Baby Steps Millionaires (1)

This weekend, I read Baby Steps Millionaires by Dave Ramsey. I got to know this book because a Google feed article on personal finance recommended it. I could have clicked “Buy Now” on Amazon ($18 or so), but I found it on the catalog of a local library, so I went to the library to borrow the book. As I discussed in my article on frugal habits, if I take into account my opportunity cost for spending 20 minutes to visit the library, it does not make economic sense, but to me visiting the library is part of leisure, so it is justified.

Anyway, the book is about how to achieve financial independence (“millionaire”) slowly but surely by following the seven “baby steps”. These steps are:

1. save $1,000 for a starter emergency fund,
2. pay off all debt except mortgage,
3. save three to six months expenses in an emergency fund,
4. save 15% of pre-tax income into retirement accounts by first maxing out company match in 401(k), then Roth IRA, and then tax-deferred plan, all in a diversified stock mutual fund,
5. fund children’s college fund through a 529 college savings plan,
6. pay off mortgage early, and
7. be generous and give.

These advices, explained in pages 13-27, are all sensible. In fact, they are pretty close to what I wrote in my article “How to get rich”. The rest of the book is devoted to concrete examples of people achieving the baby steps millionaire status, lots of encouragement like “you can do it” and quotes from the bible, and an appendix on the National Study of Millionaires, which is a survey of 2,000 millionaires conducted by the author’s firm.

I think it’s a good book for those who want to be a millionaire but don’t know anything about how to achieve it. (Though, not being a Christian, I found some religious discussions dull.) This is one of the better books on personal finance. What I especially like is that the author took time and effort to collect data to prove that the “baby steps” actually work.

After this overall positive evaluation, let me provide a few criticisms.

First, on page 20 the author states that since 1928, the S&P500 has averaged an 11.46% rate of return (with reference to this page). In my undergraduate finance course, I teach this material, so I know this is the nominal arithmetic average return. (According to my own calculation, the number was 11.43%, which is very close.) But this average return is deceptive for two reasons. First, it ignores inflation. If we account for inflation, the average return becomes 8.52%, about 3 percentage points lower. Second, the arithmetic average return is meaningless for investment. The reason is as follows. Suppose you invest for \(T\) years, and the realized gross return in year \(t\) is \(R_t\). Then the realized cumulative gross return is \[R_1\times R_2\times \cdots \times R_T.\] To obtain the same outcome by investing in the “average”, the average gross return \(\bar{R}\) needs to satisfy \[\bar{R}^T=R_1\times R_2\times \cdots \times R_T,\] or equivalently \[\bar{R}=(R_1\times R_2\times \cdots \times R_T)^{1/T}.\] This is the geometric average return, not the arithmetic average return. If we take the logarithm, we obtain \[\log \bar{R}=\frac{1}{T}(\log R_1+\log R_2+\cdots+\log R_T).\] Now the argument becomes mathematical, but because of the concavity of the logarithmic function, we can show that the geometric average return is always smaller than the arithmetic average return. In fact, it is smaller by approximately one half of the variance. (We can prove this by using the Taylor approximation.) So, getting back to the quote from the book, an average return of 11.46% is deceptive. After accounting for inflation and the fact that the geometric average return is smaller, according to my calculation, the number becomes 6.75%. This is why, in my article, I used 6% as a benchmark.

Second, on page 19 the author states that Match beats Roth beats Traditional, but the argument is inaccurate. I can no longer remember where the author wrote (I should have taken a note), but I recall the author mentioned something like Roth beats Traditional because capital gains are not taxed. Actually, capital gains are not taxed in either Roth or Traditional. As I discussed in my article “Comparing taxable, traditional, and Roth accounts”, traditional and Roth are equivalent if we ignore the timing of taxation or restrictions on withdrawal. However, I do agree that Roth beats traditional. But the reason is because Roth allows larger pre-tax investments, as discussed in my article cited above.

Third, on pages 21-22 the author discusses hiring an investment professional (such as a financial advisor) and outperforming the market. This advice is likely harmful. If you do a bit of homework, anybody can invest in a low cost index fund by opening a brokerage account and buying an ETF like VTI. Hiring a financial advisor will not change the investment outcome, and you will simply pay more fees. And while anybody can attempt to outperform the market, it is mathematically impossible for everyone to outperform the market, because the market is the average of everyone. (This is because, the market index consists of all stocks, and all stocks need to be held by somebody.) So, I would suggest that most people focus on what they are good at (their main job), and for investment, just invest in an index fund.

Fourth, the author’s Baby Step 6 of paying off the mortgage early is not necessarily optimal. Let me give you a counterexample. I bought my house in 2013 and refinanced twice, the most recent being in 2020 at an annual percentage rate of 2.85% (10-year fixed). Currently, the federal funds rate gives about 4% return (nominal). So, by not paying off my mortgage early, I am benefiting from arbitrage, borrowing at 2.85% and investing at at least 4%. The point is that, paying off mortgage early makes sense only if the mortgage rate is sufficiently high.