• The Vimes 'Boots' Theory and Financial Products

    Terry Pratchett’s famous Discworld series of books includes a novel called Men at Arms. Sam Vimes, one of the characters in this book, describes his personal theory for how poverty can be self-perpetuating. Here’s the key quote from the book:

    The reason that the rich were so rich, Vimes reasoned, was because they managed to spend less money. Take boots, for example. He earned thirty-eight dollars a month plus allowances. A really good pair of leather boots cost fifty dollars. But an affordable pair of boots, which were sort of OK for a season or two and then leaked like hell when the cardboard gave out, cost about ten dollars. Those were the kind of boots Vimes always bought, and wore until the soles were so thin that he could tell where he was in Ankh-Morpork on a foggy night by the feel of the cobbles. But the thing was that good boots lasted for years and years. A man who could afford fifty dollars had a pair of boots that’d still be keeping his feet dry in ten years’ time, while a poor man who could only afford cheap boots would have spent a hundred dollars on boots in the same time and would still have wet feet. This was the Captain Samuel Vimes “Boots” theory of socioeconomic unfairness.

    The underlying idea here is probably familiar to many: we buy some cheap product that breaks or wears out after a few uses, and realize that we would have been better off in the long run with a more durable, long-lasting product, even if it cost more initially. However, if someone cannot save up enough resources to afford that more durable product, they are stuck with the lower quality version and thus have to pay more in the long run. Vimes’s theory is that this leads to a self-perpetuating cycle of wealth disparity: not only do the rich get to enjoy a better product, they save money doing so.

    Of course, in real life, the connection between durability and price of consumer goods is not quite as strong as the fictional scenario described by Pratchett. For example, luxury cars often have more expensive upkeep and maintenance costs. Furthermore, they can have worse resale values as a percentage of value compared to something like a Civic or Corolla. So, while someone who is wealthy enough to afford a luxury car may derive additional enjoyment over it, the ability to own that car does not further exacerbate the wealth disparity between them and, say, Civic owners.

    Economists often have special names for products or goods that have certain properties, such as Veblen Goods or Giffen Goods. Let’s call a good that behaves like the high-quality leather boots in Vimes’s story a Vimes Good. That is, they are goods that a greater level of wealth gives you access to, but have a lower total cost of ownership than alternatives that are accessible with less wealth. The leather boots of Ankh-Morpork are Vimes goods under this definition, because their higher initial up front cost effectively makes them inaccessible to those that do not have a certain level of wealth or savings. Meanwhile, BMWs are not.

    As I suggested earlier, it’s not always so easy to identify Vimes goods for certain broad classes of physical products. But there’s one industry and type of product that offers a very large number of clear-cut Vimes goods: financial products. In the rest of this post, I will give some examples and explain why Vimes goods are so common in this area.

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  • What can Ben Franklin's will teach us about compound interest and leaving a legacy?

    Anyone who has read a little bit about investing and personal finance has seen tables that explain the power of compound interest. You know, the kind where we see how $1 invested at Y% interest will grow after 10 years, 20 years, 30 years, and so on. Of course, the final row is always some shockingly large amount of money. The lesson is clear: start saving early and let your money grow.

    These tables are intended to motivate people to save for retirement, so the row listings tend to stop after about 40 or 50 years. But after seeing the remarkable growth, many readers have probably done the calculation to extrapolate for a bit longer: what if the amount compounded for 60, or 70, or even a hundred years. Stretched long enough, the amount is dizzying. Of course, after a hundred years, the original saver will not be around to make use of that money. But the money could be left to heirs or charity instead. In a previous post, I wrote about how we might calculate a perpetual withdrawal rate that could then be used to draw from that accumulated sum indefinitely.

    Has anyone ever done this? Of course, there are many famous family fortunes that have been passed down through generations and charitable foundations that have lasted for a long time. But those are different from what I mean, because they usually involve some sizable initial fortune that is built through active construction of a business empire. What about growing the initial fortune just from the power of passively compounding an initial, relatively modest sum?

