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Beware the Rules of Thumb

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The other day, I was explaining the Rule of 72 to my lovely wife. It’s a simple little mathematical trick that almost epitomizes the advantages and disadvantages of rules of thumb. If you want to know how long it takes to double a sum of money, divide 72 by its interest rate.

At 10% a year, the rule says a balance doubles ever 7.2 years. It’s really closer slightly less than 7.275 years. At 5% a year, the rule says a balance doubles ever 14.4 years. It’s closer to 14.21. It’s a pretty good rule of thumb and good when you have nothing on the line. If it makes a difference whether it doubles in 14.4 years or 14.21 years, then the rule fails. (Incidentally, it’s obviously an estimate because if you have an interest rate of 100%, you don’t double it in 0.72 years, you double it in 1 year)

Should you have (120-Your Age)% of your investments in the stock market? Which stock market? Domestic? Emerging markets? Small cap? Blue chips?

Should you really be paying 30% of your income towards housing? Is this towards rent or a mortgage? Does it count utilities or is it just towards the mortgage or the rent bill? What about insurance?

As you can see, rules of thumb are good when you’re just talking about it around the room. They’re good for when there’s nothing on the line and you’re happy with a “good enough.” If you want to know with 100% certainty, you need to roll up your sleeves, grab a calculator, and do some work.

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22 Responses to “Beware the Rules of Thumb”

  1. DIY Investor says:

    I think rules of thumb are very useful as long as you take them for what they are. In talking about inflation we know we are estimating when we say inflation of 4%/year will double prices in 18 years. When we are doing the asset allocation we tend to understand that we talking about the total stock market or the S&P 500. The person who goes out and puts the stock percentage in small cap stocks deserves what he gets. In most instances I believe that rule of thumb is used to focus on what percent to put in bonds.
    One of the rules of thumb that can cause problems is the 4% withdrawal rate in retirement. People are coming to understand that the sequence of returns is critical and relying on an average can be dangerous.

  2. otipoby says:

    I did a little math in Excel. The rule of 72 is a very good estimate as long as the interest rate is not less than 3%. For example, at 8%, the Ro72 is only off by 2.3 DAYS compared to the actual calculation. Even at 50% (wouldn’t that be nice), the estimate is off by only 3.2 months. However, at rates of return less than 3%, the estimate is poor. For example, at 1%, the estimate is off by 2.34 yr.
    Any estimate / rules of thumb typically have a range of values that are reasonably accurate to estimate.
    Your premise, however, is still valid. If you are going to go to the effort to do a detailed calculation, don’t use rules of thumb if you don’t have to.

    • Jim says:

      It’s good to know the rule degrades significantly, to the point of being useless, at rates of 3% or less. Thanks for crunching to numbers to discover that!

    • knighthawk says:

      Your calculations are misleading. Sure, being off by 3.2 months isn’t as long as 2.34 years, but percentage wise that’s 18.5% off for the 50% rate and 3.25% off for the 1% rate.

      • otipoby says:

        Interesting. I think considering % difference is more misleading than considering the actual difference.
        I would rather have 1% off $200,000 (for example, buying a house) than 10% off $10,000 (for example, buying a car). I have read that humans think logarithmically (maybe a good blog post in the future). They will increase or decrease $1000 much easier when negotiating buying a house vs buying a car. In either case, $1000 is what matters.
        My $0.02.

        • These are two different concepts, though. With the accumulation of assets, taking the absolute value in favor of the relative one has a lot of merit. Bad Money Advice wrote about this a while ago.

          However, accuracy is not a practice in accumulation – it is a measurement of how close something is to the correct result – RELATIVE to the correct result, you might say. Using a percentage standard of error makes the most sense – which is why polls quote margin of error as +- 2.3% rather than +- 5 voters.

          To look at it another way:

          You ask me to measure the long end of a 5 X 7 photo. I tell you it’s 10 inches.

          I ask you to measure a 1 mile length of road. You tell me it is 5280.5 feet.

          I’m off by “only” 3 inches – you’re off by 6. But surely you did the more accurate job of measuring. Relative is better than absolute in this case.

          With regards to the rule of 72 – if you use it to determine how much money you’ll have at the end of a specific period of time (let’s say, 72 years), you’ll be much further off if you use the factor for 50% than the factor for 1%. The factor for 50% has a lower absolute error, but it compounds over time and over time eclipses the error for the 1% rate.

          But, yeah, anyway it is supposed to be for quick mental calculations. If we’re getting bogged down in the error rate for one percentage versus the other, we’re really not using it as intended.

