The Bizarro Rule of 72

April 17, 2015 by Matt McCracken

For quite some time, I have argued that the stock market is relatively expensive by historical standards and will therefore experience below average returns for the next decade. Recently, I developed a new and very simplistic means of calculating expected stock market returns in light of valuation. I’ll refer to it as The Bizarro Rule of 72.

I’m assuming that you know of the Rule of 72. If not, it goes like this. If you want know how long it will take for you to achieve a 100% return on your capital given a specific interest rate, simply divide 72 by the interest rate. It’s real easy. Say you have a bond that pays 8%. Divide 72 by 8 and you get 9, therefore, you’ll receive interest equal to your original principal in a span of 9 years. At an interest rate of 12%, it will take you 6 years and so on.

Let's consider the inverse to the Rule of 72. In honor of Seinfeld, I’ll refer to it as The Bizarro Rule of 72. Rather than starting with an assumed rate of return for stocks to figure out when I’ll get all my money back, I’m going to figure out when I’ll get all my money back to calculate an assumed rate of return for the market.

The object of this exercise is to develop a realistic expectation (not an exact prediction) for stock market returns over the next decade (in contrast to the unrealistic claims made by Wall Street purporting 10-12% gains in perpetuity.) In order to carry out this exercise, I need to make one fairly well established assumption, which is that average earnings growth for stocks in the S&P 500 will be 5%. Historically, average earnings growth has been in the 5 – 5.5% range. For the sake of easy math, I’ll use the 5% figure.

Let’s start by assuming that you’re investing in a company whose name is Total Market Inc. - TMI. You know that TMI will experience average earnings growth of 5% over the next decade. Current earnings for TMI are $5. The going rate for businesses such as TMI is an earnings multiple of 20, so the owner of TMI will not accept anything less than $100 for his beloved company. Since you got a C-note burning a hole in your britches, you buy TMI. So, how long will it take to get your money back – about 13.7 years. Now, let’s apply The Bizzarro Rule of 72. Take 72 and divide it by 13.7 and you get 5.26. Therefore, your rate of return on your investment is 5.26%.

But what if, the adjustable rate mortgage on TMI’s owner just reset and he needs cash to pay his bills and decides that he’ll take $50 (A multiple of 10) for his now not-so-beloved company. Under this scenario, you’re paypack period is right at 8 years meaning that the rate of return on your investment is 9% (72/8 = 9). So, how can this be applied to the stock market. Well, actually it’s pretty simple. When you buy the S&P at a P/E of 20 (as was the case in 2005), you’re paying 20 times today’s earnings, earnings that can be expected to grow at 5%. Therefore you can expect a return on your investment of 5.26%. However, if you bought the S&P in 1978, when the P/E was 7.5, you could have expected an 11% return (6.5 year payback and 72/6 is 11). Here’s a simple chart of stock market P/E’s and expected returns:

P/E.....Years to Recoup Investment........Rate of Return





There are certainly several factors that will impact future returns beyond current valuation levles. Here are several that will result in actual returns deviating from The Bizarro Rule of 72's predictions.

Earnings Curve. While earnings growth has averaged 5 – 5.5%, it oscillates around that average in a cyclical pattern. Currently, earnings growth is in the double digits, but in the first part of this decade/century/millennium earnings growth was negative. Depending on where on the curve we currently stand has a big impact on backward, current and forward P/E calculations. I and many others believe that we are at the top of the curve which would translate into artificially low P/E’s and therefore we should reduce our market return expectations further. Folks on Wall Street prefer to quote whichever P/E calculation that presents the rosiest picture. Currently, they are reporting forward P/E’s. In 2002, they would have focused on backward P/E’s. Be weary of what you here in the financial media.

P/E Expansion and Contraction: From 1978 through 2000, P/E’s expanded 3 fold. Therefore, a stock market investor would have experienced appreciation greater than the 11% calculation made by The Bizarro Rule of 72. However, when P/E’s contract, a stock market investor would be punished and likely realize gains less what The Bizarro Rule of 72 would estimate.

Volatility: Here’s where the real long-term disparity lies. MPTer’s (that’s my own slang for those crazy kids who believe Modern Portfolio Theory) and Wall Street brokers love to quote “average returns”. Unfortunately, the average investor doesn’t realize average returns. Huh! That’s right, volatility in the market means that compounded returns are typically 1-2% less than average returns. Therefore, while the stock market has averaged 10.4% since 1926, compounded returns have been a couple points less. When you determine return on investment, you do it in terms of compounded returns, not average. I’ll be writing a future blog post to explain, but for right now, just take my word for it.

Interest Rate Cycles: Just as Earnings are cyclical, so are interest rates. As we’ve seen in the last few years, interest rates are down, therefore, the stock market can support a higher valuation. But if interest rates go up, bonds become more attractive providing lower acceptable valuations on stocks. Finally, I’m assuming a stock market investment over a finite period of time. Most stock market investors have a fairly long-term investment outlook where earnings growth will continue to compound and provide higher rates of return. Therefore, using the The Bizarro Rule of 72 to calculate future investment returns is likely understating the longer term picture. (And that’s why I said in the beginning of this post that I’m looking to calculate expected returns for the next 10 years.) The real purpose of this entry is to help you realize that valuation really does matter. I certainly don’t believe that any simple formula that I created could have any real value in accurately predicting future stock market returns. My goal is to simply make you aware of the importance of valuation in gauging future returns and to help you realize just how expensive the market really is. Furthermore, my real objective is to get investors to start considering alternative investment strategies that will likely outperform the US equity markets. If you’d like to discuss some alternatives, please give us a call. Matt