    It turns out that there is a famous example of someone trying to do exactly that: Benjamin Franklin. In his will, he created two separate funds of £1,000 each for the cities of Boston and Philadelphia. The plan was that these funds would be used to make a series of 10 year loans to craftsmen in each of the two cities at interest rates of 5% each. After 100 years of this loan scheme, 10/13 of each city’s fund would be paid out to the city, to use for some civic improvement. The remaining 3/13 would be used to run the same loan scheme for yet another 100 years. After that, all of the remaining balances would be split between the respective cities and their states.

    What happened next has many lessons for anyone interested in savings, investment, and creating a legacy with their estates.

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  • Has the shift from dividends to buybacks made investing more confusing?

    I enjoy reading about the history of investing, finance, and business. Like any other historical subject, reading about these topics can help us gain perspective on the present. That’s especially important in the context of investing, as it can help up us understand the best ways to plan for the future.

    One thing that always shocks me when looking at older records is how high average dividend yields used to be for stocks. It’s no secret that over the past 100 years, there’s been a decline in average dividend yields. There are many reasons for this, but one contributing factor is an increasing shift to using stock buybacks instead of dividends.

    In this post, I want to explain why that shift has made things harder to understand, even if, in the end, these changes have benefits for investors.

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  • Safe Withdrawal Rates - Part 4: Perpetual Withdrawal Rates

    Recall from Part 1 that the Trinity study defined a withdrawal rate as “safe” so long as the portfolio always had enough to make withdrawals during retirement. That means if the portfolio was worth exactly $0 at the end of the retirement duration, that would count as a success. We’ve been using that same definition in the other parts of this series.

    However, many retirees would not consider such an outcome a “success”. Watching your balance drop down closer and closer to 0 would be quite nerve-racking. Moreover, many people want to be able to leave assets to their heirs or charities upon their death.

    There’s an easy (albeit conservative) way to adjust Trinity style safe withdrawal rates to guarantee a “minimum” floor for assets at death. Suppose the retiree has X dollars, and wishes to ensure that Y inflation-adjusted dollars will be available for heirs. They can simply put the Y dollars in an inflation-hedged instrument like TIPS or I-Bonds, which give a guaranteed real rate of return over inflation. Then, they can apply the usual SWR methodology to the remaining (X - Y) dollars.

    However, setting an arbitrary “base” floor that assets should never dip below seems slightly arbitrary. What if we want to ensure that the whole principal remains in tact? In other words, what if we want a perpetual withdrawal rate that can last forever.

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  • Safe Withdrawal Rates - Part 3: More Bootstrapping

    In Part 2 of this series, As we saw in the previous post, the “standard” approach of choosing a safe withdrawal rate based on what has never failed in the past is questionable. The reason is that we simply don’t have that much data. If you had tried this approach in the past, by looking at what had never failed as of 1980, you would have overestimated the actual SWR and encountered a failure.

    To try to address this, we used the stationary bootstrap to simulate alternate possible returns data. For each simulated data set, we re-ran the Trinity study methodology in order to see how different the “no failure” rate would have been. We found that in a non-trivial percentage of simulations, the “no failure” rate was much, much lower than the standard recommendations. This suggests that there is a fair degree of variability in what the Trinity study methodology could have reasonably found. So, just picking something that has never failed before does not give a good sense of how secure that withdrawal rate really is.

    To do better, we’ll again turn to the stationary bootstrap. This time, we’ll use it to estimate safe withdrawal rates directly, rather than to study the statistical behavior of the Trinity study methodology.

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  • Safe Withdrawal Rates - Part 2: Do we have enough data?

    Last time, we reviewed the definition of safe withdrawal rates and explained the origins of the popular 4% rule. The idea was to estimate how much we could safely withdraw post-retirement by simulating how retirees from 1926 through 2015 would do. For each possible year in that range and possible retirement length, we checked whether a retiree who started then and withdrew a given amount each month would run out of money. As expected, the longer the desired duration of the retirement, the less we could safely withdraw each year. This is especially important for people who want to retire early, because many studies of safe withdrawal rates focus on “normal” retirement lengths of at most 30 years.

