A Young Advisor’s View: Behavior vs. Math

I was mindlessly scrolling through Twitter, which seems to be a common occurrence over the last few months, when this tweet (see picture below) caught my eye. It caught my eye because I completely disagreed with it. When I first read it, I asked myself, “Why would you want a big tax refund? Why would you pay your smallest debt balance first or pay off your low interest rate mortgage?” My analytical and mathematical brain was screaming that all of these were poor financial decisions, but after further thought, I saw what the author was trying to get across. These might not be the most mathematically optimal decisions, but behaviorally they can make a lot of sense. So, what is more important for your future self, optimizing behavior or math?

Tax Refunds

The first behavior versus math issue addressed is that of intentionally receiving a big tax refund. From what I’ve experienced, people tend to throw logic out the window when it comes to taxes. Before diving into this issue, I want to provide a very quick explanation of how I look at taxes:

  1. The IRS is going to estimate how much you owe for the year.
  2. It is up to you to pay that estimated amount over the course of the year.
  3. You can decide to pay more or less of the estimate through your W-4 withholdings if you’re an employee or quarterly estimated tax payments if self-employed.
  4. During tax time you “true up” what you paid in versus what you actually owe.

If you receive a tax refund, it means you overpaid taxes on a monthly basis. And if you are required to pay in, it means you did not pay enough on a monthly basis. So, why is it mathematically wrong to receive a large refund?

Mathematically inclined people may explain it like this, “If you received a tax refund you gave the government an interest-free loan”. Technically, they would be right. If you do receive a refund, then you gave the government more money than needed without having received a benefit. Ramit Sethi discusses his views on tax refunds in a recent blog post. Ramit argues that giving the government an interest free loan has less of an impact than receiving a large tax bill at the end of year.

Let’s say you receive a $3,000 refund. If you would have taken that $3,000 and put it in a high yield savings account at 1.5% interest, then you would have received $45 for the year or $3.75 per month. Is that $45 going to make an impact on your financial future? I am going to go ahead and assume the answer is “no”.

Remember, I usually am a math-based person and my wife and I try to get our tax bill as close to $0 as possible. This gives us more cash flow monthly, and we don’t have to worry about owing a large amount at tax time. However, few people want to take the time to run a tax projection and adjust their W-4 accordingly throughout the year. For this reason, I tend to agree with Ramit.

If we agree that receiving a refund is better than owing when you file your taxes, then the bigger question is, “What are you going to do with your refund?” If you expect to get a tax refund each year and that money is already spoken for (meaning you have already planned how you’re going to spend it), then that probably means you rely too much on this windfall. Instead, my suggestion would be to take at least 50% of your refund and save it. This can mean putting it towards debt, an emergency fund, or retirement savings. If it’s appropriate for your personal situation, then you can take the other 50% and reward yourself for a year of hard work and have fun!

Paying Off Debt

Paying off your smallest debt first is not mathematically optimal. The most optimal way to paydown a series of debts is to start with your highest interest rate and continue working your way down from there. This will ensure that you pay the least amount of interest over time. There are a lot of people who opt to use the debt snowball method (paying the smallest balance off first) rather than the debt avalanche (paying the loan with the highest interest rate off first) even knowing the above fact. Before we dive into each groups’ reasonings, let’s make sure we have a simple understanding of how each method works.

The debt snowball method works by going through your debts and listing them in order from smallest balance to largest balance. You would make the minimum payments on all of your debts while any additional dollars (your snowball) go to paying down your smallest balance. When that first debt is paid off, you would continue making your minimum payments; however, you would add your additional dollars plus the previous smallest balance’s payment to increase your snowball. This process of adding to your snowball would be repeated until all of your debts were paid off.

The debt avalanche method works very similarly to the above process. However, you would rank your debts from highest to lowest interest rate. You would make the minimum payments on all of your debts and any additional dollars would go towards the highest interest rate debt. Once the first debt is paid off, that payment and your additional dollars would be put towards your next highest interest rate, while continuing to make the minimum payments on all other debts.

The debt snowball has much more to do with human behavior than any other factor. Those who opt to use the debt snowball method believe that quick wins (paying off smaller debts more quickly) will keep you motivated and on track. I think Dave Ramsey summarizes debt snowball advocates’ feelings with this quote, “When it all boils down, hope has more to do with this equation than math ever will”.

My personal belief on the debt snowball versus debt avalanche debate is that the debt avalanche method is the preferred method since it will ensure that you pay the least amount of interest. Let’s take a look at this example:

Assume that you have $10,000 of student loans at 5%, a $15,000 car loan at 7%, and $20,000 of credit cards at 25%. Using the debt snowball method, you would work through your student loans first and then your car loan before ever making a dent on your credit cards while incurring interest at 25% the whole time. I will concede that a debt paydown strategy is only as good as the person who is using it. So, if you are someone who really needs quick wins to maintain motivation you might consider a hybrid approach. With that in mind, a hybrid approach could be to first pay down your $15,000 car loan at 7%, then your $20,000 of credit card at 25%, and finally your student loans of $10,000 at 5%.

