The Diminishing Marginal Utility of Hoarding: Why Being a Stingy Miser Doesn’t Pay

Corey —  August 17, 2009 — Leave a comment

       The other day I was playing around with an Excel spreadsheet I made. I was looking at how much you need to save to reach your retirement goals. At one point, I thought to myself, “What happens if you save more than necessary? How much will it increase your chances of reaching your retirement goal?” The answer I found was very interesting and backs up a verse in Proverbs. But before I can tell you what I discovered, I’ll have to explain what I was doing and how I was doing it.

Monte Carlo Analysis

       In financial planning, we use Monte Carlo analysis to simulate random stock market returns among other things. When you’re planning your retirement, it doesn’t make sense to assume you’re going to get an 8% return every single year. The stock market just doesn’t work that way. Monte Carlo analysis gives a more realistic, though not perfect, representation of how the stock market actually delivers returns.

       Monte Carlo analysis uses the assumptions you give it to randomly pick numbers within a specific range. I used Monte Carlo analysis to pick random stock market returns within a range based on historic performance results. I looked at how a person’s savings would grow as they invest for 45 years to reach their retirement goals.

       Each 45 year investment period is called a “trial”. The success or failure of a trial depends on whether or not you reach your goal at the end of the period. I was testing to see whether you would have accumulated enough money to retire at the end of 45 years based on your retirement goals.

       Running just one trial isn’t enough. To get a meaningful result, you have to run thousands of trials. To figure out your success rate, you divide the number of successful trials by the total number of trials you ran. In my example, I ran 5,000 trials (that means 5,000 sets of 45 year investment periods). An 80% success rate would mean that 4,000 out of my 5,000 trials were successful.

       Monte Carlo analysis is useful because it incorporates the uncertainty of the stock market into your retirement planning. It has some limitations, but it’s the best we can do for trying to predict the future. The stock market doesn’t work exactly the way the model works, and there’s also the question of what a good result should be. Traditionally, a success rate of 80% or higher is “good” because there are so many assumptions built in to the model. Trying to go for a higher success rate means you’re placing much more importance on your assumptions being correct.

       I found that saving 20% of your desired retirement income and increasing it by inflation each year would give you an 82% success rate to reach your retirement goals. That’s pretty good, but then I wondered what would happen if you saved even more. How much would your success rate increase if you saved even more?

The Results: The Diminishing Marginal Utility of Hoarding

       So I proceeded to run a Monte Carlo analysis at different savings rates. I started at 0% and increased it by 5% for each new analysis all the way up to 100%. Here’s a graph of my results:


Success Rate As a Function of Savings


       As you can see, saving 0% gives you a 0% chance of reaching retirement – which makes sense, right? Saving 10% gives you about a 60% success rate, and saving 20% gives you an 82% success rate. But do you notice the interesting part? As you begin to save more than 20%, your chances of successfully reaching your retirement goals go up less and less. After you hit that 20% savings mark you don’t get very much bang for your buck.

       It might be easier to see what I’m talking about using this chart:


The Marginal Utility of Hoarding


       So when you go from saving 0% for retirement to saving 5%, you increase your chances of success by 37%. If you go from 5% to 10%, you increase your success rate by another 23% giving you a success rate of 60%. From 10% to 15% increases your chances of success by 13%, and from 15% to 20% gives you another 9% increase. Once you get to 20% though, saving another 5% only increases your success rate by 3%. Every little bit more that you save gives you a smaller and smaller increase in your chances of success.

       This shows what I call “the diminishing marginal utility of hoarding”. In economics, the law of diminishing marginal utility says that for each additional unit you use you get less satisfaction than you did with the last one. For example, eating one chocolate bar tastes good. A second one right after doesn’t taste quite as good, the third a little less so, and so on. Eating seven chocolate bars in a row just gives you a sick stomach.

       What we’re seeing here is the law of diminishing marginal utility applied to saving. Saving money for retirement is good. But once you get to a certain point (which depends on how long you have until retirement and how much you have already saved), saving more and more doesn’t increase your chances of success quite as much as it did before.

How Can This Be True?

       Because Monte Carlo analysis is looking at thousands of possible scenarios, you’re going to have some scenarios where the stock market loses money for several years in a row. While that’s (hopefully) not as likely in real life, saving more and more isn’t going to help you much if that happens. You’ll just keep losing the money, and the impact is even greater if you already have a lot saved. So this phenomenon is partly due to the method we’re using, but it also illustrates a fundamental truth – being stingy doesn’t help you quite as much as you might think it will.

What God Has to Say about It

       I was so excited to see these results because they help illustrate some of God’s wisdom about giving:

       24 There is one who scatters, and increases yet more. There is one who withholds more than is appropriate, but gains poverty. 25 The liberal soul shall be made fat. He who waters shall be watered also himself.

Proverbs 11:24-25 (WEB)



       Maybe you’re thinking I didn’t really prove that point, and you’d be right if you’re only thinking about dollars and cents. When Jesus talked about giving our money to the poor, He never said that it would make us rich in this life. When we give to honor God, we store up treasures in Heaven. This is precisely how one person can give away a lot of his money and become wealthier while another is stingy but becomes poor.

       Being a stingy miser won’t give you a better chance of reaching your retirement goals. Once you’re saving enough, you have to be content that you’re doing what you should and hand the rest over to God. Hoarding money for yourself doesn’t help you that much in this life, and it will severely impoverish you in the next.

       So how do you know when you’re saving enough? To find out, sign up for free updates to Provident Planning. I’ll be examining that question and many more that will help you prepare for a retirement that honors God and live a life that glorifies His name.

Corey

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Corey is currently pursuing a Master of Arts degree in religion. While he enjoys learning and writing about Christianity, another one of his new passions is writing about personal finances in order to help others make wise decisions with their money.

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