state for Maria is going to be the one where she has the most leftover savings after paying for her family’s basic living expenses. To estimate Maria’s leftover savings in a given state, we take the average annual salary for a mechanical engineer in that state and we subtract the typical annual expenses for a household with 2 adults and 3 children (leftover savings = income – living expenses). For example, in Tennessee, the average annual salary for mechanical engineers is $87,390, and the typical annual living expenses for a household with 2 adults and 3 children is $86,322. So, the leftover savings for a mechanical engineer with a spouse and 3 children is $87,390 - $86,322 = $1,068. When we do this calculation for all 50 states, we find that the “cheapest” state for married mechanical engineers with 3 children who want to save their leftover income is New Mexico (where their leftover savings would be $21,381), and the most “expensive” state is Hawaii (where their family’s living expenses would exceed their income by $62,655).</p>
<p>Finally, let’s consider Sayid and Sara, a married couple with 2 children. Sayid works as a dentist, and Sara works as a web developer. They, like Maria, want to save up all of their leftover income after paying for their family’s living expenses. To estimate Sayid and Sara’s leftover savings in a given state, we take the sum of the average annual salary for a dentist and the average annual salary for a web developer in that state and we subtract the typical annual expenses for a household with 2 adults and 2 children (leftover savings = (income1 + income2) – living expenses). For example, in Maine, the average annual salary for dentists is $179,920, the average annual salary for web developers is $62,390, and the typical annual living expenses for a household with 2 adults and 3 children is $97,454. So, the leftover savings for a dentist and a web developer with 2 children is ($179,920 + $62,390) - $97,454 = $144,856. When we do this calculation for all 50 states, we find that the “cheapest” state for a family made up of a dentist, a web developer, and 2 kids that wants to save its leftover income is Delaware (where its leftover savings would be $222,643), and the most “expensive” state is Louisiana (where its leftover savings would be $85,494).</p>
<p>Use the visualization below to find your own “cheapest” state based on your family size, your profession, and your financial goals. Keep in mind that while both the “percent of income” method and the “leftover savings” method account for how family size and profession change cost of living comparisons across states, they measure slightly different things. Use the leftover savings method if your goal is to maximize the amount of money you can save after living expenses. Use the percent of income method if you want to get the most bang for your buck spending your excess income on things other than basic living expenses. The percent of income method accounts for the fact that $5,000 of excess income goes further in a state like Wyoming than in a state like New York. Under the leftover savings method, two states with the same excess income would get the same rank. Under the percent expenses method, if two states had the same excess income, the state with lower living expenses would be ranked as less expensive than the state with higher living expenses.</p>
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<p>The typical annual living expenses estimates for this visualization come from the <a href="https://www.epi.org/resources/budget/budget-factsheets/">Economic Policy Institute’s Family Budget Fact Sheets</a>. These estimates factor in the cost of housing, food, childcare, transportation, health care, other necessities, and taxes. This data has estimates by county. To get state-level estimates, I calculated a weighted mean for each state based on the <a href="https://www.census.gov/data/datasets/time-series/demo/popest/2010s-counties-total.html">population of each county in the state</a>. The average annual salaries for this visualization come from the <a href="https://www.bls.gov/oes/tables.htm">U.S. Bureau of Labor Statistics</a>. All the data for this visualization is based on values from the year 2017.</p>
<script src="/assets/js/custom/costOfLiving.js"></script>Adam CallisterThere have been a lot of attempts to rank the 50 states by affordability, and different methodologies have come up with different answers for which state is the cheapest (Mississippi, Iowa, West Virginia). As enticing as it may be to come up with one definitive answer for the cheapest state to live in, the usefulness of these rankings is a bit dubious. Moving to Mississippi will not necessarily improve your financial situation.S&P Best of Times Wost of Times2020-07-01T00:00:00+00:002020-07-01T00:00:00+00:00/finance/2020/07/01/sp-performance<p><a href="https://www.businessinsider.com/personal-finance/warren-buffett-recommends-index-funds-for-most-investors">Investment wizards</a> tell us regular folks to buy and hold index funds. I’ve read many times that while the market goes up and down year to year, the <em>average</em> yearly return of the market is positive; patient investors will make money in the long term.</p>
<p>An average return of 7% per year sounds pretty good, but as the United States Airforce discovered, <a href="https://www.thestar.com/news/insight/2016/01/16/when-us-air-force-discovered-the-flaw-of-averages.html">averages can be misleading</a>. I want to know what’s hiding behind that average. What if I were to buy into the market right before a big crash? What if I bought in at the best possible time? What does the spread of possible returns look like? Does the spread look different for lump sum investments vs monthly investments made over a long period of time? This article will address these questions and allow you to explore S&P investment scenarios yourself.</p>