Paying Off Your Mortgage

Should I get a 15- or 30-year mortgage? Should I pay additional dollars each month to pay off my mortgage faster? These are questions that I hear a lot. A mortgage can feel very burdensome and never ending. As with the other topics in this blog, the answers to these questions come down to a behavior versus math argument. For the sake of this example, let’s call the behavior group “Peace of Mind” and the math group “Higher Return”.

The “Peace of Mind” group is striving for exactly that: freedom and security. To them, they see paying their mortgage as sacrificing a large portion of their monthly cash flow. Many in the Peace of Mind group feel that by giving up more cash flow now and getting their mortgage behind them they will have freedom to do what they want in the future. Having a mortgage can make you feel fragile and paying off your mortgage early can provide a sense of security. I think Ben Carlson says it best: “I’m not sure you’ll ever run across a person who was sad they paid off their mortgage early”.

You will know someone is a math-based person if they say something like, “You should be able to get a higher return in the market than the interest rate on your mortgage”. They believe if your mortgage rate is 3.5% and your expected return on your investment portfolio is 7%, it is better to spread your mortgage over 30-years allowing more cash flow to be invested. The bigger number wins. They also tend to believe that you are putting extra dollars into an illiquid asset (a house that cannot be quickly converted into cash) by paying off the mortgage sooner. If you were to ever need your home’s equity you would have to either sell your home, do a cash out refinance, or do a reverse mortgage (if you’re old enough). It can be challenging to access the equity of your home quickly when compared to an investment portfolio.

Let’s expand on the thought above of comparing the interest rate of your mortgage to the expected rate of return of your portfolio. If you’re in the “Peace of Mind” group and you pay off your mortgage to secure the freedom and flexibility that you’re seeking, then what are you going to do with your free cash flow? Will it all go towards spending and lifestyle creep or will you now start to invest?

For example, assume that John is 25 years old and he invests $4,000 annually and receives a 7% return while making a 30-year mortgage payment. His twin sister Jane gets a 15-year mortgage at age 25 and prioritizes paying it down without saving for retirement. She doesn’t start saving until age 40, but she saves at a much higher amount of $10,000. She expects to receive the same 7% return and they both retire at age 65. In the chart below, you can see that at age 65 John has a greater portfolio balance compared to his sister even though she saved at a much higher rate.

Another downside of a 15-year mortgage compared to a 30-year is the flexibility that you give up with a higher minimum monthly payment. Once you establish a 15-year mortgage you must continue to make those higher minimum monthly payments or otherwise refinance. I still lean towards the mathematically optimal answer on this issue as explained in the example above. However, if your 30-year mortgage keeps you up at night you can prioritize personal happiness over mathematical optimization.

Maintaining a Big Cash Balance

The final point mentioned in the above tweet is having a large cash balance. Most people have heard that you should have at least 3-6 months of living expenses in cash as an emergency fund. Is this a minimum amount? Is this an exact amount? How much cash is too much cash?

Those who argue for having a large cash balance favor holding cash more than just an emergency fund so that they maintain optionality. This optionality allows their excess cash to be deployed in any fashion they see fit. An example of when this would be beneficial was during the recent market downturn. By no means am I endorsing market timing, but if you had excess cash available you would have been able to take advantage of purchasing financial assets at low points. The value of optionality is a very hard thing to quantify, but it allows you to take advantage when others cannot and shields you when times are tough.

Those that only hold an emergency fund in cash and no cash beyond that tend to believe that any extra money is better served being invested in the market. If your basic savings account is receiving 0.01%, then it’s likely that investing any cash beyond your required 3-6 month emergency fund will yield a higher benefit over the long run. This mentality is similar to the “Higher Return” group that we mentioned above.

Personally, I always keep an emergency fund and any 1-5-year goals (such as travel) in my savings account. If our cash balance begins to grow beyond that amount I do not immediately go and invest it. I like to keep cash for optionality purposes because my wife likes the feeling of safety that the additional amount provides, and I enjoy the option of strategically deploying it. Since we had some excess cash available in mid-March, we were able to contribute funds into our Roth IRAs and invest them at a relatively low point in the market.

Behavior vs. Math

Hopefully, this blog allowed you to see a different side of financial decision-making and how the behavioral and mathematical factors play into it. This process was beneficial for me to sit down and take time to really think through the behavioral side of decisions people make and why they make them. I find myself constantly wrapped up in numbers and strategy at work that it then carries over into my own life decisions. I think the greatest value and help an advisor provides is being able to bridge the gap between emotions and math to create a plan that truly works for you.


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