  3. billsnider says:

    Another rule of thumb you hear repeatedly says that you need 70% of your income to retire. Well I am retired and this rule is a lot of baloney. Your pre retirement expenses are more or less your post retirement amount. That is the correct way to think about it.

    Bill Snider

    • Maddhatter says:

      Does that come from having a house payment versus not having a house payment? Not that when you retire your house debt goes away, but that most of the time the house is paid between that time when the kids leave and retirement. If not, that does sound like baloney. I certainly don’t plan on eating less or doing less in retirement.

    • ian says:

      I have always interpreted it to mean 70% of Gross Income. What i think I earn now (my salary), in retirement I will only need 70%. Not because my expenses dropped but because I am no longer paying income tax.

      • Ron says:

        You also stop saving for retirement after you retire. That’s 10% – 15% – 20%… oh, what’s that rule of thumb on savings again?

      • Shirley says:

        And you are also no longer paying work-related expenses such as daily commute cost or gas for the same, clothes, at work donations, bought lunches, quick to make dinners, etc. You may well spend the same amount of money on similar things, but you don’t absolutely have to. Little things really do add up!

  4. Rob Bennett says:

    The rule of thumb that drives me crazy is the one that says to save 10 percent of income. Some should be saving 0 percent (if you’re getting your degree at night, you might well not have money left to save — but you’re being 100 percent financially responsible) and others should be saving 50 percent. I saved 80 percent of post-tax income for a time. That opened up lots of opportunities for me down the road.

    It takes a little effort to know how much to save. Not a lot, but a little that pays big dividends. But we are all naturally lazy and like the idea of taking a prepackaged answer to the question “How much should I save?”

    Rob

  5. Jim, good discussion topic. I often wonder about the housing rule of thumb. Dave Ramsey says no more than 25% of your take home pay. I believe that just includes mortgage, insurance and taxes. Crown Financial Ministries says no more than 33% (family of four) of net spendable income. NSI is money left after taxes and giving. The 33% includes utilities and other housing related expenses. I think Dave’s 25% makes it pretty easy, but you also have to take into consideration how much debt you have in other areas as well as other factors. I guess the point is that it’s only a rule of thumb, but I agree you have to dig into the numbers for your specific situation. 25% may work for some people, but not for those who have a lot of credit card debt and can’t make any forward progress on their journey. A much lower percentage may be required to create forward momentum in achieve their goals.

  6. freeby50 says:

    The rule of 72 is basically mathematical fact (with a margin of error cause its an approximation).

    Most of the other financial ‘rules of thumb’ are based on opinion, often make assumptions on the future or just use some semi-arbitrary choices. They should usually be taken with a grain of salt.

  7. Eddie says:

    Rules thumb are a great starting point. It gives an easily definable starting point, provides motivation, and a goal.If not successful for everyone over the long run, at least most of them are not harmful over the short run.

    So long as a person is willing to move the goal posts as they gain education and experience, I say embrace it. Doing something is better then nothing….. the guy who saves 10% for retirement because he heard that was the rule may not be doing all he should…..but he’s better off than the guy who saves nothing!

  8. “(Incidentally, it’s obviously an estimate because if you have an interest rate of 100%, you don’t double it in 0.72 years, you double it in 1 year)”

    That’s only true if you’re compounding annually, which is atypical.

    Let’s assume quarterly compounding (which is also atypical):

    After Q1: $125
    After Q2: $156.25
    After Q3: $195.3125
    After Q4: $244.140625

    Compound weekly or daily, and you double more quickly.

    The Rule of 69 is actually more accurate, but 72 works better for “back of the envelope calculations”. It was always intended as an estimate, not as a replacement for a formal calculation.

  9. Nicole says:

    Heuristics are great if they get people to do something in the case where if they had to actually crunch the numbers they would do nothing. It is better to be close but not quite exactly right than to keep putting off the perfect decision so that no decision gets made at all. 120-your age in stocks is better than no money saved for retirement. 10% (or 15%) to retirement is better than nothing because you haven’t had time to figure out the exact number for your purposes (not that anybody knows the exact number anyway, even with the shiniest web calculator in the world).

    In other words, heuristics are a great way to satisfice when trying to optimize would cause you to be paralyzed by the Paradox of Choice.

  10. Darren says:

    Good point regarding the rule of 72. I did a somewhat detailed post about this not too long ago that shows differences between the calculated amount of time to double, and the actual time it takes to double. For some of the stated interest rates, this difference can be quite large.


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