<h2 id="the-lump-sum-case">The Lump Sum Case</h2>
<p>If you unexpectedly inherited $1000 dollars, what would you do with it? If your mind went to investing, reconsider your boring life. Just kidding! You’re in the <a href="https://en.wikipedia.org/wiki/FIRE_movement">right place</a>. Read on to experience this lame fantasy vicariously through Jim, our hypothetical heir.</p>
<p>Jim inherits $1000 from his great aunt Betsy, God rest her soul. He plans to buy into the market and hold his position for 10 years at which point he will cash out. Jim is about to call his broker when his friend Tom drops by and relates a tragic tale of losing half his fortune in the S&P! Now Jim is worried about losing money. He wants to know what his chances are. Using historical S&P prices, we can give Jim an idea of the range of possible outcomes for a 10-year investment in the S&P.</p>
<p>In this graph, we consider buying into the S&P in a given month and selling in that same month 10 years later. We will consider all such intervals from 1970-2020. Our first interval will buy into the market Jan 1970 and sell Jan 1980, our second buys in Feb 1970 and sells Feb 1980, our third… you get the idea. There are 480 such intervals from Jan 1970 to Jan 2020. Of these 480 intervals the graph below shows the best, worst and average percent returns.</p>
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<p>If Jim bought during the dotcom run up and sold before the bust, he would quadruple his initial investment in 10 years! On the flipside, buying in right before the dot com bust and selling after the 2008 mortgage crisis would cause him to lose half of his investment like his friend Tom. However, the median interval looks promising, showing a doubling of the initial investment in 10 years.</p>
<p>Now let’s take a look at the percent return of all 480 intervals. I included a dashed line at 0% return, so we can see roughly how many intervals provide a positive vs negative return.</p>
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<p>Here we can see that the majority of 480 intervals are on the north side of 0. Comforting news for Jim, showing that based on past returns a 10-year investment in the S&P can be expected to make money ~87% of the time. YOLO Jimbo, go west young man!</p>
<h2 id="monthly-investments-case">Monthly Investments Case</h2>
<p>At one time or another I’m sure <em>most</em> of us, while plugging through another work week, have thought: “Is this the rest of my life?” David Graebor’s fascinating <a href="https://www.amazon.com/Debt-First-5-000-Years/dp/1612191290">Debt the First 5000 years</a> claims the ancient Greeks would have seen modern employment as akin to slavery. We rent ourselves out for 40 hours a week for our livelihood! For most of us, the only way to buy back our time is saving enough money for retirement.</p>
<p>Most 401Ks allow you to invest a part of your paycheck into the market every month. Here we will consider investing the same <em>total</em> amount of money as the lump sum case ($1000) split up over each month in the 10-year interval. This comes out to investing $8.33 each month. Here are the investment returns for each 10-year interval in the past 50 years.</p>
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<p>Like the lump sum case, the majority of the intervals yield a positive return. However the monthly case has a slightly better win rate of ~90% compared to ~87% in the lump sum case.</p>
<h2 id="lump-sum-vs-monthly-investment-comparison">Lump Sum vs Monthly Investment Comparison</h2>
<p>Let’s take a closer look at the differences between the lump sum and monthly case by overlaying the distribution of returns for each on the same graph. We replace each histogram with a curve estimating its shape, so that we can more easily plot both distributions on the same graph.</p>
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<p>The <em>variance</em> of the monthly investment distribution of possible returns is significantly less than the lump sum distribution. By investing monthly, we hedge against the chance of choosing a <em>single</em> terrible (or amazing) 10-year entry and exit. Instead we are investing 12 times a year in each of the 10 years = 120 entry and exit intervals.</p>
<p>In this case, spacing out a sum of money into monthly investments decreases the magnitude of downside and upside on the distribution of possible returns.</p>
<h2 id="interactive-exploration">Interactive Exploration</h2>
<p>Take the data for a spin! Below I have selected investing $1000 per month for 20 years, considering 20-year intervals between 1950 and 2020. There is a million dollar spread between the best and worst outcomes. You could be the guy diligently socking away $1000 dollars per month over a 20-year career from 1962 and 1982 and be down 14% on that $240,000 dollars invested over the 20 years! Begs the question: If I invest monthly into the market, and the market falls significantly when I retire, <em>how long do I need to wait for my investment to be in the black again</em>? A question for another post.</p>
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<p>This data was compiled by <a href="http://www.econ.yale.edu/~shiller/data.htm">Mr. Robert Shiller</a>. The S&P price index used reflects dividends in addition to share price. Past performance may not indicate future returns.</p>Sam CallisterInvestment wizards tell us regular folks to buy and hold index funds. I’ve read many times that while the market goes up and down year to year, the average yearly return of the market is positive; patient investors will make money in the long term.