    When we consider longer retirement lengths, a serious question is whether we have enough data to make a safe conclusion. For example, someone retiring early at age 35 who wants to ensure they have enough money till 95 is interested in a 60 year safe withdrawal rate! But if we’re using stock data from 1927 to 2015, we have less than 90 years of data. Moreover, if we follow the Trinity study methodology of examining the outcome of each possible starting year, the last cohort we can consider is 1955 – for every starting year after that, we need data beyond 2015 to know whether they would have made it. (Of course, if they’ve already run out of money, we can know that would have been a failure. But we can’t tell how the remaining cases will turn out. I do not count such failures because it appears that the Trinity study did not either.)

    So what can we do? One possibility is to try to extend the data. I’m writing this in 2019, so we could update our ending date data by a few more years. From the other direction, some people have figured out estimates of stock and government bond returns from all the way back to 1871. That’s a lot of additional data! (Although one might wonder how relevant such old estimates are for figuring out how the market behaves today.)

    While trying to get more data is a good idea, in this post I want to look into another matter: can we estimate how much a lack of data may be hurting us? And, can we extract even more insight from the data we do have?

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  • Safe Withdrawal Rates - Part 1: The Basics

    The study of safe withdrawal rates helps answer two crucial questions about retirement savings and planning:

    • How much money do we need to save for retirement?

    • How do we make sure that our savings last throughout our retirement?

    Of course, these two questions are related. If we save too little, then it will be a struggle to stretch our savings out during retirement. On the other hand, mismanagement and excessive early spending could deplete even a seemingly large nest egg. Proper planning will help us figure out what savings rate we need to hit our targets and know when we are financially ready to retire.

    To get started answering these questions, we first need to have some estimate of what our expenses will be after retirement. This itself can be tough to figure out. In the end, this is highly personal and will vary for each individual. Moreover, expenses might change throughout retirement, sometimes dramatically so. In order to make any progress, we’ll have to make some simplifying assumptions.

    You may have heard of the 4% rule, which says that you can safely take out 4% of your original savings every year, with adjustments for inflation. For example, if you retire in 2020 with $1 million dollars in your portfolio, then the first year you withdraw $40,000. Every year after, you convert $40,000 in 2020 dollars into the current year to adjust for inflation and then withdraw the adjusted amount.

    But is this really safe? Well, it depends. The rule relies on certain assumptions. Unfortunately there is lot of misunderstanding about this on reddit and financial independence blogs! To clear this confusion up, let me explain a little bit more about where this rule comes from.

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  • Review: A Random Walk Down Wall Street

    A Random Walk Down Wall Street, by Burton Malkiel, is a classic book on personal investing. The first edition was published in 1973, and there have since been twelve editions, with the most recent released in 2019. Considering how much the market has changed in that time, its continued relevance is a testament to the book’s quality and central message.

    The book’s title is a reference to the Random Walk Hypothesis (RWH), the theory that prices of bonds and stocks can be viewed as random walks, a mathematical model in which prices increase or decrease randomly without regard to their historical value. If this model is accurate, then it’s impossible to predict whether a given stock’s price is about to rise or fall.

    In light of that, the book argues that the most sensible strategy is to buy-and-hold. Over time, the value of one’s investment will grow as prices drift upward. Since any individual stock is still likely to behave somewhat erratically, it is prudent to diversify and purchase stocks from a wide range of companies. The simplest way to do so is to purchase shares of index funds, which buy stocks from all of the companies that belong to an index like the S&P 500. Many of these funds charge very low overheads and in exchange, they handle purchasing all the stocks at the appropriate weights, rebalancing as prices change, and distributing the dividends issued by each stock.

    By now, this advice is widespread and popular, but it wasn’t always. When the first edition of A Random Walk Down Wall Street came out in 1973, there was no widely available index fund that one could invest in. The Vanguard Group, which is now one of the largest index fund managers, was founded the year after in 1974. Today, it manages over $5 trillion in assets, and many other large companies also provide funds tracking a wide range of indices.

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